THE SWIFT GRB HOST GALAXY LEGACY SURVEY. II. REST-FRAME NEAR-IR LUMINOSITY DISTRIBUTION AND EVIDENCE FOR A NEAR-SOLAR METALLICITY THRESHOLD

IRAC (Fazio et al. 2004) is a four-channel, mid-infrared imager operating on the Spitzer Space Telescope (Werner et al. 2004). Since the end of the cryogenic mission in 2009, only two of the channels are functional: channel 1, operating between 3.2 and 3.9 μm, and channel 2, operating between 4.0 and 5.0 μm. (In this paper we will refer interchangeably to the channels using their channel numbers and central wavelengths: 3.6 μm for channel 1 and 4.5 μm for channel 2.)

Prior to the start of our project, we examined the Spitzer observation catalog to determine which events within the SHOALS uniform sample (outlined in detail in Paper I) had previously been observed by the telescope. A large number (almost half) had observations already present in the archive (see Table 1 for details). We did not request reobservations of these targets. For the remaining targets we conducted new observations as part of our Cycle 9 Large Program (GO-90062; PI Perley).

Our observational strategy was based on the redshift as measured at the time of the start of our campaign (Fall 2012), with deeper observations used for more distant targets. Integration times were typically 0.2–0.5 hr for z < 1, 1.5 hr for 1 < z < 2, 3 hr for 2 < z < 3, and 6 hr for z > 3. For events at unknown redshift at the time of the proposal, we integrated for 1.5 hr. In each case a 100 s frame time was used, dithering using a medium-step dither pattern except in a few cases where the desire to avoid a nearby bright star favored a more compact dithering arrangement. For targets at unknown redshifts and for those thought to be dark/dust-obscured, we also obtained observations in channel 2 (4.5 μm) using the same exposure prescription as for the channel 1 observations.

We downloaded the PBCD (post-basic calibrated data) observations as they became available in the Spitzer Legacy Archive. We use the default astrometry provided by the pipeline without further additional alignment, effectively establishing the IRAC images (which are aligned against the Two Micron All Sky Survey with an accuracy of 03 by the IPAC pipeline) as the reference system for the survey.

Source confusion and contamination are common in even moderately deep Spitzer imaging owing to the instrument's large point-spread function (PSF; ∼18). Indeed, inspection of our images (Figure 1) demonstrates that a significant fraction of the target host galaxies are contaminated to some degree by flux from neighboring, unrelated objects. Accurate photometry requires removing this contamination.

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We manually examined each Spitzer image simultaneously with any higher-resolution ground-based or Hubble Space Telescope (HST) imaging available of the field (see Paper I) to identify the host galaxy target and any nearby objects that may contaminate the host or sky apertures. Using a custom DS9/python script, we drew a fitting box around each host position and estimated the locations and sizes of all detected sources inside it (as well as those of any bright sources outside the box edges that contribute significant flux within the box). These were then sent as initial inputs via a python wrapper to GALFIT (Peng et al. 2002) to iteratively fit and subtract all sources within the box. The default PBCD image is used as the fitter input image with the PBCD uncertainty map providing the pixel uncertainties. For the input PSF we use our own merged combination of the core and extended PRF files from the IRAC website,¹²  with the final PSF oversampled by a factor of 5 relative to the PBCD image resolution (or by a factor of 10 relative to the native pixel scale). We use a Sersic model with index fixed at n = 1 (typically circular, but elliptical if the source is visibly elongated) or a point-source model depending on the appearance and brightness of the target. The residual images were inspected after the fit, and the routine was rerun with new inputs if necessary until all sources near the host galaxy (including the host itself, if well detected) were removed as completely as possible from the final residual map. We then created a final output image by constructing a GALFIT model using the best-fit parameters for all components except for those associated with fitting the host itself, and we subtracted this model from the initial PBCD image to isolate the host galaxy. The subtracted maps are shown in Figure 2. This procedure was effective at removing contaminating flux for all of our fields, usually leaving negligible residuals except in the cores of very bright stars and galaxies.

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Our GALFIT procedure returns calibrated PSF-based magnitudes using the appropriate zero points for each image. For our final photometry, however, we employ the procedure recommended in the IRAC handbook of calculating aperture photometric magnitudes. These are calculated via the subtracted images described above using a custom IDL wrapper around the aper procedure in the Astronomy User's Library, employing an aperture radius of 18 (1.5 native pixels or 3 resampled pixels). Zero points (including aperture corrections) are based on the corresponding values reported in the Spitzer-IRAC handbook, interpolated using our PSF model (Section 2.2) to permit the use of fractional native-pixel aperture sizes not given in the handbook. Apertures are centered on the host galaxy localization as determined from our ground-based imaging or from the fitting/subtraction procedure; the aperture centers employed are given in Table 1. We estimate uncertainties via the scatter of pixel values in the sky annulus (within the aper procedure), rescaled using an empirical correction for correlated noise expected in subpixel-sampled images. We measured this correction to be a factor of 1.25 (in flux) for our PBCD images by placing a large number of random apertures in blank regions of several non-confusion-limited images and calculating the true scatter in the resulting flux values. Error estimates do not explicitly include systematics associated with the subtraction procedure, which are expected to be minor.

In many cases the host galaxy is not detected in the IRAC imaging. For these cases, we calculate an upper limit. If the host is detected in ground-based imaging, we fix the aperture location at the host position and calculate a 2σ upper limit on the flux at that location. If we do not know the host location, we center the aperture on the best-available afterglow position and calculate a 3σ upper limit. (The higher σ threshold reflects the additional uncertainty associated with not knowing exactly where to place the aperture.)

Photometry on some of the hosts presented here was also published in previous work (in particular, Laskar et al. 2011; Perley et al. 2013), but in all cases the analysis here is independent, using the semi-automated subtraction and photometry procedure above consistently for all targets. Our photometry is generally consistent with these previously published values. We note that further observations and analysis (better de-confusion and precise localization of additional host locations using deeper images) may provide additional improvements in the future, so the values reported here do not necessarily represent the final values for the survey, but we do not expect large changes and the current photometry should be adequate for the purposes of this paper.

The luminosity of a galaxy as measured in the IRAC 3.6 μm band is a good tracer of stellar mass even out to high redshifts, since it probes emission redward of the Balmer break (dominated by evolved stars and only moderately dependent on population age) at nearly all redshifts. While a precise stellar mass estimate requires a spectral energy distribution (SED) fit to many photometric data points (to incorporate age, extinction, and similar dependencies), a reasonable estimate can be obtained from Spitzer observations alone.

