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The First Fermi LAT Gamma-Ray Burst Catalog

In three years of observations since the beginning of nominal science operations in August 2008, the Large Area Telescope (LAT) on board the Fermi Gamma Ray Space Telescope has observed high-energy (>20 MeV) \gamma-ray emission from 35 gamma-ray bursts (GRBs). Among these, 28 GRBs have been detected above 100 MeV and 7 GRBs above ~ 20 MeV. The first Fermi-LAT catalog of GRBs is a compilation of these detections and provides a systematic study of high-energy emission from GRBs for the first time. To generate the catalog, we examined 733 GRBs detected by the Gamma-Ray Burst Monitor (GBM) on Fermi and processed each of them using the same analysis sequence. Details of the methodology followed by the LAT collaboration for GRB analysis are provided. We summarize the temporal and spectral properties of the LAT-detected GRBs. We also discuss characteristics of LAT-detected emission such as its delayed onset and longer duration compared to emission detected by the GBM, its power-law temporal decay at late times, and the fact that it is dominated by a power-law spectral component that appears in addition to the usual Band model.

GRBs above ∼ 20 MeV. The first Fermi-LAT catalog of GRBs is a compilation of these detections and provides a systematic study of high-energy emission from GRBs for the first time. To generate the catalog, we examined 733 GRBs detected by the Gamma-Ray Burst Monitor (GBM) on Fermi and processed each of them using the same analysis sequence. Details of the methodology followed by the LAT collaboration for GRB analysis are provided. We summarize the temporal and spectral properties of the LAT-detected GRBs. We also discuss characteristics of LAT-detected emission such as its delayed onset and longer duration compared to emission detected by the GBM, its power-law temporal decay at late times, and the fact that it is dominated by a power-law spectral component that appears in addition to the usual Band model.

Introduction
Prior to the Fermi Gamma-ray Space Telescope mission, high-energy emission from gamma-ray bursts (GRBs) was observed with the Energetic Gamma-Ray Experiment Telescope (EGRET) covering the energy range from 30 MeV to 30 GeV (Hughes et al. 1980;Kanbach et al. 1988;Thompson et al. 1993;Esposito et al. 1999) on board the Compton Gamma-Ray Observatory (CGRO;1991-2000 and, more recently, by the Gamma-Ray Imaging Detector (GRID) onboard the Astro-rivelatore Gamma a Immagini LEggero spacecraft (AGILE; Giuliani et al. 2008;Tavani et al. 2008Tavani et al. , 2009. Despite the effective area and dead-time limitations of EGRET, substantial emission above 100 MeV was detected for a few GRBs (Sommer et al. 1994;Hurley et al. 1994a;González et al. 2003), suggesting a diversity of temporal and spectral properties at high energies. Of particular interest was GRB 940217, for which delayed high-energy emission was detected by EGRET up to ∼90 minutes after the trigger provided by CGRO's Burst And Transient Source Experiment (BATSE).
The Fermi observatory was placed into orbit on 2008 June 11. It provides unprecedented breadth of energy coverage and sensitivity for advancing knowledge of GRB properties at high energies. It has two instruments: the Gamma-ray Burst Monitor (GBM; Meegan et al. 2009a) and the Large Area Telescope (LAT; Atwood et al. 2009a), which together cover more than 7 decades in energy. The GBM comprises twelve sodium iodide (NaI) and two bismuth germanate (BGO) detectors sensitive in the 8 keV-1 MeV and 150 keV-40 MeV energy ranges, respectively. The NaI detectors are arranged in groups of three at each of the four edges of the spacecraft, and the two BGO detectors are placed symmetrically on opposite sides of the spacecraft, resulting in a field of view (FoV) of ∼9.5 sr. Triggering and localization are determined from the NaI detectors, while spectroscopy is performed using both the NaI and BGO detectors. Localization is performed using the relative event rates of detectors with different orientations with respect to the source and is typically accurate to a few degrees. The GBM covers roughly four decades in energy and provides a bridge from the low energies (below ∼1 MeV), where most of the GRB emission takes place, to the less explored energy range that is accessible to the LAT.
The LAT is a pair production telescope sensitive to γ rays in the energy range from ∼20 MeV to more than 300 GeV. The instrument and its on-orbit calibrations are described in detail in Atwood et al. (2009a) and Abdo et al. (2009g). The telescope consists of a 4×4 array of identical towers, each including a tracker of silicon strip planes with foils of tungsten converter interleaved, followed by a cesium iodide calorimeter with a hodoscopic layout. This array is covered by a segmented anti-coincidence detector of plastic scintillators which is designed to efficiently identify and reject charged particle background events. The wide FoV (∼2.4 sr at 1 GeV) of the LAT, its high observing efficiency (obtained by keeping the FoV on the sky with scanning observations), its broad energy range, its large effective area (>1 GeV is ∼6500 cm 2 on axis), its low dead time per event (∼27 µs), its efficient background rejection, and its good angular resolution (∼0 • .8 at 1 GeV) are vastly improved in comparison with those of EGRET. As a result, the LAT provides more GRB detections, higher statistics per detection, and more accurate localizations ( 1 • ).
Fermi has been routinely monitoring the γ-ray sky since 2008 August. From this time until 2011 August, when a new event analysis ("Pass 7", Abdo et al. 2012) was introduced, the GBM detected about 730 GRBs, approximately half of which occurred inside the LAT FoV. In ground processing we search for LAT counterparts to known GRBs, following each trigger provided by the GBM and other instruments. In addition, we also undertake blind searches for bursts not detected by other instruments on the whole sample of LAT data, with however no independent (i.e. not detected by other instruments) detections so far.
Owing to the detection of temporally extended emission by EGRET from GRB 940217 and the interest in studying GRB afterglow emission at high energies, Fermi was designed with the additional capability to repoint in the direction of a bright GRB and keep its position near the center of the FoV of the LAT (where the effective area to γ rays is maximal) for several hours (5 hrs initially, 2.5 hrs since 2010 November 23), subject to Earth-limb constraints. This repointing occurs autonomously in response to requests to the Fermi spacecraft from either the GBM or the LAT (Autonomous Repoint Request, or ARR hereafter), with adjustable brightness thresholds, and has resulted in more than 60 extended GRB observations between 2008 October 8, when the capability was enabled, and 2011 August 1.
This article presents the first catalog of LAT-detected GRBs. It covers a three-year period starting at the beginning of routine science operations in 2008 August. In § 2 we describe the data used in this study and the list of GRB triggers that we searched for LAT detections. In § 3 we give a detailed description of the analysis methods that we applied to detect and localize GRBs with the LAT, as well as the methodology which we followed to characterize their temporal and spectral properties. In § 4 and § 5, we present and discuss our results, with a special emphasis both on the most interesting bursts and on the common properties revealed by the LAT. The physical implications of our observations are addressed in § 6, where we also discuss several open questions and topics of interest for future analysis. In Appendix A, we investigate the possible sources of systematic uncertainties via testing different instrument response functions and configurations for the analysis. Finally, in Appendix B, we discuss each individual GRB in the catalog, reporting the details of its observation and considering it in the context of multiwavelength observations.

Data Preparation
In this section we describe the data analyzed in this study and the list of GRB triggers that we searched for LAT detections.
The results of this paper were produced using two sets of LAT events corresponding to different quality levels and corresponding instrument response functions (IRFs) in the event reconstruction: the Transient event class (Atwood et al. 2009a), which requires the presence of a signal in both the tracker and the calorimeter of the LAT, and the "LAT Low Energy" (LLE) event class (Pelassa et al. 2010), which requires a signal in only the tracker and essentially consists of all the events that pass the onboard γ filter having a reconstructed direction .
The LAT event classes underwent many stages of refinement and were released as different versions (or "passes") of the data. This catalog uses the whole "Pass 6" event data set, in particular, the Pass 6 version 3 Transient event class ("P6 V3 TRANSIENT"). The LAT team has switched from using "Pass 6", which had been used since the beginning of science operations, to "Pass 7" data on the 1st of August 2011, the end of the time period covered by this catalog.
As cross checks, we repeated some of the Transient class analyses using instead the "P6 V3 DIFFUSE" event class to search for possible systematics that might arise from the choice of event selection. Both the Transient and Diffuse classes offer good energy and an-gular resolutions, along with large effective areas above 100 MeV and reasonable residual background rates 1 . The Diffuse class uses a very selective set of cuts to keep the highest quality γ-ray candidates. As a result, it has a relatively narrow point-spread function (PSF; 68% containment radius of several degrees at 100 MeV and ∼0 • .25 at 10 GeV) and a smaller background contamination with respect to the Transient class. On the other hand, the Transient class, which is defined with a less selective set of cuts, offers a significantly larger effective area, especially below 1 GeV. The LLE class corresponds to a much-loosened selection, compared to the other two classes, and is designed to provide a far larger effective area at lower energies (especially below 100 MeV) and at larger offaxis angles (especially above ∼60 • ). The LLE PSF is wide (with a 68% containment radius of ∼20 • , ∼13 • and ∼7 • at 20 MeV, 50 MeV and 100 MeV respectively) and has a much higher background contamination (∼300 Hz over the whole FoV) than the other two event classes. Since the flux of a GRB is typically a decreasing function of the energy, the LLE class provides very good statistics, which are useful for detailed studies of the temporal structure of GRB emissions. It also allows us to examine GRBs with soft spectra or occurring at a high off-axis angle, which are not detectable with the other two event classes.
Our baseline LAT-only analysis (namely localization, detection, spectral fitting, and duration estimation) uses the Transient class data. We use the LLE data only for source detection and duration measurement. As mentioned above, the LAT Diffuse data are used only as a cross-check of some of the analysis results for Transient class.
We perform joint GBM-LAT spectral fitting using the LAT Transient class data, the GBM Time-Tagged Event (TTE) data and the GBM RSP/RSP2 response files 2 . We also use GBM CSPEC data to produce our background model (see § 3.1.2).
All our analyses also use the LAT FT2 data, which contain information on the pointing history and the location of the Fermi spacecraft around the Earth. We use FT2 files with 1 s binning.

LAT Data
We select Transient class with reconstructed energies in the 100 MeV-100 GeV range. The lower limit is chosen to reject events with poorly reconstructed directions and energies. Moreover, for Pass 6, the LAT response is not adequately verified at E<100 MeV energies and the contamination from cosmic rays misclassified as gamma rays is also significantly increased. The upper limit was chosen at 100 GeV since we do not expect to detect GRB photons at such high energies due to the opacity of the Universe and the limited effective area of the LAT. We select events in a circular region of interest (ROI) that is centered on the best available GRB localization. The LAT PSF depends on the event energy and off-axis angle and has been studied using Monte Carlo simulations. We use the resulting description of the PSF to increase the sensitivity of our analyses. For the event-counting and joint spectral-fitting analyses, we select a variable ROI radius that depends on the event energy and the off-axis angle of the GRB in such a way as to select almost all the events compatible with the position of the GRB given our PSF while rejecting much of the residual cosmic-ray background, increasing the signal-to-noise ratio of the selected data. To accomplish this, we split the events in logarithmically-spaced bins in energy and for each bin we select only the events contained in a ROI around the source having a radius corresponding to the 95% containment radius of the PSF evaluated at an energy equal to the geometric mean of the bin's energy range. For the duration estimation using Transient data we deal with longer time periods; thus we dynamically adjust the radii of the energy-dependent ROIs to follow the variation of the off-axis angle with time. On the other hand, for the LLE duration estimations and the joint GBM-LAT spectral analyses we use a single set of radii calculated using the PSF corresponding to the GRB off-axis angle at trigger time. The exact dependence of the LLE PSF on the off-axis angle is not available yet. Instead, only two possible LLE PSFs are available for setting the ROI radii: one for observations with off-axis angles greater and the other for observations closer to the center of the FoV. Finally, for cases for which the GRB localization error is not negligible (i.e., for GBM or LAT localizations) we increase the radius of each ROI by setting it equal to the sum in quadrature of the localization error and the 95% containment radius of the PSF. For GRBs localized by the Fermi GBM we also added in quadrature a 3 • systematic error. The maximum-likelihood analysis utilizes the PSF information internally while calculating the probability of each event being associated with the GRB; thus no optimization of the ROI radius, as above, is necessary. For the maximum-likelihood analyses, we use a fixedradius ROI set at 12 • , a value larger than the 99% containment radius of the Transient LAT PSF evaluated for a 100 MeV event on axis.
We apply a cut to limit the contamination from γ rays produced by interactions of cosmic rays with the Earth's upper atmosphere. For our maximum-likelihood analysis we use the gtmktime Fermi Science Tool 3 to select 3 http://www.slac.stanford.edu/exp/glast/wb/prod/pages/sciTools_gtmktime/gtmktime.htm only the time intervals (the "Good Time Intervals" or GTIs) in which no portion of the ROI is too close to the Earth's limb. Because the Earth's limb lies at a zenith angle of 113 • and to take into account the finite angular resolution of the detector, we exclude any events taken when the ROI is closer than 8 • to the Earth's limb or equivalently when it intersects the fiducial line at 105 • from the local Zenith. For special cases, when the position of the GRB is very close to the Earth's limb, we compensate the loss of exposure due to this cut by reducing the size of the ROI and simultaneously increasing the maximum zenith angle to 110 • . This increases the duration of the GTI significantly, allowing deeper exposures for searches of late γ-ray activity. For all the other analyses (namely event-counting analyses and joint spectral fitting), we do not apply a cut to select GTIs as above, but rather we process the whole observation and instead reject individual events reconstructed farther than 105 • from the local Zenith.

GBM Data
The response of a GBM detector depends on the continuously-varying position of the GRB in its FoV, with its effective area decreasing as the angular distance between the detector boresight and the source (θ GBM ) increases. Because of this, when θ GBM is large, any systematic effects due to imperfect modeling of the spacecraft or the individual detectors become relatively important (Goldstein et al. 2012). For this reason we use the data from the GBM NaI detectors that have angles θ GBM < 50 • at the time of the trigger and the BGO detector facing the GRB at the time of the trigger.
We also exclude any detector occulted by other detectors or the spacecraft during any part of the analyzed time interval, as advised in Goldstein et al. (2012).
Since θ GBM usually changes with time, the GBM Collaboration released RSP2 files which contain several response matrices corresponding to short consecutive time intervals (every 2 • of slew of the detector about the source). With a suitable weighting scheme, as described in § 3.4.1, these files provide an adequate description of the GRB detector responses.
Finally, in some cases, bright GRBs trigger an ARR, causing rapid variations of θ GBM with time for some of the GBM detectors. These variations create further variations in those detector responses and background rates. In fact, due to its orbital and angular dependence the background of those detectors can be very hard to predict. Also, the RSP2 files might not be binned finely-enough in time to cover these rapid variations, we excluded data from detectors that have such rapid variations.

Input GRB List
To search for GRBs in the LAT data we use as input a list comprising 733 bursts that triggered the GBM from 2008 August 4 to the 2011 August 1 (GBM triggers bn080804456 to bn110731465).
We use the localizations provided by the GBM, unless a localization from the Swift observatory (Gehrels et al. 2004), obtained either from the Burst Alert Telescope (Swift-BAT, Barthelmy et al. 2005), the X-Ray Telescope (Swift-XRT, Burrows et al. 2005), or the UV-Optical Telescope (Swift-UVOT, Gehrels et al. 2004), is available via the Gamma-Ray Burst Coordinates Network (GCN) 4 .
We analyzed all GRBs in the input list whether or not they occurred in the LAT FoV at the time of the trigger, since a GRB that is initially outside the LAT FoV can be observable at later times due to an ARR or simply due to the standard scanning mode. As a reference, 368 GBM bursts were in the LAT 4 http://gcn.gsfc.nasa.gov/ FoV at the time of the GBM trigger, with the FoV considered to have a 70 • angular radius. In 64 of these cases, an ARR was performed. It should be noted that the sensitivity of the LLE event class extends to larger off-axis angles θ ≈90 • .
In order to characterize our detection algorithm, we also created a list of "fake" GBM triggers, by considering trigger times earlier than the true GBM trigger time by 11466 s (approximately two orbits). Since the most common observing mode for the Fermi spacecraft is to rock between the northern and southern orbital hemispheres on alternate orbits, with the exception of ARRs, the burst triggers of the "fake" sample has the desirable property of having very similar background conditions as those of the true sample.

Analysis Methods and Procedure
We implemented a standard sequence of analysis steps for uniformity. The sequence consists of event-counting analyses performed on the Transient class and LLE data for source detection and duration estimation ( § 3.3), unbinned maximum likelihood analysis performed on the Transient class data for source detection, spectral fitting, localization ( § 3.2), and a spectral-fitting analysis performed jointly on the LAT Transient class and the GBM data ( § 3.4). Details of the implementation of the analysis sequence are given in § 3.5. Estimation of the backgrounds is a central part of all the analyses and is described below.

LAT
The background in the LAT data is composed of charged cosmic rays (CRs) misclassified as γ rays, astrophysical-source γ rays coming from Galactic and extragalactic diffuse and point sources, and γ rays from the Earth's limb produced by interactions of CRs in the upper atmosphere. The backgrounds for the Transient class and LLE data are dominated by the CR component, while for the cleaner Diffuse class the backgrounds are dominated by astrophysical γ rays. The CR component of the background depends primarily on the geomagnetic coordinates of the spacecraft and on the direction of the GRB in instrument coordinates (since the LAT's effective area varies strongly with the inclination angle). The component from the Earth's atmosphere depends on the angle between the GRB and the limb (i.e., on the zenith angle of the GRB) and is strongest toward the limb. Finally, the astrophysical background γ-ray component depends on the GRB direction and is typically stronger at low Galactic latitudes.
For the Transient event class analyses, we use the Background Estimation tool ("BKGE" hereafter), which was developed by the LAT collaboration and which takes into account all these dependencies. It can estimate the total expected backgrounds for any given ROI and period of time with an accuracy of ∼10-15% (Abdo et al. 2009d). It also provides separate estimates for the Galactic diffuse emission and for everything else, namely the sum of CRs and extragalactic diffuse emission ("isotropic component"). Note that the BKGE cannot estimate the backgrounds from the Earth's limb. However, the zenith-angle cut described in §2 is very effective at reducing this component to negligible levels; thus this limitation does not generally constitute an obstacle.
Our maximum likelihood analysis of Transient class data uses a background model calculated by a combination of the isotropic component provided by the BKGE tool and the Galactic diffuse emission template provided by the LAT Collaboration 5 .
The maximum likelihood analysis using the cleaner Diffuse class data, which were per-5 http://fermi.gsfc.nasa.gov/ssc/data/access/lat/BackgroundModels.html formed for validation studies (see Appendix A), uses the Galactic diffuse emission template plus the public template describing the "isotropic background" (extragalactic diffuse emission and CR background) as a single spectrum of the intensity averaged over the whole sky. The BKGE does not produce estimates for Diffuse class events. For the time scales analyzed in this study, the contribution from point sources is typically negligible, so we do not take them into account in the background models.
For the joint GBM-LAT spectral analysis, we used as background for the LAT the estimates provided by BKGE of the total background in the energy-dependent ROI. For technical reasons related to the broad PSF of the LLE class, we cannot use the BKGE to estimate the LLE background. Instead, we evaluate it directly from the LLE data associated with each individual observation. First, in order to ensure enough events in every time bin, we bin the LLE data in time with a coarse binning of 5 s, from well before the trigger time to well after the end of the burst as measured by the GBM. We then fit the background rate as a function of time b(t) by taking into account the variation of the exposure due to the changing orientation of the LAT. Phenomenologically, we adopt the function b(t) = p 0 + p 1 C(t) + p 2 C(t) 2 , where C(t) = cos[θ(t)] and θ is the off-axis angle. The parameters p 0 , p 1 , and p 2 are obtained by fitting the "pre-burst" and "post-burst" time windows simultaneously. We use a conservative definition of these time windows based on the burst duration as measured by the GBM. In particular, the "post-burst" data start well after the end of the low-energy emission as seen by the GBM. Finally, the fit parameters allow us to compute the background rate at any time during the burst, and we use the covariance matrix from the fit to evaluate the uncertainty of this prediction. We compared this simple model to an alternative prescription b(t) = pol(t) * C(t), where the degree of the polynomial function pol(t) is increased until a good fit to the data is obtained. Typically a polynomial of degree 1 or 2 was sufficient, although in few cases a higher degree (3 or 4) was necessary. The expression above is motivated by the fact that, as a first approximation, the effective area of the LAT to CRs scales as cos (θ) and that we can model the CR contribution on-axis (θ = 0) with a polynomial. The two prescriptions gave very similar results in all cases. An example of the standard prescription is shown in Fig. 1.

GBM
We use the GBM CSPEC event data from before and after the GRB prompt phase to obtain a model for the background, similar to the procedure followed for the LLE data above. For each selected detector, we integrate the CSPEC spectra over all the energy channels to obtain a light curve, and then select two off-pulse time intervals: one before and one after the GRB prompt emission (see left panel in Fig. 2). We fit polynomial functions f (t) of increasing degree D to the data from these two time intervals, minimizing the χ 2 statistic, until we reach a good fit (i.e., with a reduced χ 2 ≃ 1). Then, we consider the light curves corresponding to each of the 128 channels separately, again with data from the off-pulse intervals, and we fit them with a polynomial of degree D by minimizing the Poisson log-likelihood function 6 . After each fit, we check by eye that the residuals are compatible with statistical fluctuations. If this is not the case, we repeat the procedure from the beginning, changing our choice for the off-pulse intervals, until a good fit has been achieved. The set of 128 polynomial functions constitutes our background model, and the predicted number of background events b i in the i-th channel of the background spectrum is the integral of the corresponding polynomial function f i (describing the rate) between t 1 and t 2 : The statistical error of the integral is computed using the covariance matrix from the fit 7 . Since the background for GBM detectors is much less predictable than for LLE data, we determine the off-pulse regions manually. In order to minimize the statistical and systematic errors (hence ensure a reliable background estimate), the off-pulse time intervals must be close to the GRB's signal, have a long-enough duration, and also possibly have a smooth part of the light curve without bumps or other structures. Moreover, the number of counts in each channel is much smaller than the total number of counts used to determine D. Thus, the larger value of D is, the more f i can pick up statistical fluctuations in some channels, giving a slightly wrong interpolation for those channels in the pulse region. Thus, we try to find off-pulse intervals well described by low-order polynomials (ideally D = 1). Unfortunately, this is not always possible. For example, for GRBs triggering ARRs, the background can vary quickly in response to the change of pointing, requiring higher-order polynomials to describe it. This effect introduces some additional noise in the spectrum, but it is unlikely to introduce any bias in the fit results, given its random nature. Note that it is not possible to fix the shape of the polynomial, since the background shows spectral evolution and thus every channel needs to be considered independently. In some cases, even with high-order polynomials, fitting the model to the background can be difficult and even impossible without being completely arbitrary (see right panel in Fig. 2 for an example). In those cases we opt for excluding the problematic detector from the analysis. These issues are not solvable at present given our current understanding of the detectors and their backgrounds. More advanced techniques to deal with the backgrounds are currently under investigation by the Fermi-GBM Collaboration (Fitzpatrick et al. 2012).

