Determining the luminosity function of Swift long gamma-ray bursts with
  pseudo-redshifts
  The determination of luminosity function (LF) of gamma-ray bursts (GRBs) is
of an important role for the cosmological applications of the GRBs, which is
however hindered seriously by some selection effects due to redshift
measurements. In order to avoid these selection effects, we suggest to
calculate pseudo-redshifts for Swift GRBs according to the empirical L-E_p
relationship. Here, such a $L-E_p$ relationship is determined by reconciling
the distributions of pseudo- and real redshifts of redshift-known GRBs. The
values of E_p taken from Butler's GRB catalog are estimated with Bayesian
statistics rather than observed. Using the GRB sample with pseudo-redshifts of
a relatively large number, we fit the redshift-resolved luminosity
distributions of the GRBs with a broken-power-law LF. The fitting results
suggest that the LF could evolve with redshift by a redshift-dependent break
luminosity, e.g., L_b=1.2\times10^{51}(1+z)^2\rm erg s^{-1}. The low- and
high-luminosity indices are constrained to 0.8 and 2.0, respectively. It is
found that the proportional coefficient between GRB event rate and star
formation rate should correspondingly decrease with increasing redshifts.
