DETECTION OF THREE GAMMA-RAY BURST HOST GALAXIES AT z ∼ 6

GRB 130606A was confirmed as a high-redshift source from optical spectroscopic observations with the Gran Telescopio Canarias $10.4\;{\rm{m}}$ telescope, giving z = 5.913 (Castro-Tirado et al. 2013). X-shooter observations by Hartoog et al. (2015), using the European Southern Observatory (ESO) Very Large Telescope (VLT), found a neutral hydrogen column density of $\mathrm{log}[{N}_{{\rm{H}}{\rm{I}}}({{\rm{cm}}}^{-2})]=19.91\pm 0.02$ based on the red damping wing of the Lyα absorption line, consistent with results from spectroscopy of the event by other groups (Chornock et al. 2013; Totani et al. 2014). Hartoog et al. (2015) estimated the average metallicity of the host galaxy to be $-1.7\lt [{\rm{M/H}}]\lt -0.9$, while multiple intervening absorption lines were detected at redshifts across the range z = 2.52 to z = 4.65, with a possible intervening system at z = 5.806. They also found host dust extinction along the line of sight, measured using the X-ray and optical spectral energy distribution (SED), to be consistent with zero and with a $3\sigma$ upper limit of ${A}_{{\rm{V}}}\lt 0.2\;{\rm{mag}}$.

GRB 050904 was confirmed as a high-redshift source from optical spectroscopic observations with the Subaru $8.2\;{\rm{m}}$ Telescope, giving z = 6.295 (Kawai et al. 2006). A detailed analysis was conducted by Totani et al. (2006), who measured a neutral hydrogen column density of $\mathrm{log}[{N}_{{\rm{H}}{\rm{I}}}({{\rm{cm}}}^{-2})]\approx 21.6$ from the damped Lyα system associated with the host galaxy, and detected an intervening absorber at z = 4.840. Thöne et al. (2013) re-analyzed the Subaru spectrum and estimated a metallicity of $[{\rm{M/H}}]\sim -1.6\pm 0.3$, based solely on the S ii ($\lambda 1253$) line (the other metal lines being saturated and/or blended). Considering the low resolution of the spectrum, this estimate should probably be regarded as a lower limit. Host extinction was determined to be ${A}_{{\rm{V}}}=0.01\pm 0.02\;{\rm{mag}}$ (Zafar et al. 2010).

A previous search for the host galaxy was conducted by Berger et al. (2007) with HST and Spitzer observations. They observed with both HST's Advanced Camera for Surveys (ACS) and Near Infrared Camera and Multi-Object Spectrometer (NICMOS), and their F850LP and F160W filters, respectively. Spitzer observations were carried out with the Infrared Array Camera in all four channels ($3.6,4.5,5.8,{\rm{and}}\;8.0\;\mu {\rm{m}}$). The host galaxy was undetected down to $3\sigma$ upper limits of ${m}_{{\rm{F160W}}}\gt 27.2\;{\rm{mag}}$ and ${m}_{3.6\mu {\rm{m}}}\gt 25.35\;{\rm{mag}}$ (see also Perley et al. 2016). The ACS data were re-reduced (Tanvir et al. 2012), and a $3\sigma$ upper limit of ${m}_{{\rm{F850LP}}}\gt 26.36\;{\rm{mag}}$ was estimated, accounting for flux loss from IGM absorption.

GRB 140515A was confirmed as a high-redshift source from optical spectroscopic observations with the Gemini-North $8.1\;{\rm{m}}$ Telescope, giving z = 6.327 (Chornock et al. 2014). Melandri et al. (2015) presented ESO/VLT X-shooter observations of the afterglow, estimating a neutral hydrogen column density of $\mathrm{log}[{N}_{{\rm{H}}{\rm{I}}}({{\rm{cm}}}^{-2})]\lesssim 18.5$ from the red damping wing of the Lyα absorption line. They determined $3\sigma$ upper limits for host galaxy metallicity, measuring $[{\rm{Si/H}}]\lt -1.4$, $[{\rm{O/H}}]\lt -1.1$, and $[{\rm{C/H}}]\lt -1.0$. An intervening absorber was detected at z = 4.804, and they also determined host extinction to be ${A}_{{\rm{V}}}\approx 0.1\;{\rm{mag}}$. In addition, Melandri et al. (2015) point out that the low hydrogen column would be consistent with GRB 140515A having exploded in a relatively low-density galactic environment.

