An improved method for estimating source densities using the temporal distribution of Cosmological Transients

TL;DR

This paper introduces an improved method for estimating the density of cosmological transient sources using their temporal distribution, leveraging invariance properties and applying it to gamma-ray burst data to predict future observations.

Contribution

The paper develops a novel, more accurate approach for constraining transient source distributions by utilizing the invariance of the peak flux--observation time relation and temporal principles.

Findings

The peak flux--observation time relation is invariant to source luminosity distribution.

The method aligns well with recent gamma-ray burst source parameter estimates.

Predictions indicate a 50% chance of detecting high-flux bursts within the next year.

Abstract

It has been shown that the observed temporal distribution of transient events in the cosmos can be used to constrain their rate density. Here we show that the peak flux--observation time relation takes the form of a power law that is invariant to the luminosity distribution of the sources, and that the method can be greatly improved by invoking time reversal invariance and the temporal cosmological principle. We demonstrate how the method can be used to constrain distributions of transient events, by applying it to Swift gamma-ray burst data and show that the peak flux--observation time relation is in good agreement with recent estimates of source parameters. We additionally show that the intrinsic time dependence allows the method to be used as a predictive tool. Within the next year of Swift observation, we find a 50% chance of obtaining a peak flux greater than that of GRB 060017 -- the highest Swift peak flux to date -- and the same probability of detecting a burst with peak flux > 100 photons s^{-1} cm^{-2} within 6 years.