A Simple Method To Test For Energy-Dependent Dispersion In High Energy Light Curves Of Astrophysical Sources

TL;DR

This paper introduces a non-parametric, unbinned method using Kolmogorov distance to detect energy-dependent dispersion in astrophysical light curves, aiding in testing quantum gravity effects with gamma-ray data.

Contribution

It proposes a novel, statistically robust technique for identifying energy-dependent dispersion in transient astrophysical signals, suitable for limited and modestly resolved data sets.

Findings

Method effectively detects energy-dependent dispersion in simulated data.

Performs well with typical gamma-ray energy resolutions (~20%).

Can constrain quantum-gravity Lorentz invariance violation effects.

Abstract

We present a method of testing for the presence of energy dependent dispersion in transient features of a light curve. It is based on minimising the Kolmogorov distance between two cumulative event distribution functions. The unbinned and non-parametric nature of the test makes it particularly suitable for searches of statistically limited data sets and we also show that it performs well in the presence of modest energy resolutions typical of gamma-ray observations (~20%). We illustrate its potential to set constraints on quantum-gravity induced Lorentz invariance violation effects from observations by the current and future generation of ground-based gamma-ray telescopes.