is very similar to the late time
decay slopes of other well studied broken or fast 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 the late stage of the decays, which most likely
is a common value of the index of the electron energy
distribution (see also Sari et al. 1999; Freedman & Waxman
2001).
The increase
from the early to the late time decay slope is different for
different physical models for GRB afterglows. For
GRB 000926 we find
from the broken
power-law fit.
This measurement we compare with different models predicting
broken light-curves: i) If the frequency separating fast
cooling and slow cooling electrons moves through the optical part of
the electromagnetic spectrum at
,
the resulting light curve would steepen by
(Sari et al. 1998); ii) If a spherical fireball slows
down to a non-relativistic expansion (Dai & Lu 1999) then
for our value of 
;
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
with a predicted steepening of
(Mészáros & Rees 1999); iv) finally, if the afterglow
arises in a sideways expanding jet, the steepening will be
(Rhoads 1999) for our value of
.
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
.
This model predicts a spectral
slope of the afterglow of
,
which is consistent with the
from the multi-band photometry.
If the density of the surrounding medium was that of stellar wind
(
with
)
we expect
(Mészáros & Rees
1999; Jaunsen et al. 2001), which is excluded by the data at the
2.2
level.
for GRB 000926 (Møller et al., in prep)
and
for GRB 000301C (Jensen et al. 2001) makes it
very convenient to compare the two. Both GRB 000301C and GRB 000926
displayed broken power-law decays. For the OT of GRB 000301C
Jensen et al. (2001) determined
and
.
In this case the best model is
that of a side-ways expanding jet in a medium of constant density,
whereas a jet with fixed opening angle is not consistent with the
data. Therefore, even though the two bursts appear similar they cannot
be explained by the same model.
GRB 000301C and GRB 000926 have very different host galaxies.
The host galaxy of GRB 000301C remains undetected despite a very
deep detection limit of R=28.5 (Fruchter et al. 2000a; Smette et al.
2001), whereas the
host galaxy of GRB 000926 is relatively bright at
(Sect. 6). Hence, the
host galaxy of GRB 000926 is more than 70 times brighter than that
of GRB 000301C. In the same way GRB 990123 and GRB 990510
occured
at nearly identical redshifts
and the host galaxy
of the former is
more than 30 times brighter than the latter (Holland & Hjorth 1999;
Fruchter et al.
1999, 2000b). If GRBs indeed trace star-formation these observations
indicate that at these redshifts galaxies covering a broad range
of luminosities contribute significantly to the over-all density of
star formation. Furthermore, as the observed R-band flux is
proportional to the star formation rate, there must be
1-2 orders of magnitude more galaxies at the R=28 level than at the
R=24 level at 
.
Otherwise it would be unlikely to detect
R=28 galaxies as GRB hosts (under the assumption that GRBs trace
star-formation). An alternative explanation is that the
faint host galaxies of GRB 000301C and GRB 990510 are faint at
rest-frame UV wavelengths due to massive extinction similar to some
sources selected in the sub-mm range (e.g. Ivison et al. 2000).
However, the low extinction derived from the optical properties of the
GRB 000301C afterglow argues against this explanation at least for this
particular burst.
Acknowledgements
Most of the optical data presented here have been taken using ALFOSC, which is owned by the Instituto de Astrofisica de Andalucia (IAA) and operated at the Nordic Optical Telescope under agreement between IAA and the NBIfAFG of the Astronomical Observatory of Copenhagen. UKIRT is operated by the Joint Astronomy Centre on behalf of the Particle Physics and Astronomy Research Council of the United Kingdom. JUF and THD acknowledges enthusiastic help and support from C. Møller and I. Svärdh during the hectic moments of finding the OT by comparison with DSS-plates. JUF acknowledges H. O. Fynbo for introducing him to CERNs MINUIT fitting programme. JG acknowledges the receipt of a Marie Curie Research Grant from the European Commission. MIA acknowledges the Astrophysics group of the Physics dept. of University of Oulu for support of his work. IRS acknowledges support from a Royal Society URF. IB was supported by Pôle d'Attraction Interuniversitaire, P4/05 (SSTC, Belgium). JMCC acknowledges the receipt of a FPI doctoral fellowship from Spain's Ministerio de Ciencia y Tecnología. KH is grateful for Ulysses support under JPL Contract 958056, and for NEAR support under NASA grants NAG5-9503 and NAG5-3500. Additionally, the availability of the GRB Coordinates Network (GCN) and BACODINE services, maintained by Scott Barthelmy, is greatly acknowledged. We acknowledge the availability of POSS-II exposures, used in this work; the Second Palomar Observatory Sky Survey (POSS-II) was made by the California Institute of Technology with funds from the National Science Foundation, the National Aeronautics and Space Administration, the National Geographic Society, the Sloan Foundation, the Samuel Oschin Foundation, and the Eastman Kodak Corporation. We acknowledge the availability of the 2MASS catalogs. This work was supported by the Danish Natural Science Research Council (SNF).
Copyright ESO 2001