2015ApJS..218...13Y

Gamma-ray bursts (GRBs) are the most violent explosions in the universe and can be used to explore the properties of the high-redshift universe. It is believed that long GRBs are associated with the deaths of massive stars. Therefore, it is possible to use GRBs to investigate the star formation rate (SFR). In this paper, we use Lynden-Bell's c^–1 method to study the luminosity function and rate of Swift long GRBs without any assumptions. We find that the luminosities of GRBs evolve with redshift as L(z) ∝ g(z) = (1 + z)^k with k = 2.43_–0.38^+0.41. After correcting the redshift evolution through L₀(z)= L(z)/g(z), the luminosity function can be expressed as ψ(L₀) ∝ L₀^{–0.14±0.02} for dim GRBs and ψ(L₀) ∝ L₀^{–0.70±0.03} for bright GRBs, with the break point L₀^b = 1.43 x 10⁵¹erg/s. We also find that the formation rate of GRBs is almost constant at z < 1.0 for the first time, which is remarkably different from the SFR. At z > 1.0, the formation rate of GRBs is consistent with the SFR. Our results are dramatically different from previous studies. We discuss a few possible reasons for this low-redshift excess. We also test the robustness of our results using Monte Carlo simulations. The distributions of mock data (i.e., luminosity-redshift distribution, luminosity function, cumulative distribution, and log N-log S distribution) are in good agreement with observations. Also, we find that there are remarkable differences between the mock data and the observations if long GRBs are unbiased tracers of SFR at z < 1.0.