1.- Introduction

The discoveries of the first X-ray afterglow (Costa et al. 1997) and Optical Transient (OT) (van Paradijs et al. 1997) of a gamma-ray burst (GRB) have led to a major breakthrough in GRB research. The determination of a redshift of 0.835 for GRB 970508 (Metzger et al. 1997), and the subsequent determination of redshifts of more than a dozen bursts with a median redshift of ~1.1, have firmly established their cosmological origin (e.g. Kulkarni et al. 2000 and references therein). One of the current goals is to use the OT properties (brightness, position within the host galaxy, light-curve shape) as diagnostic tools to study the environment of GRBs and to possibly shed some light on the nature of GRB progenitors (Bloom et al. 2000).

Essentially all viable models for forming GRBs suggest that the rate of GRBs should follow the rate of star formation (Wijers et al. 1998). One set of models predicts that GRBs occur when two collapsed objects (such as black holes or neutron stars) merge (Paczynski 1991; Woosley 1993) The time-scale for binary compact objects to merge is large (> 1 Gyr), so GRBs can occur after star formation has ended in a galaxy. The other major set of models predicts that GRBs are associated with the deaths of massive stars (supernovae or hypernovae) (Paczynski 1998; Wijers et al. 1998). In this case GRBs will coincide with the epoch of star formation in the host.

Therefore, a very appealing aspect of GRB research is the use of GRBs as cosmological probes. GRBs have been suggested as tracers of the star formation rate at the very high redshift universe (Lamb and Reichart 2000; Andersen et al. 2000).

In this paper we present the discovery of the OT of GRB 000926 and the results of the multi-colour optical photometry.

2.- Observations

GRB 000926 was detected by three instruments in the Interplanetary Network (IPN: Ulysses, Konus-WIND, and NEAR), and localized to a 35 arcmin² error box which was circulated 20.3 hours after the burst (Hurley et al. 2000). The Earth-crossing time for the burst was September 26.9927 UT. As observed by Ulysses, it had a duration of approximately 25 seconds, placing it in the "long duration" burst category.

The error-box of GRB 000926 (Hurley et al. 2000) was observed in the R--band with the 2.2-m Calar Alto telescope on 2000 September 27.8651 UT (20.937 hours after the burst). The instrumentation used was CAFOS. The large field of view of CAFOS (16' of diameter) allowed us to cover all the GRB error box with a single frame, avoiding time-comsuming mosaics. In fact, to date the 2.2-m (+CAFOS) telescope has detected 9 of the 22 GRBs with known optical/IR or radio counterpart. Thus, the 2.2m+CAFOS configuration is an ideal system for the GRB follow-up research. All the follow up observations reported in this paper were performed in real-time coordination with the NOT telescope at La palma (Dall et al. 2000).

By measuring the position of the OT relative to 80 stars in the USNO-A2.0 catalog we found the celestial coordinates of the OT to be RA(J2000) = 17:04:09.68, Dec(J2000) = +51:47:10.5 with an internal error of about 0.1 arcsec.

Comparing with red Palomar Optical Sky Survey II exposures an OT was found in the error box (Gorosabel et al. 2000). Spectra were obtained at the NOT on both September 27 and September 28. These spectra revealed a strong metal absorption system at a redshift of z=2.037±0.0034, which in all likelihood is due to gas in the GRB host galaxy (Møller et al. 2000). The OT was observed during the following weeks at the 2.2-m Calar Alto , 2.56-m NOT (this paper, Fynbo et al. 2000), 2.5-m INT (Rol et al. 2000), 1.0-m USNO (Fynbo et al. 2000, Vrba and Canzian 2000), 3.6-m CFH (Veillet 2000), 1.5-m Palomar (Price et al. 2000a), 1.1-m AZT-24 (Di Paola et al. 2000) the MDM 2.4-m telescopes (Halpern et al. 2000), 3.8-m UKIRT (Fynbo et al. 2000) the 8-m SUBARU (Fynbo et al. 2000, Kobayashi et al. 2000) A summary of our observing log is given in Table 1.

