DUST EXTINCTION IN HIGH-z GALAXIES WITH GAMMA-RAY BURST AFTERGLOW SPECTROSCOPY: THE 2175 Å FEATURE AT z = 2.45^*

The study of extinction curves outside the MW is a challenging task and has mostly been limited to galaxies in the Local Group. While the M31 extinction curve resembles that of the MW (Bianchi et al. 1996), the extinction curves of the Large and Small Magellanic Clouds (LMC and SMC) show significant variation. Lines of sight in the LMC can be broadly put into two categories, one having extinction curves similar to that of the MW ("LMC average") and the other showing extinction curves with a much less prominent bump and a steeper rise into the UV ("LMC2 supershell" Nandy et al. 1981; Misselt et al. 1999; Gordon et al. 2003). While the phrase "LMC-type of extinction" refers to extinction curves of the second type (i.e., less prominent bump and a steep UV rise), it should be kept in mind that MW sightlines also exist in the LMC. Similarly, for the SMC, the canonical SMC extinction curve shows no evidence for a bump and an even steeper rise into the UV (Prevot et al. 1984; Gordon et al. 2003) although one out of five lines of sight shows the 2175 Å bump (Lequeux et al. 1982). It is also worth noting that there are a few known lines of sight in the MW with LMC-type of extinction (Clayton et al. 2000) and a single line of sight with a measured SMC-type of extinction (Valencic et al. 2003).

Relatively little is known about dust extinction outside the Local Group as the method of measuring extinction curves by comparing the spectra of single stars is not applicable at larger distances. Several methods have been attempted, including studying statistical samples of reddened and standard quasars (Pei et al. 1999; Vladilo et al. 2008), studying individual supernova (SN) Ia light curves and using gravitationally lensed quasars. A recent overview of these studies and their results can be found in Elíasdóttir et al. (2006). The SEDs of GRBs may also be used, as discussed in Section 1.3. These studies have found varying types of extinction which can deviate significantly from MW-type extinction, leaving open the question of how common MW type dust is. In particular, prior to the present study there have only been three robust detections of the 2175 Å bump in individual extragalactic systems beyond the local group. The first is in a lensing galaxy at a redshift of z = 0.83 (Motta et al. 2002). The second is from a damped Lyα system at z = 0.524 (Junkkarinen et al. 2004). The third is in an intervening absorber at z = 1.11 toward GRB 060418 (Ellison et al. 2006).

Extinction curves are the prime diagnostic tool available to study dust in the optical/UV regime. They depend sensitively on the composition of the dust (Henning et al. 2004), allowing estimates to be made of the nature and the origin of dust and its dependence on cosmic time, metallicity, etc. Furthermore, in studies of distant objects, e.g., using SNe Ia as standard candles or determining flux ratios of strongly lensed QSOs, it has become increasingly important to accurately determine the amount and wavelength dependence of the dust extinction.

Fitzpatrick & Massa (1986) studied the 2175 Å interstellar extinction bump in the direction of 45 reddened stars in the MW, and found that it displays a peak whose central wavelength λ₀ is remarkably constant with extreme deviation of only ∼± 17 Å from the mean position of λ₀ = 2174.4 Å. As this is significantly larger than the measurement uncertainty it seems to indicate a real, but small, variation of the peak position. The full width at half-maximum (FWHM) of the bump has a larger range of intrinsic values, from 360 to 600 Å. There seems to be no correlation between the width and the central wavelength of the bump.

The fact that the 2175 Å feature becomes progressively fainter in the MW, LMC, and SMC has been attributed to the progressively lower metal abundances of the LMC and SMC (Fitzpatrick 2004) or to differences in the radiative environment (Gordon et al. 1997; Clayton et al. 2000; Mattsson et al. 2008). Gordon et al. (2003) studied the differences in the extinction of the MW, SMC, and LMC finding tentative evidence that the bump strength correlates with the dust-to-gas ratio.

Noll et al. (2007) found in their study of 108 massive, UV-luminous galaxies at 1 < z < 2.5 that there is a correlation between heavy reddening and the presence of a 2175 Å feature. The least reddened objects have SEDs consistent with the average featureless and steep extinction curve of the SMC. For their objects at 1 < z < 1.5 a significant UV bump is present in galaxies that appear disk-like and which host a rather large fraction of intermediate-age stars (i.e., from 0.2 to 1–2 Gyr old). More clumpy and irregular objects seem to have extinction curves resembling those of nearby starburst galaxies.

Several candidates have been proposed as the dust particles responsible for the bump ranging from iron-poor silicate grains (Steel & Duley 1987) to carbonaceous materials such as carbon-onions (Henrard et al. 1997), graphite grains (Stecher & Donn 1965; Draine 1989) or the polycyclic aromatic hydrocarbons (PAHs) believed also to be responsible for the prominent broad emission features found in the mid-infrared (Duley & Seahra 1998; Duley 2006; Cecchi-Pestellini et al. 2008).

