STAR FORMATION IN THE EARLY UNIVERSE: BEYOND THE TIP OF THE ICEBERG

Spectroscopy of GRB 060522 was performed by Keck roughly 12.5 hr after the burst, and revealed a strong break ∼7425 Å in the spectrum, interpreted as Lyα at z = 5.11 ± 0.01 (Cenko et al. 2006). A search for the host galaxy with the Spitzer Space Telescope found no detection to flux densities of 0.2 μJy at 3.6 μm and 2.4 μJy at 5.8 μm, implying that its rest-frame optical luminosity lies substantially below L* (Chary et al. 2007).

We obtained observations of GRB 060522 with WFC3/IR using the F110W filter. To ascertain the precise location of the burst on our HST image, we performed relative astrometry between our WFC3 observations and an image obtained at the Telescopio Nazionale Galileo (TNG) on 2006 May 22 (D'Avanzo et al. 2006). At the location of the afterglow, we measure a flux density of 7 ± 4 nJy, corresponding to a 2σ (aperture corrected) magnitude limit of F110W(AB) >28.13. Although formally this is a non-detection at 2σ  it is possible that some host flux is contributing within the aperture. Indeed visually it appears there is a somewhat more significant excess of flux which is offset slightly southwest from the GRB location (by about 03, or ∼2 kpc at z = 5.11), and if we increase the aperture size to 06 diameter then the flux density becomes 12 ± 5 nJy. This would represent a marginal detection, and corresponds to an apparent magnitude of F110W(AB) ≈28.5. While this is a plausible magnitude for a host (corresponding to M₁₈₀₀(AB) ≈ −18), the probability of a chance alignment with an unrelated object at such faint magnitude levels is also non-negligible. Specifically, considering the F110W number galaxy number counts from Thompson et al. (1999), we estimate ≈5% of random locations will have a galaxy of magnitude F110W(AB) ≲ 28.5 within 05. Thus, in a sample of six, as we have, there is a ∼25% chance of an unrelated galaxy being close enough to be possibly mistaken for a host in at least one case. For the sake of consistency with the other bursts, we will continue to use the 04 aperture limit in the remainder of the paper.

GRB 060927 was detected by Swift, and its optical afterglow was initially found in rapid, but unfiltered, Rapid Optical Transient Source Experiment (ROTSE) observations. An extensive follow-up campaign (reported in Ruiz-Velasco et al. 2007) revealed the source to be an R-band dropout, well detected in the i band. A subsequent spectrum obtained at the Very Large Telescope (VLT) showed a faint continuum redward of ∼8000 Å, as well as a weak Si ii absorption feature, consistent with a redshift of z = 5.47.

Our HST/NICMOS observations of the field of GRB 060927 were taken using the F160W filter, and were reduced as described in Fynbo et al. (2005). GRB 060927 was additionally re-observed with WFC3/IR using the F110W filter. Astrometry was performed via observations made with the VLT on 2006 September 30. To establish the position on the NICMOS images (which have a narrower field of view than WFC3), we opted to perform relative astrometry directly to the WFC3 images. The resulting rms astrometric accuracy is <001, and so it does not impact the overall error in the astrometric solution described above.

At the location of the afterglow, the photometry in each of the NICMOS and WFC3/IR observations yields limiting magnitudes of F160W(AB) >27.75 and F110W(AB) >28.57, respectively.

GRB 050904 was the first GRB at z > 6 to be located. Its optical/IR afterglow was initially found by Haislip et al. (2006), who derived a photometric redshift of z = 6.39 based on the strong spectral break between i and z bands, coupled with NIR observations showing a blue spectral slope redward of the break (see also Tagliaferri et al. 2005). The afterglow was intrinsically extremely bright, among the brightest observed for any burst, making late-time spectroscopy feasible with Subaru. This provided a measurement of the absorption redshift, hydrogen column density, and metallicity of the host (Kawai et al. 2006; Totani et al. 2006). It remains the most distant burst for which all of these diagnostics are available.

A search for the host galaxy of GRB 050904 was conducted by Berger et al. (2007) using both HST and Spitzer, which placed deep limits on any host emission. The first HST epoch, at which time both ACS/F850LP and NICMOS/F160W images were obtained, was carried out only about three weeks post-burst. No significant flux was detected in F850LP, and the faint detection in the F160W image was shown to be due to residual afterglow contamination since it was absent in a later F160W epoch (Berger et al. 2007).

