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Investigating the impact of optical selection effects on observed rest frame prompt GRB properties

Measuring gamma-ray burst (GRB) properties in their rest-frame is crucial to understand the physics at work in gamma-ray bursts. This can only be done for GRBs with known redshift. Since redshifts are usually measured from the optical spectrum of the afterglow, correlations between prompt and afterglow emissions may introduce biases in the distribution of rest-frame properties of the prompt emission. Our analysis is based on a sample of 90 GRBs with good optical follow-up and well measured prompt emission. 76 of them have a measure of redshift and 14 have no redshift. We estimate their optical brightness with their R magnitude measured two hours after the trigger and compare the rest frame prompt properties of different classes of GRB afterglow brightness. We find that the optical brightness of GRBs in our sample is mainly driven by their intrinsic afterglow luminosity. We show that GRBs with low and high afterglow optical fluxes have similar Epi , Eiso , Liso , indicating that the rest-frame distributions computed from GRBs with a redshift are not significantly distorted by optical selection effects. However we found that the rest frame T90 distribution is not immune to optical selection effect, which favor the selection of GRBs with longer durations. Finally, we note that GRBs in the upper part of the Epi-Eiso plane have fainter optical afterglows and we show that optical selection effects strongly favor the detection of GRBs with bright afterglows located close or below the best-fit Epi-Eiso relation, whose redshift is easily measurable.


Introduction
Gamma-ray bursts (GRBs) are cataclysmic explosions resulting from the collapse of massive stars or the 1 Université de Toulouse; UPS-OMP; IRAP; Toulouse, France 2 CNRS; IRAP; 14, avenue Edouard Belin, F-31400 Toulouse, France 3 Aix Marseille Université, CNRS/IN2P3, CPPM UMR 7346, 13288 Marseille, France merging of two compact objects (see Kumar & Zhang (2015) and references therein). During these events, an ultra relativistic jet is produced that is accompanied by an intense gamma-ray flash which can be seen at very high redshifts (up to z = 9 for GRB090429B; see Cucchiara et al. (2011a). The gamma-ray emission is produced in a few seconds (prompt emission) with a total energy release of up to E∼ 10 54 erg assuming an isotropic emission. This prompt emission is followed by a long-lasting and fading multi-wavelength emission from X-rays to radio (afterglow emission) which can be attributed to the external shock between the relativistic ejecta and the interstellar medium (ISM). The prompt γ-ray emission has been suggested as being due to internal shocks between shells moving at different Lorentz factors, Γ, inside the jet (see (Rees & Meszaros 1994;Paczynski & Xu 1994;Piran 1999;Kumar & Zhang 2015)). However, the physical processes at work in these shocks are still not well understood due to strong uncertainties on the physical conditions (baryon loading, energy dissipation in the jet, acceleration mechanism; see the review by Kumar & Zhang (2015)). On the contrary, the afterglow emission is better understood and can be explained by the synchrotron emission from accelerated electrons in the shock between the relativistic ejecta and the ISM (forward shock; (see Sari et al. (1998) & Granot & Sari (2002). An optical/radio flash is also expected and is sometimes observed from a reverse shock propagating into the relativistic ejecta (see (Meszaros & Rees 1993;Kobayashi 2000)). Studying the optical flash radiation from the reverse shock provides us with the opportunity to constrain the magnetization parameter of the ejecta (Zhang & Kobayashi 2005;Narayan et al. 2011), the Lorentz factor of the jet, and also on the jet composition (McMahon et al. 2006;Nakar & Piran 2004). In this framework, the dynamics of the afterglow is determined by the microphysics of the shocked material, the ISM properties, and the kinetic energy of the blast wave, E k , which depends on the prompt emission properties (the isotropic gamma-ray energy released, E iso , and the gamma-ray radiative efficiency, η). Understanding the connection between the prompt and afterglow properties would help us to better constrain the physics of GRBs and relativistic jets.
Many authors have discussed correlations between the afterglow luminosity and the prompt GRB energetics. Correlations between the afterglow optical luminosity and prompt isotropic energy have been found by Kann et al. (2010) and Nysewander et al. (2009), and between the afterglow X-ray emission and the isotropic energy by Kaneko et al. (2007) and Margutti et al. (2013). However, it is difficult to assess whether or not these relations have their origin in the physics of the GRB because some studies have shown that they could result from selection effects. Indeed, Coward et al. (2015) recently detected a strong Malmquist bias in the correlation E iso −L opt,X as we preferentialy detect the brightest GRBs. While it is clear that gamma-ray selection effects can bias statistical studies of prompt GRB properties, the impact of optical selection effects is rarely assessed. This paper is dedicated to the study of potential selection effects in the distribution of restframe prompt properties due to the need of measuring the redshift. We construct a sample of GRBs with good optical and gamma-ray data in section 2. The potential parameters (extrinsic and intrinsic) that could bias our sample are also investigated in section 3. The main conclusion of this section is that the distribution of the afterglow optical flux is mainly driven by their optical luminosities as opposed to redshift distribution. Thus, in section 4, we show how the need to detect the optical afterglow can act against the measurement of the restframe properties of some GRBs. Then, in section 5 we compare the afterglow optical flux of GRBs with their typical rest-frame prompt properties as E iso or L iso to estimate the impact of the optical selection effect. We also investigate optical selection effects on GRB restframe correlations in section 6. In section 7, we briefly discuss the consequences of our findings.