Our optical discovery triggered VLA, HST, BeppoSAX and Chandra Target of Oportunity observations (Frail et al. 2000; Price et al. 2000b, Piro et al. 2000), in order to study the multi-wavelength properties of the afterglow and the morphology of the host galaxy.

Fig. 1 shows the 2.2-m CAHA discovery image and an image taken two days later. As it can be seen the afterglow showed a clear fading in that time-span.

Figure 1: The upper panel shows the 2.2-m CAHA discovery R-band image on Sep 27.864 UT. The OT is marked with the arrow. The lower pannel shows the result of coadding seven V-band exposures two days later (Sep 29.825--29.913 UT). The OT decayed ~ 2.5 magnitudes between these two epoch.

3.1- The light-curve of the OT in the R--band

When measuring the magnitude of the OT directly on the images with Point Spread Function (PSF) photometry there will be a contribution from the underlying host galaxy. The relative strength of this contribution depends on the seeing and is therefore a source of systematic errors if not corrected for. We therefore subtracted an aligned and scaled image of the host galaxy from each of the individual R--band images listed in Table 1. For the images earlier than September 29 we found that the contribution from the host galaxy was less than 0.05 mag. We then measured the magnitude of the OT using DAOPHOT-II (Stetson 1987, 1997). The OT was last detected in the image obtained on October 2. The photometry was transformed to the standard system using photometric observations of the four secondary reference observed from the U.S. Naval Observatory Flagstaff Station (Fynbo et al. 2000).

In order to construct a well sampled light-curve we consider the R-band magnitudes measured from the 2.2-m Calar Alto , the INT, NOT and USNO telescopes (see Fig. 2). We first fitted a broken power-law to the light-curve.

which provided a good fit to the data. The parameters of the fit are given in Table 2. We then followed Beuermann et al. (1999) and fitted an empirical function of the form

where f_i(t) = k_i t^-\alpha_i and t is the time since the GRB measured in days. We performed this fit both keeping n fixed at 1 similar to Stanek et al. (1999) and with n as a free parameter. The results of these fits are also given in Table 2.

In conclusion, the data are best fit by a sharp break around t=1.95±0.12 days after the burst. In Fig. 2 we show the R--band light-curve of the OT together with the three fits and the residuals around the fits.

3.2- Other optical bands

The OT was also imaged in the U,B,V and I bands during the first four nights after the detection mainly from the 2.2-m CAHA , NOT , USNO and INT telescopes.

To precisely determine the broad band colours of the OT we used the UBRVI data obtained at the above mentioned four telescopes. We determined the colours as the offset of the broken power-law fit to the R--band light-curve that minimized the \chi² of the fit. Only points obtained earlier than Sep 30 were used in order to minimize the effect of the host galaxy. The 1\sigma errors on the colours were determined as the colours that increased the value of \chi² by 1. For all UBVI filters the fits were consistent with the (offset) broken power-law fit, which shows that the optical afterglow was achromatic to within the errors (few percent).

3.3- Infrared photometry

The afterglow was observed in the K'--band on September 29, 2000 with the IRCS instrument on the 8.2 m SUBARU telescope in a seeing of about 0.7 arcsec. Furthermore, the afterglow was observed in J, H and K bands with the UFTI imager on the 3.8-m United Kingdom Infrared Telescope (UKIRT) on September 30, 2000. The log of IR observations of GRB 000926 is given in Table 3.

We used the UBVRIJHK observations to construct the Spectral energy distribution of the afterglow (SED). The measurements were all carried out within 0.5 days from Sep 30.301 UT. We shifted the magnitudes to Sep. 30.301 UT using the broken power-law fit to the light-curve given in Table 2. Then the colours 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. For the IR bands we used the transformations given in Allen et al. (2000). Finally we calculated the specific flux using F_\nu = 10^{-0.4 × (AB+48.60)}.

