Cosmological Evolution of Gamma Ray Bursts

TL;DR

This work revisits the formation and evolution of long gamma-ray bursts (LGRBs) by leveraging an expanded Swift-based sample that includes ML-derived redshifts to reduce redshift-selection bias. Using nonparametric Efron–Petrosian analyses, it quantifies luminosity evolution via a redshift-dependent function $g(Z)$ and recovers the local luminosity function with the Lynden–Bell $C^-$ method, finding a significant evolution with $L_0=L/g(Z)$ and a smoothly broken power-law LF. The LGRB formation-rate density is modeled with a double-break law and compared to the cosmic star formation rate (SFR); results show general agreement with the SFR for $z\gtrsim 1.5$ in both catalogs, but a notable low-$z$ excess—especially in the spectroscopic sample—hinting at a possible contribution from compact binary mergers and kilonovae. These findings support a more nuanced view of LGRB progenitors and underscore the value of ML-augmented datasets for tracing GRB history and associated gravitational-wave event rates.

Abstract

Gamma Ray Bursts (GRBs) are classified as long (LGRBs) and short (SGRBs) with collapsars and compact object mergers (neutron star (NS)-NS or NS-Black hole) as progenitors, respectively. The former are expected to follow the cosmic star formation rate (SFR), while the latter follows a delayed version of the SFR. However, this division has come under question in several ways, the most prominent being the observational evidence of a significant excess of LGRBs at low redhifts by several independent investigations, summarized in arXiv:2305.15081. This could indicate that the progenitors of low-redshift LGRBs, whose formation rates are delayed, (similar to that of SGRBs) are compact mergers rather than collapsars. Two recent observations of low-redshift LGRBs show associations with kilonovae, a clear feature of compact mergers. Most results showing this separation are based on analyses of small (less than 200) samples of LGRBs with measured redshifts. The aim of this paper is to use a larger sample of LGRBs. The number of LGRBs with measured redshifts has increased by more than a factor of 2 over the last decade. To this data set we add a sample of LGRBs whose redshifts are estimated using a machine learning (ML) method (arXiv:2410.13985). This, in addition to increasing the sample size, reduces the observational selection bias arising from the process of redshift measurement. To account for this bias, we use the non-parametric, non-binning Efron-Petrosian method to establish the degree of correlation between luminosity and redshift, the luminosity evolution, which then allows us to use the Lynden-Bell $C^-$ method to obtain a complete description of the luminosity function. We find similar low redshift excess for the larger sample with measured redshifts. Adding the sources with ML-estimated redshifts, which tend to have more sources in mid-range redshifts, the excess is reduced.

Figures (7)

• Figure 1: Comparison of fractional binned redshift distributions of ML (green) and non-ML (red) samples.
• Figure 2: Flowchart of Data Processing Pipeline
• Figure 3: Power-law fit overlaid on running-average $K$-corrections.
• Figure 4: ( Left): Redshifts and Luminosities for combined GRB catalog. The black truncation line is obtained from $f_{\mathrm{lim}}$ and the average $K$. The power law fit for the bursts is shown in green. ( Right): Redshifts and Luminosities for the Non-ML Catalog
• Figure 5: Kendall’s $\tau$ statistic as a function of $k$ for the full GRB catalog (blue) and the non-ML subset (red). Solid curves show the measured $\tau(k)$. Dashed lines indicate the central (fit) guides for each dataset, while the lighter dashed bands denote the corresponding $\pm 1\sigma$ ranges.