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Connecting GRBs and ULIRGs: A Sensitive, Unbiased Survey for Radio Emission from Gamma-Ray Burst Host Galaxies at 0

Luminous infrared galaxies and submillimeter galaxies contribute significantly to stellar mass assembly and the frequency of GRBs in these systems provides an important test of the connection between the gamma-ray burst rate and that of overall cosmic star-formation. We present sensitive 3 GHz radio observations using the Karl G. Jansky Very Large Array of 32 uniformly-selected GRB host galaxies spanning a redshift range from 0<z<2.5, providing the first fully dust- and sample-unbiased measurement of the fraction of GRBs originating from the Universe's most bolometrically luminous galaxies. Four galaxies are detected, with inferred radio star-formation rates ranging between 50-300 Msun/yr. Three of the four detections correspond to events consistent with being optically-obscured"dark"bursts. Our overall detection fraction implies that between 9-23% of GRBs between 0.5<z<2.5 occur in galaxies with S_3GHz>10 uJy, corresponding to SFR>50 Msun/yr at z~1 or>250 Msun/yr at z~2. Similar galaxies contribute approximately 10-30% of all cosmic star-formation, so our results are consistent with a GRB rate which is not strongly biased with respect to the total star-formation rate of a galaxy. However, all four radio-detected hosts have modest stellar masses (~few x 10^10 Msun), significantly lower than IR/submillimeter-selected field galaxies of similar luminosities. We suggest that the GRB rate may be suppressed in metal-rich environments but independently enhanced in intense starbursts, producing a strong efficiency dependence on mass but little net dependence on bulk galaxy star-formation rate.


INTRODUCTION
One of the primary appeals of the study of longduration gamma-ray bursts (GRBs) lies in their potential to address broader questions of cosmology and galaxy evolution. As the explosions of massive stars at cosmological distances, GRBs are intimately connected with cosmic star-formation, and the evolution of the cosmic GRB rate and the changing demographics of their host galaxies with time should reflect overall cosmological trends and inform our understanding of how galaxies and the stars within them form and evolve over the Universe's history (e.g., Hogg & Fruchter 1999;Blain & Natarajan 2000;Porciani & Madau 2001;Firmani et al. 2004;Natarajan et al. 2005;Kistler et al. 2008;Butler et al. 2010;Tanvir et al. 2012;Robertson & Ellis 2012;Trenti et al. 2014).
Central to the utility of GRBs for this purpose is their extreme luminosity at all electromagnetic wavelengths, including wavelengths unaffected by absorption due to dust and gas. In particular, GRBs are first detected in hard X-rays and gamma-rays and are now routinely localized to ∼2 ′′ precision in soft X-rays using the Swift X-ray Telescope (Burrows et al. 2007), meaning thatwith sufficient follow-up effort-their host-galaxy population and redshift distribution can be constructed independent of the effects of obscuration (e.g., Hjorth et al. 2012;Jakobsson et al. 2012;. For this reason, one particular question in galaxy evolution which GRBs showed significant promise to help resolve is the relative importance of extremely luminous, dusty galaxies to cosmic star-formation (e.g., Djorgovski et al. 2001;Ramirez-Ruiz et al. 2002;Berger et al. 2003). The UV/optical tracers by which galaxy and cosmic star-formation rates are normally estimated are significantly impacted by interstellar dust. Most galaxies are predominately optically thin and the effects of dust can be corrected for via measurements of the UV spectral slope or Balmer decrement (Meurer et al. 1999;Smolčić et al. 2009). However, the most bolometrically luminous galaxies (such as submillimeter galaxies [SMGs] and local ultra-luminous infrared galaxies [ULIRGs]) contain sufficient dust so as to be optically thick at UV and optical wavelengths, causing optical/UV-based tracers to inevitably underpredict the true star-formation rates of these galaxies even after dust correction Goldader et al. 2002;Chapman et al. 2005). Instead, the star-formation rates of these objects (and therefore their contribution to the cosmic SFR) must be measured using long-wavelength tracers such as far-IR or radio continuum, but these methods have historically suffered from limited sensitivity, uncertain calibration, uncertain dust temperatures, and AGN contamination. Estimates of the importance of the most luminous and dusty galaxies to starformation have varied widely between different studiesin part due simply to varying definitions of what distinguishes a "luminous" and dusty galaxy from an "ordinary" one-but have ranged from estimates of 50% or more (Pérez-González et al. 2005;Micha lowski et al. 2010;Magnelli et al. 2013) down to only about 10% (Rodighiero et al. 2011); see Casey et al. (2014) for a review.
In principle, the contribution of dusty star-forming galaxies (or any other galaxy population) to overall cosmic star-formation could be determined simply by measuring the fraction of GRBs hosted within such galaxies: for example, if ULIRGs (galaxies with L IR > 10 12 L ⊙ ) represent 40% of all star-formation at 1 < z < 2 they should also produce 40% of all GRBs over the same redshift interval. However, this would strictly apply only if GRBs represent an unbiased tracer of overall starformation. A large volume of evidence now suggests they do not: GRB host galaxies at z 1.5 have lower masses, lower metallicities, bluer colors, and more irregular morphologies compared to what would be expected from an unbiased SFR-tracing population or when compared to the core-collapse supernova host population Modjaz et al. 2008;Levesque et al. 2010;Graham & Fruchter 2013;Kelly et al. 2014), even when including dust-obscured "dark" bursts , although c.f. Hunt et al. 2014).
Nevertheless, measuring the contribution of very luminous, dusty galaxies to the GRB rate remains important for understanding the overall link between GRBs and cosmic star-formation, and the influence of dust on our view of each. What causes GRBs to favor certain environments over others is not wellunderstood. A strong preference for low metallicity has been a long-favored explanation given the connection between line-driven winds and angular momentum loss Woosley & Heger 2006), but a variable IMF or other environmental factors (such as dynamical interaction of stars in dense stellar clusters which preferentially form in the most intense starbursting galaxies; van den Heuvel & Portegies Zwart 2013) may also help explain the observed characteristics of the host galaxy population. As extrema of the star-forming galaxy population, dusty and luminous starbursts form an excellent test-bed for distinguishing different hypotheses: in particular, they are probably very metal-rich in their interiors (Nagao et al. 2012) but also very dense and intensely star-forming (Daddi et al. 2007).
A number of previous efforts to observe GRB hosts at mid-IR, submillimeter/and or radio wavelengths have been performed over the past decade (Berger et al. 2003;Tanvir et al. 2004;Le Floc'h et al. 2005;Stanway et al. 2010;Hatsukade et al. 2012;Micha lowski et al. 2012b;Wang et al. 2012;Perley & Perley 2013;Hunt et al. 2014). However, all of these efforts have been either limited in scope (observing only small samples), limited in sensitivity (insensitive to even very luminous galaxies beyond z > 1), or subject to uncertain selection biases (most commonly a bias in favor of GRBs with afterglowbased redshift determinations that will systematically miss dust-obscured events, although other efforts have specifically targeted only the most heavily dust-obscured GRBs).
In this paper, we present results of the first GRB host galaxy survey that is simultaneously unbiased in regards to target selection, sensitive enough to detect the longwavelength emission from luminous star-forming galaxies even out to z ∼ 2.5, and large enough to usefully statistically constrain the fraction of GRBs that originate in such systems. Specifically, we survey a sample of 31 uniformly-selected GRB host galaxies (a factor of ∼ 2 larger than any previous long-wavelength survey) to a limiting radio flux density of approximately 10µJy at 3 GHz (a factor of 2-3 deeper than any other radio host survey)-detecting four in total and providing the first definitive measurement of the fraction of GRBs produced by the Universe's most luminous galaxies. Our sample selection, observations, and analysis are discussed in §2. We present our results and interpret our four detections as star-formation-associated emission from the GRB host galaxies in §3. Further discussion of individual systems, including a detailed discussion of all detections and a few notable nondetections, is presented in §4 and §5. The overall statistical properties of our sample and its implications are discussed in §6, and conclusions are summarized in §7.

