Determining the Dust Extinction of Gamma-ray Burst Host Galaxies: A Direct Method Based on Optical and X-ray Photometry
The dust extinction of gamma-ray bursts (GRBs) host galaxies, containing important clues to the nature of GRB progenitors and crucial for dereddening, is still poorly known. Here we propose a straightforward method to determine the extinction of GRB host galaxies by comparing the observed optical spectra to the intrinsic ones extrapolated from the X-ray spectra. The rationale for this method is from the standard fireball model: if the optical flux decay index equals to that of the X-ray flux, then there is no break frequency between the optical and X-ray bands, therefore we can derive the intrinsic optical flux from the X-ray spectra. We apply this method to three GRBs of which the optical and X-ray fluxes have the same decay indices and another one with inferred cooling break frequency, and obtain the rest-frame extinction curves of their host galaxies. The derived extinction curves are gray and do not resemble any extinction curves of local galaxies (e.g. the Milk Way, the Small/Large Magellanic Clouds, or nearby starburst galaxies). The amount of extinction is rather large (with visual extinction 1.6–3.4). We model the derived extinction curves in terms of the silicate-graphite interstellar grain model. As expected from the “gray” nature of the derived extinction curve, the dust size distribution is skewed to large grains. We determine, for the first time, the local dust-to-gas ratios of GRB host galaxies using the model-derived dust parameters and the hydrogen column densities determined from X-ray absorptions.
It is widely acknowledged that the long-duration gamma-ray burst (GRB) is associated with the collapse of a massive star (Woosley 1993). Observational evidence supporting this collapsar model includes the underlying supernova components in the afterglow of many GRBs (Zeh et al. 2004) and the observed location of GRBs in star-forming galaxies and active star-forming regions within their host galaxies (Paczyński 1998, Fruchter et al. 2006). In this scenario, GRBs are born and explode inside dense, dusty environments. The huge -ray energy emission of GRBs is almost unaffected by absorptions, allowing them to be detected up to rather high redshifts (e.g. see Tagliaferri et al. 2005). Therefore, to study the dust and gas properties in the surrounding vicinity of GRBs is of great significance in understanding the interstellar medium (ISM) of star-forming galaxies throughout cosmic history. In addition, an accurate apprehension of the dust and gas immediate surrounding GRBs can also help (1) to reveal the nature of so-called “dark bursts” (i.e., whether the non-detection of some optical afterglow is due to dust extinction or the afterglow is intrinsically dark; see Lazzati et al. 2002 and references therein), (2) to detect the dust evolution with cosmic time, and (3) to correct for the extinction of optical emission in GRB afterglow analysis.
The dust extinction of GRB host galaxies is traditionally modeled using either the Milky Way (MW), the Large Magellanic Cloud (LMC), the Small Magellanic Cloud (SMC), or other presumed extinction curves (e.g. see Stratta et al. 2004; Kann et al. 2006; Schady et al. 2007; Starling et al. 2007; Tagliaferri et al. 2007). Recently, Chen et al. (2006) made the first effort to determine the extinction curves for GRB host galaxies without a priori assumption of the extinction law. The derived extinction curves differ from any known extinction laws of the Milky Way and external galaxies, challenging the traditional method commonly used in determining the extinction curves of GRB host galaxies.
In this work we propose a novel, straightforward method to determine the extinction of GRB host galaxies by comparing the observed optical spectra to the intrinsic ones extrapolated from the X-ray spectra. That such an analysis is possible follows from the standard fireball model. Based on the multi-wavelength afterglow photometry (including both the X-ray and optical data), we obtain the extinction curves of four selected bursts. We then model the size distribution and composition of the dust with the silicate-graphite interstellar grain model and obtain the dust-to-gas ratios in the local environment of GRBs.
The standard fireball model (Sari et al. 1998), which has been successful in explaining the overall properties of GRB afterglow (Mészáaros & Rees 1997), predicts that the afterglow emission is produced by synchrotron radiation of electrons accelerated by the forward shock. In this model, with typical parameters, the optical to X-ray spectra can be described by a broken power law with indices for or for , where is the cooling frequency and is the electron energy distribution index. In most cases, the cooling break position is hard to determine. If the decay indices of X-ray and optical bands are different, the cooling frequency lies between them, making it difficult to calculate the intrinsic optical flux from X-ray data. However, if the decay indices of X-ray and optical bands are the same, then the optical and X-ray should lie on the same spectral segment, rendering it possible to calculate the intrinsic flux density in any optical band from , where is the X-ray afterglow spectral index that we get from fitting the X-ray spectrum, and is the X-ray flux density. After corrected for the Galactic extinction using the reddening maps of Schlegel et al. (1998), the observed spectral energy distribution (SED) of GRB at redshift can be described as . Therefore, the extinction of the GRB host galaxy can be given by
With interpolated, we can obtain the extinction curves (normalized to band) of the GRB host galaxies.