Once the galactic extinction was applied the wavelengths corresponding our UBVRIJHK measurements were blueshifted to the GRB rest frame. We realized that the SED exhibits a clear curvature from the U to the K--band. This bend can be easily explained by the presence of intrinsic extinction at z=2.037. To quantify this effect, we fitted to the SED a spectral form given by: F_\nu \alpha \nu^\beta × 10^{(-0.4 A_\nu)}, where \beta is the spectral index and A_\nu the extinction in magnitudes at frequency \nu.

The dependence of A_\nu with the frequency strongly depends on the adopted extinction law. We have considered the three extinction laws 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 parametrized in terms of (restframe) A_V. Thus, our fits allow us to determine \beta and A_V simultaneously.

5.1- The interpretation of the SED

The results of the SED fits are displayed in Table 4. For comparison we have also included in Table 4 the non-extincted case where F_\nu was fitted by a straight-line in a log-log space. The best fit was achieved for a SMC extinction law. In this case we got a modest extinction of A_V=0.18 ± 0.06 and a spectral index \beta= -1.00 ± 0.18.

For the redshift of GRB 000926 the interstelar extinction bump at 2175 is shifted into the R-band filter. This wide absorption is very prominent for the MW, moderate for the LMC and and almost nonexistent for the SMC extinction curve. Thus, for a chemically rich enviroment, like the MW, we should expect a decrease in the R-band flux. We don't see any absorption around the R-band, which makes the fits for the MW (see Table 4) irreconcilable with our experimental points. In fact, is interesting to note that the quality of the fit depends on the strenght of the 2175 absorption feature. So, the SED supports a scenario of a host in the early stages of chemical enrichment.

5.2- Interpretation of the light-curve

The temporal behavior of the optical afterglow of GRB 000926 is a clear and unambiguous example of a broken power-law decay. The fits described in Section 3.1 show that the break occurred abruptly. The late time decay slope of \alpha₂=-2.39±0.09 is very similar to the late time decay slopes of other well studied broken or fastly decaying light-curves (see e.g. Andersen et al. 2000, their Fig. 4 and Table 4). This striking uniformity suggest a common physical scenario for these late part of the decays.

The difference between the early and late time decay slopes are different for different physical models for optical afterglows of GRBs and can hence be used as discriminator between models. For GRB 000926 we find \Delta\alpha = \alpha₁ - \alpha₂ = 0.70±0.09 from the broken power-law fit. This measurement allows us to compare the predictions of four afterglow models: i) If the frequency separating fast cooling and slow cooling electrons moves through the optical part of the electromagnetic spectrum at t_b, the resulting light curve would steepen by \Delta \alpha ~ 0.25 (Sari et al. 1998); ii) If a spherical fireball slows down to a non-relativistic expansion (Dai and Lu 1999) then \Delta \alpha = -(\alpha₁+3/5)= 1.09 for our value of \alpha₁; iii) If the outflow is collimated with a fixed opening angle, the break in the light curve occurs when the relativistic beaming of the synchrotron radiation becomes wider than the jet opening angle (Mészáros and Rees 1999) with a predicted steepening of \Delta \alpha =3/4; iv) finally, if the afterglow arises in a sideways expanding jet, the steepening will be \Delta \alpha =(1-\alpha₁/3)=0.44 (Rhoads 1999) for our value of \alpha₁. The above estimates all assume a constant mean density distribution of the ambient medium. Only model iii, i.e. a jet with fixed opening angle, is consistent with the observed value of \Delta \alpha = 0.70±0.09. This model predicts a spectral slope of the afterglow of \beta = 2 \alpha₁/3 = -1.13 ±0.01, which is not consistent with the \beta = -0.34 ± 0.27 from the multi-band photometry. Thus, a more detailed theoretical afterglow model is necessary to study this enigmatic afterglow.

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