Selection effects in Gamma Ray Bursts correlations: consequences on the ratio between GRB and star formation rates

TL;DR

This study examines whether observed correlations in Gamma Ray Bursts are intrinsic or due to selection effects, and assesses the evolution of the GRB rate relative to star formation across cosmic time.

Contribution

It introduces a general method to evaluate how selection biases affect GRB correlations and applies it to the LT relation, revealing its intrinsic slope and redshift evolution.

Findings

Intrinsic slope of LT correlation is approximately -1.0.

Selection effects can bias the perceived correlation parameters.

GRB rate to star formation rate ratio shows modest evolution with redshift.

Abstract

Gamma Ray Bursts (GRBs) visible up to very high redshift have become attractive targets as potential new distance indicators. It is still not clear whether the relations proposed so far originate from an unknown GRB physics or result from selection effects. We investigate this issue in the case of the $L_X-T^*_a$ correlation (hereafter LT) between the X-ray luminosity $L_X (T_a)$ at the end of the plateau phase, $T_a$, and the rest frame time $T^{*}_a$. We devise a general method to build mock data sets starting from a GRB world model and taking into account selection effects on both time and luminosity. This method shows how not knowing the efficiency function could influence the evaluation of the intrinsic slope of any correlation and the GRB density rate. We investigate biases (small offsets in slope or normalization) that would occur in the LT relation as a result of truncations, possibly present in the intrinsic distributions of $L_X$ and $T^*_a$. We compare these results with the ones in Dainotti et al. (2013) showing that in both cases the intrinsic slope of the LT correlation is $\approx -1.0$. This method is general, therefore relevant to investigate if any other GRB correlation is generated by the biases themselves. Moreover, because the farthest GRBs and star-forming galaxies probe the reionization epoch, we evaluate the redshift-dependent ratio $\Psi(z)=(1+z)^{\alpha}$ of the GRB rate to star formation rate (SFR). We found a modest evolution $-0.2\leq \alpha \leq 0.5$ consistent with Swift GRB afterglow plateau in the redshift range $0.99<z<9.4$.