Photometry of the three galaxies was performed using GAIA ¹⁶ and its Autophotom package. A catalog of objects from each HST image was built with GAIA's native SExtractor (Bertin & Arnouts 1996) support, employing a detection threshold of $2.5\sigma \;{{\rm{pixel}}}^{-1}$ and requiring three neighboring pixels above the background to be considered objects. Identifying the objects located at each of the GRBs positions as the potential host galaxies, their count rates were measured using circular apertures centered on their barycentric catalog coordinates. Sky background was estimated with 40 circular apertures of identical radii to the galaxy aperture, distributed within $6^{\prime\prime}$ of the galaxy aperture, and taking care to avoid other objects detected in the catalog to minimize background contamination. Standard deviation of the background aperture count rates was adopted as the photometric error, which is reasonable as we are in a background-limited regime.

With a small sample, we chose to customize each source aperture radius instead of applying the more typical fixed aperture radius for all sources. Aperture radii were varied incrementally, with the background-subtracted count rates plotted into curves of growth (CoG) for each GRB host galaxy (Figure 2). Cubic spline interpolation was used to estimate values between the measured aperture radii. The total count rate can be estimated from the level at which the CoG plateaus (these peak radii are shown as the green circles in Figure 1). Although taking the peak of the CoG might systematically overestimate brightness, given that at larger radii we begin to be contaminated by neighboring sources, our approach seems reasonable. As a compromise, we chose to average the three points at the peak of the CoG to represent the point at which the source counts reach the background level. Finally, we extrapolated the count rate using the tabulated encircled energy fraction¹⁷ and adopted the WFC3-IR infinite aperture zero point¹⁸ for the F140W filter.

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Based on Galactic foreground extinction maps from Schlafly & Finkbeiner (2011), we find for each case that only small corrections need to be applied (see Table 1). At the observed pivot wavelength, we estimate apparent magnitudes of ${m}_{{\lambda }_{{\rm{obs}}}}={26.34}_{-0.16}^{+0.14},{27.56}_{-0.22}^{+0.18},$ and ${28.30}_{-0.33}^{+0.25}$, respectively. For GRB 050904, the new result is consistent with the previous upper limits as discussed in Section 2.2. The most marginal detection is the case of GRB 140515A, but even here the significance is $\sim 4\sigma$, giving us confidence that it is a real source. Subsequent photometric analysis and results are discussed in Section 4 and are given in Table 2.

Curtis-Lake et al. (2016) recently studied a sample of LBGs from Hubble deep imaging in the z = 4 to z = 8 redshift range for their rest-frame UV sizes. They quantified galaxy size as the circularized half-light radius (${R}_{{\rm{half}}}$), the radius enclosing half the galaxies' total flux (see Section 3.1). Following their methodology, we determine ${R}_{{\rm{half}}}$ from our CoGs, taking the interpolated aperture radii that intersect the estimated half-maximum count rates. Curtis-Lake et al. (2016) used fixed apertures of radius $0\buildrel{\prime\prime}\over{.} 6$. We accounted for each field's point-spread function (PSF) by fitting a central Gaussian profile to bright, unsaturated, uncontaminated stars and averaging the results.

We measured ${\sigma }_{{\rm{PSF}}}=0\buildrel{\prime\prime}\over{.} 106$ for the field of GRB 130606A, and ${\sigma }_{{\rm{PSF}}}=0\buildrel{\prime\prime}\over{.} 127$ for the fields of GRBs 050904 and 140515A. There is also an additional correction to account for the wings of the PSF which is estimated using the simulations of Curtis-Lake et al. (2016). After the total PSF correction, our half-light radii are determined to be ${R}_{{\rm{half}}}={0.15}_{-0.02}^{+0.02},{0.11}_{-0.03}^{+0.03},$ and ${0.12}_{-0.04}^{+0.05}\;{\rm{arcsec}}$ for GRBs 130606A, 050904, and 140515A, respectively.