For our analysis, we re-reduced the ACS data for GRB 050904 (since we are primarily interested in the rest-frame UV luminosity close to Lyα, this filter is the more relevant). Astrometric tying of the afterglow to field sources was done utilizing a z-band image obtained from Gemini-South on 2005 September 7. At the location of the afterglow in the F850LP frame, we measure a flux density of −5 ± 17 nJy, corresponding to a 2σ limit of F850LP(AB) >27.50 (or 27.06 at 3σ). This is in good agreement with the limits reported by Berger et al. (2007). However, since the Lyα break lies within the filter bandpass at this redshift, we must account for flux lost due to IGM absorption (i.e., the effective filter width is narrower for this host), and so we conclude a corrected magnitude limit of F850LP(AB) >26.86.

GRB 080913 was identified as a high-redshift candidate based on photometric observations with GROND showing the burst to be an i-band dropout (Rossi et al. 2008). Deep, red spectroscopy from the VLT showed a strong spectral break, interpreted as Lyα at z ∼ 6.7 (Greiner et al. 2009). A further detailed analysis of the spectrum by Patel et al. (2010) revealed a single absorption line of Si ii at z = 6.733, and we adopt this as the redshift of GRB 080913.

We obtained HST observations with WFC3/IR in the F160W filter. To tie the astrometry of our HST observations, we utilized images obtained from FORS2 at the VLT on 2008 September 13 in the z band, and images taken with NIRI on Gemini-North on 2008 September 14. We used two images independently to confirm the precise location of GRB 080913 on our HST images. For the FORS2 images, we identified nine compact sources in common, while only six sources were usable from the Gemini observations. Although the afterglow detections are of low signal-to-noise ratio (S/N), the errors on their centroids are small in comparison to the errors derived from the fit and hence we are able place the afterglow to an rms accuracy of 008. Again, no host galaxy is visible in our observations to a limit of F160W(AB) >27.92.

GRB 090423 was first identified as a candidate high-redshift object based on its afterglow being a Y-band dropout, which implies z > 7.5 (Cucchiara et al. 2009). VLT spectroscopy with both ISAAC and SINFONI allowed the identification of the Lyman break, despite low S/N, establishing the redshift z = 8.23 ± 0.07 (Tanvir et al. 2009). This value is in excellent agreement with the z = 8.1^+0.1_−0.3 determined from a spectrum obtained at the TNG (Salvaterra et al. 2009).

We obtained our first HST observations of GRB 090423 on 2010 January 24. At this stage, we acquired 20 orbits in each of the F125W and F160W filters on WFC3. Unfortunately, 15 of these 20 orbits were substantially impacted by persistence from earlier observations of bright field sources. This affected the sensitivity over wide regions of the detector, although it does allow us to measure the flux at the location of the GRB host (which was only mildly affected by persistence). Additional observations were obtained in 2010 October. All of the available observations in each filter were co-aligned and stacked via multidrizzle. These observations are extremely deep, with limiting magnitudes a factor 1.5× deeper than the WFC3 Early Release Observations of the Chandra Deep Field South/Great Observatories Origins Deep Survey (CDF-S/GOODS) fields, and only another factor of 1.5× shallower than the WFC3 observations of the HUDF (Bouwens et al. 2011b).

The location of the afterglow on our HST images was achieved by tying the astrometry to VLT/HAWK-I observations that were obtained approximately 17 hr post-burst. While the afterglow had faded since its first discovery from Hawaii, these deep observations yielded similar signal to noise, with the added advantages of a larger field of view, and a greater number of faint sources for comparison.

Within the HST image there is no obvious source at the afterglow location, and the measured 2σ limiting magnitudes are F125W(AB) >30.29 and F160W(AB) >28.36. Since both filters sample the rest-frame far-UV, we form a weighted average of the two results to provide a combined flux density measure of −0.15 ± 1.7 nJy, which is used to derive the limit on the SFR reported in Table 3. Such a small host is consistent with the non-detection of molecular gas from the GRB location (Stanway et al. 2011).