Maximum Likelihood Analysis
We perform an unbinned maximum likelihood analysis using the tools in the Fermi ScienceTools software package, version 09-26-02 8 . An overview of the method and its application for this study is given below. For 8 http://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/ref_likelihood.html more information see Band et al. (2009) and references therein.
The unbinned analysis computes the loglikelihood of the data using the reconstructed direction and energy of each individual gammaray and the assumed sky model folded through the instrument response functions of the LAT. The sky model includes the GRB under investigation modeled as a point source, typically with a power-law spectrum, as well as other components that describe the other sources that are expected to be present in the data. For the short time scales ( 10-100s) considered these are predominantly diffuse emission from the Galaxy and residual charged particle backgrounds, though in principle, a bright, nearby point source, such as Vela may be included. To estimate the spectral properties of the GRB, the model parameters are varied in order to maximize the log-likelihood given the data. Usually, the GRB coordinates are held fixed, but if a localization using the LAT data is desired, those parameters can also be varied.
The fitting in the Likelihood tools is performed using an underlying engine such as MINUIT 9 to perform the maximization. Currently, the unbinned analysis does not take into account energy dispersion. However, given the good energy resolution of the LAT ( 15% above 100 MeV), the moderate energy dependence of the LAT effective area at the energies considered, and the simple power-law spectral form that we consider, approximating the true energy by the reconstructed one is justified. The uncertainties of the best-fit values of the parameters or any upper/lower limits are estimated from the shape of the loglikelihood surface around the best-fit.
We apply the likelihood analysis to Transient class events, and as cross check, we also analyze Diffuse class events, with the data cuts described in § 2. We cannot apply a similar unbinned maximum likelihood analysis to  An example of a selected GBM detector (NaI 0 ) and its background fit (lower panel), and the angular distance between the axis of the detector and the GRB position (upper panel). The shaded regions mark the selected off-pulse intervals, while the dashed line is the best-fitting polynomial model (see text). (right) An example of an excluded detector (NaI 3 ): the change in angular distance between the detector axis and the source is too fast (upper panel), producing a change in the light curve which cannot be modeled satisfactorily with a polynomial model. the LLE data, since the PSF, energy dispersion, effective area for the LLE events and the expected backgrounds are not adequately known and/or verified yet. The analysis of LLE data is similar to that of the GBM data and is described below.
The background model is constructed as described in § 3.1. The normalization of the "isotropic background" provided by the BKGE, used for the analysis of Transient class events, is one of the free parameters of the fit and has a Gaussian prior of mean 1 and a width set to encompass any associated statistical and systematic errors (typically around 15%). The normalization of the "isotropic background" template, used for the analysis of Diffuse class data, is free to vary with no prior and no constraints. To avoid increas-ing the number of free parameters, we keep the normalization of the template for Galactic diffuse emission fixed to 1 for the analyses based on both event classes.

Source Detection
To determine the significance of the detections of sources using the maximum likelihood analysis, we consider the "Test Statistic" (TS) equal to twice the logarithm of the ratio of the maximum likelihood value produced with a model including the GRB over the maximum likelihood value of the null hypothesis, i.e., a model that does not include the GRB. The probability distribution function (PDF) of the TS under the null model is given by the probability that a measured signal is compatible with statistical fluctuations. The PDF in such a source-over-background model cannot, in general, be described by the usual asymptotic distributions expected from Wilks' theorem (Wilks 1938;Protassov et al. 2002). However, it has been verified by dedicated Monte Carlo simulations (Mattox et al. 1996) that the cumulative PDF of the TS in the null hypothesis (i.e., integral of the TS PDF from some TS value to infinity) is approximately equal to a χ 2 n dof /2 distribution, where n dof is the number of degrees of freedom associated with the GRB. The factor of ½in front of the TS PDF formula results from allowing only positive source fluxes.
Since we model the GRB spectrum as a power law with two degrees of freedom and we fix the localization, the TS distribution should nominally follow (1/2)χ 2 2 . This is formally correct if the localization of the GRB is provided by an independent data set (i.e., from another instrument). However, when the input localization is not sufficiently precise, we optimize it using the same data set used for detecting the source, thereby introducing two additional free parameters (R.A. and Dec.). In this case, the TS distribution should follow (1/2)χ 2 4 . In practice, the steps of detection and localization are iterated many times, and a detection step is performed using an ROI centered on the position found by a prior localization step. Therefore, the data sets used in each step are not exactly overlapping. For this reason, we expect some deviation from (1/2)χ 2 4 distribution. For simplicity, we set a unique threshold of TS min =20 for our analysis independent of the origin of the localization. This formally corresponds to two slightly different one-sided Gaussian equivalent thresholds, 4.1σ for χ 2 2 and 3.5σ for χ 2 4 . Additionally, we check the calibration of the detection algorithm on a sample of "fake GBM triggers" generated as described in § 2.2. With the aforementioned value of TS min we obtain zero false detections on the "fake GBM triggers" sample (see §4.1 for more details).

Localization
We compute the localizations with the LAT in two steps. The first step provides a coarse estimation of the GRB position and is performed using the gtfindsrc Fermi Sci-enceTool. At this stage, we look for an excess consistent with the LAT PSF, and we do not assume a particular background model. Although this method is quick and robust, it assumes that the likelihood function is parabolic and symmetric in azimuth around the found position, and so the provided localization error can be slightly underestimated. Therefore, this step is only used to obtain an initial seed for the follow-up analysis.
For a more accurate localization we use the gttsmap Fermi ScienceTool, which starts from the best-fit background model obtained by the likelihood fit and builds a map of the TS in a grid around the best available localization of the source. The GRB spectral parameters are fitted at each position in the grid, along with all free parameters of the background model. The grid size and spacing are set based on the localization error obtained in the first step. The final LAT localization corresponds to the position of the maximum of the TS map. Its statistical uncertainty is derived by examining the distribution of TS values around it. Following Mattox et al. (1996), we interpret changes in the TS values in terms of a χ 2 distribution with two degrees of freedom to account for the flux and spectral index of the GRB. Specifically, a confidence-level (CL) uncertainty is given by the TS map contour that corresponds to a decrease from the maximum value by a value equal to the CL quantile of the χ 2 2 distribution. For example, the 90% (68%) confidence level corresponds to a decrease of the TS from its maximum value by 4.61 (2.32).

Event probability
We estimate the probability of each γ-ray being associated with the GRB by using the gtsrcprob Fermi ScienceTool. The probability computation takes into account the spectral, spatial (extent), and temporal (flux) information of all the components in the source model, and the response of the LAT (PSF and effective area) to the particular event. The probabilities are assigned via the likelihood analysis and are computed starting from the best-fit model. In particular, the probability that a photon is produced by a component i is proportional to M i given by (1) where S i (ǫ, p, t) is the predicted counts density from the component at energy ǫ and position p, and (observed) time t, and and the integral is the convolution over the instrument response R(ǫ, p; ǫ ′ , p ′ , t). In general, the predicted count density is the sum of the different contributions S i (ǫ, p, t), including the extended backgrounds (such as the isotropic component and the Galactic diffuse emission), background point sources (nearby bright sources) and the GRB under study. Each contribution is described by a model, the parameters of which are optimized during the maximum likelihood fit. We simplify the calculation by not including nearby bright sources, as, in these short time scales, they do not contribute significantly to the total number of counts. Once we compute the maximum likelihood model for the observed number of counts, we assign to each event the probability of being associated to a particular component i.
Because the flux varies with time, we perform the calculation in several time bins so that the flux is never averaged over long time intervals. We tested schemes for defining the time intervals including linear, logarithmic, and Bayesian-blocks (Scargle et al. 2012) binnings, and the results were stable among the different choices. For consistency with the other parts of the analysis we chose the same logarithmically-spaced time bins used in the time-resolved spectral analysis described in § 3.5 below.

Event Counting Analyses
As mentioned in the previous section, the effective area of the Transient class decreases strongly for off-axis angles greater than ∼70 • or for energies less than ∼100 MeV. For this reason, in addition to the maximum likelihood analysis applied to Transient class data described above, we search for sources using the LLE class. This class provides a significantly larger effective area below 100 MeV and a wider acceptance, although with a higher background level. We use it to obtain another duration measurement as well, which is dominated by events below 100 MeV and is thus complementary to the duration measurement obtained with Transient class data.

Source Detection using LLE data
Consider a GRB as an impulse f (t) superimposed on a background signal b(t). De-pending on the unknown shape of f (t), there will be a particular time scale δt and a particular start time t 0 maximizing the quantity which is the significance of the signal in the Gaussian regime. The pair δt, t 0 corresponds to the highest sensitivity to the signal of this particular GRB. Our source-detection method searches for the closest pair to δt, t 0 by resizing and shifting the time bins and selecting the light curve that contains the single bin with the highest significance. Since the typical event rate inside the LLE ROI is not particularly large (∼10-20 Hz for the background), the Gaussian approximation implicit in Eq. 2 is not always justified. The significance S in each bin is thus derived from the Poisson probability of obtaining the observed number of counts given the expectation from the background, by converting this probability to an equivalent sigma level for a onesided Standard Normal distribution. Our algorithm starts by defining a conservative window around the trigger time, with a total duration depending on the GBM burst duration T 90 . Then, a set of 10 bin sizes δt is defined depending on the T 90 . For each of these bin sizes, the algorithm computes 11 light curves with shifted bins, i.e., with the bins centered on t 0 +(i/20) δt (i = 0...10). For each of these 10×11 light curves, the background function b(t) is fitted to the data outside the GRB window (as described in § 3.1), and the algorithm seeks the bin with the largest significance S inside the GRB window. This value is then corrected for the number of trials, i.e., by the number of bins N in the current light curve. If p is the probability corresponding to S, then the corrected-fortrials probability is p ′ = 1 − (1 − p) N . This new probability is converted to a Gaussianequivalent significance S ′ , and the pre-trials significance for the detection of the GRB is defined as S pre = max(S ′ ), where the maximum is computed over the 110 light curves. Since the data have been rebinned multiple times, a post-trial probability is finally computed to account for these not-independent trials. For this purpose, we performed 3 × 10 6 Monte Carlo simulations of the background, running our algorithm and recording S pre for each realization. The resulting distribution of S pre is well described by a Lorentzian function 1 + [(x − x 0 )/r c ] 2 ] −β , with x 0 = 1.36, r c = 7.38 and β = 41.8 (χ 2 = 43.2 with 38 d.o.f). We use this function to convert the pre-trials significance S pre into a post-trials significance S post . We consider as LLE-detected the GRBs that have post-trial significances S post > 4σ, which correspond to chance probabilities P < 3 × 10 −5 . We ran our algorithm on the 733 GRBs of the GBM sample (see §2.2), and so we expect no false-positive detections using this arbitrary threshold.

Duration measurement
We describe the duration of a GRB detected by the LAT using the parameter T 90 (Kouveliotou et al. 1993). A simple measurement of T 90 starts with the construction of the integral distribution of the number of background-subtracted events accumulated since the trigger time. As the GRB becomes progressively fainter, the distribution flattens and eventually reaches a plateau.
The calculation of the duration of the emission consists of finding the times where the integral distribution reaches the 5% and 95% levels of its total height (called T 05 and T 95 respectively), and calculating their difference T 90 ≡ T 95 − T 05 . Our duration estimation method is based on the above simple prescription, but is also extended to estimate the statistical uncertainty of the results, and accounts for the effects of effective area variations over time (for its application to the Transient class events).
Because of the unavoidable statistical fluctuations involved in the process of detecting an incoming GRB flux, a GRB observed under identical conditions by a number of identical detectors will in general produce different detected light curves, and hence different duration estimates. Our method quantifies the uncertainties on the duration estimates associated to these statistical fluctuations. In short, it accomplishes this by treating the detected light curve as the true one (i.e., that of the incoming γ-ray flux), producing a set of simulated light curves by applying Poissonian fluctuations on the detected one, estimating the durations of the simulated light curves, and calculating a single duration estimate and its uncertainty from the distribution of simulated duration estimates.
Our method starts by constructing the integral distribution of the accumulated background-subtracted events curve in small steps in time. For each step, the number of expected background events is estimated and the number of detected events is counted. At the end of each step, an algorithm checks for the presence of a plateau by searching for statistically significant increases in the average value of the points added last to the curve. If a certain number of steps does not increase the integral distribution, a plateau is reached and the construction stops. A set of simulated light curves are then produced, by adding Poisson noise to the observed light curve, and the corresponding integral distributions are produced. A duration estimation is made for each of the simulated light curves and the results (T 05 , T 95 , T 90 ) are recorded. After the durations of all the simulated light curves have been measured, the median and a (minimum-width) 68% containment interval are calculated for each distribution, and used as our measurements and ±1σ errors. In case the light curve contains multiple peaks separated by quiescent periods, the algorithm, depending on the intensity of each peak and the duration of the intermittent quiescent pe-riods, might set the beginning of the plateau at the end of the last peak or during a quiescent period. In the latter case, some of the late emission might not be fully accounted for by the produced duration. However, the returned statistical errors would be appropriately increased in both cases, indicating the uncertainty of identifying the end of the emission.
Any changes in the off-axis angle of the GRB during an observation will change the effective area of the LAT, affecting the light curve. For example, a GRB observation that involves an ARR will in general start with a moderate to large off-axis angle which will then rapidly decrease and stay small for most of the rest of the observation. Because the effective area of this observation will be small before the ARR starts, the count rate will be artificially decreased and this would cause a bias in the measurement of the T 05 if it were simply based on counts. To account for this effect, we weight the simulated light curves by the inverse of the exposure.
To illustrate this method we present in Fig. 3 the case of GRB 080916C, and the duration measurement using the Transient class data. These curves are used as the basis for the simulations. Fig. 4 shows the distribution of T 05 , T 95 , and T 90 , as measured from the simulations. These distributions are used to define the duration and associated error. In this particular case some excess events were observed at late times (about ∼400 s), as can be seen in Fig. 3. Consequently, a small fraction of the simulated light curves gave T 90 and T 95 that were very close to ∼400 s, which caused a small increase of the duration estimates and of the errors for positive fluctuations.
In some cases, a GRB observation can be interrupted before the GRB emission becomes too weak to be detectable (i.e., before reaching a plateau in the integral distribution).
Such interruptions can happen if the GRB exits the FoV of the LAT, it becomes occulted by the Earth, or the LAT enters the South Atlantic Anomaly (SAA), suspending observations. In these cases, only a lower limit on the duration can be obtained (with no errors), equal to the time interval between T 05 and the interruption of the observation.
We apply this method to both Transient class data and LLE data. In the former case we use the BKGE to estimate the background, while for the latter case we use the polynomial fit, as described in § 3.1.1. Note however that in the calculation of the duration the exposure weighting is performed only for Transient class data, since the effective area for the LLE class has not been characterized yet.
As a cross check, we also apply a different algorithm on LLE data. We consider the light curve with the binning that gives the highest significance, as obtained by the algorithm explained in § 3.3.1, and we measure T 05 , T 95 and T 90 on the integral distribution obtained from that light curve. We verified that the numbers obtained with this simple method are always within the errors obtained with the other method. Thus, we will only provide the set of results related to the first algorithm.

Joint LAT-GBM Spectral Analysis
We performed joint GBM-LAT spectral fits for every GRB detected by the LAT.

Data preparation
We start by selecting the GBM detectors as described in § 2 and estimate the expected backgrounds as described in § 3.1.2. We then use the Fermi Science Tool gtbin to extract the observed spectrum (source + background) from the GBM TTE event data. We obtain the response of a GBM detector in the interval to be analyzed (t 1 -t 2 ) using the RSP2 file for the detector for the time interval. Because the RSP2 file contains several response matrices corresponding to consecutive time intervals that in general are shorter than t 1 -t 2 , we sum the matrices of all the sub-intervals included in t 1 -t 2 using an appropriate weighting scheme. Specifically, if c i is the counts detected in the sub-interval covered by the ith matrix, and C = j c j is the number of counts detected between t 1 and t 2 , then the weight for the i-th response matrix is: To sum the matrices we use the tool addrmf 10 part of NASA HEASARC's FTOOLS 11 . For the analysis of LAT observations of all GRBs detected inside the LAT FoV, we use the Transient class events as described in § 2. We bin the LAT data in 10 logarithmicallyspaced energy bins between 100 MeV and 250 GeV, and use an energy-dependent ROI as described in § 2.1.1. We derive the observed spectrum and the response matrix using the Fermi Science Tools gtbin and gtrspgen. We also use the BKGE to obtain a background spectrum containing the contributions from all the sources of background, as described in § 3.1.1.
Note that for GRBs detected by the LLE photon counting analysis outside the LAT FoV we used only GBM data for the spectral analysis.

Spectral fit
We load the spectra and response matrices in XSPEC v.12.7 12 . For GBM data, we exclude from the fit all of the NaI channels between 33 keV and 36 keV (corresponding to the Iodine K-edge, see Meegan et al. 2009b), and ignore the channels at the extremes of the spectra (channels below 8 keV and channels 127 and 128 for NaI ; channels 1, 2, 127, and 128 for BGO). We do not exclude any energy bin in the LAT spectrum, since we already selected the data before binning them. We jointly fit the GBM and LAT data with several models (described below), minimizing the negative log-likelihood. This likelihood function is derived from a joint probability distribution, obtained by modeling the spectral counts as a Poisson process and the background counts as Gaussian process. For the latter, the Gaussian standard deviation for the i-th channel is given by σ i = σ 2 stat,i + σ 2 sys,i , where σ 2 stat,i and σ 2 sys,i are the statistical and the systematic variances respectively. The maximum likelihood principle assures that the derivatives of the likelihood function with respect to the parameters are null for the best-fitting set of parameters. Exploiting this, one can treat the means of the Gaussian functions describing the background counts as nuisance parameters, and remove them from the fitting procedure by expressing them as functions of the other parameters. This is a rather standard statistical procedure, and leads to the formulation of a so-called profile likelihood function. PGstat is defined as the natural logarithm of such function (see the XSPEC website 13 for more details). The fitting algorithms implemented in XSPEC find local minima for the statistic, but they can fail to converge to the global minimum. This is a known issue with gradientdescent algorithms (Arnaud et al. 2011). To mitigate this problem, we perform multiple fits (from 10 to 40) for each model, each time starting from a different set of values for the parameters, and we keep as the putative best fit the set giving the lowest overall value for the statistic. If while computing error contours for this set of parameters, the fitting algorithm finds an even better minimum for the statistic, we adopt that as the new putative best fit, and restart the error computation, iterating the procedure until no new minimum is found.

Spectral Models
Traditionally, GRB spectra have been described using the phenomenological "Band function" (Band et al. 1993) or a model consisting of a power law with an exponential cutoff (also called "Comptonized model"). Another common choice is the smoothly broken power law (SBPL) (Ryde 1999). Recently, the logarithmic parabola has been shown to be a good description the spectra of some GRBs, especially in time resolved analyses (Massaro et al. 2010;Massaro & Grindlay 2011). We call these 4 spectral models main components. One of the first results by Fermi was the need for multi-component spectral models for some GRBs, showing an high-energy excess over the main component which has been modeled with an additional power law Abdo et al. 2009e). In one case, Fermi observed a high energy cutoff which required the addition of an exponential cutoff to the power law component in the spectral model (Ackermann et al. 2011a), for a total of three components (Band, power law and exponential cutoff). In the following we will call the power law and the exponential cutoff functions additional components, to emphasize the fact that we add them to the main components when needed. Some authors have claimed the presence of a thermal component, modeled by a black body emission spectrum (see e.g., Guiriec et al. (2011);Zhang et al. (2011) and references therein). However, a careful time-resolved analysis is needed in order to investigate and characterize such a component, which is outside the scope of the present analysis. Thus we did not include the black body component in our spectral fits. Hereafter, N (E) is the differential photon flux (in units of cm −2 s −1 keV −1 ) expected from a model at a given energy E (in keV), and k is a normalization constant whose units depend on the model. We have 4 main model components: (I) Comptonized model (a power law with an exponential cutoff): where α is the photon index and E 0 is the cutoff energy.
(II) Logarithmic parabola, defined following equation 9 in Massaro et al. (2010): where S p is the height of the SED at the peak frequency, E p is the peak energy and b represents the curvature of the spectrum.
(III) Band model (Band et al. 1993): two power laws joined by an exponential cutoff: Note that this is the representation that uses the e-folding energy E 0 (keV) instead of the peak energy E p , where E p = (2 + α)E 0 . α and β are respectively the (asymptotic) photon index at low energy and the photon index at high energy.
(IV) Smoothly broken power-law (Ryde 1999): two power laws joined by a hyperbolic tangent function with adjustable transition length: where E piv is a fixed pivot energy, α and β are respectively the photon index of the low-energy and of the high-energy power laws, E 0 is the e-folding energy and δ is the energy range over which the spectrum changes from one power law to the other.
Here are the definitions of our additional model components: Because of the variety of spectral models, we have considered a number of functions, composed of one main component and one or more additional components: Band, Band + power law, Band + power law with exponential cutoff (≡ B(E) + kE −α e −E/E0 ), Band with exponential cutoff (≡ B(E)e −E/E0 ), Comptonized, Comptonized + power law, Comptonized + power law with exponential cutoff, Logarithmic Parabola, SBPL, SBPL + power law. To take into account the relative unknown uncertainties in the inter-calibration between the different detectors, for bright bursts we also apply an effective area correction (Bissaldi et al. 2011): we scale the model under examination by a multiplicative constant, with the constant being fixed to 1 for the LAT (taken as reference detector), but free to assume different values for all the other detectors. For GRB for which we do not use LAT data, we choose one of the NaI detectors as the reference. While for bright bursts adding such a correction changes the best fit parameters and the value of the statistic, for the other bursts it is essentially inconsequential, since in the latter cases statistical errors dominate over the inter-calibration uncertainties. For such spectra the multiplicative factors are unconstrained during the fit, and therefore we removed them. After the best fit is found, we fix all the factors to their best fit values and we proceed with the error computation. The correction factors typically have values between 0.95 and 1.05 for NaI detectors, and between 0.75 and 1.25 for the BGO detectors.

