5 Spectral energy distribution of the afterglow

Also shown in Table 4 are the colours (in the same bands) of the OT of GRB 000301C, which was also discovered at the NOT and had a very similar redshift as GRB 000926 (Jensen et al. 2001; Møller et al., in prep). As seen, the OTs of GRB 000926 and GRB 000301C had very similar colours in the optical red bands, whereas in the blue bands and in R-K the OT of GRB 000926 was significantly redder than that of GRB 000301C. In order to test whether this difference is intrinsic to the bursts or caused by a larger extinction along the line of sight to GRB 000926 we follow Jensen et al. (2001) and constrain the extinction by fitting different extinction laws to the SED.

To construct the SED we first used the colours given in Table 4 for the observed U to I bands (normalised to Sep. 27.9 UT). The J, H and K-observations were obtained on Sep. 30.3 where the host galaxy possibly contributed significantly to the flux. In order to estimate the effect of the host galaxy we used the SEDs for galaxies at redshifts z=2-3 given by Dickinson (2000, their Fig. 2). By normalising these galaxy SEDs to the observed $R(AB)=24.04\pm0.15$ for the host galaxy (see Sect. 6 below) we derived magnitudes for the host galaxy which translate into estimated corrections at Sep. 30.3 UT of $\Delta J=+0.14\pm0.08$, $\Delta H=+0.07\pm0.06$ and $\Delta K=+0.05\pm0.04$. The JHK magnitudes were then shifted to Sep. 27.9 UT using the broken power-law fit to the light-curve given in Table 3 (assuming that the burst evolved achromatically). After this the UBVRIJHK magnitudes were corrected for foreground extinction, using a value of E(B-V)=0.023 from Schlegel et al. (1998), and transformed to the AB system. For the optical bands we used the transformations given by Fukugita et al. (1995): I(AB) = I+0.43, R(AB) = R+0.17, V(AB) = V-0.02, B(AB) = B-0.14, and U(AB) = U+0.69. We assigned uncertainties of 0.05 mag to the BVR and I AB magnitudes as an estimate of the uncertainty in the transformation. For U band we assigned an uncertainty of 0.10 mag to the AB magnitude since this band is more difficult to calibrate (Bessel 1990; Fynbo et al. 1999, 2000c). For the IR bands we used the transformations given in Allen (2000): K(AB) = K+1.86, H(AB) = H+1.35, and J(AB) = J+0.87. We then calculated the specific flux using $F_{\nu} = 10^{-0.4\times(AB+48.60)}$. Finally, the wavelengths corresponding to our UBVRIJHK measurements were blueshifted to the GRB rest frame. As it can be seen in Fig. 3 the spectral energy distribution is clearly bending from the U to the K-band. This bend can be naturally explained by the presence of intrinsic extinction at z=2.037. The J-point is falling significantly below the trend of all the other points. The reason for this is not understood, but we have decided not to include this point in the analysis. Including the point does not change any of the conclusions, but it increases the $\chi^2$ of the fits.

 

 

Table 6: The fits to the spectral energy distribution of GRB000926.

	$\chi^2/{\rm d.o.f.}$	$\beta$	AV
No extinction	3.20	$1.42 \pm 0.06$	0
Pei (1992), MW			<0
Pei (1992), LMC	2.61	$0.98 \pm 0.23$	$0.27 \pm 0.12$
Pei (1992), SMC	1.71	$1.00 \pm 0.18$	$0.18 \pm 0.06$

We next fitted the function $F_{\nu} \propto \nu^{-\beta} \times 10^{(-0.4 {A}_{\nu})}$ to the SED. Here, $\beta$ is the spectral index and $A_{\nu}$ is the extinction in magnitudes at frequency $\nu$. We have considered the three extinction laws ($A_{\nu}$ as a function of $\nu$) given by Pei (1992), i.e. for the Milky-Way (MW), Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC). In the three cases the dependence of the extinction with $\nu$ have been parameterized in terms of (restframe) A_V. Thus, our fits allow us to determine $\beta$ and A_V simultaneously. Finally, we also considered the no-extinction case where $F_{\nu }$ was fitted by a straight line in log-log space.

The parameters of the fits are shown in Table 6. For the no-extinction case we find a value of $\beta$ consistent with that of Price et al. (2001). As for GRB 000301C the best fit was achieved for a SMC extinction law. We derive a modest extinction of $A_{V}=0.18\pm0.06$ (restframe V) and a spectral index $\beta=1.00\pm0.18$. For GRB 000301C Jensen et al. (2001) found $\beta = 0.70\pm0.09$. Therefore, GRB000926 was indeed intrinsically redder than GRB 000301C.

In the upper panel of Fig. 3 we show the fits using the LMC and SMC extinction laws and the no-extinction case. For the redshift of GRB 000926 (as for that of GRB 000301C) the interstellar extinction bump at 2175 Å is shifted into the R-band. This absorption bump is very prominent for the MW, moderate for the LMC and almost nonexistent for the SMC extinction curve. Thus, for a chemically rich environment, like the MW, we should expect a prominent extinction bump at 2175 Å (near the observed R-band). The data points in Fig. 3 show that there is no strong absorption bump near the R-band, which makes the fit for the MW (see Table 6) inconsistent with the data. In fact, the best MW fit implies a (unphysical) negative extinction. To illustrate the problem with the MW extinction curve we have in the lower panel of Fig. 3 plotted a $\beta =1$ power-law SED extincted by a A_V=0.2 MW extinction curve. As seen, the shape of this extinction curve is incompatible with the data. In the Milky Way the extinction curve can be different mainly for stars located in star-forming regions (Baade & Minkowski 1937; Whittet 1992) in the sense that the shape of the bump at 2175 Å is different and more importantly the curve is almost flat in the rest-frame UV at $\log(\nu)$ > 15.1. This is where the curvature is most pronounced in Fig. 3 and therefore such an extinction curve is also not compatible with the data (see also Price et al. 2001)

In conclusion, as in the case of GRB000301C, the SED supports a scenario of a host in an early stage of chemical enrichment.

Figure 3: The observed specific flux $F_{\nu }$ vs. the rest-frame frequency $\nu$ normalised to Sep. 27.9 UT. The spectral energy distribution of the afterglow from K to U is clearly curved. In the upper panel we show that this curvature can be well fitted by an underlying $\beta =1$ power-law SED with a SMC or LMC extinction law with AV=0.2. In the lower panel we show that the MW extinction law is inconsistent with the data.