Sample Selection
Given the heterogeneous nature of previous longwavelength efforts and the need to determine the fraction of luminous hosts even among both obscured and unobscured GRBs (a few dusty and luminous galaxies have been reported hosting even the latter), the primary consideration guiding the choice of targets was the need for a uniformly-constructed sample. The production of unbiased subsets out of what is now a very large (but, often, poorly and non-uniformly observed) overall GRB catalog using simple observability cuts has become increasingly widespread in recent years, starting with the efforts of Jakobsson et al. (2006) and Fynbo et al. (2009) to select subsets of GRB afterglows for population analysis and, more recently, the host-galaxy focused TOUGH (The Optically Unbiased GRB Host; Hjorth et al. 2012) and BAT6 (Salvaterra et al. 2012) samples.
For this effort we chose a subset of GRBs from TOUGH, which was well-suited to our goals for several reasons. First, the TOUGH sample size is large enough to be statistically informative but small enough to be feasible in a one-year Very Large Array (VLA) campaign. Second, deep optical host-galaxy imaging was available for all targets, needed in order to calculate accurate centroids and angular size constraints. Third, the survey boasts relatively high redshift completeness (∼85%, provided from a combination of afterglow spectroscopy available for most events and an extensive hostgalaxy spectroscopic campaign; Jakobsson et al. 2012 andKrühler et al. 2012). Finally, all GRBs in the sample date to 2007 or earlier, ensuring a long temporal baseline between explosion and the present time such that any contribution from a radio afterglow is minimal.
The original selection criteria by which the TOUGH sample was chosen out of the broader catalog of Swift GRBs are described in detail in Hjorth et al. (2012), which together establish a list of 69 GRBs. We added two additional critieria for our VLA observations. First, to ensure observability from the VLA we require a declination of δ > −30 • (since the original TOUGH criteria establish a declination maximum of δ < +27 • , this effectively limits the sample to −30 • < δ < 27 • .) In addition, we exclude any targets known to be at z > 2.5, since detecting even very luminous galaxies at higher redshift is extremely difficult at radio wavelengths. We do, however, include TOUGH GRBs in our declination range whose redshift is not yet known, to ensure that imposing a redshift cut does not produce any biases (by, for example, inadvertantly excluding dust-obscured events at z < 2.5 whose redshifts may have been missed).
These additional cuts on declination and redshift produced a final sample of 31 GRBs. Of these, 26 are known to be at z < 2.5 (although one of these does not have a unique redshift/host identification) and 5 are at unknown redshift.

VLA Observations
All of the 31 targets described above were observed with the fully-upgraded Karl G. Jansky Very Large Array, using the S-band receivers (central frequency 3 GHz) and 8-bit samplers with a bandwidth of 2048 MHz. Observations were conducted during the A-configuration cycle of fall 2012, the B-configuration cycle of fall 2013, and the BnA-configuration of winter 2014 (project codes 12B-305 and 13B-316). Integration times for each field were approximately two hours on-target. Observations employed the WIDAR correlator ) using a spectral resolution of 2 MHz and a sampling time of 4 seconds. Local phase and amplitude calibration was established via observations of a nearby source approximately every six minutes, and the flux density scale was calibrated with a single observation of 3C48, 3C138, or 3C286 using the reference scale of Perley & Butler (2013) at the beginning or end of each observation sequence. A summary of all observations is presented in Table 1.
Phase stability was very good, with typical variations of less than 10 degrees over the 6-minute calibration cycle. More troublesome were the receiver amplitude gain variations induced by transmission from geostationary satellites. As seen from the VLA's latitude, these satellites are located in a belt near a declination of −4.5 • , and examination of our data shows that observations of sources located within about 10 degrees of this declination (i.e., +5.5 • to −14.5 • ) show significant gain variations due to variable power from these satellites entering the analog signal path through the antennas' sidelobes. As the antennas track the source, the input satellite power varies as the sidelobes sweep past the satellites. These gain variations are tracked by the antennas' on-board switched power calibration system, and application of this monitoring system reduced the gain uncertainty to less than 5% for all affected sources. For those sources within ∼2-3 degrees of declination −4.5 • (050922B, 060306, 061110A) the satellite input power occasionally saturated the analog receiver system. The data from those times were deleted.
Data reduction was carried out using the Astronomical Image Processing System (AIPS). Following gain and amplitude calibration, the data were examined for sporadic radio frequency interference (RFI). Visibilities with amplitude values on the (2 MHz, 4 sec) resolution scale exceeding 5-sigma were removed. In addition, the data within the transmission bands for the XM/Sirius satellite digital radio systems (2320 to 2350 MHz) were removed for all observations. Imaging/deconvolution was done using faceting over the primary beam to reduce noncoplanar distortions. No attempt was made to account for the spectral index gradients of the background sources due to the wavelength-dependent primary beam size, as these background sources were generally far enough from the target position that the imaging errors were reduced to below the noise level at the position of the target. Effective RMS sensitivities of the final maps are between 3-4 µJy/beam for most targets. A few fields are slightly noisier (4-9 µJy), in most cases due to the influence of geostationary-belt satellites. The field of GRB 061110A suffers from significant residuals due to poor cleaning of a strong quasar in the field (and also is located near the geostationary belt).