For each of our (known-redshift) galaxies, we calculate the the quanity ${M}_{{\rm{3.6/(1+z)}}}$ = ${m}_{{\rm{obs,3.6}}}-\mu (z)+2.5{{\rm{log}}}_{10}(1+z);$ this is the luminosity (AB absolute magnitude) of the host galaxy at the rest wavelength observed by the 3.6 μm filter after cosmological redshift, i.e., the absolute magnitude at a wavelength of $3.6/(1+z)\;\mu$m. This quantity alone can be used as a reasonable stellar-mass proxy, but we also calculate stellar mass estimates directly using the following prescription. For each decade in stellar mass (10⁷ M_⊙, 10⁸ M_⊙, etc.) and for a grid of different redshifts in the range z = 0–10, we create a model galaxy SED by summing Bruzual & Charlot (2003) galaxy SED templates for a continuous star formation history between the present time and a maximum age determined by the mass (100 Myr for $\leqslant {10}^{8}{M}_{\odot },$ 300 Myr for 10⁹M_⊙, 700 Myr for 10¹⁰M_⊙, and 3 Gyr for ≥10¹¹M_⊙; if this age is greater than the age of the universe at the template redshift, we instead use the age of the universe as the maximum age). We assume modest dust attenuation (A_V of 0.05 mag for $\leqslant {10}^{8}{M}_{\odot },$ 0.1 mag for ${10}^{9-10}{M}_{\odot },$ and 0.3 mag for ≥10¹¹M_⊙)¹³ and a Chabrier (2003) initial mass function (IMF). For each SED we then calculate via synthetic photometry the same quantity that we measure using Spitzer, ${M}_{{\rm{3.6/(1+z)}}}.$ The observed magnitudes can then be translated to stellar masses via interpolation on the mass-redshift grid.

Compared to, e.g., scaling based on the rest-frame K-band luminosity, this empirical procedure avoids the use of k-corrections and allows for the expected not fully linear scaling of luminosity with mass (because lower-mass galaxies tend to be younger and have lower mass-to-light ratios). Of course, like all mass derivation procedures, it is subject to various assumptions related to the choice of stellar templates, IMF, star formation history, etc. In general, in this work we will deal with the raw observed luminosities (from which we can compare our host galaxies to each other and to observed stellar populations free of any assumptions) at most stages of the analysis, converting to mass only to add physical context or interpret our results.

In Figure 3 we plot the NIR luminosity (see above) of all galaxies in our survey as a function of redshift. Blue curves show the magnitude that would be measured for several galaxy templates of various masses as a function of redshift using the templates described in the previous section. A few GRBs have been treated specially in this plot and the ensuing analysis. For the initial 3.6 μm observation of GRB 050401 in Cycle 4, the orientation of the detector resulted in a great deal of stray light from a bright nearby star; this target was reobserved in Cycle 8 at a better orientation but at 4.5 μm only; because this image is deeper (and the expected 3.6–4.5 μm AB color close to 0.0), we use the 4.5 μm magnitude. The region near the afterglow position of GRB 090313 is strongly blended with a foreground galaxy and is omitted from the plot and subsequent analysis (pending acquiring deep ground-based data to localize the host centroid). GRB 080310 is affected by a diffraction spike from a nearby star; we attempted to model and subtract it, but it is difficult to evaluate the reality of sources at or near the host location, and a conservative estimate of the field depth does not reach our program goals, so we omit this also.

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The host galaxy luminosity distribution exhibits strong evolution with redshift, at least at the low-z end: luminous galaxies (e.g., those with M < −21) are common above z > 1.5 but effectively vanish from the host sample below z < 1. To better quantify this, we calculated the median host magnitude as a function of redshift using a moving window encompassing up to 21 objects (10 at lower redshift and 10 at higher redshifts, plus the redshift of the object at the count-center of the window). Nondetections are included; since the median magnitude is always above the limits of typical nondetectons, our lack of knowledge of their actual flux does not affect the median calculation. The uncertainty of this running median is calculated (and shown as the filled region on the diagram) via a simple resample-with-replacement bootstrap technique.¹⁴ The resulting curves are shown in Figure 3 in cyan. A marked increase of 2–3 mag in the median luminosity is evident up to z ∼ 1.4, at which point the average magnitude levels off, showing no further (significant) variation out to higher redshifts. Some of this behavior can be interpreted as the result of the shift of the effective rest-frame wavelength of the fixed filter (see the thin blue equal-mass curves); in particular, a modest downturn of up to 1 mag is expected below z < 1 as a result of the stellar bump moving out of the 3.6 μm bandpass. However, star-forming galaxy SEDs are relatively flat (in AB) for rest-frame wavelengths in the range of 0.8–2.2 μm, which most of our observations correspond to, and the strong decline in the typical luminosity (by 2–3 mag) at low redshifts is too large to be interpreted as anything other than intrinsic evolution in the population. Specifically, the characteristic mass of the host population declines by approximately an order of magnitude from z ∼ 1.5 to the present time.

An alternative visualization of the redshift evolution of the luminosity distribution is shown in Figure 4, which plots the cumulative luminosity distribution in a series of redshift bins from 0 < z < 0.5 to 4.5 < z < 6. Nondetections are represented arbitrarily as the limiting magnitude plus 1.0 and shown as a dotted line. While the two lowest-redshift bins show a distribution weighted toward low-luminosity hosts, the remaining curves are nearly identical.

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The nature of the "dark" GRB population and its implications for the GRB host galaxy population overall have been a major topic in the study of GRB environments during the past decade. Systematic follow-up of the host galaxies of these events has shown that the hosts of the dust-obscured population show dramatically higher SFRs and stellar masses and redder colors than the hosts of unobscured GRBs (e.g., Krühler et al. 2011; Rossi et al. 2012; Svensson et al. 2012; Perley et al. 2013; Hunt et al. 2014), with major implications for the nature of the GRB host population (and its connection to star formation) overall.

Given these past results, it is unsurprising that we observe a strong correlation between the existence of obscuration affecting the afterglow and the properties of the host, as illustrated in Figure 3. It is noteworthy that GRBs occurring within the most NIR-luminous quartile of GRB hosts (those at ${M}_{3.6/(1+z)}\lt -22.5$ mag, or a mass of about ${M}_{*}\gt 3\times {10}^{10}{M}_{\odot }$) are almost exclusively moderately to severely obscured. This result also emphasizes the critical role of choosing a uniformly selected sample for studies of this type: had our survey considered only those events with optical afterglow-determined redshifts (light-colored red and green points in the main panel of Figure 3), our results would have been entirely different, since nearly all of the luminous galaxies in the sample hosted GRBs whose redshifts required host galaxy follow-up.