We then fit the derived extinction curve with the standard silicate-graphite interstellar dust model which has successfully reproduced the extinction and IR emission of the MW galaxy, SMC and LMC (Weingartner & Draine 2001; Li & Draine 2001, 2002). The grain size distribution for both silicate and graphite is modeled with: , where is the grain radius (assumed spherical), ranging from = 0.005 to = 2.5, is the cut-off size. Note that it is assumed that both silicate dust and graphitic dust have the same size distribution. Let be the number fraction of graphitic dust, the mass fraction of graphitic dust is , where is the mass density of silicate material and is that of graphite.
With the fitted dust parameters, we can estimate the dust-to-gas ratio in each of the GRB host galaxies:
where is the hydrogen column density in the host galaxy; is the atomic weight of H; the factor “1.4” accounts for helium; and are the column mass density of graphite and silicate material, respectively:
is the normalized dust size distribution; The dust column density can be derived from
where and is the extinction efficiency of dust of radius at wavelength for graphite and silicate material, respectively.
We select four GRBs that have both optical and X-ray observations. Photometric data are taken from literature (see Tabled 1,2). The optical to X-ray spectra are extracted when the afterglow light-curve are in a steady power-law state (e.g. see Panaitescu & Kumar 2001, Fan & Piran 2006 for detailed analysis) to avoid complex phases (i.e. X-ray flares or re-brightening when the optical and X-ray emission are probably due to different components [Zhang et al. 2006]; see Fig. 1). For GRB 020405, GRB 030227 and GRB 060729, we adopt the spectra obtained when the cooling frequency falls below the optical band, indicating an intrinsic single power law spectrum through optical and X-ray bands as discussed above. The decay indices are all taken from literature except for GRB 060729 (around 0.35 day during plateau phase; for which is not available in literature) we derive by fitting the afterglow light curve between 0.2–0.6 day. For GRB 061126, the decay indices of X-ray and optical bands are different, indicating a break frequency lying between them. At , the R band afterglow shows a break (see Fig. 1d), which can be interpreted as the spectral break passing through the R band,111We note, however, that this burst, like many other Swift bursts, does not obey the closure relation in the standard afterglow model (Perley et al. 2007), which adds uncertainties to our analysis. But the uncertainty of break frequency does not appear to affect the shape of the derived extinction curve – as can be seen in Figure 2, the extinction curve for the other three bursts remains gray even if we ignore the GRB 061126 data. allowing us to calculate the intrinsic optical flux from .
We present in Table 3 the derived of the GRB host galaxies at every observed optical band and in Table 4 the -band extinction versus hydrogen column density () and the dust-to-gas ratio. The errors of the X-ray spectrum can bring about uncertainties on the extrapolated optical fluxes and thus on the derived . We estimate the errors of from (the X-ray spectral index) through Eq.1. Larger errors of the X-ray spectrum result in larger uncertainties in (e.g. see Table 3 and Fig. 2, GRB 020405). Most noticeably, the derived extinction curves of the four bursts are rather “gray” (see Fig. 2). Since all these extinction curves have very similar slope, we put all the extinction data of the four bursts together to fit them to the silicate-graphite grain model. The best fit parameters are , , and , with (obtained by summing up all wavebands and all GRBs, where is the uncertainty for a given GRB at a given band). A prominent feature is the considerably small (the canonical value of is 3.5), indicating a grain size distribution skewed towards substantially large grains. The main reason for is the absence of the 2175 extinction bump in the derived extinction curves which is generally attributed to small graphitic grains or PAHs.
Previous works concerning dust extinction of GRB host galaxies mostly focused on fitting the observed photometry with the intrinsic power-low spectrum reddened by certain “standard” extinction curves inferred from the Milky Way or nearby galaxies (e.g. see Starling et al. 2007). However, lacking a priori knowledge of the dust properties in high redshift galaxies harboring GRBs, we have no reason to assume that they are the same as in local universe (e.g. see Stratta et al. 2007). Chen et al. (2006), for the first time, derived the extinction curves of GRBs without a priori assumption of the extinction law, but they only used the optical data. In this work, with carefully selected afterglow data covering X-ray to optical/near-infrared bands, we obtain the extinction curve of four GRB host galaxies more directly and precisely, based only on the standard fireball model.
The “collapsar” model predicts GRBs to occur in active star-forming regions similar to Galactic molecular clouds (Jakobsson et al. 2006) which are heavily enshrouded by dust (Trentham et al. 2002; Tanvir et al. 2004). A recent dust scattering model proposed to account for the shallow-decay phase in Swift X-ray afterglow also requires large quantities of dust surrounding the GRBs (Shao & Dai 2007). Observations supporting the existence of large amount of dust include the emission and absorption features in some X-ray afterglows (Antonelli et al. 2000; Piro et al. 1999), large column densities of heavy elements revealed by optical spectroscopy studies (Savaglio & Fall 2004; Savaglio 2006), and the non-detection at optical wavelengths for more than half the well-localized GRBs (Jakobsson et al. 2004). In contradiction with these evidence, traditional SED fitting often finds small extinction, primarily because the best fit model in most cases is the SMC-type extinction which, with a steep rise into the far ultraviolet (UV), often requires a small to fit the spectrum (e.g. see Kann et al. 2006; Schady et al. 2007; Tagliaferri et al. 2007). Our work, showing considerably large compared to that fitted with traditional method, is more consistent with theoretical prediction and observations. In addition, Rol et al. (2007) found that for GRB 051022 a lower limit of was needed, which implies that at least in some GRBs the extinction is rather large.
