Determining the luminosity function of Swift long gamma-ray bursts with pseudo-redshifts

Understand

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.