Graphite has been considered a very promising, though contentious, candidate for explaining the 2175 Å bump (e.g., Stecher & Donn 1965; Fitzpatrick & Massa 1986; Mathis 1994; Voshchinnikov 1990; Sorrell 1990; Draine & Malhotra 1993; Rouleau et al. 1997; Will & Aannestad 1999; Andersen et al. 2003; Clayton et al. 2003). In an extensive investigation, Draine & Malhotra (1993) conclude that if graphite particles are the carriers of the 2175 Å peak, a variation in their optical properties must be present, e.g., as a result of varying amounts of impurities, variations in crystallinity, or changes in its electronic structure due to surface effects. The observed lack of correlation between the central wavelength and the FWHM of the peak is therefore a challenge for the hypothesis that graphite particles are the source of this peak.

Large PAH molecules are expected to at least contribute to the 2175 Å feature as the interior carbon atoms have electronic orbitals closely resembling those in graphene and an oscillator strength for each C expected to be close to the value for graphite (Draine 2003). Joblin et al. (1992) have suggested that PAHs could be entirely responsible for the feature, which has been questioned by Mathis (1994) due to the lack of an absorption feature at about 3000 Å in the spectra of PAHs. Another argument against the PAHs as the main contributors is that the constancy in wavelength along with a rather wide variation in the width, seems surprising if the bump is caused by a mixture of widely varying materials. Such properties are more likely to occur as a result of coating (or surface hydrogenation) of carbon grains (Mathis 1994; Draine & Li 2007; Cecchi-Pestellini et al. 2008).

Finally, iron-poor silicates in the form of partially hydrogenated amorphous Mg₂SiO₄ particles have been suggested as the carriers of the 2175 Å peak (Steel & Duley 1987). The absorption is observed in silicates of greatly differing composition and under a wide range of different sample preparations and outgasing conditions. However, Mathis (1996) indicated that the silicates may be problematic as carriers.

It seems most plausible that the carrier of 2175 Å peak is a composition of graphitic and amorphous carbon phases, PAHs and glassy iron poor silicates. Various models have been proposed with different compositions (see, e.g., Mathis 1996; Draine 2003, and references therein).

GRB afterglows have very simple intrinsic synchrotron spectra which are essentially featureless power laws (f_ν ∝ ν^−β) across the wavelength range of interest for measuring extinction curves (e.g., Galama et al. 1998; Granot & Sari 2002; Sari et al. 1998). This is a significant advantage over using QSOs or galaxies as background objects. In cases where the GRB physics places the cooling frequency between the optical and X-ray regime (at the time of observation) there will be a cooling break in the spectrum leading to a change in spectral slope of Δβ = 0.5 (softer spectrum in the X-rays). The X-ray slope is usually around 1.0–1.2 (see, e.g., Liang et al. 2007) and so the intrinsic optical slope is typically between 0.5 and 1.2. Moreover, the optical-NIR range is typically well described by a single power-law segment.

Reichart (1998) first attempted to constrain the extinction toward GRB 970508 (see also Reichart 2001). Several subsequent studies confirmed that a simple SMC-type/linear extinction model provided good fits to observations of several GRB afterglows (Bloom et al. 1998; Castro-Tirado et al. 1999; Jensen et al. 2001; Fynbo et al. 2001a; Price et al. 2001; Savaglio & Fall 2004; Jakobsson et al. 2004b; Kann et al. 2006). Findings of a low dust-to-gas ratios in GRB afterglows exhibiting damped Lyα absorption in the GRB host galaxy supports the apparent prevalence of SMC-type dust in GRB environments (Jensen et al. 2001; Hjorth et al. 2003; Vreeswijk et al. 2004).

Gray (wavelength-independent) extinction laws (Galama et al. 2003; Stratta et al. 2007; Perley et al. 2008; Nardini et al. 2008) or MW dust (Kann et al. 2006; Schady et al. 2007) have been suggested in rare instances for GRB environments although it should be noted that these claims are somewhat model dependent (gray dust) or statistically insignificant (MW-type dust). The 2175 Å feature itself has been searched for and ruled out in GRB 050401 (Watson et al. 2006). In GRB 000926 (Fynbo et al. 2001a) and GRB 020124 (Hjorth et al. 2003) SMC-type extinction was preferred although the existence of a 2175 Å bump was not sampled by the broadband observations. Vreeswijk et al. (2006) found a bump in the spectrum of GRB 991216 but at 2360 Å if at the redshift of the GRB (z = 1.02). To be consistent with rest frame 2175 Å it would have to be due to an even more distant absorber at z = 1.19 which was however not detected as an absorption system in the afterglow spectrum. The first (and thus far, only) clear detection of the 2175 Å bump in the foreground of a GRB, consistent with a detected intervening Mg ii absorber (z = 1.1), was reported by Ellison et al. (2006).

A significant fraction of GRB afterglows are optically `dark' (Fynbo et al. 2001b; Jakobsson et al. 2004a; Rol et al. 2005). It is likely that a large fraction of these afterglows go undetected in the optical because of extinction (e.g., Djorgovski et al. 2001). Recently Jaunsen et al. (2008) and Tanvir et al. (2008) demonstrated the validity of this dust obscuration hypothesis by detecting two highly reddened systems. These studies highlight the difficulty in probing systems with significant extinction at high redshift: GRBs with high extinction are generally not accurately localized (because of the lack of an optical afterglow position) and there are no detailed constraints on their extinction laws, particularly in the UV, for systems with of order A_V ∼ 5. Such selection effects must be kept in mind before making statistical inferences from extinction laws of GRB afterglows.