GRB 090429B is the only host within our sample that does not have a spectroscopically measured redshift. However, the photometric break between the J and H bands, coupled with the blue spectral slope between H and K provides a best-fit photometric redshift of z = 9.4 and a robust lower limit to the redshift of z ≳ 6.5 (Cucchiara et al. 2011). As we commented above, the smooth power-law spectra of GRB afterglows make photometric redshift estimates generally more reliable than they are for galaxies, since the range of intrinsic spectral variation is much less (e.g., Krühler et al. 2011). We obtained observations in F606W (ACS), F105W, and F160W; the non-detection of a host galaxy in these images, including the blue filters, provides additional support for the high-z origin for this burst, since the hosts of GRBs at z < 3 have so far always been detected in HST optical imaging. Here, we consider primarily the F160W observation, since this is the only filter redward of Lyα at the best-fit redshift z = 9.4. However, for completeness we also report results for the z ≈ 6.5 lower limit, which allows us to use both the F105W and F160W data.

We ascertained the location of the burst on the HST images via relative astrometry between our first epoch K-band observations and those obtained with HST. The 2σ limiting magnitude at this location is F160W(AB)>27.78. This is shallower than for the majority of the bursts in our sample, since only a two-orbit exposure was obtained. However, despite this the image still probes to faint limits comparable to the likely characteristic galaxy luminosity, L*, at z = 9.4.

3.1.1. Star Formation Rates

At the redshifts of the bursts in question, our NIR observations probe rest-frame wavelengths roughly in the range 1300–2000 Å. Limits on the UV luminosity at these wavelengths provide direct constraints on the host SFRs. A potentially important consideration in the UV is the effect of extinction by dust, which could lead to a significant underestimate of the true SFR if uncorrected. However, observational constraints from GRB afterglows at high redshifts (Greiner et al. 2009; Tanvir et al. 2009; Zafar et al. 2011b) suggest that extinction corrections are likely to be small. Similarly the blue colors of the z ∼ 7 candidate galaxies identified in the deep HST fields (e.g., Bouwens et al. 2010b; Finkelstein et al. 2011; but, see also McLure et al. 2011) also argue for little dust in most early star-forming galaxies. We therefore assume dust extinction can be neglected.

Following Madau et al. (1998), we estimate the SFRs based on the UV luminosity at ∼1500 Å (see also the discussion in Bunker et al. 2010):

$$\begin{equation} {\rm SFR} = {L_{1500,\,{\it UV}} \over 8 \times 10^{27}\,\mathrm{erg\, s^{-1}\, Hz^{-1}} }\,M_{\odot } \,\mathrm{yr^{-1}}. \end{equation} \tag{ 1 }$$

As discussed in Section 2.1, there is a marginal detection of what may be the host of GRB 060522 at z = 5.11, slightly offset from the burst position, but otherwise none of the hosts are significantly detected. The inferred 2σ limits on their SFRs are given in Table 3, and in Figure 2 are plotted as a cumulative histogram of upper limits, compared to the SFRs for a sample of z ∼ 7 HUDF galaxies from Bouwens et al. (2011b). The limits span the range 0.4–4 M_☉ yr⁻¹, and indicate that the total SFRs in these galaxies are modest. For comparison, the median SFR for GRB hosts at z ≲ 1 are found to be around 1–2 M_☉ yr⁻¹ (Svensson et al. 2010).

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3.1.2. Stacked Limits on Host Galaxy Emission

Although our small sample of high-z GRBs does not yet allow us to place strong constraints on the galaxy LF, we can test whether the limits on the host magnitudes are consistent with them having been drawn from the LFs suggested by other studies of galaxy populations with redshifts between 5 and 10.

The recent re-observations of the HUDF with WFC3/IR have revealed a population of z-band and Y-band dropouts, with colors consistent with galaxies at z > 7 and z > 8, respectively (Bunker et al. 2010; McLure et al. 2010; Bouwens et al. 2010a). A single candidate z ∼ 10 galaxy (J-band dropout) has also been identified (Bouwens et al. 2011a). From these samples, assuming they are substantially complete and uncontaminated, it is possible to make some statements about the form and evolution of the galaxy LF from 5 < z < 10. In particular, these authors fit their data in bins of redshift with the LFs described by a Schechter function (Schechter 1976):

$$\begin{equation} \phi (x)dx=\phi ^*x^{-\alpha }e^{-x}dx, \end{equation} \tag{ 2 }$$

where x = L/L*, with L* being the characteristic luminosity of the "knee" of the LF. Here, α is the power-law slope toward faint luminosities and ϕ* is a normalization factor. Of course, there are no strong observational reasons to expect the LF to have this form at high-z, but it is supported by theoretical work (Trenti et al. 2010).