Definition of a good fit and model selection
The main focus of the spectral analysis performed here is to characterize the GRB spectrum, which requires selecting the most appropriate spectral model. We define the best model for a given GRB as the simplest one giving a "good" value for the test statistic (PG-stat, S in the following) and no evident structures in the residuals. Since S is based on a Poisson likelihood, we do not have a simple goodness-of-fit test comparable to the χ 2 test when minimizing the χ 2 statistic. The actual expected value S * for the statistic S is a function of the number of counts N in the spectrum and of the background model and its uncertainties, and can be estimated using Monte Carlo simulations. We assume a model m 0 ( p) (for example, the Band model) with the best fitting set of parameters p 0 as the null hypothesis, and we generate 1 million realizations of m 0 ( p 0 ) and the corresponding background spectrum using the fakeit command of XSPEC. Each realization r i p0 is obtained by adding Poisson noise to the count spectrum obtained by summing the observed background spectra and m 0 ( p 0 ). Correspondingly, each realization of the background spectrum is obtained by adding Gaussian noise to the observed background spectrum, using a total variance composed of the statistical and the systematic variance of the observed background. Then we fit m 0 ( p) to r i p0 and we record the value for the statistic S i . In Fig. 5 we show an example of a distribution for S obtained using the Band model, and a χ 2 distribution for the same number of degrees of freedom as reference. Note that depending on the case, the two distributions can be very different. We can now use the distribution for S resulting from the simulations to compute the probability of obtaining the observed value for S under the null hypothesis m 0 . This approach requires a large number of simulations, so we applied it just for the subsample of GRBs for which we claim the In order to compare different models, we considered them in pairs. Let us consider the model m 0 with n 0,dof and m 1 .If S 0 < S 1 and n 0,dof ≤ n 1,dof then m 0 describes the data better using fewer or the same number of parameters and we consider it a better fit following the definition given at the beginning of this section. If S 0 ≃ S 1 and n 0,dof = n 1,dof the two models are equivalent, and we should report the results for both the models. Anyway, this never happened in our analysis. On the other hand, if S 0 > S 1 then m 1 better fits the data, and we have to decide if the improvement is significant enough to justify the added complexity. In the literature there are different ways to quantify this improvement, sometimes incorrectly (see for example discussion in Protassov et al. 2002). One of the standard methods is the likelihood-ratio test, which uses as test statistic the difference in S between the two models ∆S. In the case of nested models m 0 and m 1 , Wilks' theorem (Wilks 1938) assures un-der certain hypotheses that the quantity ∆S asymptotically follows a χ 2 distribution with n = n 0,dof −n 1,dof degrees of freedom. Unfortunately, in all the cases of interest here the theorem's hypotheses are not satisfied and the reference distribution for ∆S is not known. In general one should perform dedicated Monte Carlo simulations to obtain the reference distribution. Performing such simulations for each pair of models is not practical. Thus, we select three cases of interest (i.e., Band versus Band + power law, Band versus Band with exponential cutoff, and Band+power law versus Band + power law with exponential cutoff) and we perform several million simulations to evaluate the reference distributions. We use the same procedure as above, using the simplest model as the null hypothesis, but we fit both m 0 and m 1 to each simulated data set, recording ∆S. At the end of the simulation, the distribution for ∆S is used to compute the probability P of obtaining a ∆S greater than the observed value, which corresponds to the complement of the cumulative distribution function. In Fig. 6, we plot this function for the three cases. We fix an arbitrary threshold at P th (> ∆S) = 1 × 10 −5 , where the statistical error on the simulated distribution, visible toward the tail, is still low. P th corresponds to a significance level of ∼ 4.2σ, and defines a threshold for ∆S above which we claim a significant detection of an extra component. Specifically, P th corresponds to ∆S = 25 for Band versus Band + power law, ∆S = 28 for Band versus Band with exponential cutoff, and ∆S = 20 for Band + power law versus Band + power law with exponential cutoff.

Analysis Sequence
The sequence of analyses performed in this work is graphically represented in Fig. 7. We start our analysis using the best available localization provided via GCN typically by Swift or the GBM and in some cases by other observatories. Detections occurring in Auto-  mated Science Processing (ASP) of LAT data (Band et al. 2009) are also used as inputs. We then extract both Transient class and LLE data. We use the Transient class data to optimize the location of the GRB. However, if the reported position error is significantly smaller than the angular resolution of the LAT, there is no room for improvement and we adopt the "GCN" position. This is the case for localizations provided by Swift or by optical observatories. On the other hand, if the reported position has an error larger than the characteristic size of the LAT Transient class PSF (∼0.5 deg at 1 GeV) -most notably those typically provided by the GBM -we repeat most of the steps in our analysis sequence multiple times, starting each iteration with the best position obtained during the localization step of the previous one, until we cannot improve the localization further. Typically we repeat the analysis 2-3 times until the localization obtained in the last step is within the error on the localization of the previous iteration. This introduce a small number of trials, which are also strongly correlated since they only involve small changes in the analysis configuration/data. High confidence localization errors (90%-95%) are not affected, and we therefore decided to ignore this trial factor. The analysis of Transient class data consists of the following steps.

(I) Duration Measurement
We apply the techniques described in § 3.3.2 to compute the duration (T 90 ) of the burst, using Transient class data. We define the "LAT interval" as the time interval from T 05 to T 95 (of duration T 90 = T 95 -T 95 ) measured in this step. In case of a non-detection, the value of the LAT T 90 is not available in the following steps.
(II) Time-resolved likelihood analysis The next step consists of a timeresolved spectral analysis, which allows us to study the temporally extended emission systematically, one of the common characteristics of LAT GRBs. We analyze all data contained in Good Time Intervals (GTIs, see § 2.1.1) within 10 ks from the GRB trigger, binning them in time. We tested several binning schemes, including linear, logarithmic, and Bayesian-blocks binning, and the resulting likelihood fit parameters were consistent among the different choices. The logarithmically-spaced binning provides constant-fluence bins when applied on a signal that decreases approximately as 1/time, such as the extended GRB emissions observed by the LAT. We adopt that scheme as the starting point, we start from a bin size containing at least N events, where N corresponds to the number of parameters in the model, plus 2, and then we merge consecutive time bins until obtaining a minimum TS value.
Specifically, we divide the data into logarithmically-spaced bins, truncating bins at the edges of excluded time intervals when necessary. Then we merge bins until each of them has a number of counts at least equal to the number of parameters of the likelihood model plus 2. We then fit each bin using the maximum likelihood analysis described in § 3.2 obtaining the likelihood and the TS value corresponding to the bestfit source model. If the resulting TS value is lower than an arbitrary threshold (T S < 16 , corresponding to a pretrials significance >∼3.2-3.8σ depending on n dof ) we merge the corresponding time bin with the next one, and we repeat the likelihood analysis. This step is iterated until one of two conditions is satisfied: 1) we reach the end of a GTI before reaching T S = 16, in which case we compute the value of the 95% CL upper limit (UL) for the flux evaluated using a photon index of 2 14 ; 2) we reach T S > 16, in which case we evaluate the best-fit values of the flux and the spectral index along with their 1σ errors.
The time interval between the beginning of the first and the end of the last time bin for which TS> 16, named "LAT temporally extended time interval" (hereafter "LATTE"), constitutes a rough estimate of the time window where the GRB emission is detectable with at least a ∼ 3σ significance.
(III) Characterization of the extended emission After having characterized the GRB in each time bins separately, we study the light curve as a whole. Specifically, we select the events contained in an energy-dependent ROI (see §2.1.1) in each time bin, building a light curve of the detected counts, and we estimate the background in each time bin using the BKGE. We also compute the exposure (in cm 2 s) associated with each time bin, using the tool gtexposure 15 calculated in each energy-dependent ROI separately. This last step requires knowledge of the spectrum. For each time bin we use the corresponding best fit power-law model as found in the binby-bin analysis described before. We note here that in principle the uncertainty in the best fit parameters for the power law would translate into an uncertainty in the value of the exposure, because of the energy dependence of the effective collecting area of the LAT. In our case, such an error is typically of the order of 5%, which is smaller than the systematic uncertainty in the response of the LAT, and will be neglected.
Summarizing, for each time bin i we have the observed number of counts N i (in the energy-dependent ROI), the corresponding background estimate B i , and the corresponding exposure A i . Assuming a given model for the light curve M (t) (for example a power law), we compute the expected number of observed counts in the i-th bin between t i,1 and t i,2 as: We compare N i,pred with N i and look for the best fit parameters for the model M (t), minimizing a Poisson loglikelihood function. We actually used the PG-stat log-likelihood function implemented in Xspec v.12, which takes into account the uncertainty on B i (see §3.4.2 for details). This technique, which might seem unnecessarily complex, provides a natural way of including in the fit the time intervals during which the source is barely detected, or not detected at all. Indeed, they can be treated exactly like all the others, by comparing N i,pred with N i , even if N i ≃ B i . As a consistency check, we also have used the more conventional technique of fitting M (t) to the count-flux light curve as obtained from the likelihood analysis, minimizing χ 2 . To incorporate information from upper limits on the flux computed from the unbinned analysis 16 , we first rescaled the one-sided 95% CL UL to two-sided 68% CL confidence intervals under the assumption that the errors are normally distributed. Then, we replaced the value of the UL with the value of a point that would have the 68% CL correspond to the value of the UL. To obtain reliable values from the fit, we required at least one positive detection after the peak flux (in addition to ULs). The two methods gave virtually identical results, and so we provide only the values from the second method, the fit of the count light curve.
We consider two models for the light curve: a simple power-law model: where F 0 and α are the free parameters, and a broken power-law model: where both indices (α 1 and α 2 ) are left free, the normalization is F 0 and the break time t b . We measure the time t p at which the detected flux reaches its maximum value F p (the "peak flux") as the center of the time bin with the maximum count flux. We then consider 16 To calculate UL we use the python interface to the Likelihood package, as described here: http://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/python_usage_notes.html#UpperLimit two time intervals starting respectively at the peak t≥ t p and after the end of the prompt emission t> GBM T 95 . For each time interval, we fit the power law and the broken power-law models and we compare them by performing Monte Carlo simulations similarly to the procedures described in § 3.4.4. We consider a break significantly detected when its chance probability is smaller than 10 −3 . In the above, all times are with respect to the GBM trigger time.

(IV) Time-integrated likelihood analysis
We now perform the likelihood analysis on different time intervals, defined in Table 1. These intervals are defined using combinations of the GBM durations reported in Paciesas et al. (2012), the Transient class durations, and the "LATTE" time window. If we obtain a T S > 20 in any of these time intervals, we consider the GRB detected.

(V) Localization
We select the interval where the GRB is detected with the largest significance among those considered in the previous step, along with the corresponding likelihood model, and we generate an improved localization using the second method described in § 3.2.2. If the new localization has a greater significance and a smaller error than the current one, we repeat the analysis chain from the beginning, adopting the new improved value. Otherwise, we select the old localization and all the results of the last iteration of the analysis chain as the final ones and proceed to the next step. Note that we typically perform a few iterations of the whole chain.

(VI) LLE analysis
In parallel, we execute the LLE analysis, which consists of three steps. We first extract LLE data, then run the detection algorithm on LLE class data (see § 3.3.1). Finally, if the GRB is detected (S post > 4σ), we evaluate its duration (see § 3.3.2). Note that this part of the analysis is performed again when an improved localization is obtained using LAT Transient class data.
(VII) LAT-GBM joint spectral fits of the prompt emission We use the best available position to extract the spectrum of the GRB across the whole energy range covered by Fermi. We fit the spectrum, following the procedure described in § 3.4. We perform a spectral analysis in two time intervals: the "GBM" time interval defined in Table 1 and the time interval starting when the first LAT photon is detected in the GRB ROI and extending up to the GBM T 95 instant.

Results
In this section we describe the results from our analysis; all tables are collected in § 7 and detailed discussions for each detected GRB are in Appendix B. According to the standard definition, GRBs with GBM T 90 >2 s are defined long, while short-duration GRBs have GBM T 90 <2 s. Any upper limits from the maximum likelihood analysis are for a 95% confidence level and are calculated using a photon index of 2. We quote fluences in two Earth reference frame energy ranges: 10 keV-1 MeV and 100 MeV-100 GeV, appropriate to characterize the GRB emission as measured by the GBM and LAT respectively. For all of the quantities a subscript ("LAT, GBM, EXT") is added, to indicate the time interval used to perform the spectral analysis. Low-energy (10 keV-1 MeV) fluences of non-LAT-detected GRBs are from the GBM spectral catalog (Goldstein et al. 2012) and of LAT-detected GRBs from our joint GBM-LAT spectral analysis. A discussion on how the LAT-detected bursts fluences compare with the distribution of fluences for all the GBM-detected bursts are left for the next section.

LAT Detections
We searched for high-energy emission with the LAT for the 733 GRBs described in § 2.2 and detected 35, using the detection criteria described in § 3.3.1 and § 3.2.1. Among them, 28 were detected by our maximum likelihood analysis at energies above 100 MeV and 21 were detected using event-counting methods applied to the LLE data. Among the GCN circulars issued by the LAT team, three GRBs (listed below) were not included in this catalog as they were below the significance threshold, while we also discovered five not previously claimed bursts (GRBs 081006, 090227B, 090531B, 100620A, and 101123A). Thirty of our detected GRBs are of the long-duration class and five are of the short-duration class (GRBs 081024B, 090227B, 090510, 090531B, and 110529A).
We list the LAT-detected GRBs in Table 2 and report their trigger times, off-axis angles at trigger time, best available localizations with errors, redshifts, and references to GCN circulars. In the table we also report whether these GRBs were detected by the LLE and the maximum likelihood analyses. The LLE detection significances and the likelihood TS values can be found in Table 3.
As a cross-check of our adopted detection thresholds and to estimate the rate of false detections in our sample, we repeated the analysis on a sample of "fake GBM triggers". We generated the list of fake GBM triggers by changing the real trigger times T 0 of the input list to T 0 − 11466 s, corresponding to approximately two orbits before the true trigger. The standard operating mode for the Fermi spacecraft is to change the rocking angle every orbit, viewing alternately the northern and southern orbital hemispheres. Thus, with the exception of ARRs, the "fake" sample has very similar background conditions with respect to the true sample. Excluding the ARR, for each fake GRB trigger, we computed the TS value in a series of time intervals (of 1, 3, 10, 30, 100, 300, and 1000 s duration), kept the highest TS value we obtained for each fake GRB, and compiled them into a cumulative distribution. Figure 8 compares the cumulative distribution with the same distribution for the true GBM trigger sample. Both distributions have been normalized to unity for TS=0 [i.e. P(TS>0)=1]. For the fake triggers, we did not obtain any value for the TS greater than TS min =20 (our nominal detection threshold). The excess of the TS distribution of the true GRB sample with respect to the null distribution for TS>20 is evident. It is important to note that the full analysis chain performed on the actual data and described in the previous section also optimizes the time window to compute the likelihood analysis, a task which is not included here.
As mentioned above, in addition to the GRBs reported here, the LAT team has reported detections of 3 other GRBs via GCN, but for the reasons explained below we have not included these events in the final table as they were formally below the detection threshold set for this catalog. These are: • GRB 081224 for which a tentative onboard localization with the LAT was delivered via GCN (Wilson-Hodge et al. 2008). Further on-ground analysis did not confirm the signal excess found in the LAT data, and a retraction GCN notice was issued (McEnery 2008b). Whereas the GBM light curve is a broad single pulse event lasting ∼17 s, the LLE light curve shows a narrow spike at T 0 which is not associated with the main pulse in the GBM, with a low significance of 3.1σ only. • GRB 100707A which had a significance of 3.7 σ using the LLE data. This result confirms the early detection (Pelassa & Pesce-Rollins 2010) obtained with a dedicated event selection which was required by the burst inclination of ∼90 • at trigger time.
• GRB 081215 which was similarly observed at a large off-axis angle and the LAT team detection for the GCN circular was by means of a dedicated event selection (McEnery 2008a). However, this burst was not detected by either of our methods here, having a very low significance in both the LLE and standard likelihood analyses.
Using matched-filter techniques Akerlof et al. • GRB 081009 is a GBM-detected burst, which was not detected by Swift. In our analysis, the final value of the TS is 14, which is below our detection threshold. Also the GRB is not detected in the LLE data above our detection threshold of 4 σ, likely due to the high inclination of 94 • .5 at the trigger time.
• GRB 090228A has TS=20 after optimization of its position. However, the TS map is entirely driven by two 5-GeV events in spatial coincidence, instead of being due to several events. Moreover our LLE analysis returned a null detection. In order to accommodate two high energy events and essentially no events at low energy the photon index of this GRB should have been greater (harder spectrum) than 1, which is not very realistic as the energy (and the number of events at high energy) would tend to infinity.
• GRB 090720B is also found by our likelihood analysis, is not seen in LLE data, and will be discussed in more detail in subsequent sections.
• GRB 091208B is localized by Swift and our analysis finds the maximum TS=20. It is a marginal detection with only three events associated to the burst location. However, in this case the TS value reaches the threshold and the spectral shape is convincing, so we consider this a detection for the catalog.
• GRB 100718A is a GBM-detected burst, which was not detected by Swift. We note that the location of this GRB is only 0 • .5 (with an uncertainly of approximately 6 • ) from the position of the Vela pulsar (Abdo et al. 2009f, 2010c, which is the brightest steady γ-ray point source in the sky. The reported GBM localization error is approximately 6 • , compatible with the location of Vela. Including a point source at the position of Vela, with the flux fixed to the value reported in Nolan et al. (2012a,b), the final value of the TS is well below our threshold. Also the LLE lightcurve doesn't show any structure above threshold.
• GRB 100728A is found by our pipeline during the "LATTE" time interval with a TS=32 selecting the time interval between 5.6 and 749.9 seconds after the GBM trigger. In addition, a dedicated article has already been published (Abdo et al. 2011) by the LAT and GBM collaborations.
• GRB 100911A was detected by the GBM when the direction of the burst was very close to the Earth, with an angle from the local zenith of approximately 105 • . In order to minimize contamination from the bright limb of the Earth, we rejected any data taken during intervals for which the ROI intersected the Earth's limb, a cut that is more conservative than requiring that the GRB is not occulted by the Earth. As a consequence GRB 100911A was not detected.
• GRB 110709A is also found by our like-lihood analysis, is not seen in LLE data, and will be discussed in more detail in subsequent sections.

Emission Onset Time and Duration in the LAT
We applied our duration measurement algorithms to all of the significantly-detected GRBs as described in § 3.3.2. Our results are shown in Table 3.
Referring to the durations reported in the GBM GRB catalog (Paciesas et al. 2012), we report in the second column whether the GRB was categorized as long (L) or short (S) as determined from the measured T 90 in the 50 keV-300 keV energy bands. Our results consist of two sets of T 05 and T 95 , determined using the Transient event class (denoted as "LAT") and the LLE event class (denoted as "LLE"). We report a duration measured with an event class only if the GRB was also detected using that same event class. In two cases (GRBs 090926A and 100116A), the burst emission persisted long enough that our algorithm failed to detect a plateau before the end of the first continuous segment of observation. For these cases, we report lower limits for the LAT T 95 and T 05 . This work produced the first-ever set of GRB durations measured at high (MeV/GeV) energies.
The quantities compared in Table 3 are the onset time (reported here as T 05 and shown in Fig. 9) and the duration of the GRB emission (reported here as T 90 and shown in Fig. 10). In the top panels of Figs. 9 and 10 we compare the >100 MeV LAT Transient class duration measurements to the GBM results (in the 50 keV-300 keV energy band), while in the bottom panels we compare the tens-of-MeV LLE duration measurements to the GBM results. As shown in the top panels of both figures, the LAT-detected >100 MeV emission systematically starts later and has longer duration with respect to the GBM-detected emission. On the other hand, the bottom panels of both figures show that the durations measured using the LLE data are in better agreement with those measured by the GBM. Any deviation from the equal-duration line of the LLE versus GBM plots can be at least partially explained as due to spectral variations during the time of the GRB emission, something that can be easily observed in the light curves reported in Appendix B.
As was mentioned in § 3.3.2, the duration estimates are sensitive to the level of the background. Thus different detectors, such as the GBM and LAT, or different event selections, such as the LAT Transient and LLE class events, could produce different duration estimates as a consequence of their very different signal-to-noise ratios. This can partially explain the systematically-longer durations (T 90 ) estimated using the LAT Transient class events, but would not explain the systematically later onset times (T 05 ). We also note that a possible selection effect could arise owing to the typical GRB off-axis angles at the trigger time. Bursts that are initially at the edge of or outside the LAT FoV (i.e., having high > 60 • off-axis angles θ) enter the LAT FoV after some time (of the order of a few seconds), thus introducing a delay between the onset of the GBM and LAT observed signals. Even though we weight the LAT detected signal by the inverse of the exposure to ameliorate this effect, we cannot eliminate it since the weighting is not effective for the cases in which no GRB Transient class events are detected at all by the LAT. This effect might partially explain the delays of GRBs 090323 and 090328A. For most of the other cases, however, the GRB has a small enough off-axis angle at onset to permit sufficiently sensitive prompt observations (as shown by the θ column in Table 2).

Maximum Likelihood Analysis
We split GRB observations into 6 time intervals listed in Table 1 and performed a LAT-only spectral analysis using the maximum likelihood technique described in § 3.2. Since in the "PRE" interval the GRB is not detectable (by construction), we omit report-ing results from this interval, and we focus on the five remaining time windows. The results of this analysis, namely the TS, the bestfit photon index, the flux and fluence for the 100 MeV-10 GeV energy range are presented in Table 4. When possible, we also compute the isotropic equivalent energy E iso in the 100 MeV-1 GeV rest-frame energy band.
In the same table, we also report the number of detected events (originating from both the GRB and any possible background components), and the number of events from the GRB as predicted by the likelihood fit. These numbers are for the 100 MeV-10 GeV energy range in the observer frame. Figure 11 shows the flux and fluence measured by the LAT in the "GBM" (top two panels) and "LAT" (bottom two panels) time intervals as a function of the durations of these time intervals (i.e., GBM and LAT T 90 respectively). The fluxes and fluences presented in these figures are for the 100 MeV-10 GeV energy range. Interestingly and as can be seen in the bottom right panel of Fig. 11, within the first 3 years of operations the LAT has detected 4 very-high fluence bursts GRBs 080916C, 090510, 090902B, and 090926A that are outliers with respect to the main distribution of the LAT-detected GRBs. We will revisit these hyper-fluent bursts in § 5.2, where we discuss the energetics of Fermi-LAT detected GRBs.