In contrast, GRBs in the least luminous galaxies are only rarely obscured. Among GRBs in our sample at known redshift, only a single example is definitively dark/dusty and hosted within a galaxy with a luminosity-derived mass less than ∼3 × 10⁹M_⊙. While three others at unknown redshift are in galaxies that are very faint and—unless they are at z ∼ 5—likely hosted in similar galaxies, this is still dwarfed by the numbers of dusty GRBs in massive galaxies or by the numbers of unobscured GRBs in low-mass galaxies. A dust-obscured afterglow in a low-mass host is a very rare situation.

While a detailed analysis of the coupling between the properties of dust seen toward the GRB afterglow (A_V, extinction law, etc.) and host galaxy properties will be reserved for future work, we note in passing that the nearly ubiquitous presence of obscuration in the afterglows of GRBs originating from luminous systems provides further evidence in support of the notion that dust in massive galaxies is fairly homogeneous, or at least contains a large diffuse component. It also suggests that ongoing star formation in dense and dusty clouds in low-mass galaxies is not a large contributor to cosmic star formation and more broadly that low-mass galaxies harbor relatively little dust. (See also our discussion of this topic in Perley et al. [2013] and the discussion in Schady et al. [2014].) This is in agreement with conclusions of decreasing dust content toward fainter galaxies in deep surveys (e.g., Bouwens et al. 2009, 2014; Castellano et al. 2012; Finkelstein et al. 2012; Oesch et al. 2013) but extends these results to include optically thick, heterogeneously distributed dust (which would not manifest itself in the galaxy colors) and to galaxies with arbitrarily low masses.

We do not see obvious redshift evolution in the tendency for dust-obscured GRBs to inhabit more luminous galaxies: all but one of the dust-obscured bursts at 3 < z < 5 lies within a host galaxy with a mass above the median. This suggests that even over this redshift range, dark GRBs cannot be neglected in studies of host demographics. Several of these GRBs did have an afterglow bright enough to secure an absorption-based redshift measurement, however—which may suggest that dusty GRBs become less so between z ∼ 2.5 and higher redshifts. However, since dust-obscured GRBs represent only a modest fraction of the total at any redshift, we do not yet have sufficient number statistics to address the issue definitely.

The nature of the GRB host population at any redshift is affected by both the true distribution of star formation within galaxies and any preference that the GRB progenitor may have for particular types of environment, and the primary goal of our survey is to search for and characterize these influences. A detailed examination of this topic will require completion of the multiband survey and as such will be addressed in future publications—however, the Spitzer observations alone are already quite informative, since the Spitzer magnitude serves as a good tracer of the stellar mass distribution and can be used to produce model-independent comparisons against star-forming galaxies from galaxy field surveys with Spitzer data.

Following an approach similar to our previous study (Perley et al. 2013), in Figure 3 we also plot field galaxies from Kajisawa et al. (2011), with the area of each point scaled proportional to the SFR of each object. These galaxies come from a deep K_s-band-selected catalog (MODS) of the GOODS-North field. This survey is very deep (K_s > 24.9 AB mag at 5σ) and mass complete to a similar level to that achieved by our Spitzer observations, and it contains a large value-added catalog including dust-corrected UV and 24 μm SFR measurements. It therefore makes an appropriate field-survey comparison sample for our study, although it is susceptible to cosmic variance as a result of the small field footprint (28 arcmin² for the "wide" catalog employed here). To mitigate against cosmic variance, we also employed the catalogs derived from deep observations of the UDS field from CANDELS (Galametz et al. 2013; Santini et al. 2015)—approximately 7 times larger in area, although without the long-wavelength SFR measurements. Since both these surveys have small numbers of targets and may be incomplete at low redshift (z < 0.5), we also used the much wider (5400 arcmin²) but shallower COSMOS/Ultra-VISTA catalogs (Muzzin et al. 2013) as a comparison population for the (very limited) sample of GRB hosts in that redshift range.

The contribution of undetected galaxies to the cosmic SFR in a field survey is fundamentally uncertain without employing assumptions: extrapolating luminosity functions or relying on theoretical models. In contrast, GRBs probe star formation regardless of the detectability of their host galaxies. To fairly compare the GRB and field galaxy luminosity distributions, we trim our samples at an apparent-magnitude cut of m_3.6 < 24.25 AB, which corresponds to the completeness limit of both our host galaxy survey and MODS, and examine only the redshift range of 0.5 < z < 3, since even K-band-selected samples cannot be complete with respect to rest-frame NIR luminosity at higher redshifts. (Where relevant we use the aperture-corrected total magnitudes, not the raw catalog magnitudes.) We then calculate the median absolute magnitude of the host galaxy distribution, following the same procedure as in the previous section, and the SFR-weighted median absolute magnitude of the field galaxy sample. For this purpose, within MODS we use the ${\mathrm{SFR}}_{{\rm{IR+UV}}}$ column, which adds UV and 24 μm SFRs if detected with Spitzer-MIPS, or otherwise uses an extinction-corrected UV measurement. For UDS we use the SFR from the "14a" SED model (which employs the most flexible star formation history), and for Ultra-VISTA we employ the SED-fit SFR estimate. These median curves are plotted as thick solid blue (GRBs) and dashed black lines (MODS) in Figure 5. If GRBs were perfect tracers of the cosmic SFR (that is, the GRB rate per unit star formation were a constant regardless of environmental properties such as metallicity), then the medians of the two distributions would be statistically consistent with each other at every redshift.

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Large differences are observed between the actual average luminosity of our GRB host sample and that of the (SFR-weighted) field galaxy population at low redshift: about 1.5 mag (a factor of four) below z ∼ 1. The deviation gradually narrows with increasing redshift but does not completely disappear: at redshifts of z = 2–3 the GRB host population is still located in galaxies that are, on average, about 0.5 mag fainter than what would be predicted for a strictly uniform tracer.

A more detailed representation of this behavior is shown in Figure 6, which provides cumulative distributions for the absolute magnitude of GRB hosts in various redshift ranges, compared to the absolute magnitude distributions weighted by SFR of galaxies in several field surveys. The MODS sample is shown as a black line, and the UDS sample is shown as a gray line, except in the lowest-redshift bin, where we use COSMOS/Ultra-VISTA. The GRB distribution is heavily weighted toward low-luminosity (low-mass) galaxies out to at least z ∼ 1.5 and skewed more weakly toward higher redshifts.