Studies using the X-ray extrapolation to set limits on the total extinction (Vreeswijk et al. 1999) or using the optical spectral curvature to determine the reddening (Ramaprakash et al. 1998) have now been carried out for nearly a decade. These studies may be further improved if one obtains the largely extinction-free IR flux, typically needing observations in the mid-IR, and is the subject of our ongoing Spitzer campaign (see also Heng et al. 2008).

GRB 070802 (Barthelmy et al. 2007) was detected by Swift (Gehrels et al. 2004) on 2007 August 2.29682 UT. The ESO VLT started observations about 1 hr after the burst in rapid response mode, starting with a photometric sequence spanning from the B band through V, R, and I to the z band in excellent seeing conditions (≲0.5 arcsec) and at low air mass (≲1.4). We detected the source previously detected by Berger & Murphy (2007) in all bands (see Table 1). The source was very red and classifies as a dark burst according to the definition of Jakobsson et al. (2004a). Based on five R-band points taken from about 1 to 3 hr after the trigger we infer a decay slope of 0.62 ± 0.05 consistent with the measurement in Krühler et al. (2008) at the same time. We infer a celestial position of R.A.(J2000) = 02^h26^m3577, decl.(J2000) = −55°31'392 (calibrated against USNO-B1.0). Following the afterglow detection, spectroscopy was immediately started, using the FORS2 instrument equipped with the grism 300V (∼10 Å FWHM spectral resolution). A total of 5400 s of exposure were acquired, split into three exposures, with mean epoch of Aug 2.38935 UT (2.2 hr after the burst). The spectra were obtained in excellent seeing conditions (about 05) and a relatively small air mass of 1.2. We used a 10 slit and therefore slitloss should be negligible. The spectra were flux calibrated using a spectrum of the spectrophotometric standard star LTT1020 obtained on the same night.

The optical spectrum of the afterglow is shown in Figure 1. The afterglow spectrum is characterized by a red continuum with a broad dip centered at λ_obs ≈ 7500 Å. There is a break in the spectrum at λ_obs ≈  4250 Å blueward of which little residual flux, if any, is detected. We identify the latter feature as the imprint of the Lyα forest of absorption lines at z_abs < 2.5. Numerous narrow absorption lines are detected throughout the spectrum (see Table 2). The highest redshift absorber is a strong metal line system at z_abs = 2.4549, which we adopt as the GRB host galaxy redshift. In addition we detect two intervening Mg ii absorption systems at z = 2.078 and z = 2.292. The system at z = 2.078 is very strong with a rest-frame equivalent width of the 2796 Å line of W_r = 3.9 Å.

Zoom In Zoom Out Reset image size

2.1.1. H i Content and Metal Lines

We measured the total neutral hydrogen column density (in units of cm⁻² throughout) of the absorber at the GRB redshift by fitting a damped Lyα absorption line profile fixed at the redshift of the detected metal lines. Both the saturated core and the red damped wing of the Lyα line are constrained by the residual flux at λ_obs ⩾ 4250 Å. We derived log N(H i) = 21.5 ±  0.2 (see Figure 2).

Zoom In Zoom Out Reset image size

As listed in Table 2, a large number of metal species are identified at the GRB redshift. The detected lines from singly ionized elements are very strong compared to other GRB- or QSO-DLA sightlines. For instance, W_r = 2.9 Å for Si ii λ1526 is larger than for any LBG/GRB/QSO-DLA observed to date, hinting at a high metallicity (Prochaska et al. 2008). The rest-frame equivalent width of Si ii λ1808, W_r = 1.13 Å  is also the largest ever detected in any extragalactic sightline. Assuming the latter line is located on the linear part of the curve of growth implies that log N(Si ii) = 16.3. This is a very conservative lower limit to the actual column density and translates into a conservative lower limit on the metallicity of [Si/H]> − 0.8. Note also that Si could be depleted onto dust grains (Petitjean et al. 2002).

We further performed Voigt-profile fitting (see Table 3) using some of the weakest (least saturated) metal lines (see Figure 3). The absorption line at λ_obs ≈ 7000 Å is likely to be a blend of Zn ii and Mg i λ2026 with possibly similar strengths. It is therefore important to fit both transitions simultaneously. The other Zn ii (λ2062) line is also blended (with one of the Cr ii triplet lines). Therefore, the best line to estimate the metallicity remains Si ii λ1808. All lines were simultaneously fitted with a single component constraining their redshifts as well as their broadening parameter (assumed to be purely turbulent) to have identical values. We find [Si/H] = −0.46 ±  0.38 and also consistently get [Zn/H] = −0.50 ± 0.68. Assuming the Zn ii λ2026 line is located on the linear part of the curve-of-growth implies that [Zn/H] > − 0.35 but the actual metallicity could be lower than that due to the unknown contribution of the Mg i λ2026 line to the observed feature (see above).

Table 3. Ionic Column Densities of the GRB System

Ion	Transition lines used (Å)	log N (cm−2)
Si ii	1808	16.6(0) ± 0.3(2)
Zn ii	2026; 2062	13.6(7) ± 0.6(5)
Mg i	2026	14.4(1) ± 0.6(4)
C i	1560; 1656	14.9(5) ± 0.2(5)
Fe ii	2249; 2260a	16.1(6) ± 0.1(8)
Cr ii	2056; 2060; 2066a	14.0(4) ± 0.4(0)
Ni ii	1741	14.8(9) ± 0.2(8)
Mn ii	2576	13.8(9) ± 0.1(8)

Notes. The broadening parameter was b = 123 ±  74 km s⁻¹ in all cases. ^aEven though the FeII2249 and CrII2066 lines are not individually detected above 2σ in the spectrum we still use the appropriate regions in the spectrum to constrain the fits.