Gamma-ray data
Our gamma-ray selection criteria followed a procedure similar to that of Heussaff et al. (2013). We selected a large sample of GRBs with well-measured spectral parameters available in the literature, i.e GCN Circulars 1 . This covers GRB observations from 1997 to 2014. GRB spectra are parametrized with the Band function, Band et al. (1993), which consists of two smoothly connected power laws : where E b = α γ −β γ 2+α γ × E po . α (α > −2) and β (β < −2) are the low-and high-energy photon spectral indexes of the power law, respectively. E po is the break energy of the observed νF ν gamma-ray spectrum.
The selection was performed by applying the following cuts.
1. First, we selected GRBs with T 90 , the time for which 90% of the energy is released, between 2 and 1000 s. This criterion excludes short GRBs (T 90 < 2s), and very long GRBs that are superimposed on a varying background and whose E po is difficult to measure accurately.
2. Second, we required reliable spectral parameters. We excluded GRBs with one or more spectral parameters missing. We excluded GRBs with an error on α (the low-energy index of the Band function) larger than 0.5. We excluded a few GRBs with α < −2.0 and GRBs with β > α because such values suggest a confusion between fitting parameters. We excluded GRBs with large errors on E po , which are defined by a ratio of the 90% upper limit to the 90% lower limit larger than 3.5. When the error on β in the catalog is lacking or larger than 1.0, we assigned a typical value of 2.3 2 to β and we give no error. In a few cases, the high-energy spectral index in the GRB catalogs (HETE-2, Fermi) is incompatible with being <-2.0 at the 2 σ level, and the catalog gives the energy of a spectral break that is not E po . In these cases, we look for E po in the GCN Circulars, and if we cannot find it, then we simply remove the burst from the sample.
Finally, our analysis required GRBs with both wellmeasured γ-ray spectral parameters and an optical afterglow light curve. Consequently, we removed GRBs inaccurately localized (typically GRBs not localized by the Swift-XRT instrument) because most of the time it prevents ground-based telescope from detecting their optical afterglows.
At the completion of the high-energy selection process, we ended with 126 GRBs with a redshift and 42 GRBs without a redshift. Then, in a second step, we extracted the short list of GRBs with exploitable optical afterglow light curves.

Optical data
We collected the afterglow R-band light curves of the pre-selected 126 GRBs with a redshift and 42 GRBs without a redshift. We specifically choose the R-band because it concentrates the largest number of optical measurements. These R-band photometric measurements are issued from published articles and GCN Circulars. References are given in table 7.
Then, we used the apparent R magnitude measured 2 hr after the burst uncorrected for extinction as a proxy for the optical flux of the afterglow. The R magnitude is directly interpolated from the available measurements. To do so, we required GRBs with good optical follow-up during the first hours after the burst to accurately measure the optical flux of the afterglow.
The choice of the time (2 hr after the trigger) at which we measure the R magnitude results from various constraints.
1. We want the afterglow to be in its classical slow cooling and decaying regime, yet to be bright enough to permit reliable measurements of the magnitude.
2. We want to measure the optical flux at a time comparable to the time at which the majority of GRB redshifts are measured (in the first few hours after the trigger), so that the optical flux measurement provides a good indicator of our ability to measure the redshift of the GRBs.
We decided to exclude few GRBs with high visual extinction such that A tot V = A Gal V + A Host V > 1.2, which corresponds to a total extinction in the R-band of about 1 mag. Indeed, GRB afterglows which are strongly absorbed by dust do not provide information on their true optical brightness. This cut is a good trade-off to optimize the number of GRBs for which the afterglow flux is not as polluted by external effects (dust absorption). The galactic extinction A Gal V has been calculated from the dust map of Schlegel et al. (1998) and the host extinctions A Host V are issued from various sources. For some bursts we did not have access to the host extinction. In order to have a rough estimate of the host extinction, we performed a simple linear fit between A Host V and the intrinsic X-ray absorption NH X,i derived from the Swift-XRT catalog. We had 114 GRBs available for this fit. The best-fit gives us the following relation : A Host V = 3.9 × 10 −23 × NH X,i + 0.06 with a standard deviation of σ ∼ 0.34 mag which we considered to be an acceptable uncertainty in our A Host V estimates. We also removed those GRBs located at very high redshift since at such redshifts the Ly-α break prevents the observation of the optical afterglow in the R band. The redshift cut was fixed at z = 5.5 where the Lyman absorption starts to significantly attenuate the R band.
Finally, for GRB afterglows with only an upper limit of detection, we required that they have R magnitudes that are deeply constrained by large telescopes (at least one 2.0 m telescope). Moreover, these upper limits must be estimated from images taken close to 2 hr after the burst.
After passing the optical selection criteria, we finally ended with 76 GRBs with a redshift (75 detections and 1 upper limit) and 14 GRBs without a redshift (3 detections and 11 upper limits). These 90 GRBs constitute our full sample, which is summarized in table 4 for GRBs with a redshift and table 5 for GRBs without a redshift. This sample covers about 15 years of pre-Swift and Swift GRB observations (from 1999 to 2014). The afterglow light curves of our complete sample of GRBs can be seen in figure 1.