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A striking feature of Figures 3 and 6 is the near-total absence of GRBs in massive systems at low redshift. Galaxies more massive than 3 × 10¹⁰M_⊙ (about half the mass of the Milky Way) are responsible for more than a quarter of the cosmic SFR density at z ≲ 1 but produced no GRBs in our sample, which is 100% complete and unbiased for galaxies in this mass and redshift range. In contrast, galaxies with a 3.6 μm-derived mass only slightly less (10⁹–10¹⁰M_⊙, within a factor of a few of the LMC) produce the majority of GRBs in this interval. This suggests two things. First, it requires that the GRB rate is a quite sharp function of environment near its critical level: e.g., the GRB efficiency in 10¹⁰–10¹¹M_⊙ galaxies must be roughly an order of magnitude lower than the efficiency within 10⁹–10¹⁰M_⊙ galaxies. However, it also indicates that extremely low mass is not necessarily a boon to GRB production: while some extremely faint GRB hosts do exist, the median mass and luminosity are still well within the range that is considered "normal" for star-forming galaxies. Extremely faint galaxies are not required or even particularly favored for GRB prouction.

Our result clearly rules out models in which GRBs are entirely uniform (unbiased) with respect to star formation, as well as models in which the GRB dependence is relatively smooth. For example, the model favored by the study of Trenti et al. 2015 (largely on the basis of fitting the GRB redshift distribution, but also incorporating some limited host observations) suggests that most (∼85%) GRBs at z < 1 form via a metal-independent channel; this would predict a large number of GRBs from massive and luminous galaxies in the nearby universe and is in contradiction to our observations. (Trenti et al. themselves also note that the lack of reported luminous low-z hosts is a point of tension with their model.)

It is, however, in general agreement with previous studies of the GRB host stellar mass distribution at z < 1. For example, Figure 3 of Boissier et al. (2013) also shows an order-of-magnitude drop in GRB efficiency between a host stellar mass of 10^9.6 and 10^10.4 M_⊙, while Vergani et al. (2015) find no GRB hosts at >10¹⁰ M_⊙ in their complete z < 1 sample (requiring strong supression in this range) but measure a variation in efficiency of only a factor of a few or less below 10^9.5 M_⊙ (their Figure 4). It is also qualitatively consistent with the conclusions of Svensson et al. (2010), who compared GRB and core-collapse supernova (cc-SN) host properties.

The GRB dependence on host environment is widely speculated to intrinsically be a metallicity dependence, in which metal-poor stars form GRBs readily but metal-rich stars much less or not at all. Owing to the complex correlations between different properties in galaxies, it is difficult to be certain from photometric data alone whether or not metallicity (and not some other parameter that also correlates with mass/luminosity) is actually responsible for the mass-dependent GRB rate at low redshift—other possibilities invoke variations in the IMF/binarity associated with starburst intensity, or stellar mergers associated with dynamical interactions found only in very dense/intense star-forming regions (van den Heuvel & Portegies Zwart 2013). Direct spectroscopic metallicities of all of the massive galaxies in our sample would provide a means to evaluate this directly, but we do not (yet) have these observations for our full sample—and even with spectroscopy in hand, ambiguities associated with inhomogeneous conditions in these galaxies can introduce significant complications in interpretation.

However, our sample offers an opportunity to investigate the metallicity-limit hypothesis in a different way. The mass–metallicity relation evolves strongly with redshift (e.g., Erb et al. 2006), leading to a natural prediction (Kocevski et al. 2009) that the threshold stellar mass (and NIR luminosity) should rise with redshift, and do so in a specific way. Previous studies (Krühler et al. 2011; Perley et al. 2013) have hinted that this effect is present but have been unable to make quantitative tests of it owing to their incomplete and potentially biased redshift sampling for z > 1 objects. With our large, complete sample we are in a position to quantitatively examine this behavior for the first time.

With a simple metallicity-cut model in mind, we use our redshift-subdivided luminosity distributions (Figure 6) to test whether the increasing stellar mass with redshift that is apparent in our sample is indeed consistent with being the product of a redshift-dependent mass–metallicity relation and a redshift-invariant metallicity threshold for GRB production. For each redshift interval, we resample the field galaxy magnitude distribution such that it is uniform with respect to star formation (binning individual galaxies of similar magnitudes to produce a new distribution where each magnitude increment has constant total SFR, mirroring the way GRBs are expected to select galaxies) and perform a two-sided K-S test between this and the GRB host luminosity distribution. This procedure is then repeated for a large number of possible maximum-luminosity thresholds spanning the range of the host sample, recalculating the K-S p-value each time. We then estimate the threshold level, and its upper/lower uncertainties, by marginalization. These measurements and uncertainties are presented in Table 2.