In Figure 3, we show the preferred analytical LF fits of Bouwens et al. (2011b) and the data on which they are based, for samples at z ∼ 5, 7, and 8. Their conclusion is that the characteristic knee in the LF, L*, becomes slowly fainter with increasing redshift from 4 to 8, and at the same time the faint-end slope becomes steeper, reaching a value of α ∼ 2 by z = 8. This is in addition to the overall normalization, ϕ*, lowering (but see also McLure et al. 2010, who find a fading L* and lower ϕ* but less evidence for a steepening slope). This indicates that an increasing proportion of star formation is occurring in fainter galaxies, and indeed formally the integrated luminosity represented by a Schechter function with α > 2 diverges without some lower cutoff luminosity. However, there are important caveats which pertain to these analyses: first, the LF parameters are based on entire samples, and any incompleteness or contamination (particularly difficult to rule out at the faint end) will introduce biases; second, even the HUDF is limited to finding galaxies in the top few magnitudes of the LF, so that the conclusions about total SFR (and hence the production rate of ionizing photons) are sensitive to the untested assumption that a Schechter function is the appropriate form, and to the large uncertainties on the measurement of the faint-end slope.

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We note that at high redshift the UV LF has limitations as a way of representing the whole population of galaxies, since they are typically only visible when in the starbursting phase, and likely remain in this state for only a short duration based on the typical ages, and apparent availability of molecular gas for star formation within them. However, particularly for understanding the contribution of galaxies to the reionization of the universe, the measured UV luminosities, which are more representative of star formation occurring with the last ∼15–100 Myr, are the relevant quantities. Furthermore, since the GRB itself is a sign of ongoing massive star formation within the host, one would expect the likelihood that a GRB occurs to scale with the UV luminosity. Indeed, we would expect the region immediately underneath the burst to be extremely UV-bright, as is observed in the more local GRB population (Fruchter et al. 2006). Hence, we can meaningfully compare our limits on host emission with the observed galaxy LFs at z ∼ 7.

The 2σ luminosity limits for the GRB hosts are also shown graphically in relation to the high-z galaxy LFs in Figure 3, while their tabulated UV absolute magnitude limits are given in Table 2. As can be seen, all the hosts are apparently below M* (the AB magnitude corresponding to L*) at their respective redshifts, and in the case of our observations of GRB 090423, have the ability to probe to fainter limits than has so far been possible with the Ultra-Deep Field observations. This is because, despite the shallower depth of our images, we have prior knowledge that an object exists at this location, and so can accept a lower formal significance level for detection (since the chances of a random noise fluctuation are lower due to the much smaller area under consideration). Furthermore, since we do not need a blue "veto" filter we make more efficient use of the available exposure time, in contrast to some Lyman break searches which are limited by the depth of their short-wavelength (blueward of Lyα) imaging.

These observations of GRB host fields allow us to test the validity of the galaxy LFs that have been derived from deep-field observations. We assume that there is no dependence of GRB rate or luminosity on environmental parameters such as metallicity, which, as discussed in Section 1, is certainly plausible at high redshifts when the bulk of star-forming galaxies were generally not highly enriched. We also assume that any dust extinction is minor, as argued in Section 3.1.1. Then the probability that a galaxy produces a GRB in some unit time (the probability of more than one GRB in realistic observing times being negligible) is approximately proportional to its rest-frame UV flux, since massive stars are responsible for producing both: i.e., P_GRB∝SFR∝L_UV. Thus, because we would expect GRBs to be drawn randomly from the total stellar UV luminosity, this means that the host galaxies should be drawn from the luminosity-weighted galaxy LF.

In practice, the best-fit values for the faint-end slope α and characteristic luminosity L* at each redshift considered were determined from the fitting formulae given by Bouwens et al. (2012), and are summarized in Table 3. We can then calculate a luminosity-weighted LF, which (suitably normalized) we take to be equivalent to a probability density function (PDF) for the intrinsic host luminosity:

$$\begin{equation} y(L) = {L \phi _z(L) \over \int _{L_{\mathrm{min}}}^{\infty } L^{\prime } \phi _z(L^{\prime })dL^{\prime }}, \end{equation} \tag{ 3 }$$

where ϕ_z(L) is the LF at redshift z. We emphasize again that, since we are going to compare with the fluxes measured in apertures at the exact GRB location, we are also assuming there is no significant offset between the GRB and its parent galaxy.

