DIVERSE PROPERTIES OF INTERSTELLAR MEDIUM EMBEDDING GAMMA-RAY BURSTS AT THE EPOCH OF REIONIZATION

We first describe the physical conditions of the ISM that embeds GRBs on parsec scales. The left (right) panel of Figure 1 shows the distribution of GRB rate in the density–temperature (density–metallicity) parameter space. We see two separate concentrations of GRBs in the n–T plane, with (n_H, T) equal to (10^−2.5 cm⁻³, 10^7.5 K) and (10^4.0 cm⁻³, 10^3.8 K), respectively.

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It must be made clear that the density and temperature are defined on the local gas cell of scale of a few parsecs on which a GRB sits. The appearance of GRB afterglow spectra depends, in most cases, more strongly on the properties of gas along the line of sight rather than the gas immediately embedding them, as will be shown later. It is seen that most of the GRBs reside in the low-density, high-temperature peak, contributing to 87% of GRBs. It is easy to identify two corresponding concentrations in the Z–n plane in the right panel: the low-density, high-temperature peak corresponds the high-metallicity peak in the range [ − 1.5, 0.5] in solar units, while the high-density, low-temperature peak corresponds the low-metallicity peak in the range [ − 2, −1]. We note that super solar metallicities in hot winds driven by type II supernova explosions in starburst galaxies in conditions similar to those of our simulated galaxies are locally observed. For example, Konami et al. (2011) observe the metallicity of hot X-ray gas of two to three times the solar value in M82. Martin et al. (2002) find that the best-fit model for the hot X-ray gas metallicity in dwarf starburst galaxy NGC 1569 is solar, although a metallicity as high as five times solar still gives a χ² value only about 0.1% larger than the best-fit model; on the contrary, the model with 0.25 times solar has a much worse χ² value. The extant observations of GRB afterglow spectra do not have the capability to detect the metallicity of the X-ray absorbing medium of relatively low column density. Metallicities of lower temperature gas phases are observed and are predicted to be substantially subsolar, as will be shown later in Figure 3.

The (n_H, T) = (10^4.0 cm⁻³, 10^3.8 K) peak coincides with the cores of dense gas clouds in the simulation, where star formation is centered. The temperature of 10^3.8 K is mostly produced by atomic hydrogen cooling and the lower-temperature extension due to metal cooling is included in the simulation. As a numerical example, for a gas parcel of density 10⁴ cm⁻³, temperature of 10⁴ K, and metallicity of 1% of solar value, the cooling time is about 400 years, which is much shorter than relevant dynamic timescales. It is thus clear that the cold density phase seen in our simulation is easily understandable. However, due to lack of treatment for molecular hydrogen cooling, gas is unable to cool significantly below ∼10⁴ K. Had we included molecular hydrogen cooling and low-temperature metal cooling, we expect the gas to cool approximately isobarically to about 20 K. Thus, we prefer not to infer any observable properties of GRBs that would depend strongly on the nature of this cold gas phase, such as molecular clouds. It is more appropriate to treat (n_H, T) = (10^4.0 cm⁻³, 10^3.8 K) as bounds: (n_H, T) = (> 10^4.0 cm⁻³, <10^3.8 K). This is also why we present our results for the high-density, low-temperature regions as bounds in the abstract and conclusions sections, as well as in places where clarification is helpful.

The noticeable sub-dominance of GRBs residing in very high-density (n ∼ 10⁴ cm⁻³) star-forming regions suggests that a large number of stars are displaced from their birth clouds. This may be achieved by substantial relative motions between stars and their birth clouds due to hydrodynamic interactions of the later or dynamical effects of stars. As a numerical illustration for the former possibility, a relative motion of 10 km s⁻¹ between the birth cloud and the star would yield a displacement of 100 pc in a lifetime of 10 Myr. We note that the runaway OB stars in our simulation have typical velocities relative to the birth clouds of 20–40 km s⁻¹. Thus, the runaway OB stars have contributed significantly to displacing GRBs from their birth clouds. The GRBs being in a hot, low-density environment is also a result of supernova heating by earlier supernovae exploding in the birth clouds. We estimate that these two effects are about equally responsible for placing most of the GRBs in low-density, high-temperature regions. While it is not possible to locate GRBs within the host galaxies at high redshift at this time, observations of low-redshift GRBs may still be instructive. Le Floc'h et al. (2012) show that GRB 980425 occurring in a nearby (z = 0.0085) SBc-type dwarf galaxy appears to be displaced from the nearest H ii region by 0.9 kpc, which is in fact significantly larger than the displacement distances for the vast majority of our simulated GRBs in high-redshift galaxies.

