Distributions of Pseudo-Redshifts and Durations (Observed and Intrinsic) of Fermi GRBs

Abstract

Ever since the insightful analysis of the durations of GRBs by [Kouveliotou:93], GRBs have most often been classified into two populations: "short bursts" (shorter than 2.0 seconds) and "long bursts" (longer than 2.0 seconds). However, recent works have suggested the existence of an intermediate population in the bursts observed by the Swift satellite. Moreover, some researchers have questioned the universality of the 2.0-second dividing line between short and long bursts: some bursts may be short but actually result from collapsars, the physical mechanism behind normally long bursts, and some long ones may originate from mergers, the usual progenitors of short GRBs. In this work, we focus on GRBs detected by the Fermi satellite and study the distribution of their durations measured in the observer's reference frame and, for those with known redshifts, in the bursts' reference frames. However, there are relatively few bursts with measured redshifts, and this makes an accurate study difficult. To overcome this problem, we follow [Zhang:2018] and determine a "pseudo-redshift" from the correlation relation between the luminosity $L_p$ and the energy $E_p$, both of which are calculated at the peak of the flux. Interestingly, we find that the uncertainties in the quantities observed and used in the determination of pseudo-redshifts, do affect the precision of the individual results significantly, but they keep the distribution of pseudo-redshifts very similar to that of the actual ones and thus allow us to use pseudo-redshifts for our statistical study. We use the reduced chi-square and the maximization of the log-likelihood to statistically analyze the distribution of Fermi GRB durations. Both methods show that the distribution of the observed and the intrinsic bursts durations are better represented by two groups, rather than three.