DUST PROPERTIES IN THE AFTERGLOW OF GRB 071025 AT z ∼ 5

We started imaging the afterglow of GRB 071025 using the 1 m telescope at Mt. Lemmon Optical Astronomical Observatory (LOAO) on 2007 October 25, 04:26:54.07 UT, t ∼1080 s after the  Swift Burst Alert Telescope (BAT) trigger (Pagani et al. 2007). We obtained B-, V-, R-, and I-band imaging data up to the end of October 25 and to a part of October 26 (Im et al. 2007; Lee et al. 2010). Our data showed detections of a bright afterglow in the I and a faint counterpart in the R. The afterglow was not detected in the B and V. We reduced the data using the standard procedures of dark subtraction and flat-fielding using IRAF packages. We obtained the photometry of the afterglow and surrounding stars using SExtractor with the parameters of five pixels for DETECT MINAREA, 1.2σ for DETECT THRESH, and 1.2σ for ANALYSIS THRESH (Bertin & Arnouts 1996). The magnitudes were computed by using circular apertures with an aperture radius of 1.5 FWHM of point-spread functions and aperture corrections were derived from bright stars in the field, which amounted to 0.3–0.4 mag. We obtained the data for standard stars (SA95 and SA115) in the second night which were used to carry out the photometry calibration of the GRB 071025 field.

The J-, H-, and K_s-band data were obtained with the simultaneous quad infrared imaging device (SQIID) on the Kitt Peak Mayall 4 m telescope at Steward Observatory, with the start time of 2007 October 25, 05:56:59 UT (Jiang et al. 2007). The total exposure time in each band was 240 s and the three bands' data were taken at the same time. The photometry was calibrated using Two Micron All Sky Survey point sources brighter than J = 16.0, H = 15.5, and K_s = 14.0 mag within a 120 arcsec distance from the afterglow. Additional J, H, and K_s data were obtained at t ≃ 1.05 days with the Canada–France–Hawaii Telescope.

The results of the photometry are presented in Table 1, where the magnitudes are given in the AB system. For the conversion of the Vega-based magnitudes into AB magnitudes, we used the conversion relation of Frei & Gunn (1994) for the RI bands and Ciliegi et al. (2005) for the JHK_s bands. Galactic extinction is also corrected using E(B − V) = 0.07 (Schlegel et al. 1998), which amounts to 0.19, 0.14, 0.06, 0.04, and 0.03 mag in RIJHK_s, respectively.

Since GRB afterglows change their brightness and in some cases their colors, it is necessary to construct an SED at a given epoch for the analysis of GRB 071025. We adopt the mid-time of the JHK_s data (t = 6605 s) as the epoch for which we construct the SED, since the JHK_s data were taken simultaneously. Note that we used the form of F_{t, ν} ∼ t^−α ν^−β (Sari et al. 1998) to fit the data, where ν is the observed frequency, α is temporal index, and β is spectral index.

Before determining the SED at this epoch, we consider if it is appropriate to consider such an SED as a simple power-law SED from synchrotron radiation by analyzing its temporal evolutions. At t > 1500 s, P10 find that the light curves in the X-ray and the optical/NIR are described by simple power laws. By fitting single power-law functions to the light curves of the publicly available  Swift's X-Ray Telescope data⁵ (Evans et al. 2007) and to the I-, J-, and K_s-band data including those presented in P10, we find that over an interval of t = 1900 to 17,000 s, α_X = 1.75  ±  0.06, α_I = 1.47  ±  0.06, α_J = 1.44  ±  0.04, and α_K = 1.41  ±  0.03, or α_optical/NIR − α_X ≃ −0.25 to −0.34  ±  0.08. When the analysis is extended to t ∼ 10⁵ s, we get α_J − α_X = −0.27  ±  0.04. These results, being consistent with α_optical − α_X < −0.25 of a uniform ambient environment (Urata et al. 2007), suggest that the cooling break (ν_c) lies between the X-ray and the optical wavelengths and that the light in the optical/NIR is dominated by the afterglow from external shocks. Since we also find no late time prompt signal (e.g., flare and shallow decay) in the X-ray, we conclude that stable afterglow light characterizes the SED at t = 6605 s.

