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One of the most impressive properties of the bursts is the huge amount of
energy released (fig.
), typically ranging
between few
and few
ergs (isotropic emission).
Figure:
Energy Distribution of GRBs with known redshift in two cases:
isotropic emissions (top panel), and geometry-corrected for jet-like
emissions (bottom panel). The non-isotropic case tightly clusters the
distribution around
erg. (From [Frail et al., 2001]).
 |
Assuming isotropic emission, the case of GRB990123 is really impressive:
only in the gamma-ray domain, it released
ergs, i.e.
about twice the rest mass of the Sun.
If one supposes a jet-like emission, the energy requirements are reduced
by a factor of
with respect to the
spherical emission (
is the solid angle subtended by the emission
cone). On this subject, searches for the so-called ``orphan afterglows'',
corresponding to GRBs beamed away from our line of sight, have been performed,
only providing limits on the beaming factor.
Figure:
The two different cases of spherical and jet-like emission:
the visibility cone, defined by the time-evolving bulk Lorentz factor,
should distinguish at late times between the two cases. (From [Ghisellini, 2001]).
 |
Fig.
nicely shows what kind of observable effects should be
measured in the afterglow light curve for the two different cases of spherical
and jet-like emission: the relativistic beaming produces a visibility cone with
an opening angle of
. In the early phases,
(see Fireball
Model section) and the two cases cannot be distinguished; as the afterglow evolves,
decreases; when it is
(
is the opening
angle of the jet), the afterglow light curve in the jet-like geometry should break
and decline more rapidly, since an edge effect occurs. Indeed, the break in the
light curve is due also to another effect: the lateral spreading of the jet, since
the ejecta, encountering more surrounding matter, decelerate faster than it happens
for the spherical case. The clearest evidence for a jet can be found in the sharp
achromatic break in the light curve of GRB990510.
Also the detection of polarization for this burst ([Covino et al., 1999]) seems to agree
with the jet-like emission. Recently, [Frail et al., 2001], have tried to estimate the
opening angles
for a set of bursts with known redshifts, whose break
times
(or limits) have been estimated; the set of
coming out
includes the range
with a strong concentration around
.
The energy distribution derived is surprisingly more clustered with respect
to the spherical case, around
ergs.
Next: Theoretical Models
Up: The Afterglow Emission
Previous: GRB-SN Connection
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Cristiano Guidorzi
2003-07-31