Our observations of the field of GRB 140515A were obtained only $8.5\;{\rm{months}}$ after the GRB event, and it is therefore possible, that our photometry could be contaminated by the fading afterglow. A reasonable upper limit to this contamination can be obtained by taking the flux in a small ($0\buildrel{\prime\prime}\over{.} 1$ radius) aperture at the location of the afterglow, and assuming this is entirely due to a point source. This leads to a maximum contamination of $\approx 4\;{\rm{nJy}}$. Alternatively, considering the latest reported infrared photometry, ${m}_{J,H}=20.9$ (Melandri et al. 2015), obtained at $\approx 17\;{\rm{hr}}$ post-burst, and a typical late-time power-law decay of $F\propto \;{t}^{-1.5}$ (see, e.g., Kann et al. 2010; N. R. Tanvir et al. 2016, in preparation), we would expect an afterglow flux density at the time of observation of $F\sim 2$ nJy. We adopt this latter figure as the best compromise correction for afterglow contamination and apply it to our reported photometric results in Table 2, Section 4.3, and Figures 3–5. We note that this correction is below the level of the photometric error, although it does reduce the overall significance of the detection to $\sim 3.3\sigma$.

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The other two fields were observed much longer post-GRB, and indeed the hosts in these cases are brighter, so any afterglow contamination should be negligible.

To verify that the photometric analysis presented here is robust and the results are independent of the specific procedure followed, we carried out an independent analysis of the images using the pipeline developed by the Brightest of Reionizing Galaxies survey, which searched for high-z galaxies (see Bradley et al. 2012; Trenti et al. 2012; Schmidt et al. 2014, for a detailed description). In short, we first derived variance (rms) maps from the weight maps produced by AstroDrizzle, then ran SExtractor in dual-image mode for a preliminary identification of the sources. Finally, we normalized the rms maps to account for correlated noise by measuring the background in random positions that are not associated to any source, and ran SExtractor with the normalized rms maps to construct the final catalog.

For GRB 050904 and GRB 130606A, the procedure yielded results consistent with the optimized measurements of Table 2, within the $1\sigma$ photometric uncertainty using standard SExtractor parameters for searches of high-z faint galaxies. For GRB 140515A, a standard run to identify the host galaxy failed, but setting a lower S/N threshold for detection and aggressive deblending identified the host galaxy at ${\rm{S}}/{\rm{N}}=3.05$. Since the source is close to the detection limit of the images, and is located near an extended structure, it is not surprising that a general source detection algorithm is not recovering it as efficiently as the primary photometric approach adopted in this paper. Nevertheless, this analysis confirms that there is an excess of flux at the GRB position in all three cases.

It is possible that the three detected objects are not the host galaxies of each GRB, but are instead intervening objects at a lower redshift. Deep imaging blueward of the Lyα break is currently not available, and we cannot confirm their drop-out nature. Despite this, we can estimate the probability of chance coincidence (${P}_{{\rm{cc}}}$) of a lower redshift galaxy based on galaxy number counts (as has been used for both long- and short-GRB hosts in the past; e.g., Fong et al. 2013). Following the method of Bloom et al. (2002):

$$\begin{eqnarray}&&{P}_{{\rm{cc}}}=1-\mathrm{exp}[-4\pi {R}_{{\rm{half}}}^{2}\sigma (\geqslant m)],\end{eqnarray} \tag{ 1 }$$

where $\sigma (\geqslant m)$ is the observed number density of galaxies brighter than magnitude m. This is the appropriate formulation when a GRB afterglow is localized within the detectable light of its host galaxy, as is the case here (Figure 1). The projected offsets from the host centers are shown in Table 2, and this small sample is consistent with the roughly 50% fraction of bursts found within the (blue light) half-light radius by Bloom et al. (2002).