Interestingly, the optical afterglow luminosity has a bimodal distribution at 12 hr after trigger (Nardini et al. 2008). The bimodal distribution of volumetric density seen in the left panel of Figure 1 alone should produce a bimodal distribution of the afterglows with respect to break frequencies, luminosities, and break times, etc. (e.g., Sari et al. 1998). We cannot make detailed comparisons because the circumburst density of the high-n_H GRB subset is underestimated due to our limited resolution and because it remains uncertain if the appearance of GRB afterglows would also depend strongly on intervening material (dust obscuration, etc.). The complex situations seen in simulations may account for the observed bimodality of afterglows without having to invoke intrinsic bimodality of GRBs.

One of the most important points that this paper hopes to highlight and convey is that the appearances of the afterglows of GRBs are not solely determined by the circumburst medium in their immediate vicinity (e.g., the physical conditions shown in Figure 1 are on parsec scales centered on GRBs). They also strongly depend on the line of sight beyond the immediate circumburst medium through the ISM in the host galaxy, which we now quantify. Let us first give the meaning for our chosen value of the intervening neutral hydrogen column density $N_{\rm H\,\scriptsize{I}}=10^{19}$ cm⁻², which is used in Figure 1 to separate GRBs into separate groups. Figure 2 shows the distribution of neutral hydrogen column density integrated along the line of sight for all GRBs, separately for halos in five mass ranges. A bimodal distribution of $N_{\rm H\,\scriptsize{I}}$ is seen, peaked at $N_{\rm H\,\scriptsize{I}}\sim 10^{21-22}$ cm⁻² and $N_{\rm H\,\scriptsize{I}}\sim 10^{16-17}$ cm⁻², respectively, and well separated by $N_{\rm H\,\scriptsize{I}}\sim 10^{19}$ cm⁻². It is clear that the bimodality exists for all halo masses surveyed. The low $N_{\rm H\,\scriptsize{I}}$ peak is rather broad, extending all the way to $N_{\rm H\,\scriptsize{I}}=10^{11}$ cm⁻², suggesting some locations of GRBs well into the diffused hot ISM. There is a noticeable dip in the neutral hydrogen column density distribution at ∼10¹⁴ cm⁻² for the most massive galaxies of ⩾10¹⁰ M_☉. We attribute this to more significant shock heating in the most massive halos.

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Returning to Figure 1, it is now easy to see that the GRBs in the low-$N_{\rm H\,\scriptsize{I}}$ (⩽10¹⁹ cm⁻²) peak in Figure 2 is composed of only one set of GRBs situated in the low-density environment around (10^−2.5 cm⁻³, 10^7.5 K), shown as the red contours in Figure 1. The high-$N_{\rm H\,\scriptsize{I}}$ (⩾10¹⁹ cm⁻²) peak in Figure 2, on the other hand, consists of a combination of two separate populations with distinctly different circumburst mediums, which correspond to two separate loci of the blue contours at (10^−2.5 cm⁻³, 10^7.5 K) and (10^4.0 cm⁻³, 10^3.8 K) in Figure 1.