Hence, the probability of observing a GRB in a galaxy of luminosity L < L_host can be obtained via the cumulative probability density function (CDF):

$$\begin{equation} Y(L_{\rm host})=P(L<L_{\rm host}) = {\int _{L_{\mathrm{min}}}^{L_{\mathrm{host}}} L^{\prime } \phi _z(L^{\prime })dL^{\prime } \over \int _{L_{\mathrm{min}}}^{\infty } L^{\prime } \phi _z(L^{\prime })dL^{\prime }}. \end{equation} \tag{ 4 }$$

Setting a lower limit, L_min, for the integral is physically motivated since small dark halos (≲ 10⁸ M_☉) at z ∼ 10 are expected to retain little gas and form few stars (Read et al. 2006). Given the apparent steepness of the faint-end slope of the LF at z ∼ 8, it is also important that the value of L_min be sensibly chosen. It is not feasible to directly measure this lower limit at high redshift since it is well below the detection threshold for deep imaging, and will remain so even in the era of the James Webb Space Telescope (JWST) or ground-based ELTs. However, it is possible to provide estimates via simulations (Read et al. 2006), or from the star formation histories of the lowest mass galaxies in the local universe (e.g., Weisz et al. 2011). This latter approach suggests that the lowest mass galaxies attain total stellar masses of ∼10⁶ M_☉, over a Hubble time, implying mean SFRs of ∼10⁻⁵–10⁻⁴ M_☉ yr⁻¹. However, star formation is likely to be episodic, and characterized by periods when the SFR is markedly higher than this average, and other times when the star formation is inactive, and the galaxy is effectively invisible in the UV. Indeed, the study of Weisz et al. (2011) suggests that the SFR of local dwarfs was somewhat higher in the early universe than their average SFR over the Hubble time. Based on this, we adopt a cutoff value of L_min = 4 × 10²³ erg s⁻¹Hz⁻¹ which is equivalent to M_AB = −10, and is similar to that considered by other recent studies (Bouwens et al. 2012; Kuhlen & Faucher-Giguère 2012). This corresponds to an SFR of ≈5 × 10⁻⁴ M_☉ yr⁻¹. We note that when α < 2 (i.e., for redshifts less than z ∼ 7) the precise choice of L_min has little impact on the results.

3.2.1. Analysis I

We now consider this question: what is the probability that each host individually is fainter than the 2σ upper bound we have inferred for its luminosity? To this end, we calculate P_2σ for each host by setting L_host in Equation (4) equal to this upper bound.

The results are summarized in Table 3 and illustrated in Figure 4, which shows the CDFs for luminosity (expressed relative to L* at the redshift in question) of two bursts from our sample, together with the 2σ detection limits for the corresponding HST frames. We see that, given the above assumptions, it is not surprising to find individual hosts to be undetected since the majority of the likelihood lies below these 2σ bounds. However, the joint probability that none of the hosts are detected is only P(none) = ∏P_2σ = 0.17. While not a highly significant result, this does suggest that a non-evolving LF, in which more star formation was taking place in galaxies with luminosities around L*, would not sit comfortably with the apparent faintness of the GRB hosts.

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3.2.2. Analysis II

A weakness of the above approach is that it does not make full use of the joint probability of the formally measured fluxes at the positions of the whole sample of GRB hosts. As an alternative, we perform the following analysis, again with the aim of testing the evolving galaxy LFs proposed by Bouwens et al. (2012).

As before, we construct a CDF for host luminosity, but now turn this into an equivalent CDF for observed flux density F using the cosmological luminosity distance for the given redshift, having accounted for the aperture corrections. The next step is to convolve this with the observational errors appropriate for the given GRB field observation, in order to obtain a CDF for the observed host galaxy flux density:

$$\begin{equation} Y(F) = { \int _{F_{\mathrm{min}}}^{F_{\rm obs}} G * (F^{\prime } \phi _z(F^{\prime })){\it dF}^{\prime } \over \int _{F_{\mathrm{min}}}^{\infty } G * (F^{\prime } \phi _z(F^{\prime })){\it dF}^{\prime } }, \end{equation} \tag{ 5 }$$

where G is a Gaussian with a width σ dictated by the sky noise in each image, measured from numerous sky apertures of equal radius to the source aperture. F_obs is the formal flux measurement at the location of the GRB, and the minimum flux density, F_min, is appropriately scaled from the minimum luminosity, discussed above.