LAT Localizations
We evaluate localizations from the LAT for all GRBs detected by the maximum likelihood analysis by searching for the maximum of the TS map according to the procedure described in § 3.2.2. We present our results in Table 5, in which we report the position of the maximum of the TS map (i.e., the LAT localization) along with its 68%, 90%, and 95% statistical errors.

High-Energy Photon Events
We report the energies and arrival times of a set of interesting high-energy photons that, according to our likelihood analysis (as described in § 3.2.3), have a high probability (P>0.9) of being associated with the GRBs. Specifically, we give information for the following events: • The highest-energy Transient class LAT γ-ray in the "GBM" time window (Table 6); • The highest-energy Transient class LAT γ-ray in the interval starting from GBM T 95 and ending at the end of the "EXT" window (i.e. from the end of the measured duration in the GBM data up to the end of the LAT measured duration, Table 7); • The highest-energy Transient class LAT γ-ray detected in the time-resolved likelihood analysis (Table 8).
The results are shown in Tables 6, 7, and 8. These results show that the detection of high energy events with GRB point source probabilities P>0.9 is not strongly correlated with features in the GBM light curve. In a few cases, such as GRB 090510, such events are coincident with bright pulses in the GBM light curve, but more often the most energetic event is detected after the intense lowenergy emission, as with the 33.39 GeV event detected at T 0 +81.75 s from GRB 090902B, which is the highest energy ever observed from a burst. GRB 100728A is particularly interesting since a 13.54 GeV event was detected ∼90 minutes after the trigger time. This is the only case in which we observe such a late event, and it can potentially confirm that high-energy γ-rays can arise very late in time, as observed from GRB 940217 by EGRET (Hurley et al. 1994b). On the other hand, GRB 100728A is not significantly detected at the time the highest-energy event is observed (similarly to GRBs 090217 and 100116A reported in Table 8), thus the probability P=0.987 that the 13.54 GeV event is associated with the burst must be taken with caution. Considering the trials factors, this probability would be further reduced, weakening the case for hours-scale high-energy emission. A detailed analysis of the probability corrected by the trials factors would be non-trivial as the background strongly varies as a function of the location in orbit, and it is beyond the scope of this paper. Figure 12 shows the energies and arrival times for the highest-energy γ-rays associated with LAT GRBs. The estimated errors are computed from the energy dispersion in the Instrument Response Functions and it is of the order of 10% for energies >1GeV. When possible, we also indicate the source frame energy.  Table 8.

Temporally Extended Emission
To study the temporal decay of the extended emission detected by the LAT, we utilized the time-resolved analysis described in § 3.5. We first visualized any detected extended emission using flux light curves (shown in Appendix B), and then calculated the peak-flux value F p and the time of the peak flux t p , quantities shown in the two top panels of Fig. 14. In the time-resolved analysis we adaptively changed the size of the time bin width in order to significantly detect the source, so F p corresponds to the average flux in the time bin of the maximum, and as a result it is more precise, (i.e., with a smaller uncertainty) for bright GRBs than for faint GRBs.
The 4 most luminous bursts detected by the LAT have some of the highest peak fluxes in the ensemble, all exceeding 10 −3 cm −2 s −1 . Among the rest of the bursts, GRBs 081024B and 110721 also have notably high peak fluxes. GRB 100728A was at the edge of the FoV at the time of the GBM trigger and was detected only at later times. It has by far the lowest peak flux of all GRBs, at least an order of magnitude lower than the rest of the population; however, its value is possibly affected by large systematic errors.
We also applied the methods described in § 3.5 to the subsample of GRBs with detected extended emission. We detected temporal breaks in the decay of the extended emission of three bright GRBs: GRB 090510, GRB 090902B and GRB 090926A. In the top panel of Fig. 13 we show their luminosities as functions of rest-frame time, as well as the best fitting broken power-law models. The later points in the light curves are very important to constrain the break, but they also would be the most affected by any unaccounted-for systematic uncertainties arising, for example, from the background estimation or the exposure calculation. In the bottom panel of Fig. 13 we again report the luminosity as a function of the rest-frame time, but for all the GRBs in the subsample. In Table 9 we report the results of this analysis. For the three GRBs with temporal breaks we report the decay index starting from the peak flux and before the break α 1 , the decay index after the break α 2 , and the break time t b . For all other GRBs, we report the decay index for the whole extended emission starting from the peak flux, and the decay index for the light curve starting from the end of the low-energy (GBM) emission.
Referring to Table 9, we also define the "late-time decay index" α L , which corre- The decay of the luminosity L with time measured in the rest frame for the 3 GRBs in which we detect a significant time break. Dashed-dotted lines are the best fits of the broken power law model to each GRB, while dashed crosses are the luminosities before the peak times, which have not been used in the fits (see text). Bottom: the same quantities for all the GRBs with detected extended emission.
sponds to the decay index measured after the GBM T 95 (α L = α) for all GRBs except the three for which we detect temporal breaks, for which it corresponds to the decay index after the break (α L = α 2 ). In the third panel of Fig. 14

Joint GBM-LAT Spectral Fits
For each GRB detected with the LAT we performed joint GBM-LAT spectral analyses in two time intervals, following the procedure described in §3.4. We started by analyzing data taken in the "GBM" time window for all detected GRBs. The results of this analysis are presented in Tables 10 and 11. Since the emission at energies >100 MeV is delayed with respect to that at lower energies, we also performed a spectral analysis in the time interval between the first Transient class γ-ray detected by the LAT within the energydependent ROI of the GRB and the GBM T 95 , in order to maximize the signal-to-noise ratio at high energies (E > 100 MeV). We report the results of this analysis for all the bursts detected by the LAT in Table 12. The first table (Table 10) summarizes the model that best fits the data for each GRB, ordered by fluence. We also report the off-axis angle, which is a proxy for the detection efficiency of the LAT for equal exposure time (high off-axis angle means low efficiency). Tables 11 and 12 contain three sets of columns: the main component section, the additional component section, and two columns with the total fluence (in the 10 keV-10 GeV band) and the value of PG-stat (see §3.4.2) with the number of degrees of freedom. Each spectrum is modeled by one main component (either a Band model or a Comptonized model or a logarithmic parabola) and one or two additional components (power-law and/or exponential cutoff) when needed (see again §3.4.3). The SBPL model does not provide the best fit for any GRB in our sample, so we do not include it in either Table 11 or 12. Only the columns corresponding to the parameters of the components used in the best fitting model are entered. When a spectrum requires additional components, we report separately the fluence corresponding to the main component and the fluence corresponding to the additional components.
To elaborate on the table entries, consider the results of the time integrated analysis reported in Table 11: the first entry refers to the spectrum of GRB 080825C, which is best described by a Band model, thus only the columns referring to the parameters of the Band model are filled, and only the total fluence is reported. On the other hand, the spectrum of GRB 090926A is described by a Band model plus a power law with an exponential cutoff. Correspondingly, all columns for the parameters of those components are filled, as well as the columns for the total fluence and the fluences for the first component (Band) and the second component (power law with an exponential cutoff), respectively. The spectrum of GRB 100724B is instead described by a Band model with an exponential cutoff, so all of the corresponding columns are filled. Note that there are no partial fluences reported in this case, since the exponential cutoff is a multiplicative term. In the case of GRB 110731A, we reported in Table 11 both the Band-only fit and the Band plus power law fit, even if the extra component is not significant according to our criteria, since the power law is clearly detected in the other time interval as reported in Table 12 and thus Band plus power law is arguably a more accurate model for the "GBM" time window as well.
Some bursts have been detected only by the LLE photon counting analysis since they were outside the nominal LAT FoV (θ > 70 deg, see Table 2) at the time of the trigger. These include GRB 090227B, 100826A, 101123A, and 110625A. GRB 101014A was detected too close to the Earth's Limb at the time of the trigger, resulting in a very low exposure for the LAT due to the zenith-angle cut (see § 2.1.1). For these LLE-only detections, it is not possible to obtain a spectrum from LAT standard data, and so we use only GBM data.

Extra components
We found that four GRBs clearly require a power-law added to the Band spectrum in both time intervals that we studied. Two cases, GRB 090510 and GRB 090902B, are already known Abdo et al. 2009e). The two additional cases are GRB 080916C and GRB 110731A. During the "GBM" interval for GRB 080916C, we obtain a value of PG-stat S = 519 (with 356 d.o.f.) with the Band model alone, while we obtain S = 485 (with 354 d.o.f.) adding an extra power-law. The value ∆S = 34 is well above our detection threshold of 25 (see § 3.4.4). It corresponds to a chance probability of ≃ 1 × 10 −5 or possibly lower (see Fig. 6). The possibility for an extra component was already considered in our first publication on this GRB (Abdo et al. 2009c), but the significance of the power-law was not high enough to claim a firm detection. Now, thanks to a better understanding of the background in the LAT with the use of the BKGE, and a better calibration of the GBM instrument, we obtained convincing evidence for such a claim. We also detect an extra component in GRB 110731A, as published in Ackermann et al. (2012b). In the "GBM" time interval, the significance of this component is below our threshold, but in the LAT time interval, with a better signal-to-noise ratio, we obtain ∆S = 42. This result is fully compatible with what we already published. We also find an extra component in GRB 100414A, but in this case we highlight some possible problems with the analysis. We refer to Fig. 15 that shows the off-axis angle of the GRB as a function of the time since the GBM trigger. During the GRB prompt emission, this GRB was at the edge of the FoV of the LAT, where the effective area is small. In addition, the ARR maneuver was partic-ularly fast in terms of angular speed for this GRB and happened during the GBM T 90 , resulting in rapidly changing backgrounds and effective area at the source location, which could create large and difficult to evaluate systematic uncertainties. Indeed, in the "GBM" time interval the spectrum is better described by a Comptonized model with an additional power-law, while in the LAT time interval the statistically preferred model is a Band function. In this case we cannot significantly claim the detection of the extra power-law component.

Time since GBM trigger [sec]
We confirm the detection of a cutoff around 1.5 GeV in the extra component of GRB 090926A as previously published by Ackermann et al. (2011a), and we also significantly detect a new cutoff at lower energies in GRB 100724B. For the latter, considering again the "GBM" time interval, we find S = 977 with 469 d.o.f. using the Band model, while adding an exponential cutoff we find S = 734 with 468 d.o.f. The value ∆S = 243 is well above our threshold ∆S = 28. Discussion of the physical implication of these findings is outside the scope of the present paper. Ackermann et al. (2012b) found a hint for another cutoff at high energy with a significance of ∼ 4σ in the time interval starting from the LAT T 05 and ending at the GBM T 95 . We refer the reader to that paper for details.

Discussion
In this section, we describe the emergent properties of LAT-detected GRBs revealed by this study.

A Band model crisis?
Before the launch of Fermi, GRBs were mainly studied in the energy range from a few keV to a few MeV, with the catalog of BATSE (Kaneko et al. 2006(Kaneko et al. , 2008a, consti-tuting the largest sample available to date. Several spectroscopic analyses have been performed on that sample, showing that most of the GRB spectra are well described by a Band model, a Comptonized model, or a smoothly broken power-law (SBPL) model (Preece et al. 2000). LAT-detected GRBs are bright in the GBM energy band, which is very similar to the BATSE band, and thus we can compare our detection statistics with those found in the bright BATSE sample by Kaneko et al. (2006). In Table 10 we report all LAT-detected GRBs, ordered by fluence, and the model that best describes the spectrum over the GBM time interval. For convenience we also report their off-axis angles θ at the trigger times. We exclude GRBs outside of the nominal FoV (θ > 70 • ). We also exclude GRB 101014A which was too close to the Earth limb to allow a spectroscopic study. Kaneko et al. (2006) found that the spectra of ∼85 % of the brightest 350 BATSE GRBs are well described by a Band function, while we find that 70% of LAT-detected GRBs are well described by either a Band model or a Comptonized model, which is similar to a Band model with a very soft value of β. Given the small size of our sample, the two fractions are very similar. Additionally, Kaneko et al. (2006) found that 5% of BATSE GRBs require the more complex SBPL model, while no LAT-detected GRB requires it. Again, this is very likely to be due just to the small size of our sample.
On the other hand, Table 10 shows that the spectra of all of the brightest bursts inside the LAT FoV present significant deviations from a Band function, requiring additional components. Other GRBs, observed with low θ angle and correspondingly high effective area, show deviations as well. The phenomenological Band model, implemented for BATSE GRB observations up to a few MeV, does not seem to describe bright or well-observed LATdetected GRBs sufficiently.
For each GRB with a very high signal-to-noise ratio in the LAT data, we find that the Band model needs to be supplemented with additional components or modified with a cutoff. There is no common recipe to fit all Fermi GRBs: for the bright GRBs 090510 and 090902B, an additional power-law component, extending from low to high energies is required; for GRB 100724B a cut-off in the high energy spectrum is needed in order to explain the rapid drop-off of the flux at high energies; the case of GRB 090926A is even more complex, with both a power-law and a exponential cut-off required to describe the spectrum. Other works (Guiriec et al. 2011;Zhang et al. 2011) use a thermal component added to the Band function. This difficulty arises thanks to the greatly broadened energy coverage provided by Fermi with respect to BATSE, and accurate GRB spectroscopy in the Fermi era requires improved broad band modeling.

Energetics
Cenko et al. (2011) and Racusin et al. (2011) have studied the energetics of the afterglows of LAT-detected GRBs and concluded that they are among the most luminous afterglows observed by Swift. We start our analysis by examining the properties of LAT-detected GRBs in the context of the prompt emission and compare the highenergy properties measured by the LAT to the low-energy properties measured by the GBM.

Prompt Phase Energetics
We first study the fluence, and then continue with the subsample of GRBs that have a measured redshift and examine intrinsic GRB quantities. Even though intrinsic properties are, by far, more interesting for understanding the physics, properties measured in the observer's frame (such as the fluence or the peak flux) are sometimes more instructive from the experimental point of view, as they can reveal observational biases and selection effects.
In Fig. 16, we compare the fluence measured by the GBM in the 10 keV-1 MeV energy band for the full GBM spectral catalog (Goldstein et al. 2012) to the 10 keV-1 MeV fluence of LAT-detected GRBs. Since the LAT observations are photon-limited, the detection efficiency is directly related to the source fluence (Band et al. 2009). This is in contrast to the GBM data, which are background dominated and the peak flux is a better proxy for the detection efficiency. the LAT because it occurred outside its FoV (θ=132 • ). The second brightest GRB in the GBM catalog is the LAT-detected GRB 090902B. More interestingly, there are a few cases of bursts that were not particularly bright in the GBM, yet were detected by the LAT, namely short GRBs 081024 and 090531, which have a relatively small fluences compared to the rest of the GBM-catalog bursts, mainly because of their short durations (<20% and <30% quantile of the distribution). The former was detected by the LAT up to ∼GeV energies (Abdo et al. 2010b), while the latter was detected only at low energies by the LLE analysis. Note however that the published GBM catalog includes bursts only up to the beginning of 2010 July. Thus, it does not contain a significant part of our sample, and in particular GRB 100724B, which has the highest fluence in the GBM energy range in our sample (see Table 10).
The top panel of Fig. 17 shows the fluence measured by the LAT versus the fluence measured by the GBM in the "GBM" time window. The plotted GBM fluences were produced by the joint GBM-LAT spectral analysis in this study, in accordance with the best-fit spectral model described in Table 11. LAT fluences calculated from the LAT-only maximum-likelihood analysis and from the joint GBM-LAT spectral fits are both shown in the figure. Generally speaking, the agreement is good, however, for bright bursts the two methods produce results that are in slight disagreement. This arises because we use a two-component model in joint GBM-LAT spectral fits, with the low-energy component (a Band model or a Comptonized model) having a non-negligible contribution at high energy. Thus, both the photon index and the normalization for the power-law component are different with respect to the maximumlikelihood analysis, which uses a power law only.
The bulk of the LAT GRB population, primarily composed of long GRBs, has a ratio The three dashed lines denote the 100%, 10% and 1% fluence ratios. Colored symbols follow the convention of Fig. 9. Additionally, we also use gray circles for joint-fit results.
of high-(100 MeV-10 GeV) to low-energy (10 keV-1 MeV) fluence < ∼ 20%. It is interesting to note that the three short LATdetected bursts (red symbols in Fig. 17) have a greater ratio of high-to low-energy fluence than the bulk of the long-GRB population (blue symbols). Two short bursts GRBs 080825C and 090510 have the two highest ratios (over 100%), and the short burst GRB 090227B also has a relatively high ratio (∼10%). This reflects the well-known fact that short GRBs have harder spectra than do long duration bursts. On the other hand, since the high-energy emission typically lasts longer than the low-energy emission, and since in this plot the integration time is the same (the GBM T 90 ) for both axes, only part of the emission at high en-ergies is included in the calculation of the fluence. For this reason, we also integrate the fluence between 100 MeV and 10 GeV over the full LAT T 90 time window and in the bottom panel we compare this quantity with the fluence as measured by the GBM during the GBM time window. In this way, we better account for the energetics in the LAT energy range. The LAT measurements in this panel were all derived from the likelihood analysis of this study. Because we were not able to measure durations in the LAT energy range for all bursts, this panel has fewer entries than in the top panel. Similarly to the above, short GRBs appear considerably more efficient at radiating at high energies than at low energies.
In both panels of Fig. 17, we can see the four hyper-fluent LAT bursts, GRBs 080916C, 090510, 090902B, and 090926A, having evidently greater emission in the LAT energy range compared to the rest of the GRB population. The discrepancy increases when comparing the high-energy emission measured in the generally-longer LAT time window to the low-energy emission measured in the GBM time window, a result of the bright extended high-energy emissions of these four bursts.
It is worth examining whether the four brightest LAT bursts appear bright because they are systematically closer to us compared to the rest of the GRB population. As can be seen in Fig. 18, which shows the fluence in the LAT energy range and the LAT time window versus the redshift, this is not the case. In the figure we denote an empirical LAT-detection threshold, for which we caution the reader that since the minimum fluence at which the LAT can detect a GRB depends on the position of the GRB in the LAT FoV, as well as on the intrinsic properties of the GRB (photon index, duration, etc.), this threshold is just a crude estimate for reference.
To quantify the energy release at the source in some source-frame energy range E 1 -E 2 , we compute the isotropic equivalent energy E iso as: where d L (z) is the luminosity distance of a source at redshift z, and S(E 1 , E 2 , z) is the fluence of the source integrated in the source frame energy range E 1 and E 2 : dE describing the spectral model. The choice of the energy band used to compute the isotropic energy is important and requires some discussion. In order to calculate the bolometric isotropic energy, the energy band must be as broad as possible. On the other hand, the calculation in principle should include only the portion of the spectrum that has been directly measured (i.e., constrained by the data) or a potentiallyinaccurate extrapolation would be required. Considering the spectral coverage of the two instruments onboard Fermi, we chose to integrate between the E 1 =1 keV and E 2 =10 GeV source-frame energies. We start at 1 keV source-frame, which corresponds to a few keV observer-frame and is slightly outside of the GBM energy band, to make comparisons with some studies already in the literature. In addition, we compute the isotropic equivalent energy in a narrower band (1 keV-10 MeV), covering mainly the energy range of the GBM detectors. The latter choice allows us to directly compare our results with those of previous works, namely Amati et al. (2002); Racusin et al. (2011) who adopted a source-frame range between 10 keV and 10 MeV, Amati (2006); Butler et al. (2007) who adopted a slightly broader source-frame range extending from 1 keV to 10 MeV, and Cenko et al. (2011) who used an observerframe range between 1 keV and 10 MeV.
In Fig. 19 we plot E iso in the 1 keV-10 MeV energy range versus the redshift in the prompt . We note that although GRBs 110731A and 090510 have a moderate 1 keV-10 MeV E iso , they have been detected by the LAT. For these two bursts, the observational conditions were very favorable for detection, since they were nearly on-axis for the LAT at the times of the GBM triggers (13 • .6 for GRB 090510 and 3 • .4 for GRB 110731A off-axis angles). Before proceeding, we would like to make an important point concerning the defini-tion of "bolometric" luminosity of the prompt phase for GRBs. Before Fermi, the properties of prompt spectra of GRBs were known up to ∼ MeV energies, and there was no way to account for the higher-energy portion of the spectrum (>10 MeV) in the total energy budget. This is reasonable as long as the high-energy emission does not constitute a significant part of the total emitted energy. Using LAT detections of GRBs, it has been discovered that extra power-law components are more common in GRBs compared to what was previously thought. More importantly, even if the high-energy emission can last longer than the usual keV-to-MeV emission, in some cases (GRBs 090510, 090902B, 090926A) it contributes significantly during the prompt phase. These two considerations suggest that the total energy budget at high energies can be an important fraction of the total energy reservoir.
In Fig. 20 (top panel) we try to address this issue by plotting the amount of energy radiated by the source between 100 MeV and 10 GeV during the temporal extended emission compared to that radiated in the wider 1 keV-10 GeV energy range in the "GBM" time interval. As can be seen, the fraction of energy radiated in the form of high-energy γ rays during the temporal extended phase is typical < ∼ 10% of the total energy radiated during the prompt phase. The short GRB 090510 has an especially high fraction of ∼50%.
For the few bursts for which we can significantly separate the contributions from the extra component (power law) and the main component (the "Band" model), we can calculate the fraction of the energy during the prompt emission that is associated to each of these two spectral components. In the bottom panel of Fig. 20 we show the emitted energy corresponding to each component for the "GBM" time interval. As shown, the energy radiated during the prompt emission by the power-law component is between 10% 50% of the energy radiated by the Band component. The numerical results of this analysis can be found in Table 13.

Highest Energy Photons
Events with source-frame-corrected energy up to 50-100 GeV have been measured in GRBs by the LAT, including from high-redshift GRBs (up to z=4.35 from GRB 080916C Greiner et al. 2009). In order to produce γ rays of such high energies within the first few seconds of the burst, particle acceleration must be efficient in a GRB. Internal-opacity constraints also indicate that these high-energy-photon detections require large bulk Lorentz factors for the jet. Moreover, high-energy γ rays from high-redshift GRBs offer a valuable tool for measuring the opacity of the Universe due to interaction of >10 GeV γ rays with optical and UV photons of the Extragalactic Background Light (Abdo et al. 2010a). Finally, the short time delay observed in LAT GRBs between low and high energy events can be used to place tight constraints on any energy dependence of the speed of light in vacuum as postulated by some quantum gravity theories . Figure 21 shows the source-frame-corrected energy of the highest-energy events with a high (>0.9) probability of being associated with the GRB, detected in the time-resolved likelihood analysis, versus E iso . For long bursts, the most energetic photons appear in the brightest GRBs. Interestingly, our only short GRB with a measured redshift, GRB 090510, does not follow the correlation pattern followed by LAT detected long bursts. More statistics are needed to determine whether this pattern is significant.

