The Fermi Large Area Telescope has recently revealed a large population of gamma-ray emitting millisecond pulsars (MSPs) in our Galaxy. We aim to infer the properties of the Galactic population of gamma-ray emitting MSPs from the sample of objects detected by the Fermi-LAT. We developed a Monte Carlo model to predict the spatial and gamma-ray luminosity distribution of the Galactic MSP population and estimate their number in the Milky Way.

Based on the estimated detection sensitivity of Fermi-LAT, we split the model population in detectable and undetectable samples of MSPs. Using a maximum likelihood method, we compare the detectable sample to a set of 36 MSPs detected by Fermi-LAT, and we derive the parameters of the spatial distribution and the total number of gamma-ray emitting MSPs in the Galaxy. The corresponding undetectable sample provides us with an estimate for the expected diffuse emission from unresolved MSPs in the Milky Way. We also apply our method to an increased sample of 88 MSPs that combines firmly detected MSPs and gamma-ray sources that show characteristics reminiscent of MSPs.