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Astron. Astrophys. 364, L54-L61 (2000)

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5. Discussion

The temporal and spectral behavior of optical gamma-ray burst afterglows are in general observed to follow a power law, such that [FORMULA] ([FORMULA]), where t is the time elapsed since the GRB event. The fireball model provides the theoretical framework for this behavior and also gives the relation between the temporal slope [FORMULA] and the spectral slope [FORMULA] in various regimes (Sari et al. 1998; Piran 1999; Meszaros et al. 1998). If the afterglow is collimated (a jet), the temporal slope is modified and may change during the transition from the observer being inside the jet cone to being outside the jet cone, caused by the slowing-down of the jet (Rhoads 1999). This results in a break in the light curve, such as those observed in GRB 980519 (Jaunsen et al. 2000), GRB 990123, GRB 990510 (Stanek et al. 1999; Harrison et al. 1999), GRB 990705 (Masetti et al. 2000a), GRB 991216 (Halpern et al. 2000), and GRB 000131C (Jensen et al. 2000; Masetti et al. 2000b). In the following, we will base our discussion on the assumption that the afterglow can be described within the framework of the fireball model.

5.1. The light curve of the afterglow

The three epochs of R-band photometry can be fitted by a power-law decline with [FORMULA] and a [FORMULA], as shown in Fig. 4. A power-law decline with this slope is typical for post-break evolution of GRB afterglow emission. A value of [FORMULA] has been observed in several other afterglows, namely GRB 980326 (Groot et al. 1998), GRB 980519 (Jaunsen et al. 2000), GRB 990510 (Stanek et al. 1999; Harrison et al. 1999; Holland 2000), GRB 991208 (Hurley et al. 1999; Castro-Tirado et al. 2000), and GRB 000301C (e.g., Jensen et al. 2000). The light curve of GRB 000131 is plotted together with the light curves of these afterglows in Fig. 4. The main characteristics of these systems are summarized in Table 4. In all cases the favoured interpretation of such a steep slope is post-break decay of a collimated outflow. The light-curve breaks predicted in this scenario have indeed been observed (see Holland et al. 2000) and are believed to have occurred prior to the first observations in the other systems with [FORMULA]. The simplest interpretation of the GRB 000131 afterglow light curve is therefore that of a collimated outflow seen after the jet has slowed down.

[FIGURE] Fig. 4. R-band light curves of GRB afterglows with steep late-time decay. The solid line is a power-law fit to the GRB 000131 data (filled circles). The non-detection on March 5 is marked as an upper limit at [FORMULA]=1.52. Other afterglows are (from left to right) GRB 980326, GRB 980519, GRB 990510, GRB 000301C and GRB 991208 (which is shifted 0.4 in log(days)). Pre-break data points are omitted.


[TABLE]

Table 4. GRB afterglows with rapidly decaying light curves.


5.2. Spectral energy distribution

The optical afterglow was detected in VRIHK, but at different epochs. By assuming achromatic evolution of the afterglow (which is consistent with other afterglows), following the [FORMULA] = 2.25 power-law decline, the spectral energy distribution can be calculated for a given epoch. In Fig. 5 we plot the derived spectral energy distribution at 3.50 days after the burst trigger, i.e., at the time of the first VRI observations. Also given are the upper limits derived from our B and J observations. The spectral energy distribution has been corrected for Galactic reddening, using [FORMULA]=0.056 (Schlegel et al. 1998).

[FIGURE] Fig. 5. The spectral energy distribution, as derived from broad band photometry. The errors of the H and K fluxes include the formal error from the extrapolation of the light curve back to t=3.5 days. A fit by a power law spectrum with Lyman forest absorption and SMC reddening is shown as a dashed line. This yields A[FORMULA] = 0.18, when an intrinsic spectral slope, [FORMULA] = 0.70, and a redshift of 4.5 is assumed. The solid line shows the corresponding spectrum with its Lyman absorption edges.

For steep-decay afterglows, like those shown in Fig. 4, the large values of [FORMULA] and the relatively small values of [FORMULA] favour a scenario involving a sideways expanding jet. In this case spectral slopes between [FORMULA] and [FORMULA] are expected in the fireball model, depending on the value of the cooling frequency. With [FORMULA], this implies [FORMULA], with a preference for the low value (cf. Table 4).

The spectral energy distribution shown in Fig. 5 does not resemble a power-law with a single index [FORMULA]. This is not an artifact of extrapolating the H and K band data points from Feb. 8 to Feb. 4, as a power-law fit to the V, R, and I data points only results in a [FORMULA] and [FORMULA], which is much steeper than the value of about 1 typically observed in GRB afterglows (see Table 4). Moreover, for the H and K fluxes to be in accordance with this fit, an unphysical value of [FORMULA] of about 7.0 in the near-IR is required. Thus, a power-law spectral energy distribution is ruled out.

We have explored whether the strongly curved shape of the spectral energy distribution can be explained by reddening in the host galaxy (as in eg. GRB 000301C, Jensen et al. 2000, or in GRB 971214, Dal Fiume et al. 2000). We find that no physically plausible reddening laws can transform a power-law spectrum into the observed shape.

