The Non-homogeneous Poisson Process for Fast Radio Burst Rates

TL;DR

This paper introduces the non-homogeneous Poisson process (NHPP) as a flexible statistical model for estimating the rate of fast radio bursts (FRBs), incorporating survey details and flux distributions, and provides new rate estimates based on multiple surveys.

Contribution

It presents a tutorial on NHPP and develops a model that includes beam patterns and flux distributions to estimate FRB rates from survey data.

Findings

Estimated all-sky FRB rate: 587 events per day above 1 Jy

Flux power-law index: 0.91

Rate estimate is lower but consistent with previous studies

Abstract

This paper presents the non-homogeneous Poisson process (NHPP) for modeling the rate of fast radio bursts (FRBs) and other infrequently observed astronomical events. The NHPP, well-known in statistics, can model changes in the rate as a function of both astronomical features and the details of an observing campaign. This is particularly helpful for rare events like FRBs because the NHPP can combine information across surveys, making the most of all available information. The goal of the paper is two-fold. First, it is intended to be a tutorial on the use of the NHPP. Second, we build an NHPP model that incorporates beam patterns and a power law flux distribution for the rate of FRBs. Using information from 12 surveys including 15 detections, we find an all-sky FRB rate of 586.88 events per sky per day above a flux of 1 Jy (95\% CI: 271.86, 923.72) and a flux power-law index of 0.91 (95\% CI: 0.57, 1.25). Our rate is lower than other published rates, but consistent with the rate given in Champion et al. 2016.