Download table as:  ASCIITypeset image

Zoom In Zoom Out Reset image size

The large error bars on the measured column densities are mainly a consequence of the large uncertainty on the broadening parameter b which we find to be: b = 123 ± 74 km s⁻¹. One might argue that b could be significantly smaller (e.g., b < 30 km s⁻¹) in which case the column densities would be much larger than found in our best fit. However, it has been shown that the width of metal line profiles in DLAs is larger at higher metallicities (Ledoux et al. 2006; Prochaska et al. 2008). Therefore, a large b value is consistent with the relatively high metallicity inferred, which is among the highest measured for any GRB (Fynbo et al. 2006).

The measured abundance ratios are consistent with what is seen in other GRB- or QSO-DLAs. We find that the mean depletion of Fe-peak elements (Fe, Cr, and Mn) compared to Si is ∼0.5 dex. This is not particularly high, but yet significant implying that dust is present in this system. According to our best fit, the Si metallicity could be as large as solar. This in fact is quite likely taking into account that Si is affected by dust depletion (Petitjean et al. 2002).

2.1.2. Neutral Species

2.1.3. Non Detection of Fe ii^⋆ in GRB 070802.

2.1.4. Constraints on the z = 2.078 Foreground Absorber Extinction

The X-ray telescope onboard Swift observed the afterglow of GRB 070802 beginning observations in photon counting mode at 147 s after the trigger time (t₀= 07:07:26 on 2007 August 2). The data were extracted and reduced in a standard way using the HEAsoft software (version 6.2) and the most recent calibration files. The X-ray spectrum (with a total exposure time of 3419 s in the interval t₀ + 147–t₀ + 16800 s) was extracted and fit with a power law with absorption fixed at the Galactic level (2.9 × 10²⁰ cm⁻²; Dickey & Lockman 1990) and freely variable absorption at the redshift of the host galaxy. The best fit resulted in a power law with a photon spectral index Γ = 2.02^+0.17_−0.15 (β = 1.02^+0.17_−0.15, 68% confidence level) and an equivalent absorbing hydrogen column density of 9.7^+0.6_−0.4 × 10²¹ cm⁻² at z = 2.45 assuming solar abundances. To produce the X-ray segment of the near-infrared to X-ray SED, this X-ray spectrum was normalized to the flux level obtained from the X-ray light curve at the SED time (t₀ + 3517 s) and corrected for both absorptions. No significant evidence (above the 1σ level) was found for spectral variations over the period of the spectrum, by comparing the first 400 s and the remainder of the observation.

K- and R-band observations of the host galaxy of GRB 070802 were obtained with the ESO VLT during the nights of 2007 September 27 and 2007 October 5 (57 and 65 days after the GRB). At the afterglow position, a source is clearly detected with R = 25.03 ±  0.10 (Figure 4). A faint source is also visible in K, with magnitude K = 21.70 ±  0.25. The centroid of the host is offset by 0.15 ±  0.04 arcsec with respect to the afterglow position (1.2 kpc at z = 2.455). From the observed K magnitude (rest frame 6270 Å), and assuming a power-law spectrum consistent with the R−K color (f_ν ∝ ν^−1.3), we can estimate the absolute B-band magnitude of the host to be M_B = −21.0 (uncorrected for extinction) which is fairly luminous for a GRB host (Fruchter et al. 2006; Savaglio et al. 2009).

Zoom In Zoom Out Reset image size

If there is no cooling break between the X-ray and optical regimes, clearly the X-ray and optical emission lie on the same power law. Under this assumption, the intrinsic slope and normalization in the optical can therefore be derived from a simple extrapolation of the X-ray data. Any discrepancy between the observed optical flux and the extrapolation is then interpreted as extinction along the line of sight. A slight complication is introduced by the nonsimultaneity of the observations in different bands, since the flux decays with time. However, the uncertainty introduced by this correction is not large, since the optical photometry mean times are I = t₀ + 3517 s, V = t₀ + 3627 s, and R is interpolated between observations at t₀ + 3249 s and t₀ = 3949 s, and the X-ray flux is derived from a light curve that covers this time period.

Figure 5 shows the X-ray spectrum (scaled to the SED time, t₀ + 3517) and its extrapolation into the optical. The fluxed optical spectrum (mean time t₀ + 2.2 hr) was scaled to the R-band data point. It is worth noting that the scaled optical spectrum agrees with the observed V and I photometric data, indicating that the small temporal extrapolations are correct and that there is no significant spectral change in the optical in this period. The extinction curve, shown in the top panel of Figure 6, is then derived from the difference between the spectrum and the extrapolated slope.