Extended Phase Energetics
We have explored the energy budget of the highly energetic GRBs during the prompt phase. Now we focus on the temporally extended phase. First, we compare the energy radiated above 100 MeV during the prompt  Table 8. The symbol convention is the same as in Fig. 9.
and temporally extended phases. Since we are comparing energies in the same band, we increase the statistics of our sample by comparing fluences, a quantity that does not require knowing the redshift. Figure 22 shows the 100 MeV-10 GeV fluence measured during the "GBM" time interval versus the fluence measured in the "EXT" time interval, and Fig. 23 shows the ratio of these quantities for all GRBs with a LAT detection in both time intervals. We note that most of the ratios are compatible with unity. This implies that above 100 MeV the energy released during the prompt emission is similar to the energy released during the temporally extended emission.
To study the relative efficiencies of the Band and extra power-law components during the prompt and temporally extended emission phases we calculate the ratio of the source-frame isotropic equivalent energy, as measured by the LAT above 100 MeV in the temporally extended phase (the "EXT" time window), to the same quantity measured during the GBM time window. This is what we display in the y-axis of Fig. 24. We now know that high-energy emission can be produced during both the prompt and the temporally extended phases, and the y-axis shows the relative importance of these two phases. The GRBs in the plot occupy two regions: "γ-ray-afterglow dominated" GRBs, with E EXT iso > E GBM iso like (GRB 090510, 091003 and 090328) and "prompt-γ-ray dominated" GRBs, for which E EXT The "γ-ray-afterglow dominated" GRBs in our sample (GRB 090510, 091003 and 090328) do not necessarily have a dominant power-law component in the prompt phase. This could imply that the energy radiated by the extra component during the prompt phase can be dominated by the energy radiated by the main prompt component described by a Band  function. Note that the LAT sensitivity to GRB 090328 at the time of the GBM trig-ger was not optimal, and part of the emission may not have been detected. This is certainly true for long bursts, such as GRBs 091003 and 090328 while it is not true for GRB 090510, for which the power law component has been detected. The majority of LAT-detected bursts radiate more efficiently at high energies during the prompt GBM phase (GRBs below the horizontal line). We define such bursts as "prompt-γ-ray dominated" GRBs. The five such bursts follow an expected trend: the more important the power-law component in the prompt emission phase, the brighter the late-time emission becomes compared to the prompt high-energy γ-ray emission. As already noted, each of the four hyper-fluent GRBs has evidence of an extra component, as does GRB 110731A.

High-Energy Spectral Properties
In the previous section we discussed the energetics of Fermi-LAT GRBs, and we now consider their spectral properties. Since our primary interest is reporting observations related to Fermi-LAT data, we focus on the spectral properties at high energies, with special emphasis on the role of the extra component. We start from the LAT-only analysis. Figure 25 shows the photon indices of all GRBs detected by the likelihood analysis as measured in three different time windows. Almost all photon index values are compatible with a value of −2 for all three time windows; using the estimated errors as weights, we obtain the average values < γ GBM > = −2.08±0.04 in the "GBM" time window, < γ LAT > = −2.05±0.03 in the "LAT" time window, and < γ EXT > = −2.00±0.04, in the "EXT" time window. There is a selection effect such that any bursts with a photon index considerably softer than ∼−2 are less detectable by the LAT. Interestingly, GRB 100724B, which has the steepest photon index during the "GBM" has the second largest GBM-measured duration, while the GRB with the shortest duration, The y-axis shows the ratio between the energy released during the temporally extended emission phase and the energy released during the prompt GBM phase, and the x-axis shows the ratio between the bolometric isotropic equivalent energy radiated by the Band component over the total radiated energy during the prompt emission. The symbol convention is the same as in Fig. 9.
GRB 090510, has one of the hardest photon indices.  To further explore whether the photon in-dices depend on the duration, we plot in Fig. 26 the value of the photon index of the extra power-law as measured in the "GBM" time window Γ GBM (top panel) and in the "EXT" time window Γ EXT (bottom panel) versus the GBM T 90 . The photon index has a mild inverse correlation with the duration of the burst (top panel), in agreement with our results above and previous findings that the spectra of short duration GRBs tend to be harder (Piran 2004). On the other hand, when the spectral analysis is performed during the "EXT" time window (bottom panel), during which the signal from the GRB is no longer detected by the GBM but is still bright in the LAT energy window, this mild correlation disappears. Note that some of the GRBs (like GRB 100724B) do not have detected extended emission and are reported only in the top panel.
To further investigate this, we show in Fig. 27 the power-law photon index Γ EXT of the GRB emission in the LAT energy range as measured during the "EXT" time interval versus the value of the high-energy power-law index β of the Band function as measured in the prompt "GBM" time interval. The value Γ EXT was obtained by our LAT-only likelihood analysis and the β value was obtained by our joint GBM-LAT spectral fits. We measured β using either a Band-only or a Band-plus-power-law spectral model. For the cases where the more complex Bandplus-power-law spectral model also provided a good fit (i.e., when all the parameters were constrained and the fit converged), we selected the β value found for the more complex model. For those cases, in addition to Γ EXT we also plot the fitted values of the extra power-law component photon index α versus β. Table 11 summarizes the numerical values of the parameters of the model that best fits the LAT-GBM data. An important selection effect must be kept in mind: distinguishing an extra power-law spectral component is difficult when it is softer than the high-energy in the EXT time window. The symbol convention is the same as in Fig. 9.
component of the Band function. As can be seen in the figure, the power-law component described by Γ EXT is typically harder than the high-energy emission measured during the prompt phase by GBM, described by β. Furthermore, the two quantities do not seem to be correlated. The most extreme case, GRB 090902B, is shown in the inset of that figure, together with GRB 100414A for which we detect the temporally extended emission, while the β index of the Band function is only an upper limit. In fact for these bursts the best fit model found by our procedure were the Comptonized plus power law and the Comptonized alone, respectively. Therefore it is very reasonable that when we replace the Comptonized model with a Band function, the resulting β parameter is very steep, and not constrained toward lower values. In two cases, GRBs 090510 and 090926A, the extra power-law component that is significantly detected during the prompt emission is harder than the power-law of the extended emission. For the first case, this is probably caused by the hard-to-soft spectral evolution of the extra component, as demonstrated by the results of the time-resolved likelihood analysis shown in Fig. 53. For the case of GRB 090926A the extra power-law component during the prompt emission is significantly attenuated at high energies and the model that best fits the emission during the "GBM" time window consists of a Band function plus a Comptonized model and has a very high peak energy. The (exponential) spectral cutoff of GRB 090926A is not significantly detected at later times. Overall the temporal evolution of the extra power-law component of this GRB can be described as very soft/weak at the start, progressively becoming harder but also demonstrating a roll-off at around 10 GeV, and then becoming softer again with an index of Γ EXT ∼ −2.
In the other three cases for which we significantly detect the extra power-law component during the prompt phase (GRBs 080916C, 090902B, and 110731A) (see §3.4.4), the photon index of the extra-power law in the prompt "GBM" time interval γ is compatible with the index of the power-law in the LAT energy range measured during the temporally extended emission Γ EXT . The picture emerging from the analyses described in this subsection suggests that the high-energy (>GeV) emission is dominated by a single long-lasting component, well described by a power-law function of a photon index typically near −2, independent of burst properties such as the duration, the brightness, or the spectral properties of the lowerenergy prompt emission.

Extended Emission Temporal Decay
In Fig. 28 we report the "late-time decay index" α L as a function of the fluence mea-sured by the LAT in the GBM interval (top panel) and of the luminosity in the "GBM" time interval (lower panel). The values of α L seem to cluster around 1, which in the context of the fireball model indicates an adiabatic expansion of the fireball (see §6.2). There are two exceptions: GRB 080916C and GRB 110731A. To investigate this a little further, we plot in Fig. 29 the value of α L as a function of the intrinsic duration of the GRB at high energy. Both GRB 080916C and GRB 110731A have the shortest intrinsic LAT T 90 among long GRBs. This suggests that we have probably observed only the first steep part of the decay after the prompt phase and that we cannot exclude the existence of a flattening or a break at later times that would reconcile them with the other bursts.

LAT Detection Rate
Band et al. (2009) have reported the number of expected GRBs per year detectable by the LAT as a function of the number of excess events. This rate was estimated with Monte Carlo simulations using the predicted pointing history for the first year of observations. This calculation was performed using a standard survey profile without any pointed-mode observations (due to a positive response to ARR or planned Target Of Opportunity). The spectral model was a simple Band function, with parameters distributed according to the sample of bright BATSE GRBs (Kaneko et al. 2008b). The all-sky burst rate was assumed to be 50 GRB yr −1 full sky (above the peak flux in 256 ms of 10 ph s −1 cm −2 in the 50-300 keV band or with an energy flux greater than 2×10 −5 erg cm −2 ) in the 20-2000 keV band, derived from the BATSE catalog of bright bursts. Band et al. (2009) calculated the number of expected γrays using the bright BATSE GRB sample and also repeated the calculation with the hardest-spectrum (index β >-2) GRBs removed as the numbers of γ-rays at high energies would have been unphysically large.
In addition, Band et al. (2009) used simplified detection criteria, based entirely on the numbers of detected photons assuming a negligible contribution from background, or using a semi-analytical model to compute the value of the Test Statistic. For the latter, an isotropic background was assumed, but no additional sources were added to the simulation, including the bright Earth limb. The results of these simulations, taken from Band et al. (2009), are shown in Fig. 30. We compare these results with the numbers of events above 100 MeV predicted by the bestfit model, including all bursts from Table 4. In this comparison we use both the values obtained by integrating the spectrum in the GBM time window and in the LAT time window. Several interesting features are evident from this plot. First of all, the number of detected GRBs is somewhat less than expected. Additionally, the differences between the predicted and observed numbers of GRBs increase for bursts with many γ-rays in the LAT data. The absence of very bright bursts (with several hundreds of γ-rays detected above 100 MeV) could be due to the systematic uncertainties that are propagated in the simulation when extrapolating the Band function fits to high energies over a very-large lever arm. Especially when the high-energy photon index is close to −2, a small change of the flux value could create large uncertainties on the number of detected events at high energies, when extrapolated. This has been specifically tested using bright GBM bursts that were not detected by the LAT, and the bias introduced by fitting GBMonly data for bursts has been estimated by adding LAT upper limits in the spectral fit (The Fermi Large Area Telescope Team et al. 2012). On the other hand, intrinsic deviations from a pure Band function, such as spectral cut offs, spectral breaks, or curvature in the spectra could influence the number of predicted LAT detected GRBs.

Detectability of GBM bursts
Although many observed properties may be considered in classifying the detectability of GBM GRBs by the LAT, we limit the current analysis to the competing effects that the effective area decreases with increasing offaxis angle θ while the solid angle increases with θ.
It follows that there are more GRBs at large θ, although the LAT can detect only the brightest. Fig. 31 shows the fluence in the GBM energy band as a function of θ.
Using the sample of GRBs through August 2011 that is available at the HEASARC web site 17 , we display both the LAT and LLE detected GRBs. For LAT detections we use the fluence computed by our analysis, while for GBM-detected GRBs we use the value obtained from the GBM Burst catalog. Generally speaking, the LAT-detected GRBs are among the brightest GBM GRBs occurring in the LAT FoV. On the other hand, there are some exceptions where GRBs with a modest energy fluence or with a suboptimal viewing angle have still been detected by the LAT. These cases highlight the importance of secondary considerations other than θ or the fluence. In terms of GBM fluence, short bursts are easier to detect. Also, we note that the location in the FoV of the GRB at the time of the GBM trigger is not always representative of the quality of the exposure obtained during the burst. For example GRB 110625A was far off-axis at the time of the trigger (87 • ), but the high-energy emission was detected by the likelihood analysis a few hundred seconds after the GBM trigger when the GRB was well inside the FoV of the LAT. LLE bursts (triangles) occur typically at larger incidence angles, indicating that the FoV of the LAT is larger for LLE data sample than when using standard event classification. There is also one case of a relatively bright GBM 17 The GBM Burst catalog: http://heasarc.gsfc.nasa.gov/W3Browse/fermi/fermigbrst.html burst (GRB 110328B), where the off-axis angle was relatively small (∼32 • ) but the GRB was detected only using LLE analysis. This is explained by the results of the combined spectral analysis (summarized in Table11), which show that the best fit spectral model is a Comptonized model cutting-off approximately at 1.2 MeV, implying suppression of high-energy emission. MeV and 10 GeV in the "GBM" time interval (Top) and of the isotropic luminosity between 1 keV-10 GeV, source frame. The value of α L is ∼1, except for GRB 080916C and GRB 110731A, which notably have the shortest durations when measured in the source frame (see text). The symbol convention is the same as in Fig. 9.  Filled symbols indicate long duration bursts while empty symbols denote short bursts. Gray circles denote GBM bursts that were not detected by the LAT, stars denote LAT bursts detected using the standard likelihood analysis, and triangles denote bursts detected by the LLE analysis only. For clarity, long duration LAT-detected GRBs are plotted in blue, while short duration LATdetected GRBs are plotted in red.

Interpretation
In this study, we have characterized the high-energy emission observed from 35 GRBs detected by the LAT. While the number of LAT GRBs is a small fraction of the number detected by the GBM (Paciesas et al. 2012;Goldstein et al. 2012), there are a few emission features that show up only at high energies and distinguish the LAT GRBs: • high fluence and energy release, • temporally extended emission lasting longer than the GBM-detected emission, • delayed onset with respect to the GBMdetected emission, and • presence of an extra power-law component in the spectrum.
Here we discuss plausible interpretations of the emission properties observed with the LAT, salient features of these models, and possible issues.

Fluence and Energetics of LAT Bursts
The distribution of fluences of LAT GRBs (see Fig. 17) provides hints of two classes: a hyper-fluent class currently comprising four members, GRBs 080916C (Abdo et al. 2009c), 090510 Ackermann et al. 2010b;Giuliani et al. 2010a), 090902B , and 090926A (Ackermann et al. 2011a), and which have a typical 100 MeV-10 GeV fluence of ∼(3-8)×10 −5 erg cm −2 ; and a larger class with a lower typical fluence of ∼(2-10)×10 −6 erg cm −2 . The GBM fluences for the hyper-fluent class are also higher, ∼1.3 times the LAT fluence for the short burst GRB 090510 and ∼3-10 times the LAT fluences for the 3 long bursts (see Fig. 17, bottom panel). For comparison, we note that the typical fluence for the GBM long bursts is ∼ 2 × 10 −6 erg cm −2 in the 8 keV-1 MeV range and ∼ 10 −5 erg cm −2 in the 8 keV-40 MeV range, based on Band function fits to the spectra (Goldstein et al. 2012). It is evident that most of the LAT bursts do seem to be very bright in the GBM, especially when comparing their 10 keV-1 MeV fluences (see Figs. 31 and 16) to the 8 keV-1 MeV fluence of the typical GBM bursts (Goldstein et al. 2012).
In the cases of 9 LAT bursts for which the redshift information is available, the isotropic equivalent energy E iso in the LAT energy range (100 MeV-10 GeV) is also higher for the three hyper-fluent long bursts (see Figs. 18 and 20 top panel). The ratio of the E iso (100 MeV-10 GeV) to the total γ-ray energy E iso (1 keV-10 GeV) for the long bursts is ∼(5-25)%. Interestingly in the case of GRB 090510, the only short LAT burst with known redshift, this ratio is ∼ 70% and is clearly distinct from the long bursts. The bottom panel of Figure 20 shows that for the bright bursts, including GRB 090510 with its additional PL spectral component, the ratio of isotropic equivalent energies in the PL and Band components is concentrated at ∼ 25%. Thus the high (∼ 70%) LAT-to-GBM E iso ratio for GRB 090510 is a combination of high Band E pk , typical for short hard class, and a very hard (−1.61) PL photon index which must cut off at high energies. The bursts with 10% LAT-to-GBM E iso do not allow for the detection of an additional PL spectral component, though it could still be present. The additional PL spectral component is most likely responsible for the high fluence detected by the LAT, as also indicated in Fig. 24 for five of the eight brightest bursts.
The isotropic-equivalent energies of the LAT bursts calculated here are largely consistent with the energies calculated by Cenko et al. (2011) and show that LAT bursts possibly compose the most energetic sub-sample of GRBs (see Fig. 19). The range of E iso for short bursts in the pre-Fermi era was (0.0033-10.2)×10 52 erg (Ghirlanda et al. 2009). GRB 090510 is clearly at the high end of that range with E iso ≃ 7 × 10 52 erg. Although the sample is rather small, the detected redshifts of LAT bursts do not show a concentration of bursts at any particular range (see Fig. 19). Racusin et al. (2011) showed that the redshift distributions are statistically consistent for Swift-BAT detected GRBs, those detected by both GBM and BAT, and the small sample of LAT-detected bursts with measured redshifts. The only redshifts available for the GBM sample are for those bursts that also triggered BAT or LAT. Therefore, whether LAT-detected GRBs follow the redshift distribution of the rest of GBM-detected bursts is still an open question.
Another interesting feature of the LAT emission is that the 100 MeV-10 GeV fluences in the "GBM" and "EXT" time intervals are within a factor ∼ 2 of each other for a handful of bursts with high-significance detections (see Fig. 22). This may indicate an approximately equal efficiency of the GRB fireball to produce high-energy emission during the coasting (prompt) and deceleration (afterglow) phases, in the context of the earlyafterglow model as the origin of LAT emission.

Temporally Extended Emissions
The flux of LAT-detected emission at late times decays rather smoothly and can generally be fitted with a power law F ν ∝ t −αL (see § 4.3.4,and Figs. 13 and 14). Such behavior also is typically observed in X-ray, UV, and optical wavelengths after the prompt γray emission and is attributed to the afterglow emission. The apparent non-variation of the photon index for individual bursts (see Fig. 25) in the "EXT" time interval as compared to the "LAT" time interval also suggests that the temporally extended LAT emission resembles afterglow rather than prompt emission, for which the photon index is likely to vary with time. The burst-averaged values for the photon index in these two intervals: Γ EXT = −2.00±0.04 and Γ LAT = −2.05±0.03 are also very similar. The slightly larger values for the burst-averaged photon index Γ GBM = −2.08 ± 0.04 in the earlier "GBM" time interval could be due to a plausible contamination by the prompt emission in the LAT. Indeed, the high-energy photon index of the Band function, β Band , is systematically softer than Γ EXT in the joint fit to the GBM and LAT data (Fig. 27), suggesting that the hard spectral component becomes dominant at late times.
Remarkably, the "late-time decay index" is always close to α L = 1 (see Fig. 14 and Fig. 28), except in two cases, GRBs 080916C and 110731A, which could be affected by an observational bias (see §5.4). The clustering around α L = 1 suggests a common emission mechanism, even though our limited sample does not allow firm conclusions. In the context of afterglow emission, the bolometric flux decays as ∝ t −α , with α = 1 and α = 10/7 for an adiabatic fireball and a radiative fireball in a constant density environment (Sari 1997;Katz & Piran 1997;Ghisellini et al. 2010), respectively. The flux decay in a particular energy band is more complicated, and depends on the fast-or slow-cooling spectral models (Sari et al. 1998) as well as on the surrounding environment (i.e., whether it is uniform density interstellar medium (ISM) or with wind-type density profile (Sari et al. 1998;Chevalier & Li 2000;Panaitescu & Kumar 2000)). In particular, the relation between the flux-decay slope α and spectral index β for the flux density F ν (t) ∝ t −α ν −β varies between different parts of the spectrum. LAT-detected 100 MeV emission is likely to be from the fast-cooling part of the spectrum for which α = (12β − 2)/7 for a radiative fireball and α = (3β − 1)/2 for an adiabatic fireball, both for the ISM and wind environments (Sari et al. 1998;Granot & Sari 2002). In the LAT data, β = −Γ EXT − 1 = 1.00 ± 0.04, and α adiabatic = 1 and α radiative = 10/7, both of which are equal to their respective bolometric flux-decay indices. Thus, a simple interpretation of α L ≈ 1 flux-decay index for most LAT bursts indicates that the 100 MeV emission is more likely from an adiabatic fireball (Kumar & Barniol Duran 2009;De Pasquale et al. 2010;Razzaque 2010) rather than from a radiative fireball, as Ghisellini et al. (2010) had suggested.
For three bright bursts (GRBs 090510, 090902B and 090926A), a broken power law fits the LAT data better than a single power law (see § 4.3.4). After the time of peak flux, the initial flux decay is much steeper than the later decay. The initial steep-decay phase is likely due to a transition from the prompt to afterglow emission. An additional short-lived emission component, such as the high-latitude emission from the fireball which decays quickly (Kumar & Panaitescu 2000) and dominates the underlying afterglow emission, may in principle explain the initial steep decay.