VLA Flux Density Measurement
We evaluate the significance of host detections/limits, and measure the host-galaxy fluxes, in two different ways. First, we take the position of the host centroid in the optical images and simply measure the flux-density value in the 0.18 ′′ cell nearest to this position in the reduced, deconvolved VLA map. To measure the uncertainty we take the RMS of the same final map, evaluated directly by a Monte-Carlo sampling of the fluxes of 1000 randomly-selected cells in the central region of the image. The positions and fluxes evaluated using this method are presented in Table 2.
There is a possibility that the radio host centroid may be offset from the optical one, and there are a few fields where the exact host position is not known because the host is not detected in the available TOUGH imaging. To accomodate the possibility of an offset host galaxy, we also employ a second method in which we take the maximum value of any cell within a radius given by either the measured size of the host galaxy in the VLT optical images or (if not detected) by the size of the positional uncertainty region of the afterglow in the Swift XRT image. Flux density uncertainties are again calculated by repeating this procedure at 1000 random points across the image. In general, since the resolution of the VLA observations is larger than the angular extent of the TOUGH galaxies in almost all cases, this method produces results equivalent (within the statistical uncertainties) to the fixed-position method.
In either case, this flux measurement procedure assumes that the host galaxy is not extended at the resolution of our available imaging. This is generally a good assumption (most hosts are only marginally resolved even at the resolution of the VLT images, and the largest galaxies are only ∼2 ′′ in diameter, comparable to our beam size in most cases), although for a few fields with more extended host galaxies and/or compact beams (e.g., 060814, 060218, 051117B) our flux measurement/limit may be a modest underestimate of the true integrated value.  h GRB 070810A was observed as part of the TOUGH campaign although it technically did not satisfy the sun-angle constraint of the survey. We include it as part of our survey here. * These targets were not included as part of the statistical analysis due to the lower sensitivity. 2.4. Optical/IR Observations As discussed in the next section, four of our host-galaxy targets were detected (or are very likely detected). To investigate these systems in more detail, we also acquired deep optical, NIR, and mid-IR imaging from a variety of sources in order to perform SED modeling and measure masses and UV-based star-formation rates. Many of these data points were taken from the literature (in particular Hjorth et al. 2012, Krühler et al. 2011, including all data points for the host galaxies of GRB 060814 and GRB 070306. New observations are briefly summarized below. GRBs 051006 and 061121 were observed with the Low-Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) at Keck Observatory on a number of occasions using several different filters between 2005 and 2014. Ob- 18.72 ± 0.10 9.12 ± 0.88 Spitzer/IRAC a Apparent magnitudes of the host galaxy, not corrected for foreground extinction. SDSS filters (lowercase) are reported in the SDSS sytem (nearly AB; Fukugita et al. 1996). Other filters are reported as Vega magnitudes. b Host galaxy flux, corrected for foreground extinction. c From Hjorth et al. (2012) servations were reduced using the custom IDL pipeline lpipe 13 . Neither of these fields overlaps with the Sloan Digital Sky Survey (SDSS) footprint, so secondary standards within each field were calibrated by acquiring observations of each field with the Palomar 60-inch robotic telescope (P60; Cenko et al. 2006) in the uBgriz filters and calibrating relative to Landolt (2009) standards and to various SDSS fields observed the same night during photometric weather. Magnitudes of each galaxy are measured in the reduced images using standard aperture photometry techniques. GRB 061121 was also observed by the Wide Infrared Camera (WIRC) at Palomar Observatory in J-band using the replacement engineering-grade detector on 2014-05-10 UT. Data were reduced using custom IDL scripts; the host galaxy is weakly detected in the stack of 22 60second images. Photometry of the host was calibrated relative to 2MASS stars in the field.
GRBs 051006 and 061121 were observed by the Infrared Array Camera (IRAC) on board the the Spitzer Space Telescope during Cycle 9 (GO 90062, PI D. Perley). We used the PBCD reduced files from the Spitzer legacy archive and measure magnitudes using the standard zeropoints in the Spitzer handbook using an aperture radius of 1.2 ′′ .
All host-galaxy photometry for these two objects is presented in Table 3.

RESULTS
A mosaic of our fields is shown in Figure 1. The grayscale background image represents the TOUGH Rband optical imaging from Hjorth et al. (2012); overlaid contours are from our new VLA observations.
The large majority of the hosts are not detected (the flux at or near the GRB location is consistent with the value expected for random locations in the same image), which is no surprise-previous GRB host radio surveys have also produced low detection rates, and only a small fraction of cosmic star-formation beyond z > 0.1 is in galaxies luminous enough to be individually detected at radio wavelengths, even at these deep levels (e.g., Karim et al. 2011;Dunne et al. 2009). We do, however, clearly detect at least three (and very likely four) of our targets. Radio sources are detected at the locations of GRBs 060814, 061121, and 070306 at high significance (99.5% confidence or greater, based on our Monte-Carlo analysis). A fourth radio source at the location of GRB 051006 has somewhat lower significance (98.5%), but the point-like nature of the object and its near-exact consistency with the optical host localization suggest that it is likely real as well.
A fifth possible detection (GRB 070808), while nominally statistically significant at 99% confidence, is much less plausible. As can be seen in Figure 1, the entire area near the GRB position is elevated in flux relative to the rest of the image due to an interference-related stripe passing diagonally through this region. No point-like object is visible specifically at the host-galaxy location. We treat this observation as a nondetection.
3.1. Star Formation, Afterglow, or AGN? While it is impossible to determine with certainty whether or not any individual detection represents emission associated with star-formation in the host galaxy or some other source, it is very likely that all of these detections do indeed correspond to the host-galaxy synchrotron continuum we are seeking.
There are three possible alternatives: emission from an unrelated foreground/background source, emission from an AGN within the host galaxy, or emission from the GRB afterglow. The first case can be ruled out on statistical grounds: only about 0.1% of the sky area in our fields contains a detected source, so the probability of even one chance intersection of a source anywhere in our sample with an unrelated object is low (∼3%). An AGN origin within the host is also unlikely, for similar reasons: most sources with a radio flux density close to 10µJy flux are star-forming galaxies, not AGN (Kimball et al. 2011;Condon et al. 2012). The optical spectroscopy of these systems also shows no evidence for AGN features.
The afterglow possibility is most difficult to generically rule out: while all of our targets were observed long after the occurrence of the GRB (at least 5 years and typically 7-8 years), few GRBs have been followed to faint enough flux/luminosity limits to directly establish the "typical" distribution of afterglow fluxes on multi-year timescales. The discussion in Perley & Perley (2013) suggests that fewer than 10% of all GRB afterglows will be detectable at the flux levels and timescales of our study, but even 10% contamination would be sufficient to produce most of our detections, given the large overall sample size. However, it is possible to examine systems individually to rule out this possibly by other means: in particular, by the observation of any of the following: (1) lack of significant fading versus early-time measurements or limits; (2) physical extension of the radio source; or (3) confirmation of a star-forming galaxy-like SED from IR or submillimeter observations. GRBs 061121 and 070306 were both observed at radio wavelengths a few days after the GRB and not detected to a flux density limit of ∼ 100 µJy (van der Horst et al. 2006a;Chandra & Frail 2007). The persistance of a 10-20 µJy radio afterglow at the time of our observations would require these events to have faded by a factor of only 10 or less between ∼3 days and 2000 days, which is exceptionally unlikely given the behavior of all other known radio afterglows, which invariably show steep power-law decays beginning at ∼100 days post-GRB or earlier (Chandra & Frail 2012). In the case of GRB 061121, even the possibility of an unusually persistent/late-fading source can be ruled out directly since a second epoch showing clear fading was reported by van der Horst et al. (2006b). GRB 070306 also has sensitive FIR observations available (from the Herschel survey of Hunt et al. 2014) and the putative host is welldetected in that data, consistent with its identification as a star-forming galaxy.
GRBs 060814 and 051006 have no observations available that would enable us to directly rule out an afterglow origin: the sources do not appear obviously extended in our VLA imaging (although the beam size of both observations is comparable to the optical host diameter) and neither was observed in the radio band before our observations. However, given that our optical observations ( §4) indicate star-formation rates consistent with those inferred from our measured radio fluxes it is very likely that these detections represent host-galaxy emission as well. 14