Table 1.  Spitzer  3.6 μm Host Galaxy Photometry

GRB	z	R.A.a	Decl.a	${m}_{{\rm{3.6}}}$ b	${M}_{{\rm{3.6/(1+z)}}}$ c	log10M*d	texpe	Prog IDf
050128	<5.5	14:38:17.71	−34:45:54.6	>25.00	⋯	⋯	5400	90062
050315	1.9500	20:25:54.16	−42:36:02.1	23.43 ± 0.08	−21.29	9.77	5400	90062
050318	1.4436	03:18:51.01	−46:23:44.1	>25.22	>–18.90	<8.63	5400	90062
050319	3.2425	10:16:47.91	+43:32:54.1	24.64 ± 0.12	−21.02	9.69	7200	40599
050401	2.8983	16:31:28.79	+02:11:14.0	24.29 ± 0.39	−20.89	9.61	3700	40599
050525A	0.606	18:32:32.58	+26:20:22.4	>24.61	>–17.64	<8.11	900	3653
050726	<3.5	13:20:11.95	−32:03:51.2	>24.44			5400	90062
050730	3.9693	14:08:17.10	−03:46:17.6	>25.47	>–20.54	<9.46	7400	40599
050802	1.7102	14:37:05.84	+27:47:12.3	24.86 ± 0.29	−19.60	9.00	5400	90062
050803	${4.3}_{-2.4}^{+0.6}$	23:22:37.85	+05:47:08.8	25.49 ± 0.42	−20.66	9.53	5400	90062
050814	5.3	17:36:45.39	+46:20:21.6	24.48 ± 0.11	−22.02	10.22	6900	40599
050820A	2.6147	22:29:38.11	+19:33:36.7	24.85 ± 0.28	−20.42	9.38	3600	40599
050822	1.434	03:24:27.21	−46:01:59.7	22.60 ± 0.08	−21.50	9.85	540	272
050904	6.295	00:54:50.88	+14:05:09.5	>24.98	>–21.79	<10.07	7200	20000
050922B	${4.9}_{-0.6}^{+0.3}$	00:23:13.30	−05:36:17.8	24.59 ± 0.22	−21.78	10.08	5400	90062
050922C	2.1995	21:09:33.08	−08:45:30.2	>25.34	>–19.61	<9.01	3700	40599
051001	2.4296	23:23:48.77	−31:31:24.0	23.20 ± 0.08	−21.94	10.08	5400	90062
051006	1.059	07:23:14.09	+09:30:20.1	20.50 ± 0.01	−22.97	10.58	2700	90062
060115	3.5328	03:36:08.33	+17:20:42.6	25.40 ± 0.31	−20.41	9.43	7400	40599
060202	0.785	02:23:22.91	+38:23:04.3	22.59 ± 0.04	−20.23	9.32	5400	90062
060204B	2.3393	14:07:14.93	+27:40:36.3	22.74 ± 0.05	−22.32	10.29	5400	90062
060210	3.9122	03:50:57.37	+27:01:34.0	23.37 ± 0.06	−22.62	10.46	7200	40599
060218	0.0331	03:21:39.69	+16:52:01.8	20.77 ± 0.04	−15.01	7.20	700	90062
060306	1.559	02:44:22.91	−02:08:54.2	21.54 ± 0.02	−22.73	10.50	5400	90062
060502A	1.5026	16:03:42.63	+66:36:02.6	>24.67	>–19.53	<8.96	5400	90062
060510B	4.9	15:56:29.48	+78:34:12.1	25.15 ± 0.17	−21.22	9.81	13000	20000
060522	5.11	21:31:44.86	+02:53:09.7	>26.37	>–20.07	<9.31	13800	20000
060526	3.2213	15:31:18.34	+00:17:04.9	25.48 ± 0.29	−20.17	9.30	7200	40599
060607A	3.0749	21:58:50.4	−22:29:47.2	>25.05	>–20.52	<9.45	7200	40599
060707	3.4240	23:48:19.06	−17:54:17.7	24.10 ± 0.13	−21.66	9.99	6180	40599
060714	2.7108	15:11:26.41	−06:33:58.2	25.23 ± 0.26	−20.11	9.25	3600	40599
060719	1.5320	01:13:43.71	−48:22:51.2	22.77 ± 0.06	−21.47	9.84	1600	70036
060729	0.5428	06:21:31.78	−62:22:12.0	24.06 ± 0.19	−17.95	8.31	1600	90062
060814	1.9229	14:45:21.32	+20:35:10.5	21.44 ± 0.03	−23.25	10.82	900	70036
060908	1.8836	02:07:18.41	+00:20:31.3	24.73 ± 0.20	−19.92	9.15	3600	40599
060912A	0.937	00:21:08.12	+20:58:17.7	21.56 ± 0.03	−21.65	9.91	2700	90062
060927	5.467	21:58:12.01	+05:21:48.6	>25.77	>–20.78	<9.63	7500	40599
061007	1.2622	03:05:19.59	−50:30:02.3	23.71 ± 0.15	−20.13	9.22	5400	90062
061021	0.3463	09:40:36.13	−21:57:04.9	>24.78	>–16.22	<7.63	1600	90062
061110A	0.7578	22:25:09.84	−02:15:31.4	24.37 ± 0.29	−18.38	8.41	1600	90062
061110B	3.4344	21:35:40.40	+06:52:33.9	>25.24	>–20.52	<9.47	7400	40599
061121	1.3145	09:48:54.54	−13:11:43.2	21.50 ± 0.01	−22.43	10.31	5400	90062
061202	2.253	07:02:05.68	−74:41:55.3	23.24 ± 0.06	−21.75	9.99	5400	90062
061222A	2.088	23:53:03.40	+46:31:58.8	24.06 ± 0.08	−20.79	9.55	18500	30000
070110	2.3521	00:03:39.24	−52:58:27.3	>25.13	>–19.95	<9.16	3600	40599
070129	2.3384	02:28:00.91	+11:41:04.2	23.01 ± 0.03	−22.05	10.15	6200	40598
070223	1.6295	10:13:48.40	+43:08:00.6	23.59 ± 0.08	−20.77	9.53	5400	90062
070306	1.4959	09:52:23.31	+10:28:55.4	21.40 ± 0.03	−22.79	10.53	900	70036
070318	0.840	03:13:56.77	−42:56:46.2	>24.30	>–18.67	<8.54	1600	80153
070328	2.0627	04:20:27.65	−34:04:00.5	23.12 ± 0.06	−21.71	9.97	5400	90062
070419B	1.9588	21:02:49.78	−31:15:49.1	23.30 ± 0.09	−21.43	9.84	5400	90062
070508	0.82	20:51:11.72	−78:23:04.8	22.46 ± 0.07	−20.46	9.41	1600	70036
070521	2.0865	16:10:38.68	+30:15:22.8	21.93 ± 0.04	−22.92	10.63	1600	70036
070621	<5.5	21:35:10.05	−24:49:02.5	>24.97			5400	90062
070721B	3.6298	02:12:32.96	−02:11:40.8	>25.47	>–20.39	<9.42	10800	80054
070808	∼1.35 ± 0.85	00:27:03.30	+01:10:35.4	23.57 ± 0.10	−20.41	9.35	5400	90062
071020	2.1462	07:58:39.78	+32:51:39.6	>24.36	>–20.54	<9.43	3600	80054
071021	2.4520	22:42:34.32	+23:43:06.2	22.10 ± 0.05	−23.05	10.68	1600	70036
071025	${4.8}_{-0.4}^{+0.4}$	23:40:17.07	+31:46:42.6	24.32 ± 0.15	−22.01	10.18	4500	80153