The two apparently different groups of GRBs situated around (n_H, T) = (10^−2.5 cm⁻³, 10^7.5 K)—one with low $N_{\rm H\,\scriptsize{I}}$ ⩽ 10¹⁹ cm⁻² (red) and the other with low $N_{\rm H\,\scriptsize{I}}$ ⩾ 10¹⁹ cm⁻² (blue)—are due entirely to the line of sight through the ISM of the host galaxy. Overall, we find that 38% of GRBs have $N_{\rm H\,\scriptsize{I}}$ ⩽ 10¹⁷ cm⁻² (i.e., optically thin to Lyman continuum), whereas 44% have $N_{\rm H\,\scriptsize{I}}$ ⩾ 10^20.3 cm⁻² (i.e., containing a damped Lyα system). It is clear that various properties of the afterglows of GRBs, even sitting in the same very local environment on parsec scales, may appear different due to different intervening interstellar gas and dust along the line of sight through the host galaxy. In summary so far, there are three separate populations of GRB afterglows that are expected, if our model is correct. One might classify them in the following simple way. (1) HnHN = (high volumetric density n ∼ 10⁴ cm⁻³, high neutral column density $N_{\rm H\,\scriptsize{I}}$ ⩾ 10¹⁹ cm⁻²); (2) LnHN = (low volumetric density n ∼ 10^−2.5 cm⁻³, high neutral column density $N_{\rm H\,\scriptsize{I}}$ ⩾ 10¹⁹ cm⁻²); (3) LnLN = (low volumetric density n ∼ 10^−2.5 cm⁻³, high neutral column density $N_{\rm H\,\scriptsize{I}}$ ⩽ 10¹⁹ cm⁻²). Again, types (2) and (3) are a result of different viewing angles, where type (2) is due to viewing angles through largely hot ionized gas and type (3) viewing angles, in addition, going through cold and dense gas.

Laskar et al. (2014) analyze multi-wavelength observations of the afterglow of GRB 120521C (z ∼ 6) and re-analyze two previous GRBs at z > 6 (GRB 050904 and 090423) and conclude that the circumburst medium has a volumetric density of n_H ⩽ 0.05  cm⁻³ that is constant. The GRBs in the LnHN or LnLN group provide the right match to the observations. While the statistic is still small, it is expected that about 87% of GRBs should arise in either the LnHN or LnLN group.

Observations of GRB 050904 at z = 6.3 reveal that it contains damped Lyα (DLAs) systems in the host galaxy of column density $N_{\rm H\,\scriptsize{I}}=10^{21.6}$ cm⁻² and metallicity of Z = −2.6 to −1 (Totani et al. 2006; Kawai et al. 2006). Based on X-ray observations, Campana et al. (2007) conclude that Z ⩾ 0.03 Z_☉ for GRB 050904. The evidence thus suggests that GRB 050904 likely resides in a dense environment, although we cannot be completely sure because the metallicity range of the low-density peak (right panel of Figure 1) overlaps with the observed range. It is useful at this juncture to distinguish between the metallicity of the local environment of a GRB and that of absorbers in the GRB afterglow spectrum.

Let us now turn to the expected metallicity of UV/optical absorbers in the GRB afterflow spectra. Figure 3 shows the probability distribution functions (PDFs) of total hydrogen-column-density-weighted metallicity of gas along the line of sight, excluding gas hotter than 10⁶ K, for the three sub-populations of GRBs. We see that for all three GRB groups, the metallicity of the absorbers in the GRB spectra peaks in the range of −3 to −1. Thus, it is now clear that our model can easily account for the observed properties of GRB 050904. The additional evidence based on the analysis of the equivalent width ratio of the fine structure transition lines Si ii* λ1264.7 and Si ii λ1260.4 implies the electron density of log n_e = 2.3 ± 0.7. Furthermore, the magnitude of the optical afterglow at 3.4 days after the burst favors a high-density circumburst medium. In combination, it appears that GRB 050904 is likely in a dense environment, being of the HnHN group. This appears to be at minor odds with our model since we only expect 13% of GRBs to arise in the HnHN group. It would be highly desirable to obtain a larger sample of high-z GRBs to provide a statistically firmer test.