ANALYSIS OF DETECTED SOURCES
Since a very high star-formation rate is required for a distant galaxy to be detectable in the radio band, there is good reason to expect that the general properties of the hosts detected in our observations to differ from the overall GRB host population and from "typical" star-forming galaxies; comparison of these galaxies to other radio/submillimeter-selected galaxy populations may also provide insight into the nature of the GRBgalaxy connection overall.
Thanks to a combination of photometry from the literature and our own additional observations, we have excellent optical and infrared photometric data for all four radio-detected systems in our sample (although not yet for the nondetections). After correcting for foreground extinction (Schlegel et al. 1998), we analyzed the optical-NIR SEDs of these galaxies using a similar procedure as previously employed in , using a custom SED-fitting code based on the stellar populationsynthesis templates of Bruzual & Charlot (2003) assuming a Chabrier (2003) IMF and metallicity of 0.5 Solar. The star-formation history of each galaxy is fit as a twopopulation model with the maximum age of the older population fixed to the age of the Universe at the redshift of the host, and the maximum age of the younger population free (but required to be at least 20 Myr). Both populations are assumed to have a continuous starformation history from the maximum age until today, so the overall star-formation history is constant with an abrupt increase at an arbitrary time t burst , the age of the current ongoing starburst. Results from these fits are shown in Table 4 and Figure 2.
Radio star-formation rates are calculated from our observed VLA fluxes using Equation 17 of Murphy et al. (2011) and assuming a synchrotron spectral index (F ν ∝ ν −α ) of α = 0.75; the contribution of free-free radiation is assumed to be negligible at this frequency. We note that the calibration of radio star-formation rates is subject to some statistical uncertainty at about the level of a factor of ∼2, and the use of other relations would produce values offset by a common factor; in particular the measured SFRs and limits would drop by about 40% if we instead used Equation 15 of Yun & Carilli 2002. Since luminous and star-forming galaxies are also often very dust-obscured, the afterglow properties in relation to other GRBs (i.e., whether these bursts were optically dark or bright) are also of relevance. We generally rely on previous analysis of the afterglows of these events from the literature, supplemented by our own reanalysis where necessary.
4.1. GRB 051006 GRB 051006 was a relatively weak Swift burst with a faint X-ray afterglow. Ground-based follow-up was limited and none of it was conducted less than six hours after the burst occurred. Three optical sources near the burst location were initially identified as afterglow candidates by de Ugarte Postigo et al. (2005), but only source "B" is within the updated XRT error circle (Evans et al. 2009) and no variability was reported for it (or any other object). The lack of optical variability suggests this event may be a dark burst, although unfortunately without deeper, earlier, or redder-wavelength imaging it is impossible to know if this event was actually dust-extinguished to a significant extent or whether the nondetection was simply the result of a fainter-than-average afterglow and limited optical followup. (While we classify it as a dark burst for the purpose of subsequent discussions, in this case the assignment is not definitive.) The host galaxy of this event is easily detected in every optical filter and in Spitzer (unfortunately, no NIR data are available). Modeling of the SED shows a moderately red optical (rest-frame UV) continuum indicative of a luminous, moderately extinguished galaxy. We derive a best-fit extinction column of A V ∼ 1.7 mag and a star-formation rate of ∼100 M ⊙ yr −1 . (While a very -UV-to-radio SEDs of the host galaxies for all four radio-detected sources in our survey. The dashed curve shows the best-fit model (including the radio detection) and incorporates a component of extremely obscured star-formation; the solid curve shows a separate fit to the UV-optical data only in cases where the latter underestimates the actual star-formation rate. In two cases the modeling of the UV/optical data accurately predicts the radio flux, indicating that the starburst is optically thin. For the remaining sources the UV-inferred star-formation alone underpredicts the radio flux, and a heavily obscured nuclear starburst is also needed. All four galaxies are optically luminous and none are particularly red.
low uncertainty on this value is inferred from our SED modeling, the exact SFR value depends on the assumed star-formation history; post-starburst models with lower instantaneous SFRs also give a good fit to the data but were disallowed.) The mass of the older stellar population converged to zero in our fits, and the stellar population is dominated by the current episode with an intermediate age of about 100 Myr.
The UV/optical star-formation rate is comparable to, and possibly even in excess of, what we infer from the radio observations (∼50 M ⊙ yr −1 ), indicating that this system is a luminous, star-forming galaxy but not an extreme SMG and it does not harbor large amounts of heavily-obscured star-formation. Its stellar mass is modest, only ∼ 1.3 × 10 10 M ⊙ .

GRB 060814
GRB 060814 is a prominent dark burst, with clear detections of an afterglow in K-band but not in any bluer filters (e.g., Malesani & Patat 2006;Levan et al. 2006), unambiguously indicating an origin from an obscured region (but not an extremely obscured region, else the Kband afterglow would also be undetectable: a reasonable bracket on the dust column is 1.8 < A V < 8 mag).
The host galaxy of GRB 060814 is discussed in some detail in  as well as in Hjorth et al. (2012) and Jakobsson et al. (2012). It is well-detected in every optical/NIR band and is also one of the physically largest GRB hosts known, showing a complex, distorted morphology with an angular extent of ∼ 2.5 arcsec (21 kpc at the spectroscopic redshift of z = 1.923) that makes it easily resolved even in ground-based optical observations (Figure 1; we note that the southwest source visible in the VLT image is a foreground object at z = 0.84 but the remainder of the emission is from the host). Our SED modeling indicates a very large star-formation rate of approximately 200 M ⊙ yr −1 after correction for dust extinction.
The 3 GHz flux density of ∼15 µJy measured for this source translates to a star-formation rate of 260 M ⊙ yr −1 at this redshift. This is clearly within the range of ULIRGs and SMGs-although, again, the fact that this is in agreement with the optical SFR indicates that the galaxy is not actually optically thick but simply at the high-luminosity end of the population of ordinary, moderately-obscured galaxies. However, this galaxy is clearly in a starburst phase, given its modest mass (∼1.5×10 10 M ⊙ ) and highly distorted morphology.
A second source is also detected in the VLA image a few arcsecond to the northwest of the host galaxy. While there is no counterpart at this position in the R-band image shown in Figure 1, a very red source is clearly detected there in the NIR imaging (HST WFC3-IR, Kband, and IRAC). No redshift is available for this object, but given the relative rarity of very red objects and of faint radio sources it is possible that it may also be associated with the host system in some way.

GRB 061121
Unlike the other events in this list with radio detections, GRB 061121 was definitely not a dark burst. Its afterglow was very bright in the optical and ultraviolet at early times, was detected in all UVOT filters including UVW2 (which partially overlaps the Lyman limit at the host redshift), and its optical spectral index was relatively normal (Page et al. 2007), consistent with an unextinguished event. These are all typical properties of the optically-bright GRB afterglows commonly studied (and targeted for host follow-up) in the pre-Swift era.
Nevertheless, the event is hosted within a very luminous, radio-detected galaxy. The 17µJy source detected in the VLA image indicates a star-formation rate of 160 M ⊙ yr −1 (though with a substantial statistical uncertainty, since the RMS noise level of 5.5µJy is higher than average.) The host galaxy of this event is well-detected in all optical/NIR bands; the color is fairly blue and the inferred optical extinction is modest (A V ∼ 0.4 mag). The UV/optical star-formation rate is 30 M ⊙ yr −1 .
A secure interpretation of this system is somewhat complicated by the weak detection: nominally, the radio and optical star-formation rates are inconsistent by a factor of ∼5, but the radio measurement itself is uncertain by a factor of ∼2 simply due to the marginal detection and additional systematic uncertainties under-lie the star-formation rate derivations from UV and radio fluxes. Nevertheless, taking our current measurement at face value indicates that a (modest) additional opticallythick starburst is present in the galaxy. However, as the GRB itself shows no evidence of significant obscuration, GRB 061121 must have occurred in the relatively unobscured regions of the galaxy seen in our optical observations and not from the optically-thick component.
The stellar mass for this system is again quite modest, ∼1.5×10 10 M ⊙ . 4.4. GRB 070306 GRB 070306 was a heavily obscured gamma-ray burst (Jaunsen et al. 2008); its afterglow was detected only in K and H bands and its color between these filters was very red (consistent with A V ∼ 5.5 mag of extinction.) The optical/IR host-galaxy observations of this target are all the same as previously presented in  (which in turn incorporated data from the earlier studies of Jaunsen et al. 2008 andKrühler et al. 2011) and despite somewhat different modeling assumptions we derive nearly identical parameters, including a very modest UV/optical star-formation rate of ∼ 15 M ⊙ yr −1 . The radio (and Herschel-) inferred dust-unbiased starformation rate for this source is unambiguously much larger: approximately ∼ 140M ⊙ yr −1 , indicating the presence of substantial heavily-obscured star-formation. The large column towards the GRB is consistent with an intepretation in which the burst itself actually occurred in the dominant, heavily obscured part of the host.
The best-fit stellar mass of this galaxy is the largest of the four radio-detected hosts in our sample (∼ 5 × 10 10 M ⊙ ). HST WFC3-IR imaging is available for this source ; while the galaxy is resolved there are no obvious signs of an ongoing major merger at the resolution of the IR camera, though the galaxy does show some asymmetry (an extension to the northwest but not the southeast) and two much fainter companions (possibly, extended spiral arms) are present nearby.