Delayed Onset of LAT-detected Emission
For most bursts, the onset of the LAT-detected emission, as measured by LAT T 05 (100 MeV-10 GeV), is delayed with respect to the onset of the GBM-detected emission, measured by GBM T 05 (50 keV-300 keV) (see Fig. 9). Delays of up to 40 s have been detected in long bursts, with a few seconds being the typical value. The delay is ∼ 0.5 s for GRB 090510 and 0.05 s for GRB 081024B, both of which are short bursts. The origin of the delayed onset of the LAT emission is poorly understood.
One interpretation of the delayed LAT onset is based on the early afterglow model for the temporally-extended LAT emission (Kumar & Barniol Duran 2009;Ghisellini et al. 2010;De Pasquale et al. 2010;Razzaque 2010). The bolometric flux from a coasting fireball increases as ∝ t 2 (Sari 1997), both for an adiabatic and a radiative fireball, before it decelerates and enters a self-similar phase (Blandford & McKee 1976;Rees & Meszaros 1994). The time required for the flux to increase and be detected by the LAT corresponds to the delayed onset of the LAT emission in this scenario. It also implies that the peak-flux time of the LAT is of the order of the fireball deceleration time. The corresponding jet bulk Lorentz factor can be estimated for an ISM of constant density n =1 cm −3 as (Blandford & McKee 1976;Sari et al. 1998;Ghisellini et al. 2010), where E k,iso is the isotropic-equivalent jet kinetic energy immediately before deceleration.
In the case of a wind environment, with the wind parameter A = 3.02 × 10 35 A ⋆ cm −1 for a 10 −5 M ⊙ yr −1 mass-loss rate in the wind of velocity 10 3 km s −1 and A ⋆ ∼ 1 Chevalier & Li (2000), the jet bulk Lorentz factor can be estimated as (Chevalier & Li 2000;Panaitescu & Kumar 2000): where t peak ≈ t dec for the adiabatic and radiative fireballs. Figure 32 illustrates the range of the bulk Lorentz factors calculated using Eqs. 7 and 8 for the nine LAT bursts with known redshifts. The range depends on the uncertainty of the measurement of the peak flux time in the LAT (see Fig. 14). We assumed n = 1 cm −3 , A ⋆ = 0.1 and E k,iso is four times larger than the isotropic-equivalent γ-ray energy E γ,iso in the Band or Comptonized (in the case of GRB 100414A) component. The dependence of Γ 0 on the ISM density (∝ n −1/8 ) is rather mild. Thus, the dominant uncertainty of Γ 0 in the ISM environment comes from the peak-flux time. Note that Γ 0 needs to be large in order to explain the delayed onset and peak of the LAT emission as results of early afterglow. These estimates of Γ 0 are similar to Γ min values calculated from γγ pair production opacities for the four brightest LAT bursts (Abdo et al. 2009c;Ackermann et al. 2010b;Abdo et al. 2009a;Ackermann et al. 2011a). For GRB 110731A, detailed multiwavelength modeling suggests a wind environment. In the case of a wind environment, Γ 0 is usually smaller with milder t −1/4 dec dependence. The temporal variability of >100 MeV emission in GRBs 090902B ) and 090926A (Ackermann et al. 2011a) argues against a simple forward shock interpretation in the prompt phase, since such variability is characteristic of internal shocks. However, an energydependent transition between the prompt and afterglow contributions in the LAT flux is possible.
In the context of the internal shock scenario, the delayed onset of the LAT-detected emission could arise from late internal shocks produced via inverse Compton (IC) with plausible evolution of the microphysical parameters from the early internal shocks (Wang et al. 2006;Bošnjak et al. 2009;Toma et al. 2011). Hadronic emission such as proton/ion synchrotron radiation and/or photopioninduced cascade radiation could also account for this delay through the time required for proton/ion acceleration and cooling as well as to form cascades (Asano et al. 2009;Razzaque et al. 2010;Wang et al. 2006). However, a challenge for the internal shocks scenario is explaining the temporally extended LAT-detected emission often lasting ∼ 10 2 -10 3 s (see Fig. 10) without associated detectable keV-MeV emission. 0 8 0 9 1 6 C 0 9 0 3 2 3 0 9 0 3 2 8 0 9 0 5 1 0 0 9 0 9 0 2 B 0 9 0 9 2 6 A 0 9 1 0 0 3 1 0 0 4 1 4 1 1 0 7 3 1 A  (Fig. 14) represents the fireball-deceleration time through Eqs. (7) and (8). We also assumed a constant ISM density of n = 1 cm −3 , a wind parameter with A ⋆ = 0.1 and a kinetic energy four times the γ-ray energy, E k,iso = 4 × E γ,iso , for this illustrative plot. The range of Γ 0 in each case represents the 1σ error on t peak .

Spectral Models of LAT-detected Emissions
A power-law spectral component that dominates LAT-detected emission has been detected in the brightest LAT bursts: GRBs 080916C, 090510, 090902B, 090926A, and 110731A. This component is in addition to the Band function or the Comptonized model that typically describes the keV-MeV emission. The top panel of Fig. 26 shows that this power-law component is hard in the prompt phase (Γ GBM ∼ −2), allowing for a high-significance detection. In other bursts it can be softer, and consequently not easily detectable. In the "EXT" time window, however, the power-law component is hard (Fig. 26 The IC component contributes most significantly in the ≫ 1 GeV range. Hadronic emission models, either proton/ion synchrotron radiation or photopion-induced cascade radiation, can produce an additional spectral component as well, able to dominate the LAT-detected emission in the prompt phase (Asano et al. 2009;Razzaque et al. 2010;Wang et al. 2006). However, these models require a much larger total energy budget than the leptonic models, especially if the jet bulk Lorentz factor is high, which seems to be the case for LAT bursts.
Finally, significant cutoffs in the additional power-law component have been detected in the time-integrated prompt spectra of GRBs 090926A and 110731A. Electronpositron pair production by high-energy photons with keV-MeV photons is a plausible origin of these multi-GeV cutoffs (Krolik & Pier 1991;Fenimore et al. 1993;Baring & Harding 1997;Lithwick & Sari 2001). Detection of such cutoffs in some future LAT bursts will be helpful in determining the bulk Lorentz factors of the jets, as well as in answering whether γγ opacity plays a role in the observed low detection rate of LAT bursts.

Summary and conclusion
We have compiled a catalog of all GRBs significantly detected by the Fermi-LAT. For each of these bursts we have examined the spectral and temporal behavior of their highenergy emission. In this ensemble of bursts we have searched for common patterns in flux behavior in order to obtain an unbiased view of high-energy emission from GRBs. We have also compared the LAT-detected emission with the lower-energy emission detected by the GBM from a much greater number of bursts, and sought theoretical interpretations of the LAT observations.
In general LAT bursts are also among the brightest bursts seen by GBM. They are also the most energetic when redshift measurements allow determination of the total luminosity. Although based on only 4 bursts, there seems to be an emergent class of hyperfluent LAT GRBs.
A common characteristic of the LATdetected emission is that it is delayed with respect to the GBM emission. This delay is longer for long bursts, with some indications that the onset time increases with the energy. LAT bursts also generally have longer durations in the LAT energy range than in the GBM energy range for the same bursts.
LAT GRBs exhibit a temporally extended phase during which the LAT flux decays following a single or broken power law. The photon index in this phase is also distributed in a relatively narrow range. The index of powerlaw flux decay (later index in case of broken power-law fits) is typically close to F ν ∝ t −1 with only a few exceptions.
The temporally extended LAT-detected emission is consistent with that expected from afterglow (forward shock) emission from a relativistic blast wave. An adiabatic fireball model is favored over a radiative fireball model by the measured ∝ t −1 LAT flux-decay behavior in the majority of bursts.
The spectra of LAT GRBs are typically well described by a power-law with a fairly narrow distribution of indices, centered at −2.0 although deviations (spectral cutoffs) from a pure power law have been detected in GRBs 090926A and 110731A in the GeV range. Joint GBM-LAT spectral fits require an additional power-law component in all bright LAT bursts, indicating that the Band function alone is inadequate to fit the spectra of these bursts.
Several models exist in the literature for the delayed onset of LAT-detected emission and the additional power-law component. The early afterglow model for temporally extended LAT-detected emission can explain both the delayed onset and the additional component, but other models involving internal shocks cannot be ruled out. The detection of additional bright LAT bursts will help to characterize and explain cutoffs in the powerlaw spectra, determine the bulk Lorentz factors, and constrain GRB energetics.

Tables
In the following section, we present the results of our catalog in tabular form. Additionally, we provide all the numbers shown here in an electronic FITS 18 file format. Table 1 summarizes the intervals in which we performed the time-integrated spectral analysis described in §3.5 on page 26. Table 2 contains the list of LAT-detected GRBs, including the trigger time and position information used as input to our analysis pipeline. Each GRB was detected using the standard likelihood analysis (denoted by "Like=1" in the table) and/or the LAT Low Energy analysis (denoted using "LLE=1"). We also list the redshift (errors are omitted) and the reference number of the LAT GCN circular, if one was issued. Since the LAT localizations are obtained iteratively, we report only the final localization. Table 3 shows a comparison between the various duration estimates obtained using the standard LAT data and the LLE analysis. We also report the duration of the bursts as reported in the GBM catalog (Paciesas et al. 2012) indicating whether the burst is classified as short (S) or long (L). The final two columns report the maximum significance of the source in the likelihood analysis (Max TS) and the post-trials detection significance obtained by the LLE analysis.
Likelihood analysis results are summarized in Table 4, where we report for each interval and for each GRB, the number of events actually detected inside the ROI, the predicted number of events from the source, the detection significance, and the values of the measured photon flux, energy fluence, and isotropic equivalent energy (if a redshift is available). For the cases where the significance is below our detection threshold, we report upper limits. Three bursts detected by the LLE analysis are included in this table, 18 http://fits.gsfc.nasa.gov/ the other 4 bursts (GRBs 090531B, 101014A, 101123A and 110529A) had too few events to even compute an upper limit during the "GBM" time interval. Table 5 shows our best reconstructed direction with associated errors.
The highest-energy events associated with each GRB are summarized in Tables 6, 7, and 8. In these tables we used different timewindow to perform the analysis, and we indicate the number of events associated with the GRB, the energy, and the arrival time of the highest-energy event. We also report the probability of the event being associated with the GRB computed as described in §3.2.3.
The temporally extended high-energy emission is systematically studied in this paper, and the relative quantities are summarized in Table 9. We report the results obtained by fitting the photon flux light curves with simple power laws starting from the position of the peak flux and from the position of the GBM T 95 . When the statistics allow, we also perform a broken power-law fit. A font in bold letters indicates the parameters that best reproduce the late time decay of the γ-ray flux.
Next we summarize the results of our joint spectral-fit analyses. In Table 10 we report the spectral model that best fits the data during the "GBM" time interval. Then we present the whole range of results from the joint-fit spectral analyses as obtained in the "GBM" time interval (Table 11) and in the interval extending from the first detection of a GRB photon by the LAT up to the GBM T 95 (Table 12). Only bursts detected by the LAT (T S > 20, see § 3.5) in the "GBM" time interval are included in Table 12. In these two tables, we display the parameters of the main component and the parameters of any additional components required to describe the spectrum. For the cases that more than one component is needed, we compute the energy fluence for each spectral component sep-arately. In Table13 we report the isotropic equivalent energy in aggregate and also per spectral component for the best-fit spectral model.
Finally, we address the systematic uncertainties of our results by using a different set of data-selection cuts and we compare our standard results obtained with the Pass 6 event selection to the results obtained with the new Pass 7 data selection. This is summarized in Table 14 and described in Appendix A. Table 1 Definitions of intervals used in time-integrated spectral analysis          Table 9 Temporally extended high-energy emission s from the peak flux from GBM T 95 s 080916C 500 ± 100 6.6 ± 0.9 1.37 ± 0.07 70 ± 30 20 ± 10 1.7 ± 0.3 1.1 ± 0.4 ---110731A 220 ± 60 4.9 ± 0.7 1.8 ± 0.2 1.5 ± 0.2 --- Note.-Using numbers from this table we also define the "late-time decay index" α L , which is equal to α from GBM T 95 for all GRBs, except the 3 for which we detect the break time, for which α L = α 2 . The corresponding value is also marked with the bold font.   a These GRBs have such a large off-axis angle that the corresponding effective area for the LAT (Transient class) is negligible. Accordingly, only GBM data have been used during the spectral analysis, and the fluence has been computed extrapolating the best fit model up to the LAT energy range.
Note.-Each GRB is modeled by one main component, and eventually one or more additional components. So for example, the spectrum of GRB 080825C is well described by a Band model, thus only the corresponding columns are filled. The spectrum of GRB 090926A is instead modeled by a Band model plus a Power law times an Exponential cutoff (see main text). Note.-Each GRB is modeled by one main component, and eventually one or more additional components. So for example, the spectrum of GRB 080825C is well described by a Band model, thus only the corresponding columns are filled. The spectrum of GRB 090926A is instead modeled by a Band model plus a Power law times an Exponential cutoff (see main text).

Acknowledgments
The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariatà l'Energie Atomique and the Centre National de la Recherche Scientifique / Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden.
Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d'Études Spatiales in France.

A. Systematic Errors
In this appendix we report possible sources of systematic uncertainties in our results and how we estimate or ameliorate them.
The most important source of systematic errors arises from potentially inaccurate descriptions of the responses of the GBM and the LAT. The parametrization of the response of the LAT to incident γ rays is tabulated in instrument response functions (IRFs), produced using Monte Carlo simulations and subsequently refined based on in-flight data. Even though the results of these simulations have been verified extensively against flight data and also pre-launch using calibrated sources Abdo et al. (2009h), any imperfections in the simulation model or in the simulation procedure can propagate in the IRFs affecting all our results.
Additionally, any relative calibration errors between the GBM and the LAT and any errors in the description of the response of the GBM can affect joint spectral fits, manifesting as distortions in the spectral shapes and biases in the measured parameters.
Finally, the results of joint spectral fits also can be affected by the motion of the GRB in the instruments' fields of view which creates variations of their responses over time. These effects are minimized by producing response matrices that accurately describe the response of the instruments at any instant of the observation (see § 3.4).
Another source of systematic uncertainty is the background estimates. For Transientclass events, background estimation is performed using a procedure that has an estimated systematic uncertainty of 10-15% and negligible statistical errors (as described in § 3.1.1). For LLE and GBM data the backgrounds are estimated using interpolations of the event rate before and after the burst, a procedure the uncertainty of which primarily arises from limited statistics and is estimated to be ∼10% for LLE and less for the GBM data. For observations involving large variations of the instrument's pointing (e.g., in ARRs) or observations of locations near the Earth's limb, the systematic errors can increase possibly up to the magnitude of the statistical errors. Any mis-estimations of the LAT backgrounds can affect the final results, especially those for longer time scales such as duration estimates. The maximum likelihood analyses are not particularly sensitive to errors in the background estimates since the background level is a loosely-constrained parameter in the fitting; thus any systematic errors are partially "fit out".
In order to evaluate the impact of the above uncertainties on the maximum likelihood analysis results, we have repeated the analysis using different sets of cuts. The magnitude of the difference between the results obtained with these alternative data sets and the standard one can be used as an order-ofmagnitude estimate of the systematic uncertainties in our (standard) results.
First, we have repeated the maximumlikelihood analysis using Diffuse-class events ("Pass 6 V7 Diffuse Class"), adopting the standard isotropic template available at the FSSC site 19 as the representation of the nonrejected charged particle background. Because the Diffuse class has significantly less background contamination than Transient class, any uncertainties in the background estimates are minimal. Thus a comparison against this set of results can reveal the uncertainties arising from any inaccuracy in the background estimates for our standard set of results. Furthermore, because the two analyses employ different sets of IRFs this test is also sensitive to systematics of the IRFs in general.
We continued by splitting the Diffuse-class data sample into two independent data sets depending on which portion of the tracker each event was converted (front versus back). Events produced by photons converting in the first 12 layers of the tracker ("front") suffer on-average less multiple scattering than those converting at the next 4 layers of the tracker ("back") since the front layers have thinner converter foils (see §1 for a description of the instrument). The decreased magnitude of multiple scattering for front-converting events provides significantly better angular resolution. In addition, the front-converting events have a significantly smaller fraction of their energy measured by the calorimeter than back-converting events, which results to lower-energy (< few GeV) front-converting events being reconstructed with a worse energy resolution than back-converting events. A comparison against this sample can be sensitive to systematics of the IRFs associated to the particular properties of front-versus back-converted events.
Finally, we repeated the analysis using a more recent iteration of the set of event selection cuts for the LAT data, specifically the "Pass 7 Transient V6" selection, which benefits from more robust and accurate classification algorithms and increased refinement us-ing flight data. Again, a comparison of our results from this data set can reveal differences affecting any parts of the IRFs.
We refer to the standard configuration as "CATALOG", to the Diffuse class as "DIFF", to the front and back as "DIFF:F" and "DIFF:B" respectively, and to the "Pass 7 Transient V6" as "Pass7". Table 14 summarizes the results of the above tests, quoting for each analysis the photon flux, spectral index, index of the temporal-decay power law along with their statistical errors, and the estimated localization error. We also report the absolute difference between the CATA-LOG and each of the test configurations. In Fig. 33 we compare the results between the Pass7 and CATALOG results. The quantities compared (from top left and clockwise) are the LAT T 90 , the Fluence in the 100 MeV-10 GeV energy range during the "LAT" time interval, the index of the power-law temporal decay, and the photon index of the emission detected by the LAT. As can be seen, there are no discernible differences within errors.
We also estimated the error in the localizations obtained with the LAT. For 13 of the GRBs localized by the LAT, a Swift XRT position is also available. For those cases, we calculated the quantity ρ = δ/ǫ, which is the ratio between the angular separation (δ) between the LAT and the XRT position over the estimated LAT 1σ localization error ǫ. In Fig.34, we plot the cumulative distribution of the number of GRBs with ρ. The number of GRBs in this sample is very limited, and thus we cannot draw any firm conclusions, but we note that, as expected, the 68% quantile of the distribution is consistent with the 68% (or 1σ) estimated error.
To estimate the effects arising from relative mis-calibrations between the GBM and the LAT in the joint-spectral fit results, we introduced a flux normalization factor for each detector, letting all but one such factor be free to vary during the fit. This is basically equivalent to a rigid effective area correction across the whole bandpass of each instrument, relative to one detector chosen as reference (we chose the LAT). This procedure could give spurious results if the model used for the fit contains localized features or components, which is not the case for the models we used. We introduced these factors for the brightest GRBs of our sample: GRBs 080916C, 090323, 090328, 090510, 090902B, 090926A, 100724B, 100826A, 100414A, and 110731A. For all other GRBs, the factors were effectively unconstrained by the fit, because the inter-calibration systematic errors were small compared to the statistical errors or because the systematic errors were dominated by other components. The resulting correction was less than 5% for NaI detectors, and less than 15% for BGO detectors. According to these initial tests, relative inter-calibration uncertainties are important only in the case of bright GRBs, for which statistical errors are small. -Cumulative distribution of the number of GRBs (with good X-ray localization) over some ρ, defined as the ratio between the angular separation of the best LAT localization and the X-ray position over the 1σ statistical error of the LAT localization. The vertical band highlights the range where the cumulative distribution reaches the 68% level.
We also tested our GBM background es-timation procedure. We first considered real spectra from time intervals well outside any GRB emission. For each of these intervals I f ake , the actually observed spectrum was compared with the spectrum predicted by a background model obtained from the fit of two intervals surrounding I f ake , obtained with the procedure described in § 3.1.2. We selected a couple of GRBs, and we defined different background models by selecting different time intervals around the GRB times.
These validation studies showed that the procedure has, under normal circumstances, a systematic error of ∼ 3%, which we have added to all of our predicted background spectra.

B. Fermi LAT Gamma-Ray Bursts
In this appendix we give detailed information on individual LAT-detected GRBs. We summarize the information previously published in refereed papers and GCN circulars. We also include figures showing the GBM/LAT composite light curves as well as, when possible, the results of the LAT time-resolved spectral analyses.

B.1. Conventions and Styles for Figures
Each composite light curve consists of either 4 or 5 panels, showing the emission (in counts) recorded by the GBM NaI's (first two panels from the top), by the GBM BGO (third panel), by the LAT within the LLE event selection (fourth panel) and, if any, the selected LAT Transient-class events above 100 MeV (bottom panel).
• The GBM NaI light curves were obtained by summing all the NaI detectors (typically 2 or 3) for which the GRB position was within 50 • from the detector normal pointing axis. We also selected the BGO detector that faces the burst. We used GBM TTE data and selected the channels corresponding to the energy ranges of 8-20 keV and 20-250 keV for the NaI detectors, and 0.2-5 MeV for the BGO detector.
• The LLE light curve corresponds to the selection cuts discussed in § 2.1.1, which were applied to LAT events with energies above 10 MeV. As the gamma-ray signal in the LAT is proportional to the LAT effective area, it depends strongly on the GRB off-axis angle θ (and spectrum) at any time. In order to reflect the amplitude of this modulation, the grey curve displayed in the LLE panel shows the cos[θ(t)] function (ranging from 0 to 1 over the full extent of the panel).
• In the last light curve, we selected the LAT Transient-class events in a 12 • ROI which have a reconstructed energy above 100 MeV. We represent, as filled circles, the events which also have a probability >0.9 of being associated with the GRB (see § 3.2.3).
• In each panel, vertical dashed lines indicate the GBM trigger time (in red, at T=0), the GBM T 05 and the GBM T 95 (both in green). Other lines indicate the time of the LAT highestenergy event associated with the GRB within the GBM T 90 (in magenta, from Table 6) and during the LAT emission (in blue, from Table 8). If the two events are identical, then only the blue line is displayed.
When possible, we add a figure for the >100 MeV flux light curve, showing how the temporally extended emission develops and then decays as a function of time F (t).
• The GBM T 95 is indicated by a vertical red dashed line.
• For each time bin where the GRB was significantly detected (i.e. TS>16, see step 2 in § 3.5), we also show the value of the photon index (we use here the convention N (E) ∝ E β where N is the fitted photon flux and β is typically negative).
• For the bins with no detection, we fixed the power-law index to β=-2.0 and then report the value of the flux upper limit.
• When the statistics are large enough, we give the decay indices from the fit F (t) ∝ t −α of a power-law (starting from the latest time between the peak flux time t p and the time of the GBM T 95 ) and of a broken power law (starting from t p ). If a significant break is found in the latter fit, the broken power law is displayed as a filled grey line and the power law as a dashed grey line. The line styles are reversed in the opposite case.
In two cases (GRBs 090323 and 090328) where the ARR maneuver caused a particularly bright increase of the background during the GBM prompt emission we also show the LLE light curve and the relative background estimation.

B.2. GRB 080825C
The long GRB 080825C triggered the GBM flight software at T 0 =14:13:48 UT on 25 August 2008 (trigger 241366429, van der Horst & Connaughton 2008). Although this faint burst had an off-axis angle of 60 • .3 at the trigger time, where the effective area is a factor ∼3 less than on axis, the LAT detected it significantly and the LAT preliminary localization was delivered via GCN (Bouvier et al. 2008), with a statistical error of 0 • .95. A detailed analysis was published by the Fermi LAT collaboration in Abdo et al. (2009d). The composite light curve (Fig. 35) shows a multi-peak structure in the GBM signal, while the number of counts is not large enough at high energy to study the temporal profile in details. The LAT emission, especially above 100 MeV, seems to coincide with the second bright pulse in the GBM. The high-energy emission is also clearly visible at later times, and the highest-energy event (0.57 GeV) is detected at T 0 +28.29 s, i.e. after the end of the GBM emission. However, as the temporally extended high-energy emission is faint, the LAT time-resolved likelihood analysis returned a significant flux in two time bins only (Fig. 36).
Note that an LLE light curve of GRB 080825C was reported in the paper on GRB 090217 published by the Fermi LAT collaboration ), which indicated a ∼5σ signal after integration over the first ∼4 s, slowly increasing to ∼9σ after ∼30 s. We could not confirm this signal excess in LLE data as our analysis is based on a different detection algorithm, which is not tuned to slowly accumulating signals. This algorithm is mostly sensitive to the short variability time scales as it looks for the highest-significant excess among all considered time bins in the LLE light curve (see § 3.3.1). A 3.2σ post-trial significance (4.2σ pre-trial) was found, thus no LLE results are reported for this burst in the catalog.