071112C	0.8227	02:36:50.97	+28:22:16.5	23.59 ± 0.11	−19.34	8.89	2700	90062
080205	${2.72}_{-0.74}^{+0.24}$	06:33:00.69	+62:47:32.0	23.79 ± 0.13	−21.55	9.91	5400	90062
080207	2.0858	13:50:02.97	+07:30:07.3	20.98 ± 0.02	−23.87	11.11	1600	50562
080210	2.6419	16:45:04.01	+13:49:35.6	>24.62	>–20.67	<9.50	1600	80153
080310	2.4274	14:40:13.80	−00:10:30.7	23.84 ± 0.25	−21.29	9.78	3500	80054
080319A	2.0265	13:45:20.01	+44:04:48.4	22.63 ± 0.03	−22.16	10.21	5400	90062
080319B	0.9382	14:31:41.00	+36:18:08.6	24.57 ± 0.22	−18.64	8.50	3600	11116
080325	1.78	18:31:34.22	+36:31:23.7	21.09 ± 0.02	−23.45	10.91	1600	70036
080411	1.0301	02:31:55.19	−71:18:07.3	>24.66	>–18.75	<8.54	2700	90062
080413A	2.4330	19:09:11.75	−27:40:40.4	>24.15	>–20.99	<9.64	3600	80054
080413B	1.1014	21:44:34.67	−19:58:52.3	23.22 ± 0.09	−20.33	9.30	2700	90062
080430	0.767	11:01:14.71	+51:41:08.4	24.55 ± 0.34	−18.22	8.33	1600	90062
080603B	2.6892	11:46:07.67	+68:03:39.8	25.43 ± 0.24	−19.89	9.15	10800	11116
080605	1.6403	17:28:30.04	+04:00:55.7	21.61 ± 0.10	−22.77	10.53	1600	80153
080607	3.0368	12:59:47.24	+15:55:10.8	22.96 ± 0.06	−22.58	10.45	4500	70036
080710	0.8454	00:33:05.63	+19:30:05.4	>23.52	>–19.47	<8.95	2700	90062
080721	2.5914	14:57:55.83	−11:43:24.6	>24.30	>–20.96	<9.63	3600	80054
080804	2.2045	21:54:40.18	−53:11:04.8	24.76 ± 0.23	−20.19	9.28	3600	80054
080805	1.5042	20:56:53.44	−62:26:39.4	22.70 ± 0.08	−21.50	9.86	1600	80153
080810	3.3604	23:47:10.49	+00:19:11.5	23.57 ± 0.07	−22.15	10.24	10800	80054
080916A	0.6887	22:25:06.22	−57:01:22.6	22.81 ± 0.10	−19.73	9.12	1600	90062
080928	1.6919	06:20:16.83	−55:11:58.7	>24.20	>–20.24	<9.29	1600	80153
081008	1.967	18:39:49.87	−57:25:53.0	>24.75	>–19.98	<9.18	5400	90062
081029	3.8479	23:07:05.36	−68:09:19.7	>25.61	>–20.35	<9.39	10800	80054
081109A	0.9787	22:03:09.57	−54:42:40.4	20.79 ± 0.02	−22.51	10.35	500	80153
081118	2.58	05:30:22.22	−43:18:05.6	25.27 ± 0.41	−19.98	9.18	3600	80054
081121	2.512	05:57:06.14	−60:36:09.8	25.09 ± 0.34	−20.11	9.24	3600	80054
081128	<3.4	01:23:13.09	+38:07:38.8	25.20 ± 0.31			5400	90062
081210	2.0631	04:41:56.17	−11:15:26.8	22.63 ± 0.04	−22.20	10.23	5400	90062
081221	2.26	01:03:10.17	−24:32:52.0	21.78 ± 0.03	−23.22	10.78	1600	70036
081222	2.77	01:30:57.57	−34:05:42.5	24.48 ± 0.21	−20.90	9.61	3600	80054
090313	3.375	13:13:36.21	+08:05:49.8	>23.54	>–22.19	<10.26	1600	80153
090404	${3.0}_{-1.8}^{+0.8}$	15:56:57.49	+35:30:57.5	22.14 ± 0.04	−23.38	10.85	1600	70036
090417B	0.345	13:58:46.61	+47:01:04.5	20.94 ± 0.02	−20.05	9.44	500	70036
090418A	1.608	17:57:15.17	+33:24:20.9	23.39 ± 0.11	−20.95	9.61	5400	90062
090424	0.544	12:38:05.11	+16:50:14.4	21.35 ± 0.03	−20.66	9.62	1600	90062
090516A	4.109	09:13:02.61	−11:51:14.6	22.92 ± 0.04	−23.15	10.71	10800	80054
090519	3.85	09:29:07.00	+00:10:48.9	>25.50	>–20.46	<9.44	10800	80054
090530	1.266	11:57:40.50	+26:35:37.9	>24.34	>–19.51	<8.93	5400	90062
090618	0.54	19:35:58.48	+78:21:24.7	22.63 ± 0.07	−19.36	9.04	1600	90062
090709A	${1.8}_{-0.7}^{+0.5}$	19:19:42.63	+60:43:39.3	23.58 ± 0.09	−20.98	9.63	4500	70036
090715B	3.00	16:45:21.61	+44:50:20.4	23.45 ± 0.06	−22.07	10.18	10800	80054
090812	2.452	23:32:48.56	−10:36:17.2	>24.80	>–20.35	<9.35	3600	80054
090814A	0.696?	15:58:26.39	+25:37:53.2	22.98 ± 0.09	−19.58	9.05	1600	90062
090926B	1.24	03:05:13.94	−39:00:22.5	21.42 ± 0.02	−22.38	10.28	5400	90062
091018	0.971	02:08:44.74	−57:32:54.1	22.28 ± 0.04	−21.01	9.62	2700	90062
091029	2.752	04:00:42.62	−55:57:20.0	>24.03	>–21.34	<9.81	3600	80054
091109A	3.076	20:37:01.81	−44:09:30.1	25.49 ± 0.35	−20.08	9.25	10800	80054
091127	0.490	02:26:19.87	−18:57:08.6	23.21 ± 0.12	−18.57	8.66	1600	90062
091208B	1.0633	01:57:34.11	+16:53:22.9	>25.22	>–18.26	<8.28	2700	90062
100305A		11:13:28.07	+42:24:14.3	>25.27			5400	90062
100615A	1.398	11:48:49.34	−19:28:51.5	23.84 ± 0.14	−20.21	9.27	4500	70036
100621A	0.542	21:01:13.02	−51:06:22.4	21.35 ± 0.03	−20.65	9.61	900	70036
100728B	2.106	02:56:13.46	+00:16:52.1	>24.74	>–20.13	<9.25	3600	80054
100802A	<3.1	00:09:52.43	+47:45:18.5	25.47 ± 0.43			5400	90062
100814A	1.44	01:29:53.55	−17:59:43.7	23.35 ± 0.07	−20.76	9.52	5400	90062
110205A	2.22	10:58:31.20	+67:31:31.0	23.80 ± 0.10	−21.17	9.72	11100	90062
110709B	2.09?	10:58:37.11	−23:27:16.8	24.82 ± 0.31	−20.03	9.20	5400	90062
120119A	1.728	08:00:06.95	−09:04:53.6	22.89 ± 0.07	−21.59	9.91	5400	90062
120308A	<3.7	14:36:20.12	+79:41:11.9	24.98 ± 0.27			5400	90062

