Bayesian Model Comparison and Analysis of the Galactic Disk Population of Gamma-Ray Millisecond Pulsars

TL;DR

This paper presents a Bayesian analysis of gamma-ray millisecond pulsars, modeling their spatial and luminosity distributions while accounting for distance uncertainties, and identifies the most supported population model.

Contribution

It introduces a self-consistent Bayesian framework for analyzing MSP populations, including a new Python package for distance uncertainty estimation and model comparison.

Findings

Broken power law luminosity function is preferred.

Best-fit spatial distribution aligns with radio MSPs.

Number of gamma-ray MSPs estimated consistently with previous radio studies.

Abstract

Pulsed emission from almost one hundred millisecond pulsars (MSPs) has been detected in $\gamma$-rays by the Fermi Large-Area Telescope. The global properties of this population remain relatively unconstrained despite many attempts to model their spatial and luminosity distributions. We perform here a self-consistent Bayesian analysis of both the spatial distribution and luminosity function simultaneously. Distance uncertainties, arising from errors in the parallax measurement or Galactic electron-density model, are marginalized over. We provide a public Python package for calculating distance uncertainties to pulsars derived using the dispersion measure by accounting for the uncertainties in Galactic electron-density model YMW16. Finally, we use multiple parameterizations for the MSP population and perform Bayesian model comparison, finding that a broken power law luminosity function with Lorimer spatial profile are preferred over multiple other parameterizations used in the past. The best-fit spatial distribution and number of $\gamma$-ray MSPs is consistent with results for the radio population of MSPs.