The Cosmic Star Formation History: Insights from Kilonova-Associated Gamma-Ray Bursts

TL;DR

The paper addresses whether kilonova-associated GRBs (KN/GRBs) can serve as clean tracers of the cosmic delayed SFR, circumventing contamination in $T_{90}$-based classifications. It assembles a sample of 20 KN/GRBs with redshifts and spectra, computes bolometric luminosities with $L = 4\pi d_L^2(z) F K$ using CPL/Band fits, and removes selection biases via Lynden-Bell's $c^{-}$ method alongside EP-L de-evolution with $g(z)=(1+z)^k$ (found $k=6.46$). The KN/GRB luminosity function follows a smoothly broken power law with break at $L_0^b \approx 1.15 \times 10^{49}$ erg s$^{-1}$, and the de-evolved FR declines with redshift, showing a low-$z$ excess relative to the SFR and delay-SFR models. The results indicate KN/GRBs do not straightforwardly trace the delayed SFR, likely due to sample size, high-redshift sparsity, or evolving progenitor/environmental factors, underscoring the need for larger KN/GRB surveys to clarify their role in cosmic star-formation history.

Abstract

The origin of the Universe and its material content remains one of the most fundamental questions in science. Gamma-ray bursts (GRBs), with their extreme luminosities and high-redshift detectability, provide a unique window into the history of cosmic formation and chemical evolution. Consequently, the GRB formation rate (FR) has been employed to trace the star formation rate (SFR) across cosmic time. GRBs are conventionally classified into long and short categories (lGRBs and sGRBs) based on their $ T_{90} $ duration. sGRBs are widely employed as tracers of the delayed SFR, owing to their origin linked to the inspiral timescales of compact binary systems. However, some studies suggest that the detection of supernova-associated sGRBs may indicate potential contamination by core-collapse events. In this work, we move beyond the $ T_{90} $ classification and focus exclusively on GRBs with confirmed kilonova signatures, which provide unambiguous evidence of binary compact star mergers, to reassess their connection with the delayed SFR. Through analysis of a kilonova-associated GRB (KN/GRBs) sample, we find that even within this robust subset, the KN/GRB FR displays a trend contrary to that of the delayed SFR at low redshifts ($ z < 1 $). This result challenges the conventional theory by indicating that low-redshift KN/GRBs may not accurately trace the delayed SFR, independent of core-collapse contamination, while further validation with larger KN/GRB samples is essential to determine the reliability of compact binary mergers as probes of delayed SFR.

Figures (3)

• Figure 1: Distributions and correlations for the KN/GRBs sample: Left top: Duration ($T_{90}$) distribution of KN/GRBs events; Right top: Bolometric luminosity distribution where individual points represent different KN/GRBs, with the line indicating the sensitivity limit of $1.0 \times 10^{-8}\,\mathrm{erg\,cm^{-2}\,s^{-1}}$; Left bottom: In the Kendall $\tau$ correlation test, the red dotted line represents the null hypothesis ($\tau = 0$), and the measured correlation strength of $k = 6.46$ suggests that the evolutionary dependence between luminosity and redshift has been effectively removed; Right bottom: De-evolved luminosity function following $L = L_{0}(1 + z)^{6.46}$ for our sample of 20 KN/GRBs, removing the redshift evolution component.
• Figure 2: Left: The distribution of cumulative luminosity function $\psi({L_0})$, which is normalized to unity at the lowest luminosity. The function is fitted by red solid line with broken power law. The luminosity function can be expressed as $\psi ({L_0}) = L_0^{-0.15 \pm 0.04},{L_0} < L_0^b$ and $\psi ({L_0}) = L_0^{-0.43 \pm 0.03},{L_0} > L_0^b$; Right: Normalized cumulative redshift distribution.
• Figure 3: Comparison KN/GRBs rate and SFR. The thick colored curves display the best fits achieved by applying merged delay models to each distribution. The SFR data and fit line were collected from 2014ARAA..52..415M (Brown dots). The blue line are the formation rate of fitting 20 KN/GRBs sources. The error bar gives a 1 $\sigma$ poisson error 1986ApJ...303..336G. These fitting lines are normalized at z=1.