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Probing Cosmic Dust of the Early Universe through High-Redshift Gamma-Ray Bursts

We explore the extinction properties of the dust in the distant universe through the afterglows of high-redshifted GRBs based on the"Drude"model which, unlike previous studies, does not require a prior assumption of template extinction laws. We select GRB070802 at z~2.45 (which shows clear evidence for the 2175\AA extinction bump) and GRB050904 at z~6.29, the 2nd most distant GRB observed to date. We fit their afterglow spectra to determine the extinction of their host galaxies. We find that (1) their extinction curves differ substantially from that of the Milky Way, the Small and Large Magellanic Clouds (which were widely adopted as template extinction laws in literature); (2) the 2175\AA extinction feature appears to be also present in GRB050904 at z~6.29; and (3) there does not appear to show strong evidence for a dependence of dust extinction on redshifts. The inferred extinction curves are closely reproduced in terms of a mixture of amorphous silicate and graphite, both of which are expected supernova condensates and have been identified in primitive meteorites as presolar grains originating from supernovae (which are considered as the main source of dust at high-z).


Introduction
Dust is present in the high-redshift (z > 2) universe, as evidenced by the reddening of background quasars, the depletion of heavy elements in quasar absorption systems, and the far infrared (IR) to millimeter (mm) thermal emission of distant quasars. Dust plays a crucial role in the formation and evolution history of stars and galaxies in the early universe. The importance of correcting for dust extinction in the universe is now widely recognized. In order to reveal the structure and evolution of the early universe, to use Type Ia supernovae (SNe) as standard candles, and to infer the cosmological star formation rate, it is essential to correct for the effects of dust extinction.
Gamma-ray bursts (GRBs), owing to their intense luminosity (emitting up to ∼ 10 53 erg), allow their detection up to very high redshifts at z 10 (Lamb & Reichart 2000). Particularly, the association of long-duration bursts with massive stars (and therefore with dusty regions of high-mass star formation) and the featureless, power law-like spectral shapes of their afterglows, make GRBs an excellent probe of the dust at high-redshifts.
In this Letter we explore the dust extinction of the host galaxies of GRB 070802 at z ≈ 2.45 and GRB 050904 at z ≈ 6.29. We aim at a quantitative examination of the nature of the dust in the early universe and attempt to address one of the hotly-debated questions in high-z astrophysics: do the dust properties evolve as a function of redshift (particularly at z > 5 where the dust source may be different)?

Dust Extinction Model
We characterize the dust extinction properties of GRB hosts with the extinction quantity (e.g. A Vr , the rest-frame visual extinction) and the wavelength-dependence of the extinction (i.e. A λ /A V or A ν /A V if expressed in frequency ν, often known as the "extinction curve" or "extinction law"). We derive A Vr and A λ /A V (or A ν /A V ) by fitting the ultraviolet (UV), optical, and near-IR afterglow photometry with a dust-reddened power-law model through where F ν is the afterglow photometry (with the Galactic foreground extinction corrected), β is the intrinsic power-law slope of the afterglow, F o is a normalization constant, A (1+z)ν is the rest-frame extinction, and z is the GRB redshift.
Unlike previous studies which often assume a template extinction law for A λ /A V (i.e., the extinction curves of GRB hosts are assumed to resemble that of the Milky Way [MW], the Small Magellanic Cloud [SMC], the Large Magellanic Cloud [LMC], the "Calzetti" attenuation law of starbust galaxies [Calzetti et al. 1994], or the relatively flat "Maiolino" curve of AGNs [Maiolino et al. 2001]), we take the "Drude" model proposed in Li et al. (2008a). This approach approximates the wavelength-dependence of the extinction by a simple formula consisting of four dimensionless parameters (c 1 , c 2 , c 3 , and c 4 ) where λ is in µm, the first term in the right-hand side represents the far-UV extinction rise, the second term and the third term respectively account for the near-IR/visible extinction and the 2175Å extinction bump.
Compared to models based on template extinction curves, the "Drude" model is preferred because (1) it eliminates the need for a prior assumption of template laws -after all, there is no reason to assume that the "true" extinction curves of GRB hosts should resemble any of those templates, and (2) the analytical formula (eq.2) on which the "Drude" model is based restores the widely-adopted MW, SMC, LMC, "Calzetti", and "Maiolino" templates -if the "true" extinction curve of a GRB host happens to resemble a certain template law, the "Drude" approach will allow us to restore it (see Li et al. 2008a).