NOTABLE NON-DETECTIONS
Since the radio star-formation rates inferred for two of our detections are close to the values inferred from UV/optical observations of the same galaxies (ruling out sinificant optically-thick star formation), we also examined our sample to determine if any of our nondetections imply radio luminosities close to our measured limits, which would also rule out additional optically-thick star formation. The available TOUGH data only provide two filters (R and K s bands) which are not adequate to evaluate the dust-corrected UV star-formation rates of these sources (dust corrections are critical even for reasonably optically thin galaxies). However, in two cases additional data are available that suggest star-formation rates comparable to our radio limits, discussed below.

GRB 060306
The host galaxy of GRB 060306 was studied in . Its optical/IR SED indicates a very luminous and dust-obscured galaxy; we previously derived an estimated star-formation rate of 245 +130 −67 M ⊙ yr −1 at the favored redshift of z = 1.55 ). Our limiting radio star-formation rate of SFR <260 M ⊙ yr −1 is not inconsistent with this figure, but indicates that the galaxy-while probably a ULIRG, based on the bolometric luminosity implied by our fit-contains minimal optically-thick star formation. This conclusion is similar to the one reached for this system from our previous study of dark GRB hosts with the VLA using C-band observations (Perley & Perley 2013) but significantly more constraining. This target is at a declination near the satellite belt and the observation was strongly impacted by satellite RFI; had similar noise levels been achieved for this field as the majority of our other targets, we predict that the host would have been detected.

GRB 060218
GRB 060218 is by far the lowest-redshift event in the sample and represents something of a special case: it is extremely optically underluminous compared to almost any class of galaxy, is physically very small (∼1 kpc), and clearly has little in common with the LIRG-like systems which our survey otherwise targets. Nevertheless, given the close proximity of this galaxy (redshift z = 0.033) the radio limit reaches very low star-formation rates. This source was observed only in A-configuration and the beam (0.6 ′′ FWHM) is significantly smaller than the full optical extent of the host, but the core of the galaxy (in which the large majority of the star-formation is occurring) is very compact: Kelly et al. (2014) estimate a halflight radius of only 0.31 ′′ from HST imaging, so at least half of the galaxy's star-formation is contained within one VLA beam. Conservatively allowing for a factor of ∼2 loss in sensitivity for this reason, our observations place a limit on the radio-derived SFR of <0.04 M ⊙ yr −1 , similar to the optically-derived value of 0.03-0.04 M ⊙ yr −1 (Wiersema et al. 2007;Levesque et al. 2010). Radio observations of very young, dwarf starburst galaxies often underpredict the optically derived star-formation rates because the ongoing starburst has not had sufficient time to produce enough supernova remnants to accelerate the electrons which produce the radio continuum (Roussel et al. 2003), so a mild discrepancy would not be surprising for this system.

Stacked Observations
To provide a limit on the average flux density of the host galaxies in our sample, we summed all 24 images in which no significant host emission was detected and which were not highly adversely affected by RFI, using the host position from the VLT images as the alignment point. Both a direct sum and a sum weighted using the inverse of the RMS were performed. In neither case is significant emission detected at the position of the stacked host galaxies. We measure an averaged flux density of 1.03 ± 0.87 µJy in the unweighted stack, or 0.77 ± 0.80 µJy in the weighted stack. At the mean redshift of the stacked sample of z = 1.54, this corresponds to a 2σ limiting average star-formation rate of 30 M ⊙ yr −1 , although we caution that the flux-SFR conversion is a strong function of redshift and significant evolution is expected in the population across this period.
Somewhat more informative limits can be determined by stacking in limited redshift intervals. Using the same procedure as in the previous paragraph, we stacked the images of 5 fields at 0.5 < z < 1.0 and 9 fields at 2.0 < z < 2.5; in the weighted stacks we do not detect a source -3 GHz radio fluxes (or 3σ limits) of TOUGH galaxies from the VLA (yellow data points), compared to measured or predicted radio fluxes from galaxies inside GOODS-N (grey circles). To calculate the fluxes of the field galaxies, we use the reduced VLA map of this field presented by Morrison et al. (2010) to directly match against the galaxy catalog of Kajisawa et al. (2011), scaling the 1.4 GHz flux density from that survey to 3 GHz using an average spectral index of α = 0.75. For sources which are not detected, we calculate the predicted radio flux density based on the UV+IR star-formation rate estimates in Kajisawa et al. (2011). Galaxies with hard X-ray detections are excluded (open circles). We also evaluate the fraction of cosmic star-formation occurring in detected radio galaxies using this method by directly summing the star-formation rates of all galaxies above and below our 10µJy survey threshold. The solid lines show a linear fit to the redshiftdependent 50th and 88th percentiles. We also show the limits resulting from stacks of our nondetections at 0.5 < z < 1.0 and 2.0 < z < 2.5.