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Analyses of observations of GRB 130606A at z = 5.9 indicate that it likely contains a sub-DLA system of $N_{\rm H\,\scriptsize{I}}\sim 10^{19.8}$ cm⁻² in the host galaxy (Totani et al. 2013; Castro-Tirado et al. 2013). The inferred low metallicity of −1.8 to −0.8 in solar units (Castro-Tirado et al. 2013) and −1.3 to −0.5 (Chornock et al. 2013), in conjunction with the $N_{\rm H\,\scriptsize{I}}$, suggests that GRB 130606A may reside in a low-density environment with a foreground sub-DLA system in the host galaxy. This proposal is consistent with the evidence of detection of highly ionized species (e.g., N v and Si iv; Castro-Tirado et al. 2013). It seems likely that GRB 130606A belongs to the LnHN group.

It is easy to see that in our model the metallicity distribution of UV/optical absorbers in GRB afterglow spectra is wide, which itself is due to the very inhomogeneous metallicity distributions in the ISM of the host galaxies. Thus, it would be a rather chancy practice trying to infer the metallicity of the host galaxy solely based on a small number (typically one) of GRB afterglow absorption spectra.

The reader has already clearly seen that the distributions of all concerned physical quantities, including metallicity, density, and total and neutral hydrogen column density, are wide. We will add yet one more quantity and show the cumulative distributions of the ratio of neutral hydrogen to total hydrogen column density for the three groups in the right panel of Figure 4. We see that for GRBs in the LnLN group, the neutral hydrogen to total hydrogen column ratio is significantly less than unity. Even for the HnHN and LnHN groups, (10%, 14%) of GRBs have a ratio less than 0.1. In other words, it is generally a pretty poor assumption that the apparent absorbers in the GRB afterglow spectra are mainly neutral. This indicates that the so-called "missing gas problem" (e.g., Schady et al. 2011) may be accommodated in this model.

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The left panel of Figure 4 shows the PDFs of the total hydrogen column density for the three sub-populations of GRBs, which are most relevant for probing GRB X-ray afterglows and hence a useful test of our model. One expectation from our model is that the vast majority of GRBs sitting in low-density circumburst medium (LnHN + LnLN) do not have Compton-thick obscuring gas. This prediction is verifiable with a combination of afterglow light curves and X-ray observations. On the other hand, one expects from our model that a significant fraction of the GRBs sitting in high-density circumburst medium (HnHN) have an extended high-N_H tail and dominate the GRBs with N_H ⩾ 10²³ cm⁻². Quantitatively, we find that (45%, 3%) of GRBs have N_H ⩾ (10²³, 10²⁴) cm⁻²; it is noted that these two numbers are likely lower bounds due to possible numerical resolution effects. As already noted earlier, it is seen from the right panel that the GRBs in the LnLN group are intervened by highly ionized gas peaking at an average neutral fraction of ∼10⁻⁴, with no cases having a neutral fraction exceeding 10⁻¹. In contrast, for GRBs in both the LnHN and HnHN groups, more than 50% of them have an average neutral fraction greater than ∼10⁻¹.

We now turn to the issue of dust obscuration. The left panel of Figure 5 shows the PDFs of visual extinction A_V. It is noted that the simulation does not follow dust formation explicitly. Thus, we have adopted the well-known empirical relation between metal column density and visual extinction: A_V = (N_H/10²¹  cm⁻²)(Z/ Z_☉) (Draine 2003). While the applicability of the relation derived from local observations is uncertain, detailed analysis of galaxy colors at EoR suggests that the simulated galaxies based on this relation give rise to self-consistent results when comparing to observations (Kimm & Cen 2013; Cen & Kimm 2014). Moreover, direct observations of dust suggest that this relation holds well in other galaxies locally and in galaxies and damped Lyman alpha systems at moderate to high redshift (e.g., Draine et al. 2007; De Cia et al. 2013; Draine et al. 2014; Fisher et al. 2014). Nevertheless, it is possible that the normalization factor in front of the relation is probably uncertain to the order of unity.