Zoom In Zoom Out Reset image size

To study the properties of the extinction curve, we fit it to the four previously mentioned extinction laws with the additional constraint that the extinction must go to zero for infinite wavelengths. The derived extinction and the fits are shown in the top panel of Figure 6 and the parameters of the fit are given in Tables 4 and 5. The freedom of the FM parameterization allows for a good fit (χ²/dof = 261/968), the LMC also provides a reasonable fit (χ²/dof = 815/975), while the SMC and MW fail to reproduce the extinction curve. However, the infrared photometry points of Krühler et al. (2008) clearly do not agree with any of the fits and require the extinction curve to take a very sharp break in its steepness at x < 1.5 μm⁻¹ which would suggest that the host of GRB 070802  has a very strange form of extinction law. However, a more plausible explanation is that the assumed intrinsic slope is wrong, either due to the extrapolation or because of the presence of a cooling break in the spectrum (see Section 3.2).

From Figure 5 we see that due to the several order of magnitudes extrapolation, the 1σ difference in β translates into a difference of ∼1 mag in the optical. While going toward steeper slopes will make the apparent "break" in the extinction curve greater, a shallower slope will act to reduce it as seen in Figure 6. Redoing the analysis for a shallower slope corresponding to 1σ deviation (i.e., β = 0.87) results in the extinction curve shown in the middle panel of Figure 6. The parameters of the fit, for both 1σ deviations are given in Tables 4 and 5. The goodness of fit for the MW, SMC, and LMC is improved for the shallower slope, while the effect on the FM fit is minimal. The fits are also more consistent with the additional photometric points in the infrared of Krühler et al. (2008). We note however that most GRBs have β_X > 1 (see, e.g., Liang et al. 2007, their Figure 3, with Γ = β + 1).

A cooling break in the intrinsic spectrum occurring between the X-ray and the optical data, i.e., β = β_X − 0.5, would result in an intrinsic spectrum at optical wavelengths of the form

$$\begin{equation} f^{\rm intr}_{\nu}=\tilde{f}_{\nu,0}\left(\frac{x}{x_0}\right)^{-\beta }=\tilde{f}_{\nu,0}\left(\frac{x}{x_0}\right)^{-(\beta _X-0.5)} \end{equation} \tag{ 8 }$$

where the normalization $\tilde{f}_{\nu,0}$ depends on the location of the cooling break, x_break, by

$$\begin{equation} x_{\mathrm{break}}=x_0\left(\frac{f_{\nu,0}}{\tilde{f}_{\nu,0}}\right)^{2}. \end{equation} \tag{ 9 }$$

The absolute extinction is then given by

$$\begin{eqnarray} A_{\lambda }&=&-2.5\log _{10}\left(\frac{f_{\nu }}{\tilde{f}_{\nu,0}}\left(\frac{x}{x_{0}}\right)^{\beta }\right) \end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray} &=&-2.5\log _{10}\left(\frac{f_\nu }{f_{\nu,0}}\left(\frac{x}{x_0}\right)^{\beta }\right) - A_{\infty }. \end{eqnarray} \tag{ 11 }$$

The first term of the sum can be determined as before from the X-ray data, while the second part of the sum

$$\begin{equation} A_{\infty }\equiv 2.5\log _{10}\frac{f_{\nu,0}}{\tilde{f}_{\nu,0}}=2.5\log _{10}\left(\frac{x_{\mathrm{break}}}{x_0}\right)^{0.5} \end{equation} \tag{ 12 }$$

is an additional unknown to be added to the fits. Its effect is to shift the extinction curve up or down (i.e., the value of A_λ + A_∞ at x = 0 is A_∞). Constraining the break to occur between the optical and X-ray regimes translates into constraints on the allowed values of A_∞ corresponding to setting x_break to be the upper x of the optical data and the lower x of the X-ray data. An additional requirement is that the extinction remains positive.

We fit the three local extinction laws (MW, SMC and LMC) to the curve in addition to the FM parameterization. Again we find that of the three local extinction laws the LMC provides the best fit (χ²/dof = 311/974), but the FM parameterization still gives the best overall fit (χ²/dof = 253/967). In this instance, the infrared photometric points of Krühler et al. (2008) agree with the extrapolated LMC and FM fits.

The MW extinction law provides a poor fit to the observed extinction, in part because the observed bump is shallower than the predicted MW bump and the rise into the UV is steeper (see e.g., Figure 6). However, as Figure 7 shows, such effects can be caused if part of the extinction is due to a foreground object without a bump.

Zoom In Zoom Out Reset image size

The spectrum of GRB 070802 shows two intervening Mg ii absorption systems which might also cause part of the reddening. Neither foreground system shows any signs of a 2175 Å bump. If the foreground absorber had a 2175 Å bump in its rest frame, it would act to broaden and shift the peak of the observed bump in the rest frame of the host, which is inconsistent with the data. Therefore, the most straightforward way to model them is with an SMC-type extinction law. As this extinction law is roughly linear, there is no way of separating the effect of two systems without additional constraints on the dust content of the two systems. As the absorber at z = 2.29 has much weaker absorption lines, and therefore by assumption much weaker extinction, we will only look at the possible contribution from the system at z = 2.078.

We will therefore limit ourselves to studying the possibility of the extinction being of the form

$$\begin{equation} A_\lambda =A_{\lambda}^{\rm host}+A_{\lambda}^{\rm fore} \end{equation} \tag{ 13 }$$

where A^host_λ is the extinction in the host galaxy and A^fore_λ is the extinction in the foreground Mg ii absorber. We have already seen that the extinction curve is poorly fit by an SMC-type extinction, as it lacks the characteristic bump. We will therefore parameterize the extinction of the host galaxy of GRB 070802  as either an MW (with fixed R_V = 3.1) or an LMC type, while the foreground absorber will be parameterized as an SMC type. In addition, we place the limit A^fore_V < 0.25 for the foreground absorber based on the discussion in Section 2.1.4.