The remaining task is to synchronize R- and I-band photometry to this epoch. One of the I-band images from LOAO is nearly contemporaneous with the JHK_s data, lagging behind the NIR observation by only 209 s. To correct for the small difference in the observed time, we interpolate the I-band data with the power-law model.

We fit the I-band light curves with our own data only, and with additional I-band data from P10. The fitted values of α are 1.44 ± 0.11 and 1.47 ± 0.06 without or with the P10 data, respectively. The necessary correction to derive the contemporaneous I-band magnitude from the t = 6814 s data point is +0.050 mag with α = 1.47 and +0.049 mag with α = 1.44. The difference in the correction due to the choice of α is negligible, hence we adopted the correction of 0.05 mag to compute the I-band magnitude at 6605 s, which gives I = 19.18 ± 0.16 mag.

For R-band photometry, we used two methods. First, we extrapolated the R-band detection at t = 1500 s to t = 6605 s assuming an achromatic decay of the light curve during this period, as found in P10. This gives the R-band photometry of R = 21.3 mag. For the second approach, we derived a limit in the R-band photometry from a stacked image made of seven 300 s R-band frames around t = 6605 s. In the stacked image, no afterglow was detected, giving an upper limit in R-band photometry at 21.1 mag at 3σ. These two methods give consistent results, therefore we adopt R = 21.3 mag for the R-band photometry at t = 6605 s. For the 1σ uncertainties of data, 0.16 mag is used in I band to reflect the uncertainty in α. In the case of R-band, we adopt the error, 0.3 mag, of the R frame at t = 1500 s.

We derive the redshift of GRB 071025 before proceeding to a detailed comparison of the best-fit models using different extinction curves. By fixing the redshift, direct comparison between different models becomes more straightforward. Fixing the redshift to a single value can be justified if the derived redshift is not strongly dependent on the models.

In order to determine the redshift, we fit the observed SED with different extinction curves with four free parameters: redshift, A_V, β, and the normalization factor. We find that the derived redshifts are all between 4.60 and 4.85^+0.05_{− 0.1} due to the sharp break at R (R − I ≃ 2.0) which can be explained by intergalactic absorption of the light below Lyα, consistent with the value reported in P10. Since the dependence of the redshift on the assumed dust extinction curves is small, we will fix the redshift of GRB 071025 to a fiducial value of 4.8 in the following analysis of the extinction property. We tried the same analysis using different values for the redshift and find that the main conclusion is not affected by the choice of redshift. The differences between the χ²_red of best-fit SNe-dust models and less favorable models are always greater than 3 over the plausible redshift range.

Figure 1 shows the result of the SED fit with various dust extinction curves (SMC, MW, Calzetti, and Maiolino). As in P10, we observe an inflection in the observed SED shape—as we go from the shorter to the longer wavelength, IJHK_s data points move up and down with respect to a simple power-law model SED. While the best-fit models with SNe-dust have χ²_red values less than 1, models with the dust extinction curves of LMC, SMC, MW, and Calzetti produce the χ²_red values of about 4–5. The MW and the LMC extinctions are characterized by a 2175 Å bump which is absent in the SED of GRBs, and the best-fit A_V values of these models converge to zero. The SED with the Calzetti curve is featureless and similar to the SED with no extinction. Although the adoption of the SMC extinction curve improves the goodness of the fit a little bit compared with the MW or the Calzetti curves, it cannot reproduce the observed changes of slopes between JHK_s bands as well as the SNe-dust extinction curves.

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Since some of the fits converge to no extinction, we tried a fit without dust extinction, which has the benefit of reducing one free parameter. The fit returns the χ²_red of 2.55, an improvement over the fits with the MW and the LMC extinction curves. However, the best-fit spectral slope is too steep at β = 1.6, which we argue as unfavorable below.