Detection Rate and Connection to Cosmic
Star-Formation The successful detection of four objects with SFRs ranging up to ∼300 M ⊙ yr −1 clearly indicates that GRBs can form in extremely luminous galaxies in at least some circumstances, while at the same time the low overall detection rate (approximately 15%: 4 out of 24 low-RMS fields at known z < 2.5, or 4 out of 29 including unknownz) indicates that most GRB hosts are not systems of this type. While this qualitative observation obviously rules out the most extreme models (e.g., in which GRBs are never produced by very luminous galaxies, or are produced only within very luminous galaxies), we wish to be more quantitative: is the observed detection rate above, below, or consistent with the detection rate expected if GRBs neither prefer nor avoid the Universe's most luminous galaxies?
We followed two different approaches to predict the expected numbers under this SFR-tracing null hypothesis. First, we numerically integrated long-wavelength luminosity functions from both Spitzer (the 24µm luminosity  Fig. 4.-Fraction of star-formation detectable to the approximate average sensitivity of our EVLA survey (F 3GHz > 10µJy) as a function of redshift, as calculated by three different means: integrating the Herschel-PACS luminosity functions of Gruppioni et al. (2013), integrating the Spitzer-MIPS luminosity functions of Pérez-González et al. (2005), and directly matching sources detected at 1.4 GHz in Morrison et al. (2010) to the catalogs of Kajisawa et al. (2011). Between approximately z = 0.5 and z = 2.5, radio observations probe about the same fraction of cosmic SFR with little variation with redshift, even though the absolute star-formation rate sensitivity limit (right axis and dotted line) varies strongly with redshift. Our GRB detection fraction is shown as a single bin, since our sample size is not yet large enough to provide redshift-resolved constraints.
functions of Pérez-González et al. 2005, converted to total infrared luminosity), and Herschel (the bolometric IR luminosity functions of Gruppioni et al. 2013) to determine the quantity of star-formation occurring in galaxies with SFRs large enough to be detected in our survey at each redshift, using 10 µJy as a characteristic flux limit of our survey. Specifically, we calculate the quantity: Here, L limit is the total IR luminosity of a star-forming galaxy with F 3GHz = 10 µJy (our radio flux limit) and φ L (L, z) is the IR luminosity function as taken from the literature. 15 For the Herschel-based luminosity functions of Gruppioni et al. (2013) the radio-detectable fraction drops gradually from 40% to 25% over our redshift range of interest (0.5 < z < 2.5). The Spitzer-based fraction is flat at 20% between 0.5 < z < 1.5; it then rises sharply above z > 1.5 although 24 µm-based luminosities are highly uncertain at these redshifts (Figure 4).
Taking a more direct approach, we also calculated a sum of the actual inferred SFRs of all radio-detected galaxies from GOODS-N, using the redshift and SFR catalogs of Kajisawa et al. (2011) matched with detected sources in the 1.4 GHz radio map of Morrison et al. (2010), which has similar resolution and sensitivity as our S-band observations. We independently measured 1.4 GHz flux densities of sources in this map using the same procedure as for our GRB hosts, and scaled these values to 3 GHz using an average spectral index of α = 0.75; galaxies with hard X-ray detections were excluded as AGN-dominated. We then calculate the detectable fraction: f det (z min , z max ) = galaxies with F >10µJy SFR all galaxies SFR where both sums are restricted to galaxies over the range z min < z < z max . Since the field is small this method is more affected by small-number statistics then the Herschel/Spitzer maps, but the overall result is similar, between 5-15% on average between z = 0.5 − 2.2.
Note that despite the fact that there is rapid cosmic evolution with redshift over this range (the characteristic luminosity of galaxies increases by over an order of magnitude) and strong variation in sensitivity with redshift in the radio bands, these two effects largely cancel out, and our survey is sensitive to about the same proportion of cosmic star-formation at every redshift: specifically, at any redshift between z = 0.5 and z = 2.5, the galaxy population at or above our sensitivity limit is responsible for ∼5-30% of the cosmic SFRD at that time. Therefore, regardless of the actual redshift distribution of the sample (as long as it is within this range), for an unbiased star formation tracer we expect a detection rate of 5-30%.
This range agrees quite well with our measured fraction of 15%, so our radio data alone are consistent with the hypothesis that GRBs represent unbiased tracers of star-formation. However, note that the prediction is systematically uncertain to a factor of ∼2-3 depending on the comparison study, and our own measurement is statistically uncertain to within a factor of ∼2-3 ( §6.2), so this is not yet a highly constraining test on its own. Fortunately, we know much more about these galaxies than simply their radio fluxes and star-formation rates and can apply additional, more constraining tests using additional parameters; we will return to this issue in §6.3.

Intrinsic Flux and Luminosity Distributions
The convenient scaling between sensitivity and characteristic luminosity discussed above means that the detection fraction alone provides perhaps the most informative constraint on the degree to which GRBs prefer or avoid the most luminous galaxies, as long as it is understood that "most luminous" is treated as a relative statement (versus other galaxies at the same redshift) as opposed to an absolute one (e.g., above some fixed luminosity threshold). 16 Still, it is informative to produce formal constraints on the intrinsic flux distribution inferred from our survey and on the luminosity distribution as a function of redshift.
While we have treated our detection fraction as a single value above a single flux point, in reality our sensitivity limits do vary from field to field (from 7.1 µJy for 070306 to 18.6 µJy for 060306 and 070621, at 2.5σ). Translating our results into a statistical constraint on the actual fraction with flux density above a specific value therefore requires a prior on the shape of the flux density distribution of the underlying population. We assume it follows a single flux-weighted Schechter function (dN/dS ∝ S × (S/S * ) α e −S/S * , with α = −1.1 and S * a free parameter)-a reasonable assumption if GRBs approximately trace star-formation given the redshiftindepenence of the characteristic flux as described in the previous paragraph-although the results are not particularly sensitive to the choice of model. Based on a simple Monte-Carlo analysis using the distribution of 2.5σ sensitivity limits achieved by our survey and including the effects of measurement noise, we calculate that, intrinsically, between 5 and 25 percent of all z < 2.5 GRB hosts have S 3GHz > 10µJy at 80% confidence (between 4 and 40 percent at 90% confidence.) If the weighted-Schechter assumption is relied upon more heavily, a significantly more constraining upper limit of 8.6% (or 13% at 90-percent confidence) can be placed given the 2.77 µJy limit (2.5 σ) in our stack of nondetections. However, this conclusion is much more strongly dependent the assumption of a single fluxweighted Schechter function should be treated with additional caution; if GRBs do not trace star-formation uniformly with respect to galaxy SFR or if the redshift evolution of L * (z) and L(F, z) differ significantly it would not be valid.
We do not have enough detections to constrain the flux density function shape in a meaningful way, but it is worth noting that we detect no host galaxies with a flux density greater than 20µJy at any redshift, so the luminosity function is at least moderately steep (as indeed is expected for the high-luminosity exponential tail of a Schechter-like population). This observation produces some tension with the pre-Swift study of Berger et al. (2003), which reported a detection rate of 20% at a 2.5σ radio sensitivity level of 20-30 µJy in X-band (equivalent to 40-60 µJy in S-band for α = 0.75). The distribution of redshifts for the targets in their survey, and for their reported detections, is similar to what is seen in our own. We suspect that some of their reported detections may have either been noise fluctuations or affected by latetime contribution from the GRB afterglow, and/or that their detection of several intrinsically rare, luminous objects in such a small sample was a statistical fluke.
Again assuming that the ratio of host luminosity sensitivity and characteristic star-forming galaxy luminosity can be assumed to be constant over our redshift range, the flux-distribution constraint can be translated to an equivalent SFR-distribution constraint at any redshift within a factor of ∼2 simply by calculating the equivalent limiting star-formation rate for our 10µJy limiting flux at each redshift. For example, we estimate that 5-25% of GRB hosts at z ∼ 0.6 have SFR > 14M ⊙ , 5-25% of hosts at z ∼ 1.0 have SFR > 50M ⊙ , 5-25% of hosts at z ∼ 1.5 have SFR > 125M ⊙ , and 5-25% of hosts at z ∼ 2.0 have SFR > 250M ⊙ .