Afterglow optical flux and potential biases
The afterglows of our 90 GRBs span a large range of optical flux from mag R 2h = 13.02 to mag R 2h = 23.9 (see figure 2). We noted that GRBs without a redshift have faint optical counterparts, which is not due to high visual extinction since they pass our optical selection criteria. These GRBs may be high-z GRBs or GRBs with sub-luminous afterglows. Our GRBs with a redshift are also distributed over a wide range of redshift from z = 0.168 to z = 4.11 and we need to understand whether or not the distribution of the R magnitudes is dominated by the redshift distribution. To verify this hypothesis, we divided our 76 GRBs with a redshift into three equally populated classes of optical flux.

The class of bright GRBs is composed of 26
GRBs with an afterglow R magnitude brighter than R = 17.9.
2. The class of intermediate flux GRBs is composed of 25 GRBs with an afterglow R magnitude in the range 17.9 < R ≤ 19.1.

The class of faint GRBs is composed of 25
GRBs with an afterglow R magnitude weaker than R = 19.1.
We will refer to these classes throughout this paper.

Impact of the redshift on the afterglow optical flux distribution
We compared the redshift distribution of our three GRB classes with a Kolomogorov-Smirnov statistical test (KS test; see figure 3). The KS test clearly reveals that the redshift distributions of the three classes are similar. The results of the statistical tests are summarized in table 1. We conclude that the redshift is not the main driver of our optical flux distribution. This observation is explained in figure 6, which shows a shift in the GRB population to higher luminosities with the redshift. At large redshifts, the combination of the increased volume and the GRB density evolution allow us to see very luminous GRBs, which are too rare to be visible below z ∼1. This luminosity shift nearly compensates for the effect of distance, leading to similar fractions of bright and faint GRBs at all redshifts.

Impact of the visual extinction on the afterglow optical flux
Although we have selected GRBs with relatively low total visual extinction (A tot V < 1.2), we checked if this parameter could bias our afterglow flux distribution, i.e, whether afterglows with faint optical flux are more obscured by dust. We again performed a KS test to compare the A tot V distributions of our three classes of GRB afterglow flux. We found that the three populations of GRBs are drawn from the same underlying distribution (see figure 4 and table 1). We conclude that GRBs with faint afterglow optical fluxes are not more obscured than the bright ones, and thus visual extinction does not bias our afterglow optical distribution.

Afterglow optical luminosity
As the extrinsic factors (redshift, visual extinction) do not seem to play a major role in the observed optical flux distribution, we investigated the impact of the intrinsic optical luminosity of the afterglow. We calculated the optical luminosity density (in units of erg.s −1 .Hz −1 ) two hours after the burst using the following formula: where F R is the optical flux density corrected from the Galactic and host extinction measured at t obs = 2h after the burst, z is the GRB redshift, D L (z) is the luminosity distance, β o is the optical spectral index and α o the optical temporal index, ν R is the typical frequency of the R-band (Vega system), and ν obs is the observed frequency (here ν obs = ν R ). For GRBs with no optical detection, we used their optical upper limits to compute F R and the median values of the α o (|α med o | = 0.975) and β o (|β med o | = 0.65) distributions to estimate an upper limit on their optical luminosity density. Finally, for GRBs without a redshift, we also calculated their optical luminosity density as function of the redshift, (considering 0.168 < z < 6.0) using the method decribed above. Since their derived luminosity (or upper limit) depends on the redshift, they produce tracks in the z − L R plane as shown in figure 6.
Then, we compared the optical luminosity densities of the three classes of GRB afterglow fluxes (bright, intermediate, and faint; see figure 5). The KS test clearly reveals that GRBs with low optical flux are also less luminous in the optical domain.  We conclude that our afterglow optical flux dis-tribution is strongly shaped by the optical luminosity densities of the GRB afterglows. This result is valid for GRBs with a redshift but, interestingly, GRBs without a redshift also follow this trend. Indeed, they have the afterglows with the lowest optical fluxes (figure 2), and at any redshift most of them would have had subluminous afterglows, see figure 6. Thus, we conclude that the aferglow optical flux of the GRBs in our sample is very likely dominated by their optical luminosity. As a consequence, a large population of GRBs with sub-luminous afterglows may escape detection in the optical domain, creating a strong bias in the observed afterglow luminosity distribution. In particular, we note that GRBs with L R < 10 30 erg.s −1 .Hz −1 have no redshift measurement beyond z ∼ 1 (see figure 6), except for GRB090519 which is discussed in more details in the Appendix.

