# A statistical method to detect non-stationarities of gamma-ray burst jets

## TL;DR

This paper introduces a statistical method to identify non-stationarities in gamma-ray burst jets by linking variability measures to jet angles, supported by simulations across different jet profiles.

## Contribution

The study develops a novel approach connecting gamma-ray burst variability to jet characteristics, validated through Monte Carlo simulations for various jet profiles.

## Key findings

- Anti-correlation between variability and jet angle for uniform and power-law profiles.
- Correlation between variability and jet angle for Gaussian profiles.
- 50 to 237 observations needed for 3σ to 5σ detection depending on jet profile.

## Abstract

We propose a method to detect possible non-stationarities of gamma-ray burst jets. Assuming that the dominant source of variability in the prompt gamma light curve is the non-stationarity of the jet, we show that there should be a connection between the variability measure and the characteristic angle of the jet derived from the jet break time of the afterglow. We carried out Monte Carlo simulations of long gamma-ray burst observations assuming three radial luminosity density profiles for jets and randomizing all burst parameters, and created samples of gamma light curves by simulating jets undergoing Brownian motions with linear restoring forces. We were able to demonstrate that the connection between the variability and the characteristic angle is an anti-correlation in case of uniform and power-law jet profiles, and a correlation in case of a Gaussian profile. We have found that as low as $50$ $(144)$ gamma-ray burst observations with jet angle measurements can be sufficient for a $3\sigma\ (5\sigma) $ detection of the connection. The number of observations required for the detection depends on the underlying jet beam profile, ranging from 50 (144) to 237 (659) for the four specific profile models we tested.