Notes.

^aLocation of IRAC aperture center (J2000). For targets with a detected host at any waveband this is the host galaxy centroid; for nondetected hosts the best afterglow position is given. ^bMeasured IRAC aperture magnitude (3.6 μm, AB) and 1σ uncertainty. ^cAbsolute AB host magnitude at a wavelength of λ = 3.6 μm/(1 + z). For targets with photometric redshifts we assume the best-fit redshift given in the table. ^dLogarithm of the stellar mass, as derived from the Spitzer-measured luminosity. ^eIRAC exposure time in seconds. ^fSpitzer Program ID number. Programs are: 272—PI Le Floc'h, "Probing the Dark Side of the Cosmic Evolution Using Dark Gamma-Ray Bursts"; 3653—PI Garnavich, "Gamma-Ray Burst Physics in the Spitzer/Swift Era"; 20000 and 30000—PI Berger, "Gotcha! Using Swift GRBs to Pinpoint the Highest Redshift Galaxies"; 40598—PI Jones, "GRBs as Beacons of Star Formation at High Redshifts"; 40599—PI Chary, "Unveiling the Galaxy Counterparts of Damped Lyα Absorbers using GRB-DLAs"; 50562—PI Levan, "The nature of dark gamma-ray burst host galaxies"; 70036—PI Perley, "The Host Galaxies of Dust-Obscured Gamma-Ray Bursts"; 80054—PI Berger, "Probing the z > 2 Mass–Metallicity Relationship with Gamma-Ray Bursts"; 80153—PI Perley, "Understanding the Environmental Dependence of High-z Dust with GRB Hosts"; 90062—PI Perley, "Spitzer Observations of GRB Hosts: a Legacy Approach."

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Despite the large size of our survey, we remain strongly limited by the number counts of the GRB host population in each bin, and the uncertainty on the threshold measurement is large (typically 0.5–1.0 mag). However, at all redshift bins at which we can carry out this analysis, a model with no luminosity cut is ruled out (95%–99.99% confidence, depending on redshift). We do, however, find a good match to the distributions at every redshift if a luminosity cut is applied to the field galaxy sample.

Our measured luminosity thresholds (and uncertainties) can then be translated into stellar masses using the same procedure described in Section 2.4. From there, they can be converted into metallicity values using the analytic expressions for the redshift-dependent mass–metallicity relation of Zahid et al. (2014).

If the GRB efficiency is controlled only by metallicity (and not other factors that are varying over the universe's history, such as the average specific SFR), we would expect to measure a consistent metallicity threshold at each redshift. Indeed, we find that all of our observations are consistent with a redshift-independent GRB metallicity threshold of 12 + log[O/H] = 8.94 on the KK04 system with a scatter of only σ = 0.04 among the different redshift bins. Converting using the relations of Kewley & Ellison (2008), this is equivalent to 12 + log[O/H] = 8.64 on the Pettini & Pagel (2004; PP04) system. In either case this is close to the solar value (∼8.7; Asplund et al. 2009).

Given that the original Zahid et al. relation was derived from a fit only to z < 1.7 data, the extension of their analytic prescription to higher redshifts is purely an extrapolation, and it is somewhat surprising that we continue to see agreement between our measured threshold and their mass–metallicity–redshift relation even at z = 2.25 and (to some extent) at z = 3. The actual mass–metallicity relation at higher redshifts has been investigated directly by other surveys (e.g., Savaglio et al. 2005; Erb et al. 2006; Maiolino et al. 2008)¹⁵ but remains uncertain, in part because the ionization properties of high-redshift galaxies appear to be quite different from those at lower redshifts (e.g., Steidel et al. 2014; Sanders et al. 2015), putting the calibration of popular diagnostics and prescriptions developed at z ∼ 0 into doubt at these epochs. Our observations may actually help shed some light on this topic: given the good consistency between the GRB host luminosity function and the evolving mass–metallicity relation from z ∼ 0.5 to z ∼ 2.0 with a fixed, approximately solar metallicity limit, the continued avoidance of GRBs from massive (∼10¹¹M_⊙) galaxies out to z ∼ 3 suggests that massive systems are metal enriched at or above at least the solar value (and would favor the use of abundance diagnostics/calibrations consistent with this evaluation). If so, this would be an interesting reversal: while the metallicity sensitivity of the GRB progenitor has long been seen as an obstacle for its use to measure the cosmic SFR density, this property may in the end turn out to be valuable by making GRBs an independent tracer of chemical evolution.

Turning to low redshifts, although our inferred cut value provides a good explanation for the luminosity distrubution of galaxies over the full range of redshifts well probed by our survey, it is somewhat higher than the effective metallicity cuts measured by spectroscopic surveys at low redshift. For example, Modjaz et al. (2008) infer a cutoff value of ∼8.5 (on the Kewley & Dopita [2002] abundance scale, equivalent to 8.67 on KK04) based on four objects at z ∼ 0.1; the updated analysis of Graham & Fruchter (2013) finds reasonable agreement with this cut value for the bulk of their population (although fully 5 of their 14 hosts have measured metallicities above this). Wolf & Podsiadlowski (2007) find a cutoff value of 8.7 ± 0.3 (KK04) using a photometric analysis of published low-z hosts. Given the large uncertainties on these earlier values (associated with the small sample size), they might not be inconsistent with our new measurement. In addition, it must be remembered that the sample of local, low-luminosity GRBs has properties quite different from the cosmological population observed at high redshift (e.g., >5 orders of magnitude in E_iso and in observed volumetric rate; low-luminosity GRBs are also quasi-spherical and probably not jetted; Bromberg et al. 2011). Most low-redshift samples are also still based primarily on pre-Swift GRBs whose selection is particularly heterogeneous and difficult to model; future studies of low-z events from the more uniform, better-understood Swift population should help better constrain the true nature of the low-redshift population.

