Event Weighted Tests for Detecting Periodicity in Photon Arrival Times

TL;DR

This paper develops likelihood-based event weighting tests to improve detection of periodic signals in photon arrival data, such as gamma-ray pulsars, by incorporating auxiliary information and assessing template deviations.

Contribution

It introduces a principled likelihood-based framework for event weighting in periodicity detection, accounting for auxiliary data and template deviations.

Findings

Derived expressions for test power and efficacy of weight functions

Quantified impact of template deviations on detection power

Provided a method to compare different weighting schemes

Abstract

This paper treats the problem of detecting periodicity in a sequence of photon arrival times, which occurs, for example, in attempting to detect gamma-ray pulsars. A particular focus is on how auxiliary information, typically source intensity, background intensity, and incidence angles and energies associated with each photon arrival should be used to maximize the detection power. We construct a class of likelihood-based tests, score tests, which give rise to event weighting in a principled and natural way, and derive expressions quantifying the power of the tests. These results can be used to compare the efficacies of different weight functions, including cuts in energy and incidence angle. The test is targeted toward a template for the periodic lightcurve, and we quantify how deviation from that template affects the power of detection.