The most likely interpretation of the spectral break is therefore the onset of Lyman forest blanketing, hence implying that GRB 000131 was at a high redshift (z[FORMULA]4). To examine this interpretation further we have fitted the spectral energy distribution with power-laws modified by the effects of Lyman forest blanketing and internal reddening in the host galaxy. This technique was first used by Fruchter Fruchter (1999) for GRB 980329 and discussed in detail by Reichart Reichart (2000). For the reddening we use the SMC extinction law assumed to best represent a chemically less-evolved environment at redshifts of 4 to 5. To model the effects of Lyman forest blanketing we follow Moller and Jakobsen Moller & Jakobsen (1990): for each pair of values of [FORMULA] and z, the visual rest-frame absorption [FORMULA] and the [FORMULA] of the fit is obtained. We find that all kedit lvuv11.f7 values of [FORMULA] allowed by the fireball model are possible, with a preference for low values. The corresponding range of internal reddening is 0.11 [FORMULA] [FORMULA] [FORMULA] 0.20, with a preference for high values. For values of [FORMULA] around 0.65, the possible range (2 [FORMULA]) of redshifts is [FORMULA], while the redshift is [FORMULA] for [FORMULA] = 1.0. This result is not affected by the choice of reddening law.

5.3. The spectroscopic redshift of GRB 000131

Our analysis of the photometric observations implies the presence of a Ly[FORMULA] absorption edge in the range 6500 Å to 6900 Å. This implication is confirmed by the spectroscopic observations. After smoothing the FORS1 spectrum to a resolution of 30 Å a clear indication of such an absorption edge at 6700 Å is revealed. The recorded spectrum was very faint, at the level of less than 2% of the continuum of the night sky, which is dominated by emission lines through the red part of the spectrum. The noise in the spectrum is therefore dominated by uncertainty in the sky subtraction. An improved representation of the continuum was obtained by rebinning the spectrum to a resolution of 200 Å, omitting spectral bins coincident with sky lines. The smoothed and the rebinned spectra are shown in Fig. 6 together with a model of the spectrum, assuming a redshift of 4.5, [FORMULA] = 0.70 and a reddening, [FORMULA], as derived from a fit to the photometry (see Fig. 5).

[FIGURE] Fig. 6. The spectrum of the GRB 000131 afterglow: a smoothed to a resolution of 30 Å, b rebinned to a resolution of 200 Å. The dotted curve shows the noise per bin, while the dot-dashed line is the model spectrum shown in Fig. 5.

The model spectrum is normalized to the R-magnitude of the afterglow, obtained immediately before the spectroscopic observations began, and corrected for slit losses of 35%, as would result from using a [FORMULA] slit in a seeing of about [FORMULA]. The model spectrum is seen to be in very good agreement with the binned spectrum for wavelengths below 7200 Å. The average observed flux in the Lyman forest region (between Ly[FORMULA] and Ly[FORMULA]) is [FORMULA] nJy, which is in reasonable agreement with the level of 79 nJy predicted by the model. Beyond 7200 Å the spectrum is dominated by an atmospheric band and strong sky lines, which are not well resolved at a spectral resolution of 9 Å. This effectively renders the spectrum useless in this spectral region.

As the spectral region from 6590 Å to 6810 Å is essentially free from sky lines, the location of the absorption edge is well defined (see Fig. 7). We measure its location to be at [FORMULA] Å from which a redshift of [FORMULA] is inferred. The reality of the absorption edge and the interpretation that it is due to Ly[FORMULA] is most convincingly seen by integrating the flux of the spectrum and the model, as shown in Fig. 7. The integrated spectrum is very smooth and follows the model nicely on the red side of the edge, while there are significant deviations on the blue side of the edge. Comparing 100 Å intervals on the blue and red side of the absorption edge, the standard deviation of the spectrum is found to be 65% larger on the blue side, consistent with the interpretation that the blue side is located in the Lyman forest. Hence, the VLT spectrum is in excellent agreement with the photometric observations and provides independent evidence that the redshift of GRB 000131 is [FORMULA].

[FIGURE] Fig. 7. a A region of the spectrum, centered on the Ly[FORMULA] absorption edge and smoothed to a resolution of 13 Å. The dotted line gives the noise per bin, while the dashed curve is a model absorption edge spectrum corresponding to a redshift of 4.511, and redshifts of 4.509 and 4.513 (dot-dashed curves). b The integrated flux of the full resolution spectrum and the model absorption edge spectra shown in a . The integrated flux is normalized to a common level at 6750 Å .

In the VLT spectrum of GRB 000301C, Jensen et al. Jensen et al. (2000) detected a strong damped Ly[FORMULA] absorption line at the redshift of the GRB. If a similar damped Ly[FORMULA] absorption line is present in the spectrum of GRB 000131 the redshift as determined from the spectral break will be slightly overestimated since the red wing of the damping profile will move the spectral break 10-20 Å (depending on the HI column density) towards the red. Therefore, the inferred redshift from the spectral break depends on the assumed HI column density of the GRB self absorption. With the signal-to-noise of the spectrum, it is not possible to constrain the HI column density. An indirect indication that GRB 000131 had significant self absorption is obtained from the estimate of A[FORMULA]. Assuming an SMC extinction law and minimum dust-to-gas ratio (Pei 1992) and the maximum value of A[FORMULA], as derived from the fit of the spectral energy distribution, an HI column density of up to [FORMULA] cm-2 is estimated. An estimate of the likely error of the redshift may therefore be obtained by fitting a HI line corresponding to this column density to the spectrum. We derive a redshift of 4.490 [FORMULA]0.002 for this column density, which allows us to conservatively conclude that the redshift of GRB 000131 is [FORMULA].

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© European Southern Observatory (ESO) 2000

Online publication: December 15, 2000
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