Interpolating H-band number counts measured by Metcalfe et al. (2006) and using our calculated ${R}_{{\rm{half}}}$ measurements, we determine ${P}_{{\rm{cc}}}$ values of ≲2% (see Table 2) for all three objects. This statistic indicates that these are all likely the GRB host galaxies, and that the probability that two or even all three detections are lower redshift interlopers is very low.

An alternative approach to addressing this question is to directly measure the fraction of our images covered by visible galaxies. To do this we ran SExtractor to find all non-stars (using the same parameters discussed in Section 3.1). Summing their total area, we find that only $\approx 0.5$% of each HST image coincides with detectable galaxies, suggesting that the ${P}_{{\rm{cc}}}$ values evaluated above are, if anything, rather conservative for our fields.

As is common in spectroscopy of high-redshift continuum sources, absorption lines of intervening systems at lower redshifts are seen in all three GRB afterglows studied here (see Section 2). These absorption systems (in particular C iv at $z\gtrsim 2$) are typically associated with galaxies with impact parameters that are tens of kiloparsecs (many arcseconds) from the line of sight (Adelberger et al. 2005). Thus, a priori, it would be surprising if the galaxy responsible for absorption happened to coincide spatially with the GRB location. Indeed, there is no evidence for particularly strong absorption or dust attenuation that would be suggestive of these GRBs being directly behind a lower redshift galaxy.

Converting our apparent magnitudes from the observed pivot wavelength to literature comparison wavelengths of 1500–1600 Å requires knowledge of the underlying spectrum and its spectral index (${\beta }_{{\rm{UV}}}$), where the UV continuum is typically assumed to be a power-law with ${f}_{\lambda }\propto {\lambda }^{{\beta }_{{\rm{UV}}}}$. Duncan & Conselice (2015) compare a variety of UV continuum studies and find little difference between $z\sim 6$ and $z\sim 7$ (see their Figure 2) in the parameterization of the UV spectral index

$$\begin{eqnarray}&&{\beta }_{{\rm{UV}}}=(-2.05\pm 0.04)+(-0.13\pm 0.04)\times ({M}_{{\lambda }_{{\rm{rest}}}}+19.5).\end{eqnarray} \tag{ 2 }$$

We assume that this parameterization is applicable to our host galaxies and find ${\beta }_{{\rm{UV}}}$ values in the range −2.2 to −1.9. We also adopt an intrinsic scatter of ${\sigma }_{{\beta }_{{\rm{UV}}}}\approx 0.25$ based on the results of Rogers et al. (2014). Magnitudes are converted using the following equation:

$$\begin{eqnarray}&&{M}_{\lambda }={M}_{{\lambda }_{{\rm{obs}}}}-2.5\times ({\beta }_{{\rm{UV}}}+2)\times \mathrm{log}((1+z)\times \lambda /{\lambda }_{{\rm{obs}}}).\end{eqnarray} \tag{ 3 }$$

We estimate absolute magnitudes (M₁₆₀₀) in the range −20.5 to −18.5, a difference of only 0.02–0.03 from the observed wavelength (absolute) magnitudes. Considering the size of our observational errors, this difference is negligible.

Bouwens et al. (2015) present results for the UV galaxy LF from z = 4 to z = 10, based on large samples of LBGs with photometric redshifts. The LF is conventionally described using the Schechter function (Schechter 1976):

$$\begin{eqnarray}&&{LF}(x){dx}={\phi }^{* }{x}^{-\alpha }{e}^{-x}{dx},\end{eqnarray} \tag{ 4 }$$

where $x=L/L*$, with L* being the characteristic luminosity break between the faint end power-law slope (α) and the bright end exponential cutoff, while $\phi *$ is a normalization factor. Bouwens et al. (2015) present a parameterization of ${M}_{1600}^{* }$ (the magnitude corresponding to L*) using a linear fit as a function of redshift:

$$\begin{eqnarray}&&{M}_{1600}^{* }=(-20.95\pm 0.10)+(0.01\pm 0.06)\times (z-6).\end{eqnarray} \tag{ 5 }$$

