Bayesian model comparison and analysis of the Galactic disc population of gamma-ray millisecond pulsars

Pulsed emission from almost one hundred millisecond pulsars (MSPs) has been detected in γ-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 (available from http://github.com/tedwards2412/MSPDist) 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 parametrizations 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 parametrizations used in the past. The best-fitting spatial distribution and number of γ-ray MSPs is consistent with results for the radio population of MSPs.