B.3. GRB 080916C
The long, bright GRB 080916C triggered the GBM at T 0 =00:12:46 UT on 16 September 2008 (trigger 243216766, Goldstein & van der Horst 2008). This burst would have been bright enough to trigger an ARR of the Fermi spacecraft, but the repointing capability of the spacecraft was enabled only a few weeks later, on 8 October 2008. GRB 080916C was easily detected by the LAT, which delivered a localization via GCN (Tajima et al. 2008), with a statistical error of 0 • .09. It had an off-axis angle of 48 • .8 at the trigger time and it exited the FoV of the LAT after ∼3000 s. Swift Target of Opportunity (TOO) observations started ∼17 hours after the trigger time (Stratta et al. 2008). A possible X-ray counterpart was found by Swift-XRT 3.1 arcmin away from the LAT position (Kennea 2008), and further observations confirmed the existence of a fading source (Perri et al. 2008). Follow-up observations with the Gamma-Ray burst Optical/Near-infrared Detector (GROND) yielded a high photometric redshift of z=4.35±0.15 (Greiner et al. 2009) which, combined with its brightness, makes GRB 080916C the most energetic burst ever detected, with an isotropic equivalent energy E iso ≃ 6.5 × 10 54 erg (1 keV-10 GeV, within the GBM T 90 ).
The LAT emission peaked ∼5 s after the trigger time, coinciding with the second GBM bright pulse (Fig. 37). Approximately 180 Transient-class events are recorded above 100 MeV within the LAT T 90 ∼210 s, including many GeV events. The highest-energy event (13.22 GeV), which is detected at T 0 +16.54 s, does not coincide with any noticeable feature in the GBM light curve. In the first paper published by the Fermi LAT collaboration (Abdo et al. 2009c), the prompt emission spectrum of GRB 080916C was fitted over six decades in energy by the empirical Band function. This previous analysis also searched for possible deviations from the Band function, and did not provide any evidence for a deficit or a signal excess at the highest energies in the LAT. In particular, the significance for an additional power-law component was found to be small, ∼2σ. We repeated the analysis and found that an additional power law is actually required (4-5σ, see § 4.4.1). It is worth stressing the improvements which have been brought to the analysis procedure since the first post-launch GRB studies and which support this new result. First of all, we now use the Background Estimator tool (see § 3.1.1) which provides a much more accurate description of the backgrounds in the spectral fits. In addition, we benefit from a better calibration of both the GBM and the LAT instruments. Finally, we base our assessment of the significance of any new spectral feature on dedicated and extended Monte-Carlo simulations. These improvements, along with a new choice of the time intervals (based on our estimates for the durations of the emission in the GBM and the LAT) as well as a different spectral shape, also explain the differences in our results (Tables 11 and 12) with respect to the original publication.
The high-energy emission of GRB 080916C lasts much longer than the GBM estimated duration. The LAT time-resolved likelihood analysis resulted in a well sampled light curve of the high-energy flux up to ∼560 s (Fig. 38). Its first point suggests that the spectrum is significantly softer than the LAT emission at later times, where the photon index fluctuates consistently around β=-2. The decay of the flux as a function of time follows a simple power law starting from the GBM T 95 , with a decay index α=1.78±0.33. This steep decay is similar to the first part of the decay observed in GRBs 090510, 090902B and 090926A (Table 9) for which a significant break was found in the flux light curve. This suggests that GRB 080916C was observed during the transition from the prompt phase to the afterglow phase as discussed in § 6.2.

B.4. GRB 081006
The long GRB 081006 triggered the GBM at T 0 =14:29:34 UT on 6 October 2008 (trigger 244996175, van der Horst 2008). It was a faint burst, both in the GBM and in the LAT (despite an initial off-axis angle of 11 • ). No significant emission was detected in the LLE light curve (Fig. 39) despite a 2.7σ fluctuation observed shortly after the trigger time. More interestingly, this burst was detected and localized by the LAT likelihood analysis using Transient-class events above 100 MeV, with a maximum TS∼72 (see Table 4). Taking into account uncertainties in the calculation of the LAT T 90 , the high-energy emission could be simultaneous with the low-energy emission (i.e. happening on very similar time scales) or it could last much longer as a significant signal excess is detected above the estimated background up to ∼T 0 +115 s. This time corresponds to the entrance of the LAT in the South Atlantic Anomaly, and was thus reported as a lower limit to the duration in Table 3. In spite of this hint for a temporally extended high-energy emission, the LAT likelihood analysis did not find any significant signal in the "EXT" time interval, and could not provide good time-resolved spectral measurements (Fig. 40).

B.5. GRB 081024B
GRB 081024B triggered the GBM at T 0 =21:22:41 UT on 24 October 2008 (trigger 246576161, Connaughton & Briggs 2008) and it was the first LAT detection of a short burst. The LAT preliminary localization was delivered via GCN (Omodei 2008), with a statistical error of 0 • .16. Follow-up observations by Swift and ground-based telescopes did not find any conclusive evidence for an afterglow counterpart (Guidorzi et al. 2008). Historically, GRB 081024B represents the first clear detection of a temporally extended emission from a short GRB at GeV energies (Abdo et al. 2010b;Corsi et al. 2010). Whereas the low-energy emission observed by the GBM lasts ∼0.5 s, the highenergy emission is visible up to ∼3 s after the trigger time (Fig. 41). The highest-energy event (3.07 GeV) is detected at T 0 +0.49 s, i.e. very close in time to the end of the GBM emission. A LAT T 90 could not be derived due to the small number of Transient-class events above 100 MeV, however the LLE duration (∼2.3 s) indicates a significantly longer duration of the LAT emission at tens-of-MeV energies. Due to the low photon statistics, the LAT likelihood analysis did not find any significant signal in the "EXT" interval, and could not provide good time-resolved spectral measurements (Fig. 42).

B.6. GRB 090217
The long GRB 090217 triggered the GBM at T 0 =04: 56:42.56 UT on 17 February 2009(trigger 256539404, von Kienlin 2009a. The LAT preliminary localization was delivered via GCN (Ohno et al. 2009b), with a statistical error of 0 • .36. A detailed analysis was published by the Fermi LAT collaboration in Ackermann et al. (2010a). No X-ray counterpart was found in Swift TOO observations of the LAT preliminary localization that covered only the center of the LAT error circle (Godet 2009), and therefore no redshift is available for this burst. GRB 090217 is a bright burst both in LLE and in LAT Transient-class data above 100 MeV. The LLE light curve shows a series of pulses coincident with the GBM emission (Fig. 43). The highest-energy event (0.87 GeV) during this prompt emission is detected at T 0 +14.83 s and is not associated with any noticeable structure of the GBM light curve. The LAT T 95 =68 +109 −40 s is not accurate enough to conclude if the high-energy emission extends later than the low-energy emission (GBM T 95 ∼35 s). The off-axis angle of GRB 090217 remained below 60 • until T 0 +500 s, but no additional signal was found and upper limits are reported up to 10 ks (Fig. 44).

B.7. GRB 090227B
The short GRB 090227B triggered the GBM at T 0 =18:31:01.41 UT on 27 February 2009(trigger 257452263, Guiriec 2009a. GRB 090227B had an initial off-axis angle of 71 • from the LAT boresight and the ARR triggered by the GBM brought it down to ∼20 • after ∼300 s. The triangulation of the burst by the Interplanetary Network (IPN) provided a position with a 3σ error box area of 1.5 square degrees (Golenetskii et al. 2009) which we used in our analysis. The GBM light curve of GRB 090227B consists of one single pulse which was also significantly detected in the LLE data, with comparable durations (Fig. 45). A TS∼30 was obtained by the LAT likelihood analysis based on the 3 Transient-class events recorded above 100 MeV during the GBM time window, thus the burst is included in the catalog. However, due to the position of the burst in the LAT FoV during the main emission, no LAT T 90 could be derived due to the paucity of events. We could also not improve upon the IPN localization as no reliable TS map could be obtained. For the same reason, no time-resolved likelihood analysis could be performed with the LAT.

B.8. GRB 090323
The long, bright GRB 090323 triggered the GBM at T 0 =00:02:42.63 UT on 23 March 2009(trigger 259459364, Ohno et al. 2009a. It had an initial off-axis angle of 57 • .2, where the LAT effective area is low, but it triggered an ARR of the Fermi spacecraft which allowed the LAT to detect its late emission phase and to localize it with a statistical error of 0 • .09 (Ohno et al. 2009a). Specifically, GRB 090323 was detected by the LAT on-gound Automated Science Processing (ASP) which searches for LAT counterparts to known GRBs. Swift TOO observations started ∼19.5 hours after the trigger time. A possible X-ray counterpart was found by Swift -XRT 1.9 arcmin away from the LAT position (Kennea et al. 2009a), and further observations confirmed the existence of a fading source (Perri & Stratta 2009). Follow-up observations of the X-ray afterglow with GROND in 7 bands started ∼27 hours after the trigger time, providing a preliminary photometric redshift of z=4.0±0.3 (Updike et al. 2009c). Chornock et al. (2009 reported a spectroscopic redshift of z=3.57 based on observations of the optical afterglow using the Gemini Multi-Object Spectrograph (GMOS) mounted on the Gemini South Telescope. Combined with its brightness, this makes GRB 090323 the second most energetic LAT-detected burst after GRB 080916C, with an isotropic equivalent energy E iso ≃ 4.1 × 10 54 erg (1 keV-10 GeV, within the GBM T 90 ). The burst was also detected in the radio band (Harrison et al. 2009;van der Horst 2009). A dedicated analysis of the near-infrared and optical follow-up observations of GRB 090323 is presented in McBreen et al. (2010).
The GBM light curve of GRB 090323 consists of several pulses and lasts ∼150 s (Fig. 46). The LLE light curve shows two bright long pulses which somehow coincide with two broad pulses observed in the GBM light curve. The ARR caused the GBM and LAT orientations to change very rapidly with time, requiring a careful evaluation of the instruments' responses and backgrounds as the spacecraft is slewing. In particular, the burst Zenith angle increased from 67 • at T 0 to 84 • at T 0 +300 s, causing a rise in the LAT count rate due to the entrance of the Earth's limb in the instrument's FoV. As illustrated in Fig. 47, the analysis of LLE data accounts for this effect, following the background estimation method discussed in § 3.1. In the LAT likelihood analysis, we reduced the contamination from the Earth's limb by simply rejecting the time intervals in which the burst Zenith angle was larger than 105 • . Indications of long-lasting high-energy emission are seen in the LAT Transient-class data where multi-GeV events were recorded well after the GBM emission, similarly to the 7.50 GeV event detected at T 0 +195.42 s. The LAT T 95 =294 +55 −25 s confirms the temporal extension of the high-energy emission, and the LAT time-resolved likelihood analysis returned a significant signal up to T 0 +422 s, with a temporal decay index α=0.85±0.29 (Fig. 48). GRB 090323 became occulted after ∼570 s and, in the next orbit, the spacecraft entered the SAA only ∼50 s after the burst exited occultation, thus only upper limits are reported at later times, up to ∼10 ks.

B.9. GRB 090328
The long, bright GRB 090328 triggered the GBM at T 0 =09:36.46 UT on 28 March 2009(trigger 259925808, McEnery et al. 2009b. GRB 090328 had an initial off-axis angle of 64 • .6 in the LAT and the ARR triggered by the GBM brought it down to ∼10 • after ∼300 s. The LAT preliminary localization was delivered via GCN (McEnery et al. 2009b), with a statistical error of 0 • .11. Swift TOO observations started ∼16 hours after the trigger time (Marshall et al. 2009). A possible X-ray counterpart was found by Swift -XRT ∼10 arcmin away from the LAT position (Kennea 2009), and further observations confirmed the existence of a fading source (Rowlinson & Page 2009). Observations of a candidate optical afterglow were also reported by Kennea et al. (2009b) and Oates (2009). More observations of the afterglow were conducted in the optical (Allen et al. 2009), in the optical/NIR with GROND (Updike et al. 2009a), and in the radio band (Frail et al. 2009). Cenko et al. The GBM light curve of GRB 090328 consists of several pulses and lasts ∼70 s (Fig. 49). The LLE light curve shows one single, long bright pulse which coincides with the second broad pulse observed in the GBM light curve. In addition, the first narrow spike in the GBM light curve has no LLE counterpart, indicating an initially soft spectrum. The ARR caused an increase in the background rate in the LLE light curve as the burst off-axis angle was decreasing (third panel of Fig. 49). Fig. 50 shows the results of the background estimation in the analysis of LLE data.
In the preliminary analysis of LAT data, Cutini et al. (2009) reported that GRB 090328 highenergy emission lasted until ∼900 s post trigger. Our analysis of the LAT Transient-class data above 100 MeV provided a LAT T 95 =653 +134 −45 s which confirms the temporal extension of the burst emission in the LAT. We could also confirm that the highest-energy events detected by the LAT which are spatially coincident with the burst position arrived hundreds of seconds after the trigger time. Multi-GeV events were recorded well after the GBM emission, in particular two 3.83 GeV and 5.32 GeV events detected at T 0 +264.42 s and T 0 +697.80 s, respectively. Unlike GRB 090323, the ARR for GRB 090328 was excellent and started just after the burst exited occultation. During the next two orbits, observations were only interrupted by occultations, with no passage through the SAA. As a result, the LAT time-resolved likelihood analysis detected a significant signal up to T 0 +1.78 ks, with a temporal decay index α=0.95±0.19 (Fig. 51). The short, bright GRB 090510 is the only burst detected so far by the LAT onboard flight software (trigger 263607783). The LAT onboard localization was delivered via GCN (Ohno & Pelassa 2009), with a statistical error of 7 arcmin. Combined with an initial off-axis angle of 13 • .6, GRB 090510 caused an exceptionally bright emission in the LAT as reported in the follow-up analysis by Omodei et al. (2009), and it triggered an ARR of the Fermi spacecraft. GRB 090510 was also significantly (>5σ) detected by the AGILE-GRID above 100 MeV (Longo et al. 2009a;Giuliani et al. 2010a). At lower energies, GRB 090510 triggered both the Swift -BAT (Hoversten et al. 2009a,b)  As shown in Fig. 52, the GBM triggered on a precursor in GRB 090510 light curve. The main emission in the GBM consists of several pulses, with a maximum at T 0 +0.6 s and a duration of ∼0.6 s. The temporal structure of the LAT emission shows fast variability on timescales as short as 20 ms. The LLE light curve shows a series of short spikes coinciding with the GBM pulses and appearing on top of a smoother and longer single pulse. Two of the three LAT Transient-class events recorded above 100 MeV at the time of the precursor (between T 0 to T 0 +0.2 s) have high probabilities to be associated with the burst. The main emission in the LAT starts at T 0 +0.6 s and lasts much longer than the GBM estimated duration, with 180 Transient-class events recorded above 100 MeV within the LAT T 90 ∼45 s (see Table 4). many GeV events are recorded during and well after the GBM emission, similarly to the 31.31 GeV event detected a T 0 +0.83 s in coincidence with a short bright spike in the GBM light curve. This photon candidate has been used by the Fermi LAT collaboration to set the best lower limit on the energy scale at which postulated quantum-gravity effects create violations of Lorentz invariance, disfavoring models which predict a linear variation of the speed of light with photon energy below the Planck energy scale E Planck =1.22×10 19 GeV ).
In the time-resolved spectral analysis published by the Fermi LAT collaboration , the prompt emission spectrum of GRB 090510 was fitted over more than six decades in energy by the combination of the empirical Band function with a high-energy power law. The hard power law is detected from the onset of the main emission in the LAT, and it dominates the Band function not only at high energy but also below ∼20 keV. Our GBM-LAT joint spectral analysis in the GBM time window confirms these results, yielding a peak energy E p ∼3.6 MeV for the Band function and a spectral slope of 1.60±0.04 for the additional power-law component. The total isotropic equivalent energy is (7.3 ± 0.3) × 10 52 erg (1 keV-10 GeV, within the GBM T 90 ).
The LAT time-resolved likelihood analysis resulted in a well sampled light curve of the highenergy flux up to T 0 +178 s (Fig. 53). No significant spectral evolution was detected. The decay of the flux as a function of time can be fitted with a simple power law starting from the GBM T 95 , with a decay index α=1.82±0.17 somewhat steeper than the index of 1.38±0.07 reported in De Pasquale et al. (2010). However, the fit of the flux light curve with a broken power law from the peak flux time t p =T 0 +0.9 s up to T 0 +∼8 ks (including flux upper limits after T 0 +178 s) returned a significant break at t b =7.0±1.5 s, along with a steeper initial decay (α 1 =2.21±0.27) and a smoother decay (α 2 =1.13±0.12) at later times. Swift -XRT (Sbarufatti et al. 2009) instruments. It is a relatively faint burst, both in the GBM and in the LAT (despite an initial off-axis angle of 21 • .9). Only a few LAT Transient-class events above 100 MeV are compatible with the Swift localization, therefore no significant emission was found in the likelihood analysis. GRB 090531B was detected in the LLE data only, and the LLE light curve shows a significant signal excess which is temporally coincident with the first pulse detected by the NaI and BGO detectors (Fig. 54).

B.12. GRB 090626
The long GRB 090626 triggered the GBM at T 0 =04:32:08.88 UT on 26 June 2009(trigger 267683530, von Kienlin 2009b. It was also detected by the LAT on-gound ASP which searches for LAT counterparts to known GRBs, and the LAT preliminary localization was delivered via GCN (Piron et al. 2009), with a statistical error of 0 • .32 (95% confidence level). The GBM light curve of GRB 090626 consists of several bright pulses and lasts ∼55 s (Fig. 55). The LLE light curve shows one single, faint short pulse which coincides with the second bright pulse observed in the BGO light curve. However, this signal excess was not significant enough to claim an LLE detection (see Table 2). In the preliminary analysis of LAT data, Piron et al. (2009) reported that GRB 090626 high-energy emission lasted until T 0 +∼250 s. Our analysis of the LAT Transient-class data above 100 MeV provided a LAT T 95 =300 +338 −53 s which confirms the temporal extension of the burst emission in the LAT. In addition, a 2.09 GeV event is recorded at T 0 +111.63 s. The LAT time-resolved likelihood analysis returned a significant flux in three time bins only up to T 0 +750 s (Fig. 56).