For illustration, the CDFs for two of our bursts are shown in Figure 5 (red curves), along with the CDFs for true host flux for comparison (blue curves). The green lines indicate the formal measured flux density at each GRB position. Note that for GRB 090423 we take a weighted average of the results for both filters, since they straddle 1500 Å, while in the analysis of GRB 060927 we use the F110W flux density, being the closest match to 1500 Å. If the assumptions we have made are correct, then we would expect these measured flux densities to be drawn randomly and uniformly from 0 to 1 on the cumulative probability axes. We can quantify this by calculating the average value for 〈Y(F_obs)〉 = 0.46, consistent with an expected value of 0.5 ± 0.12 from the Central Limit Theorem.

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However, we can also repeat the analysis, but this time fix the LF parameters for all the hosts to be that found at lower redshift. Specifically, we first choose α = 1.73 and M* = −20.97, as measured at z ≈ 3 by Reddy & Steidel (2009). Thus, we are testing here whether the hosts could be drawn from an LF whose shape (but not normalization) does not evolve from z ∼ 3 to high redshift. The results in this case for the same two bursts are shown in Figure 6. Now all the measured flux densities at the GRB locations are close to or below the Y = 0.5 level, with a mean 〈Y(F_obs)〉 = 0.29, thus rejecting the model at ≈96% confidence (≈98% if we took z = 6.5 for the redshift of GRB 090429B and averaged the F105W and F160W limits). An alternative test would be to fix the parameters to those found at z = 6–7 by McLure et al. (2010), α = 1.71 and M* = −20.08. Again, this model is weakly rejected at the ≈90% level (≈94%).

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Our result is not a highly significant, but does support an evolving galaxy LF, with an increasing proportion of star formation occurring in faint galaxies. It also demonstrates that a larger sample and/or deeper limits on host emission can begin to provide important tests of the high-z galaxy LF.

Whether UV radiation from star-forming galaxies is sufficient to bring about and sustain the reionization of the IGM above z ∼ 6 is a long-standing question (e.g., Loeb 2009). Recently, a number of authors have argued that an increasingly steep faint end to the galaxy LF, motivated by theoretical considerations, may be able to achieve this, without resorting to extremely high Lyman continuum escape fractions (e.g., Bouwens et al. 2012; Lorenzoni et al. 2011; Kuhlen & Faucher-Giguère 2012). However, the form, steepness, and faint-end cutoff of the galaxy LF at z > 7 are very poorly constrained by current data, since HST (and even in the longer-term JWST and ground-based 20–40 m class optical/NIR telescopes) can only directly probe the bright end of the LF.

If GRBs are sampling star formation in an unbiased way, as we argue they may be at early times, then they provide an alternative window on the total SFR which would ultimately circumvent the necessity to detect the individual galaxies in which the star formation is occurring. Our results, even from the small sample of high-redshift bursts currently available, already support an evolving galaxy LF over a non-evolving one, and therefore suggest that reionization may be brought about primarily from stars born in very faint protogalaxies.

It is worth considering further possible physical effects which may be biasing our conclusions. If a significant amount of star formation at high-z is actually dust enshrouded, which we believe is unlikely, then it would impact the observability of GRBs and their hosts, as well as the LBG samples. One would generally expect that the GRBs for which afterglows are detected and redshifts estimated would typically be in the lower dust systems, if there is indeed a wide range, and so in that sense, their hosts could still be compared directly to the (also preferentially dust free) LBG samples. From the point of view of reionization, of course it is the low-dust star formation that is more likely to have a high escape fraction of ionizing radiation, so our conclusions are likely to be valid in that respect.

As discussed in Section 1, we should also be concerned about possible GRB metallicity sensitivity. Both theoretical considerations and observational evidence (the blue colors of the LBG samples) argue that few star-forming galaxies at z > 6 will have high metallicities (e.g., supersolar) and therefore the low rate of GRBs in such systems seen at low redshift is not likely to be an important factor at high-z. Of course, it could be that a contrary effect becomes important at some point, for instance if very low metallicity populations produce fewer and/or fainter GRBs. However, if that were the case then we would expect to lose, if anything, the lower mass halos, where any metals produced are most easily lost. Hence, such an effect would seem unlikely to result in finding an unusually faint population of hosts, and so again our basic conclusion would only be strengthened.