Results
We apply the "Drude" model to GRB 070802 at z ≈ 2.45 and GRB 050904 at z ≈ 6.29. They are selected for the following reasons: (i) they span a wide range of redshifts, from the moderately high redshift of z ≈ 2.45 (GRB 070802) to the 2nd highest redshift observed to date of z ≈ 6.29 (GRB 050904); (ii) the afterglow photometry of GRB 070802 provides the most definite evidence for the presence of the 2175Å extinction feature in a GRB host galaxy (Krühler et al. 2008;Elíasdóttir et al. 2008); and (iii) the peculiar UKIRT z band (λ rest ≈ 1275Å) flux suppression of the GRB 050904 afterglow at 0.5 days and 1 day after the burst Stratta et al. 2007) was interpreted as evidence for an evolution of the dust properties at z > 6 ( Stratta et al. 2007).
Using eqs.(1,2) and the Levenberg-Marquardt minimization algorithm, we fit the broadband spectral energy distributions (SEDs) of the afterglows of these GRBs 1 with β, A V , c 1 , c 2 , c 3 and c 4 allowed to vary as free parameters. 2 Therefore, in the SED modeling we have six free parameters. 3 It is unfortunate that the number of model parameters (N para = 6) exceeds the number of photometry data points N data for GRB 050904 (N data = 4 for all three epochs; Haislip et al. 2006;Tagliaferri et al. 2005). With N data = 7, GRB 070802 has a better wavelength coverage. 4 We therefore use χ 2 /N data as a quality measure of the fit.
In Figure 1 we plot the "Drude" model fit to the afterglow SED of GRB 070802 as well as the derived extinction curve. The results for GRB 050904 at three different epochs after the burst are shown in Figure 2. We see in these figures that (1) the "Drude" model provides excellent fits to the observed SEDs; (2) the derived extinction curves differ substantially from the widely-adopted template extinction laws; (3) the 2175Å extinction feature appears to be also present in the afterglow spectra of GRB 050904, the 2nd most distant GRB observed to date, at epochs of 0.5 days and 1 day after the burst; (4) at an epoch of 3 days after the burst, the 2175Å feature appears to be absent in GRB 050904, suggesting that its carrier may have been destroyed by the burst; 5 and (5) there does not appear to show strong evidence for a dependence of dust extinction on redshifts (although the extinction curve does vary from one burst to another), as supported by a systematic study of > 20 GRBs at z > 2: the overall wavelength dependence of extinction, the steepness of the far-UV extinction rise, and the presence and strength of the 2175Å extinction bump, do not appear to show any dependence on redshifts (S.L. Liang & A. Li 2008, in preparation). The model parameters are tabulated in Table 1.
the overall flux level.