The extinction curve derived in our work is flat, almost independent of wavelength, and is even “grayer” than the gray type of extinction curve obtained by Chen et al. (2006), similar to the Calzetti et al. (1994) law suitable for local starburst galaxies. This result is in good agreement with other works fitting the SEDs of these bursts (e.g. Stratta et al. 2005; A. Li et al. 2007, in preparation). In particular, Perley et al. (2007) found that for GRB 061126 the extinction curve is gray. Gray extinction has also been observed in Galactic dense clouds (Cardelli et al. 1988) and in the circumnuclear region of some AGNs (see Li 2007 for a review). Gray extinction is produced by a dust distribution biased towards large grains (see §4), which may form from (1) grain coagulation naturally expected in the dense circumstance near GRBs (Maiolino et al. 2001a,b), (2) the biased evaporation of smaller grains due to the intense X-ray and UV radiation up to 20 parsecs from the GRB (Waxman & Draine 2000, Fruchter et al. 2001, Savaglio et al. 2003), and (3) preferential destruction of small grains by high energy ions in fast shocks (Jones 2004). Perna et al. (2003) computed the extinction curve that is obtained if standard Galactic dust is exposed to a GRB lasting more than a few tens of seconds (three of the four bursts in our sample meet this requirement, see in Table 1) and found that the extinction curve can be very flat, chiming with our result. We favor the grain growth hypothesis since the preferential destruction of small grains only occurs in the immediate GRB environment (10–20 pc from the burst).
It has long been proposed that GRB afterglow radiation, as well as the prompt emission, can destroy dust grains and cause to decrease with time (e.g. see Vreeswijk 1999). We test this effect for GRB 060729, which is exceptionally bright in X-rays as well as at UV/optical wavelengths showing an unusually long unanimous plateau phase ( day). We derive at day (in the plateau phase) and at days (in normal decay phase) respectively (see Tables 1, 4), showing no significant dust destruction during this time. Detailed studies of dust destruction by GRBs will be presented in a forthcoming paper (Z. Jin et al. in preparation).
In accordance with previous works, we find that the average is smaller than that in the Milky Way,222An exception to this is GRB 060729, for which the derived dust-to-gas ratio is 10 times higher than that of the Milky Way (see Table 4). We note that, in estimating the dust-to-gas ratios, one uncertainty is the equivalent hydrogen column densities which is derived from the X-ray data by assuming a solar metallicity. If we take a metallicity of for GRB 060729 which is typical for GRB host galaxies (e.g. Fynbo et al. 2006; Stanek et al. 2006), the resulting dust-to-gas ratio of GRB 060729 (for which the current value seems to be too high, see Table 4) would shrink by roughly an order of magnitude, close to that in local galaxies. Besides, photoionization of the gas in GRB vicinities by the intense X-ray emission can result in a decrease of (Lazzati & Perna 2002). Richer observations combined with more detailed absorption spectroscopic studies will help clarify this issue in the near future. which is usually ascribed to a lower dust-to-gas ratio in GRB vicinities (e.g. see Watson et al. 2006). However, there is no obvious reason why the amount of dust is low in the dense environment surrounding GRBs. We note that the dust extinction is very sensitive to the dust size distribution, for larger grains the extinction (on a per unit mass basis) is low, but the amount of dust may be still high (e.g. see Li 2007). In fact, based on the model fit dust parameters, the dust-to-gas ratios for most bursts are larger than that in the Milky Way. On the other hand, grain growth through coagulation in dense molecular clouds enshrouding GRBs is expected and this would result in a dust size distribution biased in favour of large grains, a flat extinction curve, and a reduced .
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Note. – is the redshift of the burst; is the intrinsic optical/UV to near-IR spectral index derived from the standard afterglow model; is the X-ray flux density at 1 keV; is measured from the burst trigger time; is the duration of the burst; and , respectively the temporal decay index at optical and X-ray bands, are all taken from literature except GRB 060729, for which we obtain and by fitting the the afterglow light curve between 0.2–0.6 day. References. – (1) Berger et al. 2003; (2) Stratta et al. 2005; (3) Castro-Tirado et al. 2003; (4) Mereghetti et al. 2003; (5) Dirk Grupe et al. 2007; (6) Perley et al. 2007. 11footnotetext: Data are taken during the plateau phase. See §5 for discussion
Note. – The flux densities measured in the observer frame are taken at the time of the vertical lines reported in Fig. 1. All the data have been corrected for Galactic extinction
Note. – is the rest-frame -band extinction of GRB host galaxies; is the rest-frame equivalent column densities of hydrogen measured from X-ray absorption assuming a solar metal abundance at the same time when the multi-band spectra were taken (see §2)