Milli-second pulsars and the Galactic center excess

Since the early operational years of the Fermi-LAT, an unexpected excess of γ rays has been observed in the Galactic Center, now known as the Galactic Center Excess (GCE). This remains one of the most intriguing unresolved problems in astroparticle physics. In this work, we explore the hypothesis that the GCE is due to a population of unresolved Milli-Second Pulsars (MSPs). We focus on selecting and implementing the most effective method to simulate an MSP population and examine their characteristics in the Outer Galaxy region. The simulation considers both the spatial distribution of MSPs, modeled using a Lorimer-Disk distribution, and their luminosity function, described by a Log-Normal distribution. By combining these simulations, we generate a model of the MSP population in terms of their expected flux. Using a One-point Probability Distribution Function (1pPDF) analysis, we compare our simulations to observational data also below the Fermi threshold level. These comparisons allow us to constrain the parameters of the luminosity function. Assuming that both the disk and bulge populations share the same luminosity function, our results provide constraints on the MSP population that could potentially explain the GCE. This analytical method can be readily applied to constrain other luminosity functions or to explore different characteristics of the GCE.