Intensity Distribution and Luminosity Function of the Swift Gamma-Ray Bursts

Using the sample of long Gamma-ray bursts (GRBs) detected by Swift-BAT before June 2007, we measure the cumulative distribution of the peak photon fluxes (log N - log P) of the Swift bursts. Compared with the BATSE sample, we find that the two distributions are consistent after correcting the band pass difference, suggesting that the two instruments are sampling the same population of bursts. We also compare the log N - log P distributions for sub-samples of the Swift bursts, and find evidence for a deficit (99.75% confident) of dark bursts without optical counterparts at high peak flux levels, suggesting different redshift or Gamma-ray luminosity distributions for these bursts. The consistency between the log N - log P distributions for the optically detected bursts with and without redshift measurements indicates that the current sample of the Swift bursts with redshift measurements, although selected heterogeneously, represents a fair sample of the non-dark bursts. We calculate the luminosity functions of this sample in two redshift bins (z<1 and z>1), and find a broken power-law is needed to fit the low redshift bin, where dN/dL \propto L^{-1.27\pm0.06} for high luminosities (L_{peak} > 5e48 erg/s) and dN/dL \propto L^{-2.3\pm0.3} at for low luminosities, confirming the results of several studies for a population of low luminosity GRBs.