Discussion
In deriving the extinction of GRB hosts, a major problem with the models based on template extinction laws is that the wavelength-dependence of the extinction is fixed. For a featureless, power-law-like afterglow SED, this often leads to a preference of a SMCtype extinction and a small amount of A V (usually < 0.2 mag): obscured by a SMC-type extinction (which is roughly a power-law A λ ∝ λ −1.2 ), an intrinsic power-law-like afterglow SED remains featureless and becomes a steeper power-law. However, if the dust is "gray" (i.e. the extinction A λ only weakly varies with λ), the resulting dust-obscured afterglow SED will still be a featureless power-law, with the intrinsic power-law exponent unchanged. The possible presence of gray extinction has been suggested by a number of authors (e.g. see Savaglio et al. 2003, Savaglio & Fall 2004, Stratta et al. 2004, Chen et al. 2006, Li et al. 2008b, Perley et al. 2008. The "Drude" approach allows us to break the degeneracy between "gray" extinction and SMC-type extinction. Attempts have also been made to fit the afterglow SEDs with the MW, SMC and LMC template extinction laws. As shown in Figures 1,2, no acceptable fits are obtained, except that the MW model for GRB 070802 and the SMC model for GRB 050904 at an epoch of 3 days after the burst fit the observed SEDs reasonably well. But even for these two cases, the "Drude" approach fits better as can be seen in Figs. 1,2 and indicated by χ 2 /N data (see Table 1). Elásdóttir et al. (2008) tried to fit the VLT/FORS2 spectroscopy and the GROND photometry with the Fitzpatrick & Massa (1990; hereafter FM) parametrization as well as the MW-, LMC-, and SMC-type extinction. They found that satisfactory fits could be achieved only if one assumes a cooling break in the intrinsic spectrum, with the FM parametrization providing the best fit. However, one should caution that the FM parametrization is only valid for λ < 2700Å, while the GROND photometry of GRB 070802 extends from ∼ 1400Å to ∼ 6400Å (in the GRB rest-frame).
The afterglow SEDs of the bursts discussed here all show a flux suppression at λ ∼ 4 − 6 µm −1 and deviate appreciably from a power-law (except for GRB 050904 at 3 days after the burst). As shown in Figures 1,2, the flux suppression is closely accounted for in terms of dust with a 2175Å bump in its extinction. For GRB 070802, the derived 2175Å bump is comparable or even slightly stronger than that of the MW: for MW c 4 ≈ 0.05 while c 4 ≈ 0.06 for GRB 070802. To validate the suggested detection of the 2175Å extinction feature, we have also tried to fit the afterglow SEDs with the "Drude" approach but setting c 4 = 0 (i.e. no 2175Å extinction bump). It is found that the fits (with c 4 = 0) are much worse, as reflected from the substantially increased χ 2 /N data (see Table 1).
The 2175Å bump, first detected by Stecher (1965), is the strongest spectroscopic interstellar extinction feature. This feature is seen in extinction curves along lines of sight in the MW and LMC. 6 But it is rarely seen in the afterglow spectra of GRBs. So far, its possible detection is only reported in four bursts: GRB 970508 (Stratta et al. 2004), GRB 991216 (Kann et al. 2006, Vreeswijk et al. 2006, GRB 050802 (Schady et al. 2007), and GRB 070802 (Fynbo et al. 2007, Krühler et al. 2008, with the latter showing the clearest presence of the 2175Å extinction feature in its afterglow spectrum. In addition, Ellison et al. (2006) reported the detection of this feature in an intervening absorber at z ≈ 1.11 toward GRB 060418. But the host galaxy of GRB 060418 at z ≈ 1.49 seems to have a SMC-type extinction law.
Although the precise nature of the carrier of the 2175Å extinction feature remains unknown, it is generally accepted that it arises from small graphitic dust or a cosmic mixture of polycyclic aromatic hydrocarbon (PAH) molecules (Li & Draine 2001). In view of the detection of presolar graphite dust with a SN origin in primitive meteorites, it is not unreasonable to expect a 2175Å extinction bump for high-z objects since the dust at z > 5 6 Most SMC extinction curves have no detectable 2175Å bump (Prévot et al. 1984). But there exist regional variations in the SMC extinction curve. The SMC sight lines which show no 2175Å bump all pass through the SMC Bar regions of active star formation (Prévot et al. 1984;Gordon & Clayton 1998). The 2175Å bump is seen at least in one line of sight, Sk 143 (AvZ 456), which passes through the SMC wing, a region with much weaker star formation (Gordon & Clayton 1998). York et al. (2006) found no evidence for the 2175Å bump in the composite absorption spectra of 809 intervening QSO MgII absorbers at 1 < z < 1.9.
is thought to originate from Type II SNe. On the other hand, PAHs have been detected in ultraluminous IR galaxies and submm galaxies at z > 2 through their vibrational bands at 6.2, 7.7, 8.6 and 11.3 µm (see Lutz et al. 2005, Yan et al. 2005. PAHs were also seen in the Cloverleaf lensed QSO at z ≈ 2.56 (Lutz et al. 2007). If PAHs are indeed responsible for the 2175Å extinction, it would not be surprising to see this feature in high-z galaxies.
Finally, we fit the inferred extinction curves using a mixture of spherical amorphous silicate and graphite dust each with an exponential-cutoff power-law size distribution (e.g. see Kim et al. 1994) where the lower (upper) cutoff size a min (a max ) is taken to be 50Å (1 µm) for both silicate and graphite dust; the power-law indices α sil , α gra and the exponential-cutoff sizes a c,sil and a c,gra are treated as free parameters; A sil and A gra are related to the abundance of each species; and C sil ext (C gra ext ) is the extinction cross section of silicate (graphite) dust. As shown in Figure  1c and Figure 3, the silicate-graphite model closely reproduces the inferred extinction curves for both GRBs, including the 2175Å extinction bump (see Table 2 for the size parameters). The major mismatch occurs at λ ∼ 7 µm −1 which is probably due to the sudden rise of the silicate electronic absorption (see Kim & Martin 1995). We note that both silicate and graphite are expected SN condensates (Todini & Ferrara 2001, Nozawa et al. 2003. They have been identified as presolar grains in primitive meteorites originating from supernovae which are considered as the main source of dust at z > 5 (see Dwek et al. 2007).
By fitting the afterglow SEDs of GRB 050904 (z ≈ 6.29) with the extinction curve inferred for the distant BAL QSO at z ≈ 6.2 (which displays a plateau at λ −1 ∼ 3.3 − 5.9 µm −1 , Maiolino et al. 2004), Stratta et al. (2007) argued that the dust properties may evolve beyond z > 5. This seems to be supported by that the dust at z > 5 is probably produced by Type II SNe while in the local universe AGB stars are a major source of dust. However, this study together with a preliminary analysis of > 20 GRBs at z > 2 based on the "Drude" approach does not indicate any dependence of the dust extinction on redshift. A more thorough and systematic study of the dust extinction and IR emission properties of high-z GRBs is in progress and will be used to further explore whether the dust properties vary as a function of redshift.
We thank V.P. Kulkarni, S. Savaglio, G. Stratta, D. Watson and D.M. Wei for very helpful comments and suggestions. We are supported in part by a NASA/Swift Theory