Shiwei Wu, Dong Xu, Daming Wei
Gamma-ray bursts (GRBs) are brief but intense emission of soft {\gamma}-rays,
mostly lasting from a few seconds to a few thousand seconds. For such kind of
high energy transients, their isotropic-equivalent energy ($E_{\rm iso}$) can
be reliably measured and may be more scientifically meaningful when compared
with GRB isotropic-equivalent luminosity function ($L_{\rm iso}$) as well as
cosmic GRB formation rate, as the traditional luminosity function refers to
steady emission much longer than a few thousand seconds. In this work we for
the first time construct the isotropic-equivalent-energy function for a sample
of 95 bursts with measured redshifts (z). Using a {\tau} statistical technique,
we find cosmic evolution between $E_{\rm iso}$ and z, i.e., $E_{\rm
iso}\propto(1+z)^{1.8^{+0.36}_{-0.63}}$, which is comparable to that between
$L_{\rm iso}$ and z, i.e., $L_{\rm iso}\propto(1+z)^{2.30^{+0.56}_{-0.51}}$
(both 1{\sigma}). The local isotropic-equivalent-energy function can be
reasonably fitted by a broken power-law, in which the dim and bright segments
are $\psi(E_{\rm iso})\propto E_{\rm iso}^{-0.27\pm0.01}$ and $\psi(E_{\rm
iso})\propto E_{\rm iso}^{-0.87\pm0.07}$, respectively. For the cosmic GRB
formation rate, it increases quickly in the region of $0\leq z \lesssim 1$, and
roughly keeps constant for $1\lesssim z \lesssim 4$, and finally falls with a
power index of $-3.80\pm2.16$ for $z\gtrsim 4$, in good agreement with the
observed cosmic star formation rate so far. In future a larger GRB sample with
known redshifts shall better address the consistency/inconsistency between
these two formation rates.
View original:
http://arxiv.org/abs/1112.2029
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