The Stellar Masses of GRB-Selected Submillimeter
Galaxies In the study of  we examined the influence of several parameters on the rate at which a galaxy produces GRBs relative to stars in general (the GRB production "efficiency", ǫ ≡ R GRB /SFR). The total star-formation rate of a galaxy had no discernable effect on its efficiency for GRB production over the redshift range we examined (z ∼ 0.5 − 3). The consistency of the number of radio detections in our TOUGH-VLA sample with the expected number for an unbiased tracer ( §6.2) can be seen as an extension of this conclusion up to the highest star-formation rates. On the other hand, we previously found that mass had a strong effect (GRBs in the most massive galaxies are much rarer than expected given the contributions of such galaxies to overall cosmic star-formation), so it is relevant to investigate the masses of the luminous galaxies detected in this effort as well.
Our optical/NIR SED modeling provides firm estimates of the stellar masses of all four-radio detected galaxies ( §4) 17 , enabling us to evaluate whether or not their mass distribution is consistent with that which would be expected for the most luminous members of a star-formation-sampled galaxy population. Results are plotted in Figure 5; note that we have applied a redshift scaling to the star-formation rates to decrease the impact of redshift evolution over the range spanned by our sample. The masses of our radio-detected hosts (large yellow squares) are well below the masses of almost all high-luminosity (scaled SFR > 100 M ⊙ yr −1 ) galaxies in the GOODS-N field as estimated by Kajisawa et al. 2011, with the exception of GRB 070306 whose stellar mass is fairly typical for a luminous galaxy.
Because the GOODS-N field is small, galaxies with the highest masses and star-formation rates are not wellsampled and this comparison may be biased by cosmic variance. However, wide-area FIR and submillimeter surveys select galaxies out of the underlying field population in a manner similar to the way in which our four detections were selected out of the parent TOUGH sample, and provide a comparison sample over a much larger volume suitable to evaluate the GRB-SFR connection within luminous galaxies in more detail. In Fig Figure 1) and Gruppioni et al. 2013 (their Figure 15).
The stellar masses of submillimeter galaxies are subject to some systematic uncertainty, with the values derived varying by up to a factor of almost ten depending on the assumptions considered in modeling the stellar populations (in particular the star-formation rate history, choice of stellar templates, and IMF; see Micha lowski et al. 2012aMicha lowski et al. , 2014a for an in-depth discussion of this issue). The offset of the Micha lowski et al. (2012a) SMGs and the Herschel samples in Figure 5 is largely a reflection of this. In our own modeling we have assumed a twocomponent stellar population, which tends to lead to 17 Of course, stellar masses in this and all other studies are subject to systematic uncertainties related to the input assumptions. As discussed earlier, our modeling assumes a Chabrier IMF and a two-population star-formation history, which are thought to be the most realistic assumptions for fitting galaxies of this type (Micha lowski et al. 2012a(Micha lowski et al. , 2014a. However, even when employing alternative star-formation histories we derived consistent results, and in this analysis we scale all comparison studies to the same IMF. higher masses when applied to SMGs. However, even when compared to SMG mass catalogs derived using assumptions leading to lower masses, very few such galaxies are of masses comparable to the GRB hosts in our sample (three out of four of the GRB hosts in our sample have a mass below 2 × 10 10 M ⊙ , SMGs below this value are extremely uncommon.) 18 Our sample size is small (4 hosts), but can be expanded by considering additional submillimeter/radio-detected GRB hosts from previous work (although these were not selected out of an unbiased GRB sample, and one of which was detected in radio but undetected at submillimeter wavelengths and could conceivably be afterglowcontaminated; §6.1). Micha lowski et al. (2008) analyzed the SEDs of four submillimeter-or radio-detected GRB hosts (all at z = 1 − 2), and derived stellar masses within the relatively narrow range of 1.0 − 2.1 × 10 10 M ⊙ for all four cases. This result is fully consistent with the distribution observed within our own sample and provides additional support to the notion that, even within submillimeter galaxies and at z ∼ 1.5, GRBs exhibit a strong aversion against the most massive galaxies.
GRBs in more massive submillimeter-like galaxies do exist, particularly among dark GRB hosts: combining the dark GRB samples of Perley & Perley (2013) and Hunt et al. (2014), four galaxies with masses of > 5 × 10 10 M ⊙ have been detected by Herschel or VLA. However, it is important to keep in mind that these are not unbiased samples, but are selected out of the much larger parent pool of the hundreds of Swift and pre-Swift GRBs and subject to very specific selection criteria, explicitly favoring heavily reddened afterglows and IRACbright (massive) galaxies.
Further long-wavelength observations of unbiased samples will be necessary to confirm this interpretation, but these results offer support to the notion that GRBs preferentially explode in low-mass galaxies (albeit without entirely excluding massive galaxies) across the entirety of the host luminosity range.
6.4. GRBs from Optically Thick Super-Starbursts? Traditional submillimeter galaxies are extremely heterogeneous systems, with dense, intensely star-forming cores that dominate the bolometric output (and overall star-formation rate) as well as less-obscured outer components that dominate the UV/optical luminosity despite their minor contributions to the total energy budget. Since the degree of obscuration to a GRB can be determined from afterglow observations, it is possible to crudely discern where within the host galaxy the burst occurred: the central, optically-thick starburst inferred from long-wavelength observations or the outer, optically-thin regions seen in optical/UV observations. 18 An additional systematic issue concerns the completeness and purity of the submillimeter and Herschel samples discussed here. While recent Herschel papers claim very high redshift completeness (80-100%; Gruppioni et al. 2013), it is not inconceivable that some Herschel sources are incorrectly identified with bright counterparts in the Herschel beam when in fact they should be associted with fainter, lower-mass sources, leading to a bias in favor of larger masses and lower redshifts. ALMA follow-up will be necessary to clarify this issue unambiguously, but since our survey targets a relatively nearby redshift range (z = 1 − 2.5) at which counterpart matching is fairly secure we will treat the published Herschel/JCMT results at face value. -Stellar masses and star-formation rates of GRB host galaxies and field galaxies from our sample and from the literature at 0.8 < z < 2.2. In addition to the four radiodetected targets presented here (large squares), we plot GRB hosts with FIR/submillimeter/radio detections from Micha lowski et al. (2008) and Hunt et al. (2014) (small squares), as well as events from Perley & Perley (2013) which were not detected at radio wavelengths, showing the range between the UV/optical SFR as a minimum and the radio SFR as a maximum in the form of vertical lines. Pre-Swift GRB hosts are also shown, plotted as lower limits since sensitive radio/submillimeter limits are generally not available. For the GOODS-N field galaxies (Kajisawa et al. 2011) we take 24µm SFRs when available or dust-corrected UV SFRs otherwise, correcting by an IMF adjustment factor of 1.6 to convert from Salpeter to Chabrier/Kroupa. To minimize the impact of redshift evolution and varying radio luminosity-sensitivity over this broad interval we have scaled all star-formation rates by a factor of (z/1.5) −1.8 . Compared to field galaxies of comparable luminosities and compared to SMGs (small circles indicate individual systems from Micha lowski et al. 2010; the large red ellipse represents the region of parameter space inhabited by SMGS in Gruppioni et al. 2013), the most luminous GRB hosts have unusually low stellar masses.
This also represents an important indicator of the connection between GRB production and star-formation, since the dusty inner regions are likely to be much more metal-rich than the unobscured regions but are also more intensely star-forming. Different physical hypotheses for the origin of the variations in the GRB rate have opposing predictions for the rate of GRBs in such environments: if the GRB efficiency is governed primarily by metallicity we would expect GRBs to avoid the obscured regions; if the GRB efficiency is governed primarily by star-formation intensity then we would expect GRBs to be abundant in obscured regions.
Only two of the galaxies in our sample show strong dust-heterogeneity, as evidenced by significantly discrepant radio versus dust-corrected UV-optical starformation rates: the hosts of GRB 061121 and GRB 070306. These two sources offer a split verdict on the location of the burst within these hosts. The bright, blue afterglow of GRB 061121 is clearly not heavily obscured: Page et al. (2007) estimate between A V = 0.4 − 1.6 mag depending on the assumed dust law and intrinsic spectral index. This is consistent with the mean obscuration inferred from the host UV/optical observations in our SED modeling and clearly situates the event outside the heavily obscured star-forming region that our data (tentatively) indicate is also present. On the other hand, GRB 070306 was extremely obscured and this event is quite consistent with having occurred within the dusty starburst region of a submillimeter galaxy.
Two events are not sufficient to give a definitive answer as to whether or not GRBs preferentially prefer or avoid any particular area of this type of galaxy. Again, however, comparison to other literature results can offer a hint. Among the four pre-Swift submillimeter host galaxies discussed in Micha lowski et al. (2008)-all of which showed evidence for dust heterogeneity as discussed above-three were optically bright and therefore unobscured; only one, GRB 000210, was consistent with an obscured origin. While it is conceivable that this is a selection effect (few optically-obscured dark bursts were sufficiently well-localized in the pre-Swift era to perform a host galaxy search), dedicated studies of dark GRBs have failed to turn up many counterexamples: all of the submillimeter or radio-detected galaxies of dark GRBs in the studies of Hunt et al. (2014) and Perley & Perley (2013) have corresponded to optically reddened galaxies in which the gap between the extinction-corrected UV and the FIR/radio star-formation rates is small. This may be a selection effect on its own (in Perley & Perley 2013 we explicitly favored events with redder optical colors and higher inferred dust-corrected star-formation rates; Hunt et al. 2014 observed only hosts previously targeted with, and detected by, Spitzer ), but even so, additional analogs of GRBs 070306 and 000210 have proven remarkably elusive considering that the bolometric luminosity of obscured regions of typical submillimeter galaxies can exceed the luminosities of the unobscured regions by huge factors.
Larger, preferentially unbiased, campaigns to observe GRB host galaxies at submillimeter/radio wavelengths will be required to resolve this question unambiguously. However, the small numbers of GRBs found to date within heavily obscured regions of very luminous, blue galaxies (two) in relation to the much larger number found in unobscured regions of similar galaxies (as many as five, although c.f. our discussion in §6.1) may point toward nonuniform efficiency for GRB production across the different parts of these hosts: preference for outer, unobscured regions and for blue, moderatelyextinguished ULIRGs, and an aversion against the central, dusty starburst.