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It is evident that a significant fraction of GRBs in the high HnHL group (blue solid curve) are heavily dust obscured, where (53%,16%) of GRBs in the HnHL group have A_V ⩾ (1, 10). At the other extreme, we see that the GRBs in the LnLN group (red dashed curve) have negligible dust columns with no case of A_V ⩾ 0.3; nevertheless, it is worth pointing out that even for this set of GRBs, 12% has an A_V ⩾ 0.03 due largely to dust in high-temperature gas. The GRBs in the LnHN group (green dotted curve) are situated in between the above two groups, with a small but non-negligible fraction (7%) at A_V > 1. Observationally, the issue of dust in high-z GRB hosts is less than settled. Zafar et al. (2010), based on a reanalysis of the multi-epoch data of the afterglow of GRB 050904 at z = 6.3, conclude that there is no evidence of dust. Given that the neutral column density of the in situ DLA for GRB 050904 is $N_{\rm H\,\scriptsize{I}}=10^{21.6}$ cm⁻² and low-metallicity Z = −2.6 to −1 (Totani et al. 2006; Kawai et al. 2006), an A_V ∼ 0.01 is possible, if one adopts the lower-metallicity value that is statistically allowed in our model (see the right panel of Figure 1). Thus, both the low extinction and a standard ratio of dust to metals are still consistent with the observations. Our model indicates that 9% of GRBs have A_V ⩾ 1. Thus, with a z ⩾ 6 GRB sample of size 11, one expects to see one GRB with n_H ∼ 10⁴ cm⁻³ that is significantly obscured by dust with A_V > 1. This may be testable with SWIFT data relatively soon.

The right panel of Figure 5 shows the PDFs of average gas temperature weighted by N_HZ, excluding gas with temperature greater than 10⁶ K (the exclusion is a crude way to say that dust in gas hotter than 10⁶ K is destroyed). The purpose of this plot is to provide an indication of the diversity of intervening gas with dust. One notes that the lines of sight of HnHL GRBs contain dust in cold medium (T ⩽ 10⁴ K), whereas those of high LnHN GRBs are dominated by dust residing in gas T ∼ 10^{4 − 5} K, and the LnLN GRBs are intervened by dust in hotter gas of T ⩾ 10⁵ K. Under the assumption that the hotter gas is presumably produced by shocks, which are more destructive to larger dust grains, one might infer that dust becomes increasingly grayer from HnHL to LnHN to LnLN. One expectation is that for some lines of sight, especially those for the LnHN and HnHN groups, the total dust column arises from multiple different temperature regions. This may provide a physical explanation for the observational indications of multiple dust components (e.g., Zafar et al. 2012).

As a side note on the star formation rate (SFR) of GRB hosts, Basa et al. (2012) place the SFR of GRB 080913 at z = 6.7 to be less than 0.9 M_☉ yr⁻¹. Berger et al. (2007) obtain an upper bound on the SFR of GRB 050904 at z = 6.3 less than 5.7 M_☉ yr⁻¹. From the simulations, we find that (42%, 57%, 66%) of GRBs occur in galaxies with an SFR less than (0.3, 1.0, 3.0) M_☉ yr⁻¹. Thus, while simulations and observations are in good agreement, larger data sets are needed to place the comparisons on a solid statistical ground.

Finally, we must stress that the analysis performed here has focused on the ISM embedding the GRBs at EoR. The exact details of the state of the IGM at EoR are uncertain both observationally and theoretically. The theoretical difficulty is in part computational because we do not have the capability to simulate a large enough volume to capture the reionization of the IGM self-consistently, while still having enough resolution for the ISM. The goal of this work is to present the signatures of the ISM theoretically, which is lacking. It may be argued that the properties of ISM in galaxies are somewhat detached from the properties of the IGM on large scales; in other words, the observed spectra of GRB afterglows at EoR may be considered to be imprinted by both ISM and IGM as a linear superposition. Consequently, a proper understanding of the ISM will not only aid in the interpretation of the ISM of galaxies at EoR but also is highly necessary for proper interpretation of the properties (neutral fraction, topology, etc.) of the IGM at EoR.