Probing evolution of Long GRB properties through their cosmic formation history aided by Machine Learning predicted redshifts

TL;DR

This study addresses how long GRB properties evolve across cosmic history by leveraging redshift estimates predicted without cosmology-dependent correlations, derived from prompt and afterglow observables. It builds two samples (PS and CS) and uses luminosity evolution corrections via $L' = L/(1+z)^{k}$ and KS-based flux limits to compute the LGRB rate density $\rho(z)$ from the cumulative distributions $\sigma$, then compares to the observed rate and to the cosmic SFRD MD14. The results show that simple evolutionary scenarios, including $(1+z)^{\delta}$ or beaming evolution, can explain the $z \in [1,2]$ region but fail at low and high redshift, suggesting a more complex evolution or sample heterogeneity, and pointing to stronger constraints achievable with larger, multiwavelength training sets and upcoming facilities. The approach demonstrates the value of ML-equipped redshift inference for GRB demographics and informs future observational strategies to connect GRB formation with star-formation history.

Abstract

Gamma-ray Bursts (GRBs) are valuable probes of cosmic star formation reaching back into the epoch of reionization, and a large dataset with known redshifts ($z$) is an important ingredient for these studies. Usually, $z$ is measured using spectroscopy or photometry, but $\sim80\%$ of GRBs lack such data. Prompt and afterglow correlations can provide estimates in these cases, though they suffer from systematic uncertainties due to assumed cosmologies and due to detector threshold limits. We use a sample with $z$ estimated via machine learning models, based on prompt and afterglow parameters, without relying on cosmological assumptions. We then use an augmented sample of GRBs with measured and predicted redshifts, forming a larger dataset. We find that the predicted redshifts are a crucial step forward in understanding the evolution of GRB properties. We test three cases: no evolution, an evolution of the beaming factor, and an evolution of all terms captured by an evolution factor $(1+z)^δ$. We find that these cases can explain the density rate in the redshift range between 1-2, but neither of the cases can explain the derived rate densities at smaller and higher redshifts, which may point towards an evolution term different than a simple power law. Another possibility is that this mismatch is due to the non-homogeneity of the sample, e.g., a non-collapsar origin of some long GRB within the sample.

Figures (8)

• Figure 1: Left: The $\tau$-k distribution for the predicted sample. We select the k value corresponding to $\tau=0$ to make the luminosity and $\mathrm{1+z}$ independent of each other. Right: The $\tau$-k distribution for the combined sample. We select the k value corresponding to $\tau=0$ to make the Luminosity and $1+z$ independent of each other.
• Figure 2: Left panel: The fit to $\sigma$ of the predicted sample with the best parameters derived from the sigmoid function. The best-fit parameters to this function are noted in the first row of Table \ref{['tab:sigma_fit_params']}. Right panel: The fit to $\sigma$ of the combined sample with the best parameters derived from a piecewise function. The data points below $z_{cut}=3.01$ are best fit with a 4th-order polynomial, while the data points above $z_{cut}$ are best fit with a sigmoid. The best-fit parameters to these functions are noted in the second and third rows of Table \ref{['tab:sigma_fit_params']}.
• Figure 3: The comparison of $\rho_{PS}(z)$ and $\rho_{CS}(z)$ in this study, with rate densities from the X-ray study of K25 and the optical study of 2024ApJ...967L..30D. All other data points/lines correspond to various SFRD in the literature as specified in the legend. All curves/data points are renormalized to the predicted sample for better comparison.
• Figure 4: Example figure of $\rho_{LGRB}(z)$ in 1+z space. The orange-filled circles represent the $\rho_{OS}$ taken from K25. The red-filled and blue-filled circles represent $\rho_{PS}$ and $\rho_{CS}$, respectively. The black solid curve is $\rho_{theor}$ derived from Equation \ref{['eq: Drake_eqn']} and multiplied with $(1+z)^{\delta}$. We choose $\delta$ = 1.6 as an example for this figure. The interactive figure is available in the online version of the journal, which contains a slider that allows $\delta$ to change, thus accounting for the evolution of GRB/progenitor properties.
• Figure 5: Left panel: The $z$-distribution of the total sample, which contains all GRBs with X-ray plateaus detected by Swift and the distribution of the PS. Right panel: The KS test of the two samples in the left panel. We include four cases of $F_{lim}$ corresponding to a 5%, 10%, 15%, and 20% cut from left to right. The 5% cut has the highest p-value.