The results are shown in Figure 8 and tabulated in Tables 4 and 6. We find that for the LMC, the addition of the foreground contributor does not improve the fits and the best fits are found by setting A^fore_V to be zero. For the MW, the fits are improved and the best fit is found by setting A^fore_V to its maximum value of 0.25. The MW fits are still worse than the LMC leading us to conclude that the extinction of GRB 070802 is not well fitted by an MW-type extinction.

Zoom In Zoom Out Reset image size

Figure 9 shows the scaled extinction curve for GRB 070802 for β = 0.87. We clearly detect the 2175 Å bump in the extinction curve of GRB 070802. The data sample the bump very well and its detection does not depend on whether we assume cooling breaks or not in the spectrum of the GRB. It is one of the most robust detections of the bump in extragalactic environments to date and currently the highest redshift detection at z = 2.45 (corresponding to 2.5 Gyr assuming a flat universe with Ω_m = 0.3, Ω_Λ = 0.7, and H₀ = 73 km s⁻¹ Mpc⁻¹).

Zoom In Zoom Out Reset image size

For the three local extinction laws, the LMC provides the best fit (i.e., it has the lowest χ² per degree of freedom (dof)) to the shape of the derived extinction curve, regardless of whether we assume there is a cooling break or not between the X-rays and the optical, and whether we take into account a possible contribution from the foreground absorbers or not (see Tables 4 and 6). The SMC clearly provides a poor fit in all cases as the bump is completely missing, while the bump of the MW extinction law is too strong and the rise into the UV not steep enough. A foreground absorber with SMC-type extinction could make the bump shallower and the UV rise steeper (see Figure 7); however, the absorption would need to be larger than the upper limits placed on A^fore_V in Section 2.1.4.

The best fits are obtained using the FM parameterization. This is not surprising, as it has more freedom in tracing the shape of the curve (see the Appendix). The three parameters giving the shape of the bump are only weakly dependent on the assumed β and whether we assume a cooling break or not (Table 5). The bump is found to be centered at x_c ≈ 4.6 ± 0.1 μm⁻¹, the width of the bump is found to be γ ≈ 1.08 ± 0.05 μm⁻¹, while the "strength" (i.e., its height above the linear extinction, see the Appendix) is c₃ ≈ 2.7 ± 0.1. Therefore, both the area of the bump Δ_bump ≡ πc₃/(2γ) and its maximum height above the linear extinction E_bump ≡ c₃/γ² are well defined. The relative strength of the bump A_bump/A_V = c₃/(γ²R_V) (as defined by Gordon et al. 2003) is also well defined, although here the uncertainty is dominated by the uncertainty in A_V (or equivalently R_V). We note that the value of c₃ is the same as the average c₃ = 2.7 ± 0.1 that Gordon et al. (2003) find for the LMC average sample while the width γ is a bit wider compared to their γ = 0.93 ± 0.02 μm⁻¹ (although it is still within their scatter). The value of c₃ is however higher than Gordon et al. (2003) find for the LMC2 sample (c₃ = 1.5 ± 0.1) although it is within the scatter.

We estimate the amount of dust extinction to be A_V = 1.341 ± 0.002 for β = 1.02 and A_V = 1.259 ± 0.002 for β = 0.52 given the FM parameterization. The LMC fits correspondingly give A_V = 1.474 ± 0.002 for β = 1.02 and A_V = 1.27 ± 0.02 for β = 0.52. Taking into account the possible 1σ deviation of the slope (excluding steeper slopes than β = 1.02, as this would be in strong disagreement with the photometric points of Krühler et al. 2008), we estimate A_V = 0.8–1.5 in the host along the line of sight to GRB 070802.

As mentioned in Section 1.2, based on evidence from the MW, LMC, and SMC, the simplest hypothesis would be that the strength of the 2175 Å bump is simply controlled by the metallicity. However, Savaglio et al. (2003) infer a metallicity of [Zn/H] =−0.13 ± 0.25 for GRB 000926 (compared to [Zn/H]=−0.50 ± 0.68 we derive for GRB 070802) and the H i column density for GRB 000926 is similar to that of GRB 070802. This would indicate that the extinction curve of GRB 000926 should also have a bump if metallicity was its only driver. However, the extinction curve derived for GRB 000926 is inconsistent with those of the MW and LMC and fully consistent with that of the SMC, i.e., without a 2175 Å bump (Fynbo et al. 2001a).

Gordon et al. (2003) suggested that the average extinction properties of the SMC, LMC, and MW were described by the same underlying extinction law, which could be described by the R_V parameter of the MW extinction and one additional parameter characterizing the strength of the bump and the UV slope. They suggested the gas-to-dust ratio as the second parameter and showed that for the LMC and SMC there is a correlation between the gas-to-dust ratio and the UV slope (i.e., c₂/R_V) and an anticorrelation between the gas-to-dust ratio and the strength of the bump (i.e., A_bump/A_V = c₃/(γ²R_V)), albeit with a large scatter.