From z = 5.913 to z = 6.327, ${M}_{1600}^{* }$ varies only by 0.004 mag, and hence we adopt the value ${M}_{1600}^{* }=-20.95\pm 0.12$. Converting our GRB host galaxies into comparable ratios gives 0.1–0.6 ${L}_{z=6}^{* }$ (see Table 2). This range is consistent with that found in deep LBG samples given the low extinction inferred from the afterglows, and these galaxies would likely also satisfy the color selection criteria for inclusion in these LBG samples (Bouwens et al. 2015).

Using our adopted cosmology, we convert our ${R}_{{\rm{half}}}$ values into kiloparsecs, giving the range 0.6–0.9 kpc (see Table 2). We plot these sizes against magnitudes in Figure 3, together with the LBG sample of Curtis-Lake et al. (2016). All three GRB host galaxies have typical ${R}_{{\rm{half}}}$ for their magnitudes. We also note that our GRB host galaxies have comparable ${R}_{{\rm{half}}}$ values to those of Lyα-selected galaxies at $z\sim 6$ (Malhotra et al. 2012).

The host galaxies were observed in the rest-frame 1900–2000 Å range, where the emission is dominated by the light of young, massive stars. Therefore, our photometry provides constraints on their star-formation histories. To investigate this, we employ the BPASS stellar population synthesis models (Eldridge & Stanway 2009; Stanway et al. 2016), which incorporate prescriptions for binary stellar evolution. We also choose to adopt their preferred broken power-law model for the differential stellar initial mass function, which has a slope of −1.3 between 0.1–0.5 M_⊙ and a slope of −2.35 between 0.5 and 100 M_⊙. Given the abundance constraints discussed in Section 2, from the GRB afterglow spectra, we use the lowest metallicity ($Z=0.001;$ i.e., $\sim 5 \% \;{Z}_{\odot }$) BPASS models.

We consider two cases that span a broad range of plausible histories. Model (A) has a continuous star-formation rate for $100\;{\rm{Myr}}$, which is reasonable given the age of the universe of $\sim 900\;{\rm{Myr}}$ at $z\sim 6$. Our alternative model (B) assumes just a single short-lived burst of star formation $10\;{\rm{Myr}}$ prior to the observation epoch, which would be reasonable if the GRB progenitors were born in the same starburst. Their likely high masses would imply a lifetime of this order. It is interesting to note that despite its young age, this model results in significant near-IR emission due to the contribution of red supergiants.

Starting with the SED BPASS models¹⁹ , we folded these through the radiative transfer program Cloudy ²⁰ (Ferland et al. 1998) to obtain the underlying nebular continuum and line emission spectrum excited by the BPASS stellar spectra. Next, we scaled the emission lines to an intrinsic spectral resolution of R = 1000. Finally, we transformed these models to the observed redshifts of the bursts and scaled them to our photometric results. For model (A), our inferred star-formation rates are $\mathrm{SFR}=5.3\pm 0.7,1.8\pm 0.3,$ and $0.8\pm 0.2\;{M}_{\odot }\;{\mathrm{yr}}^{-1}$, while the total mass of stars formed instantaneously in model (B) are ${ \mathcal M }=24.3\pm 3.4,8.4\pm 1.5,$ and $3.7\pm 1.1\;\times {10}^{7}\;{M}_{\odot }$ for the hosts of GRBs 130606A, 050904, and 140515A, respectively. These scaled models are shown for each GRB host in Figure 4.