The physical picture
The population of GRBs with a redshift suffers from two different selection effects. The "γ-ray selection effect" prevents the detection of GRBs with low peak flux while the "optical selection effect" prevents measuring the rest-frame properties of GRBs with faint optical afterglows. In both cases, the final result is that we lose a significant fraction of GRBs for statistical studies dealing with their rest-frame prompt properties. The relative influence of the two selection effects is difficult to assess, but we try to quantify it by comparing the two quantities related to the two selection effects in figure 7 : 1. the observed peak flux (erg.cm −2 .s −1 ) in the Swift band (15-150 keV) connected to the detectability of a GRB in γ-rays; and 2. the uncorrected R magnitude of the afterglow related to our ability to measure the redshift of a GRB via the spectroscopy of the optical afterglow.
For each GRB, we simulated the evolution with the redshift of its peak flux and optical afterglow flux. In particular, we checked whether a given GRB located at higher redshift would first disappear from our sample because it becomes undetectable in γ-rays or because its afterglow is becoming too faint to allow measuring its redshift. Thus, for each GRB, we define . Upper limits are plotted as downward triangles. The red dashed lines indicates the iso-magnitude of the optical afterglow as a function of the redshift (up to z = 6.0). They define our three classes of optical afterglow flux (bright are GRBs with R≤17.9, intermediate are GRBs with 17.9 < R ≤ 19.1, and faint are GRBs with R > 19.1). As discussed in section 6, the green circles represent GRBs below the best-fit E pi -E iso relation while black squares represent GRBs located above the best-fit E pi -E iso relation. For GRBs without a redshift, the color of the dashed-dotted line indicates whether the GRB is located below the best-fit E pi -E iso relation (green) or above it (black). z max γ and z max opt as the maximum redshifts that the GRB could have before being limited by the γ-ray detection threshold (z max γ ) or the optical threshold related to the redshift measurement (z max γ ). To do so, we define a peak flux limit below which the GRB is supposed to be undetectable in γ-rays at z = z max γ . We decided to choose the faintest peak flux of our sample (except for GRB090519, which is an exceptional burst), i.e. that of GRB140626A with P 15−150keV = 0.7 ph.cm −2 .s −1 . For the R magnitude limit that defines z max opt we choose the weakest measured R magnitude of our GRB sample with redshift (again we remove GRB090519 from the list), i.e that of GRB090812 with R mag. = 21.15.
For instance, GRB080605, with z max opt ∼ 2.85 and z max γ ∼ 6.45 would be limited by its optical afterglow flux, as shown in figure 7. On the contrary, a GRB like GRB 050820A would be limited by the γ-ray detection with z max opt > 10 much 3 larger than z max γ ∼ 4.55 3 Note that here we do not take into account the effect of the Lyman break in the R band which appears at z ∼ 5.5 − 6. For very high-z GRB (z > 6), the optical threshold for a redshift measurement has to be preferentially defined based on the infrared afterglow flux (IJHK band). Note.-The indicated probabilities correspond to the p-values, i.e, the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. "F", "I" and "B" refers to the three classes of afterglow optical flux : Faint, Intermediate, and Bright, respectively.
. In the end, we find that about 20% of our GRBs with redshift would predominantly suffer from optical selection effects if they were located at higher redshift (z max opt < z max γ ), while about 80% of GRBs would definitely disappear because the GRBs themselves becomes too faint to be detected (z max opt > z max γ ). Clearly, the computation of V/V max or other measures of the detectability of GRBs with a redshift have to take into account that some GRBs will be effectively limited by their γ-ray visibility (z max γ ), while others (∼ 20 % of the GRBs with a redshift in our sample) will be firstly limited by their optical afterglow flux (z max opt ) and our ability to determine their redshift. In addition, as suggested by figure 2, we confirm that most of the GRBs in our sample without a redshift are dominated by optical selection effects (∼ 85% of them) since their peak flux does not prevent them from a γ-ray detection (see figure 7).
We conclude that optical selection effects play a significant role in shaping the observed population of GRBs with a redshift. The next question is as follows : do these optical selection effects create a significant bias in the observed distribution of the rest-frame properties of GRBs? Below, we discuss the method used to assess the significance of the selection effects associated with the measure of the redshift.

A method to assess the significance of optical selection effects
The impact of measuring the redshift is assessed by comparing the properties of GRBs with different optical fluxes (R magnitudes measured 2 hr after the trigger). If GRBs with different optical fluxes show no dif-ference in the distribution of a given parameter, then it is expected that the measure of the redshift, which depends strongly on the optical flux of the afterglow, will not impact the distribution of this parameter. If, on the other hand, GRBs with different optical fluxes show significant differences in the distribution of a given parameter, then the measure of the redshift will impact the distribution of this parameter.
Of course, one limitation of this method is that it cannot be used to measure the biases between the population of GRBs with a redshift and GRBs without one, that is, it can only be used to measure differences between subpopulations of GRBs with a redshift. The scope of this paper is thus restricted to an evaluation of the prompt GRB properties which may be biased by the measure of the redshift. A detailed evaluation of the biases between GRBs with and without a redshift would require the construction of a GRB "world model" which takes into account many parameters of the GRBs and their afterglows and their correlations, a task which is beyond the scope of this paper (see, however, Shahmoradi (2013); Kocevski (2012)).