B.13. GRB 090720B
The long GRB 090720B triggered the GBM at T 0 =17:02:56.91 UT on 20 July 2009 (trigger 269802178, Burgess et al. 2009). The GBM light curve consists of one short hard pulse followed by a wider pulse (Fig. 57). GRB 090720B had an off-axis angle of 56 • .1 in the LAT at the trigger time, where the effective area is a factor ∼3 less than on axis. The burst was not significantly detected in the LLE data and the LAT likelihood analysis returned a TS∼25 based on the 3 Transient-class events recorded above 100 MeV during the GBM time window, including a 1.45 GeV event at T 0 +0.22 s. No LAT T 90 could be derived due to the large Zenith angle of the burst. The LAT time-resolved likelihood analysis returned a marginal detection in one time bin only, ending at T 0 +75 s (Fig. 58). B.14. GRB 090902B The long, bright GRB 090902B triggered the GBM at T 0 =11:05:08.31 UT on 2 September 2009 (trigger 273582310, Bissaldi & Connaughton 2009). In spite of an initial off-axis angle of 50 • .8, GRB 090902B caused exceptionally bright emission in the LAT and it triggered an ARR of the Fermi spacecraft. The LAT preliminary localization was delivered via GCN (de Palma et al. 2009b), with a statistical error of 0 • .04. Swift TOO observations started ∼12.5 hours after the trigger time (Stratta et al. 2009b). A possible X-ray counterpart was found by Swift -XRT 3.2 arcmin away from the LAT position (Kennea & Stratta 2009), and further observations confirmed the existence of a fading source (Stratta et al. 2009a). Follow-up detections in the optical were reported by the Swift -UVOT team (Swenson & Siegel 2009;Swenson & Stratta 2009) and by several observers operating ground-based telescopes (Perley et al. 2009a;Guidorzi et al. 2009;Pandey et al. 2009). GRB 090902B was also detected in the optical/NIR (Olivares et al. 2009a) and in the radio band (van der Horst et al. 2009;Chandra & Frail 2009). Cucchiara et al. (2009b reported a spectroscopic redshift of z=1.822 based on observations of the optical afterglow using the GMOS spectrograph mounted on the Gemini South Telescope. Combined with its brightness, this makes GRB 090902B the third most energetic LAT-detected burst after GRB 080916C and GRB 090323, with an isotropic equivalent energy E iso ≃ 3.4 × 10 54 erg (1 keV-10 GeV, within the GBM T 90 ). A dedicated analysis of the near-infrared and optical follow-up observations of GRB 090902B is presented in McBreen et al. (2010).
As shown in Fig. 59, the GBM light curve of GRB 090902B is complex both in the NaI and BGO detectors, probably resulting from the overlap of many small pulses. After a plateau phase of ∼6 s similar to what is observed at lower energies, the LLE light curve shows a series of short spikes on top of two broad and partially overlapping pulses, which seem to coincide with two distinct emission episodes visible in both the NaI and BGO light curves. The temporal structure of the LAT emission shows fast variability on timescales as short as ∼100 ms. In the first paper published by the Fermi LAT collaboration , the prompt emission spectrum of GRB 090902B was fitted over more than six decades in energy by the combination of the empirical Band function with a high-energy power law. The hard power law is detected from the trigger time, and it dominates the Band function not only at high energies but also below ∼50 keV as already reported in the preliminary joint analysis of GBM and LAT data (de Palma et al. 2009a). Our GBM-LAT joint spectral analysis in the GBM time window confirms these results, yielding similar parameters for the Band function and a spectral slope of 1.94±0.01 for the additional power-law component. Note that alternative spectral models have been studied in details (Ryde et al. 2009;Liu & Wang 2011), and that the peculiar spectrum of GRB 090902B has also been used to constrain several theoretical models (Barniol Duran & Kumar 2011;Pe'er et al. 2012).
The LAT emission contains many GeV events during and well after the GBM emission, similarly to the 33.39 GeV event detected at T 0 +81.75 s. This photon candidate has the highest energy ever observed from a burst and it has been used by the Fermi LAT collaboration to probe the Extragalactic Background Light as a function of redshift in the optical-UV range (Abdo et al. 2010a). The temporally extended high-energy emission reaches at least the end of the first GTI (LAT T 95 >825 s) and ∼300 Transient-class events are recorded above 100 MeV until this time (see Table 4). The LAT time-resolved likelihood analysis resulted in a well sampled light curve of the high-energy flux up to T 0 +750 s (Fig. 60). No significant spectral evolution was detected. The decay of the flux as a function of time can be fitted with a simple power law starting from the GBM T 95 , with a decay index α=1.40±0.10, in agreement with the result reported by Abdo et al. (2009a). Similarly to GRB 090510, however, the fit of the flux light curve with a broken power law from the peak flux time t p =T 0 +8.7 s up to T 0 +∼8 ks (including flux upper limits after T 0 +750 s) returned a significant break at t b =130±50 s, along with a steeper initial decay (α 1 =1.70±0.19) and a smoother decay (α 2 =1.27±0.12) at later times. ). An X-ray counterpart was found by Swift -XRT 4 arcmin away from the LAT position (Vetere et al. 2009a), and further observations confirmed the existence of a fading source with some flaring activity (Vetere 2009). The optical afterglow of GRB 090926A was discovered by the Skynet-PROMPT telescopes (Haislip et al. 2009b,a,e,c,d) and also detected by Swift -UVOT (Gronwall & Vetere 2009;Oates & Vetere 2009). Malesani et al. (2009 reported a spectroscopic redshift of z=2.1062 based on observations of the optical afterglow using the Xshooter spectrograph mounted on the ESO-VLT UT2. Combined with its brightness, this makes GRB 090926A the fourth most energetic LAT-detected burst, with an isotropic equivalent energy E iso ≃ 2.4 × 10 54 erg (1 keV-10 GeV, within the GBM T 90 ).
As shown in Fig. 61, the light curve of GRB 090926A exhibits a bright, short pulse at ∼T 0 +10 s, in all energy bands covered by the GBM and the LAT. In the preliminary analysis of GBM and LAT data,  fitted the emission spectrum of this pulse by the combination of the empirical Band function with a high-energy power law. In the time-resolved spectral analysis published by the Fermi LAT collaboration (Ackermann et al. 2011b), the high-energy power-law component was found to start at the time of the bright pulse and to persist until ∼T 0 +22 s. In this study, a spectral break was also found at the highest energies, with a cutoff energy E c ∼400 MeV during the bright pulse and E c ∼1.4 GeV for the time-integrated spectrum. Our GBM-LAT joint spectral analysis in the GBM time window confirms these results, yielding E c ∼1.5 GeV and a similar spectral slope of 1.73±0.03 for the high-energy power-law component (Table 11).
The LAT emission contains many GeV events during and well after the GBM emission, similar to the 19.56 GeV event detected at T 0 +24.83 s. The temporally extended high-energy emission reaches at least T 0 +225 s, and ∼230 Transient-class events are recorded above 100 MeV until this time (see Table 4). The LAT time-resolved likelihood analysis resulted in a well sampled light curve of the high-energy flux up to T 0 +295 s (Fig. 62). The decay of the flux as a function of time can be fitted with a simple power law starting from the GBM T 95 , with a decay index α=1.60±0.28, in agreement with the result reported by Ackermann et al. (2011b). Similarly to GRB 090510 and GRB 090902B, however, the fit of the flux light curve with a broken power law from the peak flux time t p =T 0 +11.7 s up to T 0 +∼8 ks (including flux upper limits after T 0 +295 s) returned a significant break at t b =40±5 s, along with a steeper initial decay (α 1 =2.88±0.32) and a smoother decay (α 2 =1.06±0.14) at later times. The right hand plot of Fig. 62 also suggests that the photon index in the first phase is steeper than the one in the final decay part. No significant emission was detected in the LLE light curve (Fig. 63). The highest-energy event (2.8 GeV) is detected at T 0 +6.47 s and does not coincide with any noticeable feature in the GBM light curve. Although the LAT T 95 =453 +86 −376 s suffers from a large uncertainty due to the relatively small statistics (∼30 events), the burst was detected up to this time with high significance by the LAT likelihood analysis of the Transient-class data above 100 MeV. The LAT time-resolved likelihood analysis returned a significant flux up to T 0 +316 s, with a temporal decay index α=0.96±0.20 (Fig. 64).

B.17. GRB 091031
The long GRB 091031 triggered the GBM at T 0 =12:00:28.85 UT on 31 October 2009 (trigger 278683230, McBreen & Chaplin 2009). The LAT preliminary localization was delivered via GCN (de Palma et al. 2009c), with a statistical error of 0 • .2. This burst was significantly detected in the LLE light curve (Fig. 65) and above 100 MeV by the likelihood analysis up to the LAT T 95 =206 +12 −43 s. The LAT time-resolved likelihood analysis returned a significant flux up to T 0 +100 s (Fig. 66). The highest-energy event (1.19 GeV) is detected with two other high-energy events at T 0 +79.75 s, well after the end of the GBM emission.  (Pagani et al. 2010). A fading and uncataloged X-ray source was found and Swift -UVOT detected a bright afterglow candidate consistent with the XRT localization (de Pasquale & Pagani 2009;Pagani et al. 2009). Several telescopes detected the bright optical transient (Xin et al. 2009;Kinugasa et al. 2009;Andreev et al. 2009;Updike et al. 2009b;Xu et al. 2009;Cano et al. 2009;Nakajima et al. 2009;Yoshida et al. 2009;de Ugarte Postigo et al. 2009). A spectroscopic redshift measurement of z=1.063 was obtained using the GMOS spectrograph mounted on the Gemini North Telescope (Wiersema et al. 2009b), later confirmed by the HIRES-r spectrometer mounted on the 10 m Keck I telescope (Perley et al. 2009c). Using the XRT refined position (Osborne et al. 2009), the LAT likelihood analysis found a marginal detection (TS=20) during the GBM T 90 , based on three Transient-class events associated to the burst. The highest-energy event (1.18 GeV) is detected at T 0 +3.41 s. Due to the paucity of events (Fig. 67), no LAT T 90 could be derived and the LAT time-resolved likelihood analysis returned a significant flux in one time bin only, ending at T 0 +42 s (Fig. 68).

B.19. GRB 100116A
The long GRB 100116A triggered the GBM at T 0 =21:31:00.24 UT on 16 January 2010 (trigger 285370262, Briggs & Connaughton 2010). The LAT preliminary localization was delivered via GCN (McEnery et al. 2010), with a statistical error of 0 • .17. As shown in Fig. 69, the GBM triggered on a precursor in GRB 100116A light curve. A very intense pulse is observed at ∼T 0 +90 s, with a slow rise and a fast decay, probably due to the overlap of many smaller pulses during the rising part. LAT low-energy events are recorded in temporal coincidence with this bright GBM pulse. More interestingly, the Transient-class events above 100 MeV which are compatible with the burst position appear to be slightly delayed (∼20 s) with respect to both the LLE and GBM emission, and the highest-energy event (2.2 GeV) is detected at T 0 +105.71 s, right at the end of the GBM emission. This temporally extended high-energy emission reaches at least the end of the first GTI (LAT T 95 >141 s). The LAT time-resolved likelihood analysis returned a significant flux up to T 0 +178 s (Fig. 70). A 13.12 GeV event with a probability higher than 99% to be associated with the burst is detected at ∼T 0 +296 s (see the discussion in § 4.3.3). . Only a few LAT Transient-class events above 100 MeV are actually compatible with the burst position, therefore no LAT T 90 could be derived and no significant emission was found in the likelihood analysis. GRB 100225A was detected in the LLE data only. The LLE light curve consists of a long duration pulse which mimics the light curve seen in the NaI detectors (Fig. 71).

B.21. GRB 100325A
The long GRB 100325A triggered the GBM at T 0 =06:36:08.02 UT on 25 March 2010 (trigger 291191770, von Kienlin 2010a). The LAT preliminary localization was delivered via GCN (de Palma et al. 2010), with a statistical error of 0 • .6. The light curve in the NaI detectors consists of several overlapping pulses, whereas the burst is not visible in the BGO light curve and only marginally detected in the LLE light curve (Fig. 72). Due to the paucity of events, no LAT T 90 could be derived. A cluster of four Transient-class events above 100 MeV are recorded within 0.57 s right after the trigger time, and the LAT time-resolved likelihood analysis returned a significant flux up to T 0 +23.7 s (Fig. 73). More interestingly, the time-integrated spectrum of GRB 100325A during the GBM T 90 is best represented by a Band function, with a hard value for the low-energy spectral slope α = −0.33 ± 0.11. The GBM light curve of GRB 100414A consists of a single slowly rising pulse which ends abruptly after culminating at T 0 +23 s (Fig. 74). No significant emission was detected in the LLE light curve. Although the LAT T 95 =289 +90 −111 s suffers from a large uncertainty due to the relatively small statistics (∼20 events), the burst was detected up to this time with high significance by the LAT likelihood analysis of the Transient-class data above 100 MeV. The LAT time-resolved likelihood analysis returned a significant flux up to T 0 +316 s, with a temporal decay index α=1.08±0.43 (Fig. 75). More interestingly, the time-integrated spectrum of GRB 100414A during the GBM T 90 is best represented by a Comptonized model with an additional power-law component with a spectral slope of 1.75±0.07. However, as discussed in § 4.4.1, this additional component is seen in the "GBM" time interval only (Tables 11 and 12) and its existence is uncertain due to possible systematic effects in the GBM-LAT joint spectral analysis during the ARR maneuver.

B.23. GRB 100620A
The long GRB 100620A triggered the GBM at T 0 =02:51:29.1134 UT on 20 June 2010 (trigger 298695091). The best localization reported in the GBM catalog (Paciesas et al. 2012) was used as an initial seed for our analysis. Using LAT Transient-class events above 100 MeV, we could improve upon the GBM localization. The LAT localization, which has a statistical error of 0 • .71 (Table 5), is the final best position. GRB 100620A is a faint burst in the GBM, with no emission in the BGO detector nor in LLE data (Fig. 76). No LAT T 90 could be derived due to the paucity of events, but accumulating signal in the LAT time-resolved likelihood analysis allowed us to detect a significant flux up to T 0 +316 s (Fig. 77).

B.24. GRB 100724B
The long GRB 100724B triggered the GBM at T 0 =00:42:05.98 UT on 24 July 2010 (trigger 301624927, Bhat 2010). Its off-axis angle in the LAT was 48 • .9 at the trigger time, and remained greater than 40 • for 2700 s despite the ARR triggered by the GBM, as the Fermi spacecraft remained in survey mode as long as the Earth avoidance angle condition was not satisfied. The LAT preliminary localization was delivered via GCN (Tanaka et al. 2010b), with a statistical error of 0 • .6. The burst was also significantly detected by both the AGILE-GRID and the AGILE-MCAL (Marisaldi et al. 2010;Giuliani et al. 2010b).
GRB 100724B is very bright in the GBM and in LLE data, with two main emission episodes (Fig. 78). Surprisingly, it is not exceptionally bright in LAT Transient-class data above 100 MeV, and the highest-energy event (0.22 GeV) is detected at T 0 +61.75 s, during the second episode. No LAT T 90 could be derived due to the large Zenith angle of the burst, but the burst was detected up to T 0 +125 s with high significance by the LAT likelihood analysis above 100 MeV. This analysis actually revealed a fairly steep high-energy spectrum, with a photon index of −4.96 ± 0.94 during the GBM T 90 and −4.85 ± 0.92 in the "LATTE" time interval. Similar indices were measured in the LAT time-resolved likelihood analysis (Fig. 79). More interestingly, the time-integrated spectrum of GRB 100724B during the GBM T 90 is best represented by a Band function with a hard value for the high-energy spectral slope β = −2.00 ± 0.01 and with an exponential cutoff at E c = 40 ± 3 MeV (Table 11 and Table 12). The spectral analysis performed by Guiriec et al. (2011) was based on GBM data only and yielded similar results except for the spectral break whose detection requires the addition of LAT data. Conversely, our analysis is not in agreement with the results reported by Del Monte et al. (2011), who found a single power-law spectral shape extending up to 100 MeV with a photon index β = −2.13 +0.05 −0.04 . This difference could be explained by the larger effective area and the deeper calorimeter of the Fermi-LAT (Atwood et al. 2009b), which provides more sensitive spectral measurements than the AGILE instruments. Owing to its long duration (∼120 s in the GBM) and despite the relatively low peak energy E p = 263 ± 4 keV and the spectral break at MeV energies, GRB 100724B is the most fluent burst in the catalog, with a The GBM light curve of GRB 100728A shows a multi-peaked structure lasting approximately ∼190 s (Fig. 80). Most of the emission is detected at low energy, and the time-integrated spectrum of the burst during the GBM T 90 is best represented by a Comptonized model. GRB 100728A had an initial off-axis angle of 59 • .9 in the LAT and the ARR triggered by the GBM brought it down to ∼10 • after ∼300 s. Only a few LAT Transient-class events above 100 MeV are compatible with the burst position, therefore no LAT T 90 could be derived and no significant emission was found in the likelihood analysis. Accumulating signal in the LAT time-resolved likelihood analysis allowed us to detect a significant flux in one time bin, ending at T 0 +750 s (Fig. 81). This detection confirms the temporal coincidence of the high-energy emission of GRB 100728A with its flaring activity in X-rays, as published in Abdo et al. (2011). The implications of the Fermi-LAT observation and the possible connection between the gamma-ray emission and the X-ray activity of GRB 100728A have also been discussed in He et al. (2011) andMao &Wang (2012). A 13.54 GeV event with a probability higher than 98% to be associated with the burst is detected ∼90 minutes after the trigger time (see the discussion in § 4.3.3). This represents the only evidence in our catalog that high-energy events (>10 GeV) can arrive very late in time, confirming the results from Hurley et al. (1994b) and suggesting that such events are rare. Only a few LAT Transient-class events above 100 MeV are compatible with the burst position, therefore no LAT T 90 could be derived and no significant emission was found in the likelihood analysis. GRB 100826A was detected in the LLE data only (McEnery & Omodei 2010). The LLE light curve has a very similar structure to the GBM broad peak, with the maximum count rate occurring at ∼T 0 +22 s (Fig. 82). The burst is bright in the GBM and its time-integrated spectrum during the GBM T 90 is best represented by a Band function, with a hard value for the high-energy spectral slope β = −2.03 ± 0.02.

B.27. GRB 101014A
The long GRB 101014A triggered the GBM at T 0 =04:11:52.62 UT on 14 October 2010 (trigger 308722314, Tierney & Goldstein 2010) and it has the longest GBM duration (T 90 ∼450 s) in the catalog. It had an initial off-axis angle of 54 • in the LAT and the ARR triggered by the GBM brought it down to ∼10 • after ∼200 s. Because of the burst's proximity to the orbital pole, there was substantial contamination in the surrounding region owing to gamma-ray emission from the Earth's limb (Tanaka et al. 2010a). As a result, no LAT Transient-class events are left above 100 MeV after our selection cuts ( § 2.1.1). We could thus not improve upon the GBM localization and no likelihood analysis was possible. GRB 101014A was detected in the LLE data only. Whereas the GBM light

B.29. GRB 110120A
The long GRB 110120A triggered the GBM at T 0 =15:59:39.23 UT on 20 January 2011 (trigger 317231981, Lin 2011). In spite of an initial off-axis angle of 13 • .6, GRB 110120A was relatively faint in the LAT. The LAT preliminary localization was delivered via GCN , with a statistical error of 0 • .4. The GBM light curve of GRB 110120A consists of two overlapping pulses (Fig. 85). The LLE light curve shows a small signal excess which coincides with the GBM emission, but this excess was not significant enough to claim an LLE detection (see Table 2). Our analysis of the LAT Transient-class data above 100 MeV provided a LAT T 95 =113 +21 −30 s which indicates the temporal extension of the burst emission in the LAT. In addition, a 1.82 GeV event is recorded at T 0 +72.46 s. The LAT time-resolved likelihood analysis returned a significant flux in two time bins only, up to T 0 +75 s (Fig. 86).

B.31. GRB 110428A
The long GRB 110428A triggered the GBM at T 0 =09:18:30.41 UT on 28 April 2011 (trigger 325675112, Tierney & Fitzpatrick 2011). It had an initial off-axis angle of 34 • .6 in the LAT and the ARR triggered by the GBM brought it down to ∼5 • after ∼200 s. The LAT preliminary localization was delivered via GCN (Vasileiou et al. 2011b), with a statistical error of 0 • .15. Swift TOO observations started ∼55.6 ks after the trigger time and a possible X-ray counterpart was found by Swift -XRT (Melandri et al. 2011b). Further observations confirmed the existence of a fading source (Melandri et al. 2011a).
The GBM light curve of GRB 110428A consists of several overlapping pulses (Fig. 88). No significant emission was detected in the LLE light curve. The highest-energy event (2.62 GeV) is detected at T 0 +14.79 s and does not coincide with any noticeable feature in the GBM light curve. Although the LAT T 95 =408 +93 −336 s suffers from a large uncertainty due to the relatively small statistics (∼16 events), the burst was detected up to this time with high significance by the LAT likelihood analysis of the Transient-class data above 100 MeV. The LAT time-resolved likelihood analysis returned a significant flux in two time bins only, up to T 0 +178 s (Fig. 89). More interestingly, the time-integrated spectrum of GRB 110428A during the GBM T 90 is best represented by a Band function, with a steep value for the high-energy spectral slope β = −2.90 ± 0.10. This value is very different from the hard photon index of -1.73±0.20 which is found by the likelihood analysis at late times (Fig. 89). In the catalog, GRB 110428A is thus among the bursts which show the strongest spectral evolution between the prompt and late emission phases.

B.32. GRB 110529A
The short GRB 110529A triggered the GBM at T 0 =00:48:42.87 UT on 29 May 2011 (trigger 328322924, Burgess & Guiriec 2011). Only a few LAT Transient-class events above 100 MeV are compatible with the burst position, therefore no significant emission was found in the likelihood analysis. The burst was detected in the LLE data only (McEnery et al. 2011), and the light curve consists of a short spike in coincident with the GBM emission (Fig. 90). of the Fermi spacecraft. However, its initial off-axis angle of 87 • .9 in the LAT resulted in a very poor photon statistics above 100 MeV (Fig. 91) and no LAT T 90 could be derived. In addition, the Fermi spacecraft continued its maneuver toward the GBM flight software reconstructed position, which was off by 68 • from the enhanced Swift -XRT position (Page 2011), providing non-optimal exposure for LAT follow-up observations. Accumulating signal in the LAT time-resolved likelihood analysis allowed us to detect a significant flux in two time bins, up to T 0 +562 s  and Fig. 92), confirming the earlier detection by Tam & Kong (2011). The highest-energy event (2.42 GeV) is detected at T 0 +272.44 s.

B.34. GRB 110709A
The long GRB 110709A triggered the GBM at T 0 =15:24:27.37 UT on 09 July 2011 (trigger 331917869, Connaughton 2011) and the Swift -BAT at 15:24:29 UT (Holland et al. 2011a). Swift -XRT observations started 65.6 s after the BAT trigger and a bright, uncataloged X-ray source was immediately located (Holland et al. 2011b). Further analysis refined the position of the X-ray source (Evans 2011; Osborne et al. 2011). In spite of numerous follow-up observations (Ivanov et al. 2011;Xin et al. 2011;Tello et al. 2011;Kuroda et al. 2011;Kelemen 2011b;Holland 2011), no optical afterglow was detected. GRB 110709A was bright enough to trigger an ARR of the Fermi spacecraft. However, its initial off-axis angle of 53 • .4 in the LAT resulted in a very poor photon statistics above 100 MeV (Fig. 93). The LAT time-resolved likelihood analysis returned a significant flux in one time bin only, ending at T 0 +42 s (Fig. 94). In addition, no LAT T 90 could be derived due to the large Zenith angle of the burst.

B.36. GRB 110731A
The long GRB 110731A triggered the GBM at T 0 =11:09:29.94 UT on 31 July 2011 (trigger 333803371, Gruber 2011) and the Swift -BAT at 11:09:30 UT (Oates et al. 2011a). The LAT preliminary localization was delivered via GCN (Bregeon et al. 2011), with a statistical error of 0 • .2. GRB 110731A was bright enough to trigger an ARR of the Fermi spacecraft. Its initial off-axis angle was 3 • .4 in the LAT, thus the repointing had little impact on the prompt emission phase observations and permitted excellent observations of the extended emission for 2.5 hours after the trigger time. High quality continuous observations of the burst are available until the first Fermi passage into the SAA at ∼T 0 +1400 s. The ARR continued for another 90 minutes after Fermi had exited the SAA. Swift -XRT observations started 56 s after the BAT trigger (Oates et al. 2011b). A bright, uncataloged X-ray source was found and Swift -UVOT detected a bright afterglow candidate consistent with the XRT localization (Oates et al. 2011a). Further analyses refined the position of the burst (Krimm et al. 2011;Beardmore et al. 2011) and further observations confirmed the existence of a fading X-ray (Littlejohns et al. 2011) and optical afterglow (Oates 2011;Tristram et al. 2011). Tanvir et al. (2011 reported a spectroscopic redshift of z=2.83 based on observations of the optical afterglow using the GMOS spectrograph mounted on the Gemini North Telescope. After a weather-induced delay, GROND detected GRB 110731A at a mean time of 2.74 days after the trigger time. A dedicated analysis of the near-infrared to GeV observations of GRB 110731A in its prompt and afterglow phases using data from Fermi, Swift , MOA and GROND is presented in Ackermann et al. (2012b).
The high-energy emission of GRB 110731A lasts much longer than the GBM estimated duration. A 1.90 GeV event is detected at T 0 +8.27 s, right after the end of the GBM emission (Fig. 97). The LAT time-resolved likelihood analysis resulted in a well sampled light curve of the high-energy flux up to ∼562 s (Fig. 98). The decay of the flux as a function of time follows a simple power law starting from the GBM T 95 , with a decay index α=1.53±0.19, in agreement with the result reported by Ackermann et al. (2012b). This relatively steep decay is similar to the first part of the decay observed in GRBs 090510, 090902B and 090926A (Table 9) for which a significant break was found in the flux light curve. This suggests that GRB 110731A was observed during the transition from the prompt phase to the afterglow phase as discussed in § 6.2. Moreover, the time-integrated spectrum of GRB 110731A is best represented by a Band function with an additional power-law component. As discussed in § 4.4.1, the detection of this additional component is marginal in the "GBM" time interval but significant in the other time interval (Tables 11 and 12), in agreement with Ackermann et al. (2012b).