Our light curve analysis indicates that the afterglow emission follows the external shock model with $F(t,\nu) \sim t^{\frac{3(p-1)}{4}}\, \nu ^{\frac{p-1}{2}}$ for the optical/NIR, where p is electron power-law index (Sari et al. 1998). From our optical/NIR light curves, we get p ∼ 2.97 and consequently β ∼ 0.99. With the external shock model, β_X should follow β_X = β + 0.5 ∼ 2.1 if β ∼ 1.6, but we find that β_X is only β_X = 1.07 ± 0.1 at t = 3000–11, 000 s.⁶ Furthermore, GRB afterglows are known to have β ∼ 0.6 and β ≲ 1.1 for all the well-studied cases (Kann et al. 2006, 2010; Zafar et al. 2011).

The SNe-dust models perform far better than those with other dust extinction laws, confirming the previous result from P10.

H05 and H08 allow us to test various SNe-dust production scenarios with a broad progenitor mass range from 13 to 170 M_☉, with or without mixing of heavy elements inside the He-shell, and with or without shock destruction of dust. Dust grains can be destroyed by the SNe shock, modifying the grain size distribution and eventually the extinction curve. In H08, the shock destruction is implemented with the destruction efficiency depending on the ambient gas density, which is varied from 0, 0.1, to 1 cm⁻³. Here 0 cm⁻³ is the case for no destruction and 1 cm⁻³ for the most efficient destruction. If the gas density is much larger than 1 cm⁻³, the dust destruction is so efficient that there would be almost no dust extinction (Nozawa et al. 2007).

For this analysis, we introduce a Y-band data point at t = 6605 s by interpolating two epochs of data (2653 and 11526 s) from P10. Applying α = 1.47 ± 0.06 of the I-band, we estimate Y = 18.30 ± 0.21 mag. We did not add other data sets such as RIJHK_s from P10, since such data do not significantly improve photometric accuracies in the same bands. Figure 2 and Table 2 summarize our findings after the GRB 071025 data are fitted with these models.

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First, we discuss whether the mixed or the unmixed core model fits the data better using 25 M_☉ progenitor models as references. The left panel of Figure 2 shows that the unmixed core model fits the data better than the mixed core model. Mixed core produces only oxidized molecules, since most carbons are locked in CO. Extinction is dominated by SiO₂ in such cases, regardless of progenitor mass. Since the SiO₂-dominated extinction curve monotonically increases with 1/λ without any change of the slope, it cannot explain the inflexed SED shape of GRB 071025. We find that the same argument applies to models with different progenitor masses; therefore, we will focus on unmixed core progenitors in the following.

Next, we examine if the dust destruction is needed to account for the observed SED. The triple-dot-dashed and the dotted lines represent models with dust destruction at n_H = 0.1 cm⁻³ and 1 cm⁻³, respectively. The destruction affects small grains and the effect is reflected in the model SED in the left panel of Figure 2. After the destruction, the extinction curve becomes featureless, resembling the SMC or the Calzetti curves, and the afterglow model SEDs with the dust destruction fit the data as poorly as models with the SMC or the Calzetti curves. Therefore, we conclude that the dust destruction is negligible for GRB 071025. We checked that this conclusion holds for models with other progenitor masses.

Finally, we discuss the most likely progenitor mass of the SNe responsible for the dust. For this, we compare the best-fit models with the 13, 20, 25, 30, and 170 M_☉ progenitors with unmixed core and no dust destruction (the right panel of Figure 2). Figure 2 shows that the models with a progenitor mass of 13 or 25 M_☉ fit the data significantly better than the others (the χ²_red ≲ 1 versus ∼4). This is because the inflexed SED shape between the I- and K_s-bands can be explained by extra absorptions at the rest frame 1200–2000 Å and at around 3000 Å due to the increased contribution of carbon grains (13 M_☉), or Mg₂SiO₄ and FeS grains (25 M_☉) with respect to Si grains. The 30 M_☉ progenitor model fails to fit the data because of the excessive increase of Si grains. The 170 M_☉ model, given as a representative case for pair-instability supernovae, which could be abundant in the early universe (Heger & Woosley 2002), also gives poor fits to our data. This results from the high contribution of Si grains which make the curve look more or less monotonically increasing and the deficiency of the extra extinction from Fe that introduces a plateau in the model SED at shorter wavelengths.