Optical selection effects on the rest-frame prompt properties of GRBs
We compare the distributions of various parameters of the prompt emission for the three classes of afterglow flux. The four parameters discussed here are the isotropic γ-ray energy, E iso , the isotropic γ-ray luminosity, L iso , the intrinsic peak energy of the νF ν γ-ray spectrum, E pi = E po × (1 + z), and the duration of the burst, T rest 90 = T 90 /(1 + z). We performed KS tests to compare the distributions   GRBs without a redshift measurement are represented in black (stars for GRBs afterglows with a well-measured R magnitude, downward triangles for optical upper limits). The red dashed lines represent the limiting peak flux and the limiting R magnitude for GRB detection and redshift measurement, respectively. The black dashed line divides the population of GRBs that would undergo the γ-ray selection effect before the optical one (above this line) from those that firstly suffer from the optical selection effect (below this line).
of the four parameters listed above for GRBs in the three classes of afterglow flux (see figure 8). These tests are based on the population of 76 GRBs with a redshift when comparing the E iso , E pi and T rest 90 distributions, and only 73 GRBs for the L iso distributions because three GRBs had unsecured peak flux measurements. The results of the KS test are summarized in table 2. We found no significant differences between the L iso and E pi distributions. Nevertheless, we noted that the T rest 90 distributions differ by more than 2.5σ between GRBs with faint and bright afterglows. This marginal discrepancy highlights the fact that GRBs with low afterglow fluxes could be shorter on average than GRBs with high afterglow fluxes. Finally, we note that GRBs with faint afterglow fluxes seem to have slightly lower E iso than the rest of the GRB population (intermediate and bright GRB afterglows). This difference is not significant, and so no conclusive statement can be made. The low significance of the KS test applied to E iso can be explained by two rea-sons. First, the afterglow dynamics are driven by both the kinetic energy of the jet (E k = E iso × 1−η η , where η is the γ-ray radiative efficiency) and the density of the shocked ISM. Thus it is not straightforward to connect E iso with the afterglow optical flux. Second to the first order, E iso can be roughly estimated from the averaged γ-ray luminosity < L iso > integrated over the T rest 90 duration, E iso ∼< L iso > ×T rest 90 . Since we observed no bias in the L iso distribution but a marginal one in the T rest 90 distribution, the combination of the two distributions leads to a similar but lower bias in the E iso distribution compared to what we observed for T rest 90 . In the end, no clear trend emerges from these statistical tests and we conclude that the rest-frame prompt properties of GRBs are not significantly biased by optical selection effects

Optical selection effects on rest-frame prompt correlation
The study of biases in GRB spectral energy correlations has led to many studies concerning γ-ray se-lection effects. However, the role of optical selection effects on these correlations has not been explored as much. If such an optical bias exists, then we expect to find a link between the afterglow flux and the positions Note.-The indicated probabilities correspond to the p-values, i.e, the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. "F", "I" and "B" refer to the three classes of afterglow optical flux, Faint, Intermediate, and Bright, respectively.
of GRBs in the corresponding parameter space of the correlation. We decided to study such a connection using the E pi − E iso and E pi − L iso relations (respectively reported for the first time by Amati et al. (2002) and Yonetoku et al. (2004)) as they are among the most robust GRB correlations, yet are highly debated in the GRB community.
6.1. Our GRB sample in the E pi -E iso plane As shown in figure 9, the 76 selected GRBs with a redshift follow a standard E pi -E iso relation. The best-fit E pi -E iso relation for this sample is E pi = 145 E 0.463 52 keV, where E 52 is the GRB isotropic energy in units of 10 52 erg. This best-fit relation is consistent with the E pi -E iso relation found by other authors (e.g. Nava et al. 2012;Gruber et al. 2012), showing that our sample is not significantly biased for what concerns the distribution of GRBs with a redshift in the E pi -E iso plane. The dispersion of the points around the best-fit relation along the vertical axis, σ = 0.31, is also comparable to the values found by Nava et al. (2012) and Gruber et al. (2012) (σ = 0.34). In the following, we compare the positions of our three classes of GRBs in the E pi -E iso plane using the mean distance to best-fit the Amati relation as a criterion for this comparison.

Comparing the vertical distances with respect
to the E pi -E iso relation The vertical distance is defined as log 10 (E pi ) − log 10 [best fit (E pi )], where best-fit (E pi ) is the value measured on the best-fit relation. In figure 9, we show the complete GRB sample (90 GRBs) in a plane displaying the vertical distances to the best-fit E pi -E iso relation as a function of the afterglow optical flux. We performed a KS test to compare the vertical distance distributions for our three classes of GRBs with a redshift. The KS tests reveal that GRBs with intermediate and bright afterglow fluxes follow similar distributions, while GRBs with low afterglow fluxes differ by more than ∼ 3σ from GRBs with high afterglow fluxes and by ∼ 2.6σ from GRBs with intermediate afterglow fluxes. Because the faint GRBs seem to behave unlike intermediate and bright GRBs, we compared the vertical distance distributions of these two groups of GRBs (faint versus intermediate+bright). The KS test reveals that the distribution of faint GRBs in the E pi -E iso plane is not compatible with that of the intermediate and bright GRBs with a probability of 99.96% (∼ 3.7σ). The results of the different statistical tests are summarized in table 3. This table shows that GRBs with faint afterglows are mostly located in the upper part of the E pi -E iso plane compared to the other GRBs. This suggests that an extended population of GRBs with low afterglow fluxes may fill the upper part of the E pi -E iso plane even above the 2σ limit of the E pi -E iso relation but cannot be seen due to optical selection effects that prevent us from measuring their redshift.