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The above estimates implicitly assume negligible dust extinction, as is frequently done for galaxies at these redshifts (although see Wilkins et al. 2013, who argue for modest UV extinctions of 0.35–0.5 mag based on colors of $z\sim 7$ LBGs). For our cases, the observations of the afterglows support the proposition that the dust content is generally low, with ${A}_{{\rm{V}}}\lesssim 0.1\;{\rm{mag}}$ in each case (see Section 2). If we take these afterglow dust estimates as representative of the internal extinction in their hosts, we can find rest-frame extinctions at $\sim 2000\;\mathring{\rm{A}}$, as observed. Depending on the adopted extinction law, we find ${A}_{2000}\approx 2\mbox{--}3\;{A}_{{\rm{V}}}$ (Pei 1992; Calzetti et al. 2000). Hence, our star-formation rate values could increase by up to $\sim 30 \%$ if corrected for dust extinction.

It is interesting to compare the properties of our detected $z\sim 6$ hosts with the population of GRB hosts at lower redshifts. One problem in doing this is that samples of GRBs and their hosts tend to be inhomogeneous, incomplete, and biased, in particular against GRBs occurring in dusty galaxies for which no optical afterglows were found (e.g., Perley et al. 2013). The Optically Unbiased GRB Host (TOUGH) survey attempted to define a more statistically representative sample of hosts by identifying them using their X-ray localizations, and hence obtaining redshifts directly from the hosts, where an afterglow redshift was unavailable. The net result is a sample of 69 hosts for which 61 have redshifts and all but 1 of the remainder have photometric constraints placing them at $z\lesssim 6$ (Hjorth et al. 2012; Jakobsson et al. 2012).

Beyond $z\sim 3$ the TOUGH sample suffers from small number statistics, and we supplement it with additional hosts for which photometry is available in the literature. Although these additional data are more subject to optical selection effects and include some non-Swift GRBs, the larger sample size likely does provide a fuller picture of the host luminosity distribution at higher redshifts. The $1600\;\mathring{\rm{A}}$ UV luminosities of TOUGH VII (Schulze et al. 2015), Greiner et al. (2015), and Tanvir et al. (2012) are plotted in Figure 5 together with our new hosts. To ensure that the samples of TOUGH VII and Greiner et al. (2015) are comparable, we re-analyzed the latter sample using the methodology of TOUGH VII (Schulze et al. 2015). We also plot ${M}_{1600}^{* }$ as a function of redshift. At low redshifts ($z\lesssim 1$) the bulk of hosts are sub-L*, as expected if GRBs trace primarily sub-solar metallicity star formation (e.g., Levesque et al. 2010; Graham & Fruchter 2013; Trenti et al. 2015; Vergani et al. 2015). From $z\sim 1$ to $z\sim 6$ the break of the LF evolves rather little. While some hosts are found with $L\gt {L}^{* }$ up to $z\sim 4$, at higher redshifts such bright hosts are absent, consistent with a steepening galaxy LF (see Bouwens et al. 2015), with star formation predominantly occurring in faint galaxies.

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Our primary comparison images were obtained with the United Kingdom Infrared Telescope (UKIRT) Wide Field Camera (WFCAM) in the Z, J, and K bands. These wide-field images are astrometrically calibrated to the Two Micron All-Sky Survey (2MASS) system. We made use of 12 field stars which were well detected in the WFCAM images and visible in the HST fields.

In fact, the independent estimates of the afterglow position from the three bands agree to better than this error, so we average them to obtain the final best estimate.

In this case, our primary astrometric comparison was with several UKIRT/WFCAM images taken in the J, H, and K bands, which we co-added to increase the S/N. A rather higher scatter in the mapping to the HST image was noticed for stars in this field, possibly due to small proper motions during the intervening decade from the burst occurrence. We therefore utilized four compact galaxies as well as three stars to make the astrometric comparison.

We also analyzed the HST/NICMOS image reported by Berger et al. (2007), finding a consistent location within the errors, although the S/N of the afterglow was rather low.

We used Gemini-North Gemini Multi-Object Spectrograph (GMOS) imaging as the astrometric comparison, utilizing eight stars that were also on our HST images. The seeing was good on the GMOS image ($\approx 0\buildrel{\prime\prime}\over{.} 5$), and the S/N high ($\approx 100$).