Monte Carlo evaluations of gamma-ray and radio pulsar populations
Based on well-grounded Galactic neutron star populations formed from radio pulsar population syntheses of canonical pulsars (CPs) and millisecond pulsars (MSPs), we use the latest Fermi-LAT catalog (4FGL-DR4) to investigate the implications of proposed $γ-$ray luminosity models. Using Monte Carlo techniques, we calculate the number of CPs and MSPs that would comprise the sample of pulsar-like unidentified sources (PLUIDs) in 4FGL-DR4. While radio beaming fractions were used to scale the sizes of the populations, when forming the mock 4FGL-DR4 samples, we make the simplifying assumption that all $γ-$ray pulsars are beaming towards the Earth. We then explore the observable outcomes of seven different $γ-$ray luminosity models. Four of the models provide a good match to the observed number of PLUIDs, while three others significantly over-predict the number of PLUIDs. For these latter models, either the average beaming fraction of $γ-$ray pulsars is more like 25--50\%, or a revision in the luminosity scaling is required. Most of the radio detectable MSPs that our models predict as part of the PLUIDs within 4FGL-DR4 are, unsurprisingly, fainter than the currently observed sample and at larger dispersion measures. For CPs, in spite of an excellent match to the observed radio population, none of the $γ-$ray models we investigated could replicate the observed sample of 150 $γ-$ray CPs. Further work is required to understand this discrepancy. For both MSPs and CPs, we provide encouraging forecasts for targeted radio searches of PLUIDs from 4FGL-DR4 to elucidate the issues raised in this study.