Comparing the afterglow optical flux above and below the best-fit E pi -E iso relation
In order to confirm the suggestion that GRBs located above the best-fit Amati relation have fainter afterglows than GRBs located below the best-fit Amati relation, we compared the optical flux of the GRBs located above and below the best-fit E pi -E iso relation. In order to include GRBs without a redshift, we calculated their minimum and maximum vertical distances the E pi -E iso plane with its 2σ limit (dashed line). The red circles corresponds to the population of GRBs with bright afterglows, the black diamonds corresponds to the GRB afterglow with intermediate flux, and the blue squares corresponds to the faint GRB afterglows. Top right: distribution of the 14 GRBs without a redshift in the E pi -E iso plane with its 2σ limit (dashed line). They all appear in the class of GRBs with faint afterglows (blue solid line). Bottom left: Distribution of the uncorrected R magnitude as a function of the vertical distance to the best-fit to the E pi -E iso relation for our global sample of GRBs (90 GRBs). Bottom right: cumulative distribution function of the uncorrected R magnitude between GRBs located above the best-fit E pi -E iso relation (dashed line) and those located below the best-fit E pi -E iso relation (solid line). This analysis used a sample of 76 GRBs with a redshift and 8 GRBs without one.
to the best-fit E pi -E iso relation which depends on the redshifts (considered here between 0.168 < z < 6.0). Then, we only kept those which are strictly located above the best-fit E pi -E iso relation (i.e, those for which the minimum and the maximum distances to the best-fit E pi -E iso relation are always positive) or strictly below it at any possible redshift. Eight GRBs without a redshift were selected, all of which were located strictly above the best-fit E pi -E iso relation. Therefore, we finally used 84 GRBs in this analysis. Figure 9 compares the afterglow optical flux of GRBs located above and below the best-fit E pi -E iso relation. A KS test shows that the two distributions strongly differ with a p-value of 4.77 × 10 −6 (∼ 4.5σ).
The high significance of this test confirms that GRBs located below the best-fit E pi -E iso relation have, on average, brighter afterglows than GRBs located above it. The average difference in magnitude between the two groups of GRBs is 1.76. We also noted that this result becomes less significant when we only consider GRBs with a redshift. Thus, GRBs without a redshift seem to confirm the trend that GRBs with low afterglow fluxes are mainly located above the E pi -E iso relation and that they can suffer from a lack of redshift measurement.

Our GRB sample in the E pi -L iso plane
To compute the standard E pi -L iso relation we removed 3 GRBs from our sample of 76 GRBs with a redshift because of unsecured peak flux measurements. The best-fit E pi -L iso relation for this sample (73 GRBs) is E pi = 304 L 0.428 52 keV, where L 52 is the GRB isotropic luminosity in units of 10 52 erg.s −1 . This best-fit relation is consistent with the E pi -L iso relation found by other authors (e.g. Nava et al. 2009Nava et al. , 2012. The dispersion of the points around the best-fit relation along the vertical axis, σ = 0.34, is also comparable with the values found by Nava et al. (2012), (σ = 0.30). We then produced the same analysis and the similar figures than for the E pi -E iso relation (see figure 10 and table 3).

Comparing the vertical distances to the E pi -L iso relation
For this analysis, our complete GRB sample is now composed of 87 GRBs since 3 GRBs have unsecured measured peak fluxes. The KS test that compares the vertical distances to the E pi -L iso relations of our classes of afterglow optical flux reveals that the three populations of GRBs follow nearly the same statistical distribution. Contrary to the E pi -E iso relation no clear connection can be determined between the afterglow optical flux and the positions of the GRBs in the E pi -L iso plane.

Comparing the afterglow optical brightness
above and below the best-fit E pi -L iso relation In this analysis, we could use 73 GRBs with a redshift and add 6 GRBs without a redshift which are all located above the best-fit E pi -L iso relation, so that we used a total of 79 GRBs.
The KS test reveals that the two distributions of afterglow optical flux marginally differ with a p-value of tional biases due to the measure of redshift. According to figure 8, the measure of the redshift may select GRBs which are about two times longer than average (i.e. with a larger T rest 90 ). This bias is in addition to, and may partially compensate for, the biases resulting from the γ-ray selection effects discussed by Kocevski and Petrosian (2013). A detailed analysis of the γ-ray light curves would be helpful to assess more precisely the differences between the light curve of GRBs with bright and faint optical afterglows.