If the GRB efficiency is close to uniform in galaxies with luminosities/metallicities below our inferred threshold, our observations can be used to provide an independent means of estimating what fraction of all star formation occurs in the least luminous and lowest-mass galaxies at each redshift. At the completeness level of MODS (approximately m_3.6 = 24.25, slightly shallower than the level achieved in our host galaxy survey) the star-forming fraction in fainter galaxies can be read directly from our plots in Figure 7 as the fraction where the completeness magnitude intersects the GRB host curve. Given the depth of the survey, this fraction is unsurprisingly quite low at z < 2: 10%–20% in every well-sampled redshift bin. At higher redshifts the implied survey-detectability fraction drops significantly: the fraction of faint hosts is ∼30% at z = 2.25 and ∼50% at z = 3. Our survey goes deeper than MODS at z ∼ 3 (m_lim ∼ 25) and gives an even tighter constraint to this depth; only about 30% of star formation is in galaxies fainter than that level (about 3 × 10⁹ M_⊙).

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Extending this constraint to even higher redshift (z > 3.5) is contingent on the assumption that the GRB host distribution probes the entire galaxy population (i.e., that even the most massive galaxies have metallicities below our inferred threshold), an assessment we cannot test directly because no mass-complete field galaxy samples exist at these redshifts.¹⁶ However, at the depths achieved on our deep high-z fields (m_3.6 ∼ 25.5 mag, corresponding to ∼few × 10⁹ M_⊙) we continue to detect approximately half the GRB population out to the redshift limit of the sample (z ∼ 5.5), indicating that about half of star formation occurs in galaxies less luminous/massive than this threshold. If GRBs continue to avoid high-mass galaxies even in this redshift range, the implied fraction of undetectable star formation would be less than this.

Figure 7 also allows us to measure directly the fraction of star formation at each epoch that does versus does not produce GRBs (except possibly at a much reduced rate)—this is simply the fraction of the plot below versus above (respectively) the horizontal dotted line. In the last column of Table 2 we provide this measurement, which is ∼0.85 at z ∼ 3 (indicating that GRBs track star formation well in all galaxies except for those responsible for 15% of cosmic star formation) but drops to 0.5 at z ∼ 1.5 (indicating that half or more of the star formation in the universe does not produce GRBs, except perhaps in unusual circumstances) and even lower at lower redshifts.

Table 2.  Redshift-dependent Cutoff Values

za	${M}_{3.6/(1+z)}$ b	log($\displaystyle \frac{{M}_{*}}{{M}_{\odot }}$)c	12+log[O/H]d	${M}_{3.6/(1+z),8.94}$ e	fSFf	pbestg	p8.94h	p∞i
0.1–0.5	⋯	⋯	⋯	−20.30	⋯	⋯	⋯	⋯
0.5–1.0	$-{21.33}_{+0.34}^{-0.31}$	${9.82}_{-0.15}^{+0.14}$	${8.91}_{-0.05}^{+0.04}$	−21.53	0.33	0.71	0.43	<0.0001
1.0–1.5	$-{23.17}_{+0.97}^{-1.23}$	${10.70}_{-0.52}^{+0.57}$	${9.05}_{-0.11}^{+0.05}$	−22.23	0.43	0.24	0.06	0.044
1.5–2.0	$-{22.41}_{+0.54}^{-0.36}$	${10.34}_{-0.30}^{+0.20}$	${8.91}_{-0.10}^{+0.05}$	−22.57	0.50	0.13	0.12	0.003
2.0–2.5	$-{23.31}_{+0.62}^{-0.38}$	${10.83}_{-0.34}^{+0.20}$	${8.99}_{-0.09}^{+0.04}$	−22.92	0.62	0.70	0.19	0.017
2.5–3.5	$-{22.97}_{+0.48}^{-0.27}$	${10.64}_{-0.25}^{+0.14}$	${8.88}_{-0.08}^{+0.04}$	−23.39	0.77	0.87	0.16	0.012

Notes.

^aRedshift range. ^bInferred AB absolute magnitude threshold and 15%–85% confidence uncertainty interval, measured from the data. Confidence interval does not include uncertainty due to cosmic variance in the field survey. ^cStellar mass corresponding to column (b). ^dOxygen abundance corresponding to column (c), converted using the analytic mass–metallicity relation of Zahid et al. (2014). ^eAbsolute magnitude threshold predicted, assuming a metallicity cutoff of 12 + log[O/H] = 8.94 at all redshifts. ^fFraction of cosmic star formation at that epoch that readily produces GRBs. ^gp-value calculated from a two-sided K-S test betwen the GRB host magnitude distribution and the SFR-weighted galaxy distribution clipped at the best-fit magnitude threshold. ^hp-value if clipped at the magnitude threshold corresponding to 12 + log[O/H] = 8.94. ⁱp-value if not clipped at all (if GRBs are assumed to be "unbiased" tracers of SFR).

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This allows us to correct the cosmic GRB rate estimated in Paper I to examine whether or not the same model that explains the evolution of the luminosity distribution can also explain the redshift distribution and in particular the apparent excess of GRBs at high z (or equivalently, the deficiency at low z). We use a polynomial fit to interpolate between the redshift bins for the values in Table 2 and simply divide each bin by the resulting value of f_SF.

The result is plotted in Figure 8 (left panels). The correction procedure greatly reduces the discrepancy; while the z > 2 data points are still above the SFR density curves, the excess is less than a factor of two and always less than 2σ significance.

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Since our GRB rate derivation procedure (using E_iso from a fluence-limited sample) differs from previous work, in the right panels of Figure 8 we also show the rate derived in the more conventional fashion using the average flux/luminosity of each burst, $F=S/{T}_{{\rm{90}}}$ (we continue to use a k-correction to the 45–450 keV band instead of bolometric corrections). Results are nearly identical, with the exception that this procedure recovers two z > 8 bursts that were dropped by our fluence cut (090423 and 090429B; Salvaterra et al. 2009; Tanvir et al. 2009; Cucchiara et al. 2011), which would imply a very high rate at this epoch. This may imply different behavior entering the reionization era (in the burst rate or perhaps in burst properties—both events were remarkably short after taking into account time dilation) but may also be a fluke. More searches for very high z GRBs will be needed to investigate this.

Otherwise, our analysis provides further support to the notion that the entire GRB rate behavior—both as a function of galaxy mass and as a function of redshift—can be explained in terms of the chemical history of the universe. Above z ≳ 3 GRBs track star formation; below this point massive galaxies build up metals and cease GRB production, shifting the host luminosity distribution to fainter galaxies and reducing the cosmic GRB rate.