GRBs typically originate in host galaxies with low dust-to-gas ratios (i.e., high gas-to-dust ratios Hjorth et al. 2003; Jakobsson et al. 2004c; Vreeswijk et al. 2004; Kann et al. 2006; Prochaska et al. 2007; Schady et al. 2007; see Table 7 for specific example). While the column density, N_H, of the host of GRB 070802 is not exceptionally large, it does have a very large A_V, leading to a low gas to dust. This is shown in Figure 10, where we have plotted N_H/A_V versus the strength of the bump A_bump/A_V for the SMC, LMC, MW, and GRB 070802. Also plotted is the region where GRBs for which an extinction curve analysis exists in the literature lie. The plot shows that the anticorrelation between the bump strength and the gas-to-dust ratio found by Gordon et al. (2003) for the SMC and the LMC also holds for the GRBs, and GRB 070802 in particular, although with large uncertainties in the values.

Zoom In Zoom Out Reset image size

GRB 070802 is, to our knowledge, the first GRB to date to show prominent C i in its afterglow spectrum and also the first GRB to show the 2175 Å feature, which is suggestive of a link between these two components. Should such a link be established by further observations it constitutes a constraint on the environment in which the 2175 Å feature occurs. The ionization potential of neutral carbon is lower than that of hydrogen (11.3 versus 13.6 eV) and neutral carbon is therefore only expected in regions without intense UV radiation. This would be consistent with the general lack of the 2175 Å feature in GRB host galaxies, as GRBs arise predominantly from star-forming regions where the UV radiation is expected to be strong (Fruchter et al. 2006; Chen et al. 2009).

To test whether this suggested correlation holds in general, we have looked at the other three robust detections of the 2175 Å bump in individual systems beyond the local group. For the lensing galaxy reported by Motta et al. (2002) and the intervening absorber toward GRB 060418 reported by Ellison et al. (2006), the existing data do not cover the wavelength range where one would see the C i absorption line if present. However, for the intervening damped Lyman-α system toward AO 0235+164 reported by Junkkarinen et al. (2004) we see tentative evidence for the C i λ1656 absorption line. The regions around C i λ1560, λ1656 are shown in Figure 11 for GRB 070802 and AO 0235+164. For comparison we also show the same region in the afterglow spectrum of the high-metallicity burst GRB 000926 which shows no significant evidence for the C i absorption features (and no bump in its extinction curve).

Zoom In Zoom Out Reset image size

It would be of interest to further check whether the sightlines to the MW, LMC, and SMC for which extinction curve analysis exist are consistent with this correlation. Such a study is beyond the scope of this current work, but we note that a quick and incomplete search of the literature resulted in two more lines of sight consistent with this correlation. The first is a detection of C i in the line of sight toward HD 185418 in the MW by Sonnentrucker et al. (2003). This line of sight is included in the sample of Fitzpatrick & Massa (1986) and has the 2175 Å bump in its extinction curve. The second is a line of sight toward the SMC, which has C i detected in the MW but only as an upper limit in the SMC (Welty et al. 1997). Although this sightline does not have an extinction curve analysis, it is consistent with our prediction that most lines of sight in the SMC should not show significant C i absorption.

The presence of the C i absorption feature in GRB 070802 suggests that the UV radiation field is weaker than in typical GRB environments—see Section 4.3. Gordon et al. (2003) reached the tentative conclusion that the shape of the extinction curve is affected by the UV flux density in the environment of the dust. In particular, a weaker UV flux density is found to correlate with the presence of the bump. Continuing our comparison to the bump-less GRB 000926 host, we find evidence that GRB 070802 does indeed have a weaker UV radiation field. (1) The GRB 000926 absorption system has stronger high ionization lines and much weaker lines from neutral species (e.g., C i, see Figure 11) than the GRB 070802 system. (2) The host galaxy of GRB 000926 appears to have a stronger UV flux density as illustrated by the very strong Lyman-α emission line (Fynbo et al. 2002b). For GRB 070802 we can exclude the presence of such a strong Lyman-α emission line (Figure 1 and B. Milvang-Jensen et al. 2009, in preparation). This supports the conclusion reached by Gordon et al. (2003).

It is not immediately clear what the physical significance of the possible correlation of strong C i and the 2175 Å bump is. Given that the bump is generally believed to be carried by carbonaceous material, and that carbonaceous grain growth and formation requires free, neutral carbon and molecules (Henning & Salama 1998), it would not be surprising to find both observed properties in the same environments. The simultaneous presence of C i and the 2175 Å bump as well as the lower overall ionization state of the gas, relatively (though not exceptionally) high metallicity, and large dust-to-gas ratio may be explained in a scenario in which the dust column is strongly enriched by the presence of asymptotic giant branch (AGB) stars.