Redshift and GRB correlations
We have found a significant correlation between the optical magnitudes of GRBs and their locations in the E pi -E iso plane. In our sample, GRBs with a large optical flux concentrate in the region located below the best-fit E pi -E iso relation, while GRBs with low optical flux preferentially fill in the region located above the best-fit E pi -E iso relation, like a majority of GRBs without a redshift, which have very faint optical afterglows. This optical bias could explain the apparent contradictory results obtained between GRBs with a redshift, which seem to follow the E pi -E iso relation Note.-The indicated probabilities correspond to the p-values, i.e, the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. "F", "I" and "B" refer to the three classes of afterglow optical flux, Faint, Intermediate, and Bright, respectively. relation quite well, and the whole GRB population, which seems to contain a significant fraction of outliers. Our observations also show that GRBs with a redshift underestimate the true width of the E pi -E iso relation correlation. We propose an explanation for this observation in the next section.
On the contrary, we observe no clear correlation between the afterglow optical brightness and the positions of GRBs in the E pi -L iso plane. This means that the E pi -L iso relation does not suffer as much from optical selection effects. If biases affect the observed E pi -L iso relation then they should mostly come from the γ-ray detections.

Why Do GRBs below and above the Best-fit E pi
-E iso relation have different R magnitudes? Figure 6 clearly shows that the excess of bright optical afterglows among GRBs located below the bestfit E pi -E iso relation is due to a bunch of GRBs with R < 17.9 and z < 1.5 (log(1 + z) < 0.4). Above z = 1.5, on the other hand, the bright GRBs are equally distributed with respect to the E pi -E iso relation. This led us to study the E pi -E iso relation below and above redshift z = 1.5. We find that the best-fit moves from E pi = 128 E 0.397 52 keV for GRBs with z < 1.5 to E pi = 211 E 0.400 52 keV for GRBs with z ≥ 1.5. Assuming that GRBs below and above z = 1.5 follow different E pi -E iso relations, the bright GRBs are now distributed equally above and below the best-fit E pi -E iso relation for GRBs with z < 1.5. Using the same method as in section 6, we compared the R magnitudes of GRBs with a redshift located below their best-fit E pi -E iso relation to those located above it and now found an insignificant result with a KS test p-value = 0.0329. Thus, we observe that the correlation between optical brightness and the location of GRBs in the E pi -E iso plane disappears.
We conclude that there is no real difference between GRBs located below and above the E pi -E iso relation. Instead, the E pi -E iso relation evolves with redshift or changes with GRB luminosity, leading to the observed correlation between the location of GRBs in the E pi -E iso plane and the magnitude of their afterglows when a single E pi -E iso relation is considered in the full redshift range. A similar conclusion was proposed by Li (2007) and Lin et al. (2015).
Based on the present statistics, it is not possible to determine whether the change of the E pi -E iso relation below and above z = 1.5 is due to an evolution of the E pi -E iso relation with the redshift or to different relations for GRBs with small and large E iso . Considering that the location of GRBs in the E pi -E iso plane is an intrinsic property, like their energy E iso we tend to favor the second possibility.

Using the E pi -E iso relation for cosmological purposes
The simplest way to use the E pi -E iso relation for GRB standardization is to consider that it as an intrinsic GRB property that does not evolve with redshift or with the properties of the GRBs. However, this simple view is being challenged by growing evidence that the E pi -E iso relation is a boundary in the E pi -E iso plane and not a true correlation (e.g. Heussaff et al. (2013)), and by the possibility that the E pi -E iso relation evolves with redshift (Li (2007); Lin et al. (2015); see, however, Ghirlanda et al. (2008)).
We have shown here that the selection effects due to the measure of the redshift cannot be neglected when discussing the E pi -E iso relation as a genuine restframe prompt property of long GRBs or when attempting to use it for cosmology. In addition, our study suggests that GRBs which can be calibrated with Type Ia supernobvae (at redshifts z < 1.5) are not representative of the GRB population at higher redshift, which raises important concerns for GRB cosmology based on the E pi -E iso relation(see for example Liang et al. (2008)).
We conclude that GRB standardization is a complex issue that cannot rely on the construction of a GRB Hubble diagram simply based on the measure of E pi and the redshift and an "ideal" E pi -E iso relation. It requires a better understanding of the nature of the E pi -E iso relation (boundary or true correlation), of its dependence on GRB parameters, of its possible evolution with redshift, and of the biases resulting from current observations.

