The rate and luminosity function of long Gamma Ray Bursts

Understand

We derive, adopting a direct method, the luminosity function and the formation rate of long Gamma Ray Bursts through a complete, flux-limited, sample of Swift bursts which has a high level of completeness in redshift z (~82%).

• We parametrise the redshift evolution of the GRB luminosity as L = L_0(1+ z)^k and we derive k = 2.5, consistently with recent estimates.
• The de-evolved luminosity function of GRBs can be represented by a broken power law with slopes a = -1.32 +- 0.21 and b = -1.84 +- 0.24 below and above, respectively, a characteristic break luminosity L_0,b = 10^51.45+-0.15 erg/s.
• Under the hypothesis of luminosity evolution we find that the GRB formation rate increases with redshift up to z~2, where it peaks, and then decreases in agreement with the shape of the cosmic star formation rate.