For massive stars to move onto the AGB requires at least 600 Myr and typically much longer for a large population (Maeder 1992). The star-forming environment at such an age will be intrinsically relatively benign, with a softer UV field, and one in which a large amount of dust and molecular and free carbon is produced (Andersen et al. 2003; Gautschy-Loidl et al. 2004). Furthermore, the interstellar medium (ISM) is likely to be reasonably metal-rich and dust-rich. These properties are in contrast to the normal environments of GRB hosts which are typically metal-poor. However, some GRB hosts may be fairly metal-enriched (Fynbo et al. 2006) but still have hard radiation fields and young stellar populations (Le Floc'h et al. 2003; Christensen et al. 2004; Prochaska et al. 2004) and in particular, low dust-to-gas ratios (Fynbo et al. 2006; Jakobsson et al. 2006; Watson et al. 2007). This is consistent with the above scenario since the metal-enrichment timescale could well be much shorter than the ≳10⁹ yr required to have a reasonable number of AGB stars producing dust (Schneider et al. 2004). Such a scenario is then also consistent with the fact that GRB 070802 is the only GRB host galaxy so far discovered with a 2175 Å bump. It should also be noted that the host galaxy of GRB 070802 is fairly luminous and red for a GRB host (Savaglio et al. 2009), suggesting that it is a massive, evolved system, which would be in agreement with the claim of Noll et al. (2007) that the presence of the bump requires an evolved population.

This parameterization was introduced by Pei (1992) and is given by

$$\begin{eqnarray} A_\lambda &=&A_B \sum _{i=1}^{6}\frac{a_i}{(\lambda /\lambda _i)^{n_i}+(\lambda _i/\lambda)^{n_i}+b_i} \end{eqnarray} \tag{ A1 }$$

where the six terms are all positive and represent different parts of the extinction curve. The parameters can be found in Pei (1992). The five terms with n_i = 2 are equivalent to Drude profiles with a peak at λ_i. The only free variable in the fit is the overall amount of extinction. The original Pei (1992) paper scales it to A_B but we choose to scale it to A_V to be consistent with the other parameterizations. Note that the Pei (1992) law can also be used to describe MW-type of extinction.

Gordon et al. (2003) present new and updated average extinction curves for the SMC and LMC extinction curves. Their analysis is based on using the Fitzpatrick & Massa (1990) parameterization which differs from the updated FM parameterization we use (see below) in keeping c₅ fixed. The Gordon et al. (2003) analysis presents a more nuanced picture of the extinction in the SMC and LMC with lines of sight showing different type of extinction (see Section 1.1). However, we find that their "LMC2" average extinction curve and their "SMC Bar" extinction curves are very similar to the LMC and SMC extinction curves of Pei (1992; see Figure 12), thus justifying our use of the commonly used Pei (1992) parameterization.

Zoom In Zoom Out Reset image size

This parameterization of the MW extinction law was proposed by Cardelli et al. (1989). It depends on only two parameters, E(B − V) = A(B) − A(V) and R_V = A(V)/E(B − V) which is the ratio of total to selective extinction. It is given by

$$\begin{eqnarray} A_\lambda & = & E(B-V) \left[R_V a(x) + b(x)\right] \\ & = & A(V) \left[ a(x) + \frac{1}{R_V} b(x)\right],\nonumber \end{eqnarray} \tag{ A2 }$$

where A(λ) is the total extinction at wavelength λ, a(x) and b(x) are polynomials and x = λ⁻¹. The advantage of this parameterization over the one of Pei (1992) for the MW is that it allows for a varying R_V.

The parameterization for the UV (i.e., valid for x > 3.7 μm⁻¹) is given by

$$\begin{eqnarray} A_\lambda &=&E(B-V)\left(k\left(\lambda -V\right)+R_V\right) \end{eqnarray} \tag{ A3 }$$

$$\begin{eqnarray} & = & A(V)\left(\frac{1}{R_V}k\left(\lambda -V\right)+1\right) \end{eqnarray} \tag{ A4 }$$

where

$$\begin{eqnarray} k(\lambda -V) = \left\lbrace \begin{array}{@{}ll@{}} c_1 + c_2 x + c_3 D(x,x_c,\gamma) & x \le c_5 \\ c_1 + c_2 x + c_3 D(x,x_c,\gamma) \\ \quad + c_4 (x-c_5)^2 & x > c_5, \end{array} \right. \end{eqnarray} \tag{ A5 }$$

and

$$\begin{equation} D(x,x_c,\gamma) = \frac{x^2}{\big(x^2-x_c^2\big)^2 +x^2\gamma ^2}. \end{equation} \tag{ A6 }$$

The parameters c₁ and c₂ define the linear component underlying the entire UV range, c₃, x_c and γ give the 2175 Å bump (although its central wavelength is not fixed in the parameterization) and c₄ and c₅ give a far-UV curvature component. The extinction properties in the infrared and optical are not parameterized in the FM2007 description but are derived using spline interpolation (see Fitzpatrick & Massa 2007, for details). As our data set does not reach into these regions in the rest frame, we do not constrain the extinction curve in this region. Therefore, for display purposes, we have chosen to set these parameters to "typical" values found by Fitzpatrick & Massa (2007) to create "normal" smooth continuation of the curve toward x = 0. We note that the choice of these parameters does in no way affect our fits for the UV parameters and, vice versa, that the FM fits do not constrain this part of the curve.

As explained in Fitzpatrick & Massa (2007), additional useful quantities can be defined using the UV parameters. The first one (1) Δ1250 = c₄(8.0 − c₅)² gives the value of the far-UV curvature term at 1250 Å and measures the strength of the far-UV curvature, (2) Δ_bump = πc₃/(2γ) is the area of the bump, and (3) E_bump = c₃/γ² is the maximum height of the bump above the linear extinction.