Conclusion
Large samples of GRBs with a redshift are required in order to obtain a correct understanding of the intrinsic properties of GRBs and their afterglows. Such samples suffer from combined selection effects due to the need to detect the GRBs and the need to measure their redshift. The connections that exist between the prompt emission and the afterglow imply that these selection effects will impact both the observed properties of the prompt emission and those of the afterglow.
Here, we have studied the potential impact of mea-suring the redshift on the observed properties of the prompt emission. According to our results, the redshift measurement slightly alters the observed distribution of GRB durations, leading to a longer-than-average selection of GRBs. A stronger effect is observed for the E pi -E iso relation. We have found a correlation between the location of a GRB in the E pi -E iso plane and the optical R magnitude of its afterglow, we interpret this observation as being due to the dependence of the E pi -E iso relation on the GRB energy or its evolution with redshift.   Note.-(1) GRB name; (2) redshift; (3) rest-frame peak energy of the gamma-ray spectral energy distribution; (4) isotropic gamma-ray energy; (5) isotropic gamma-ray luminosity; (6) duration, in seconds, during which 90% of the burst fluence was accumulated starting by the time at which 5% of the total fluence has been detected; (7) R mag is the apparent R magnitude 2 hr after the burst not corrected from the galactic and host extinctions ( indicates it is an upper limit on R mag); (8) L rest R is the optical luminosity density taken 2 hr after the burst (in the rest-frame); (9) galactic extinction from Schlegel et al. (1998); (10) host extinction (*) indicates that the host extinction is estimated from the NH X,i measurement), otherwise the references for the host extinction are listed in table 7; (11) the references are listed in table 7. Note.-(1) GRB name where ( ) indicates that for this GRB a strong constraint on the redshift was determined by Volnova et al. (2014f); (2) observed peak energy of the νF ν spectrum; (3) observed γ-ray fluence in the 15-150 keV energy band; (4) Observed 1s-peak photon flux in the 15-150 keV energy band; (5) and (6) galactic and host visual extinctions, respectively, where (*) indicates that the host extinction is estimated from the NH X,i measurement); (7) apparent R magnitude measured 2 hr after the burst not corrected for the galactic and host extinctions ( : upper limit on R mag. † : calibrated with the V-band magnitude).  (2003) Table 7 References for the redshifts and Host extinctions A. The case of GRB090519 and the need for a ground-based observational strategy GRB090519 is an exception as it is a very faint GRB with a redshift of z = 3.85. It was detected by both Fermi and Swift on 2009 May 19 at 21:08:56 UT (see Perri et al. (2009)). Swift-XRT and Swift-UVOT rapidly observed the field of GRB090519 (<130s after the burst). An X-ray counterpart was clearly identified by Swift-XRT, allowing for a refined localization of the burst at R.A.(J2000) = 09 h 29 m 06.85 s and decl(J2000) = +00 d 10 48.6". However, no significant optical counterpart was detected by Swift-UVOT and a corresponding 3σ upper limit of 19.6 mag (white filter) was estimated ∼ 200s after the burst. On the ground, fast robotic telescopes rapidly responded to the GCN notice, such as TAROT at Calern observatory in France ), FARO at Chante Perdrix Observatory in France (Klotz & Kugel (2009)), and BOOTES-1B in Spain (Jelinek & Kubanek (2009)). No optical counterpart was detected and a limiting magnitude of R > 18.5 at t ∼ 230s after the burst was estimated based on the TAROT Calern observations. The low galactic extinction (A Gal V = 0.13) suggested that GRB090519 is a high-z GRB or was embedded in a very dusty environment. In the next hours, NOT (see Thoene et al. (2009a)), and the GROND telescope (see Rossi et al. (2009b)), detected a new fading optical source in the XRT field of view which was associated with the afterglow emission from GRB090519. The magnitude measured by NOT at t∼ 0.33hr after the burst was R∼ 22.8, reavealing that the afterglow of GRB090519 was among the faintest afterglows ever observed (figure 1). The faintness of the afterglow was due to a combination of a high-redshift value and an intrinsic weak luminosity of the afterglow (see figure 6). Greiner et al. (2011) found AV Host ∼ 0.01 by fitting the broadband afterglow spectrum built form GROND and Swift-XRT data. We therefore exclude a very dusty environment surrounding GRB 090519. Although faint, the redshift of GRB090519 was determined by the VLT (see Thoene et al. (2009b)) thanks to a fast response to the GCN notice. We can reasonably assume that a delay of a few additionnal hours in the VLT observation would have made the afterglow of GRB090519 unreachable for a redshift measurement and useless for GRBs studies.
This exceptional case is a good example which demonstrates the need for an observational strategy designed to quickly determine the redshift of such under-luminous GRBs. Suc a strategy will help us to better understand the optical selection effects and reduce their impact on GRB rest-frame studies by extending the observed population of GRBs with a redshift toward the least luminous ones.
Consequently, the designs of the future telescopes devoted to GRBs must include large apertures (above one meter), rapid slewing (less than one minute), and the ability to quickly perform low-resolution (to estimate redshifts at +/-0.2) and near infrared spectrometry (to detect GRBs at redshifts higher than 9). According to that requirement, the next GRB mission SVOM will optimize the GRB detection mostly toward the antisolar direction in order to detect more easily optical afterglows from the ground. One-meter class telescopes, as previously described and largely spread over the world, will be important to avoid biases against GRBs that are too faint for the current observatories or not observable because of local observational constraints. Lin, H.-N., Li, X., Wang, S., et al. 2015, MNRAS, 453, 128-132 Lipkin, Y. M., Ofek, E. O., Gal-Yam, A., et al. 2004, ApJ, 606, 381 Littlejohns, O., Butler, N., Watson, A. M., et al. 2013a, GRB Coordinates Network, 15420, 1 Littlejohns, O., Butler, N., Watson, A. M., et al. 2013b, GRB Coordinates Network, 15436, 1