CONCLUSIONS
We have presented sensitive radio observations to search for host-galaxy synchrotron emission at the locations of 31 GRBs selected from the TOUGH host-galaxy survey. Among 24 sources of known redshift and not compromised by RFI, we securely detect three (and probably detect a fourth), indicating that approximately 15% of all GRBs occur in the most luminous galaxies (those detectable at radio wavelengths).
As about 15% of all cosmic star-formation occurs in galaxies of similar radio luminosity over this redshift range, our results suggest that GRBs are not particularly biased tracers of cosmic star-formation with regard to bulk galaxy star-formation rate, neither markedly preferring nor avoiding galaxies with the highest luminosities. However, the stellar masses of the systems we de-tect with the VLA are about an order of magnitude lower than what would be expected for an unbiased luminositylimited population. Both of these results are consistent with the trends seen in , in which the GRB host population had significantly lower mass than an SFR-weighted field sample but matched the expected distribution of UV-based star-formation rates.
Why would GRBs appear to preferentially avoid massive galaxies, yet not avoid the most actively star-forming galaxies, when it is well-established that the most massive galaxies are, on average, the most-star-forming? Our results indicate that the GRB efficiency, while depressed in massive galaxies, must also be enhanced in galaxies with high specific star-formation rates, allowing moderate-mass starburst galaxies to compensate for the underabundance of GRBs in non-starbursting highmass galaxies. This effect probably operates at the lowmass end as well, given the remarkable abundance of GRBs within low-mass, modest total-SFR, extremely high-sSFR galaxies (blue points in Figure 5, or Figure 13 from ; see also Christensen et al. 2004 andSvensson et al. 2010) which contribute almost negligibly to overall cosmic star-formation.
The traditional hypothesis for the fundamental factor controlling the GRB rate is a metallicity effect, since such an effect is predicted theoretically in many models (e.g., Yoon & Langer 2005) and several observational studies have found a strong trend for the GRB population to favor lowmetallicity galaxies (Modjaz et al. 2008;Levesque et al. 2010;Graham & Fruchter 2013). Since mass and metallicity are strongly correlated (e.g., Tremonti et al. 2004), this naturally explains why GRB hosts also seem to favor low-mass galaxies. Evidence for an additional dependence on specific star-formation rate (independent of that on mass) does not necessarily nullify this conclusion, since high-sSFR galaxies may be more metal-poor than low-sSFR galaxies of the same mass (Mannucci et al. 2010;Lara-López et al. 2010)-but the sSFR-metallicity trend is not particularly strong, so it remains to be seen whether the distribution of GRB host properties is truly consistent with a model in which the GRB efficiency depends only on metallicity and no other factors. Direct measurements of the metalliticies of the systems studied here (and of other low-metallicity galaxies) should provide some insight: are these galaxies actually significantly less chemically enriched than others of the same mass, or simply more active? In the latter case, this would provide evidence for alternative scenarios in which another parameter instead of or in addition to metallicity governs the GRB efficiency, such as a variable IMF or binary interactions in dense clusters (van den Heuvel & Portegies Zwart 2013). Some independent evidence for such a scenario is provided by the spatially resolved characteristics of GRB host galaxies: HST studies have shown that GRB hosts are more compact than core-collapse supernova hosts and that the GRB itself preferentially occurs in or near the brightest, densest regions of each galaxy Svensson et al. 2010;Kelly et al. 2014;Micha lowski et al. 2014b).
While only four radio-luminous systems have been identified in an unbiased manner so far, the path to identifying more is now well-established: it is now possible to efficiently survey large numbers of fields with the VLA, and an extension of this technique could easily identify many new submillimeter/radio-luminous host galaxies in the next few years. Our survey demonstrates the depths necessary to detect an appreciable fraction of GRB hosts out of an unbiased sample (10 µJy at 3 GHz to identify ∼15%, independent of the redshift of the host population being targeted as long as it is z 2.5) a limit achievable in only ∼2 hours of observation. ALMA observations will be even more sensitive, reaching an order of magnitude fainter and probing GRB hosts beyond z > 3, as has already been demonstrated by Wang et al. (2012) for two objects. A complete understanding of the entire GRB host population, from the least to the most luminous galaxies and from the nearby universe out to high redshifts, is clearly within reach. Support for this work was provided by NASA through Hubble Fellowship grant HST-HF-51296.01-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The W. M. Keck Observatory is operated as a scientific partnership among the California Institute of Technology, the University of California, and NASA; the Observatory was made possible by the generous financial support of the W. M. Keck Foundation. We extend special thanks to those of Hawaiian ancestry on whose sacred mountain we are privileged to be guests. This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. Partial support for this work was provided by NASA through an award issued by JPL/Caltech. It is also based in part on observations with the NASA/ESA Hubble Space Telescope, obtained from the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. These observations are associated with program GO-12949. We thank F. Owen for discussions regarding deep radio field surveys, C. Casey for advice regarding the star-formation rates and masses of submillimeter-and Herschel-selected galaxy populations, and D. A. Kann for helpful comments. This manuscript was completed during the "Fast and Furious: Understanding Exotic Astrophysical Transients" workshop at the Aspen Center for Physics, which is supported in part by the NSF under grant No. PHYS-1066293.