Constraining the Galactic millisecond pulsar population using Fermi Large Area Telescope

Context. The Fermi Large Area Telescope (Fermi-LAT) has recently revealed a large population of gamma-ray emitting millisecond pulsars (MSPs) in our Galaxy. Aims. We aim to infer the properties of the Galactic population of gamma-ray emitting MSPs from the samples detected by the Fermi-LAT. Methods. We developed a Monte Carlo model to predict the spatial and gamma-ray luminosity distribution of the Galactic MSP population. Based on the estimated detection sensitivity of Fermi-LAT, we split the model population into detectable and undetectable samples of MSPs. Using a maximum likelihood method, we compared the detectable sample to a set of 36 MSPs detected by Fermi-LAT, and we derived the parameters of the spatial distribution and the total number of gamma-ray emitting MSPs in the Galaxy. The corresponding undetectable sample provided us with an estimate for the expected diffuse emission from unresolved MSPs in the Milky Way. We also applied our method to an extended sample of 66 MSPs that combines firmly detected MSPs and.-ray sources that show characteristics reminiscent of MSPs. Results. Using the sample of 36 MSPs detected by Fermi-LAT, our analysis suggests the existence of 9000-11 000 gamma-ray emitting MSPs in the Galaxy. The maximum likelihood analysis suggests an exponential radial scale length of similar to 4 kpc and an exponential vertical scale height of similar to 1 kpc for the underlying MSP population. The unresolved population of Galactic gamma-ray emitting MSPs is predicted to contribute a flux of similar to 2 x 10(-6) ph cm(-2) s(-1) sr(-1) to the Galactic diffuse emission observed from the central radian above 100 MeV. This value corresponds to similar to 1% of the total observed gamma-ray flux from that region. For latitudes vertical bar b vertical bar >= 40 degrees the expected average intensity amounts to similar to 2x10(-8) ph cm(-2) s(-1) sr(-1) above 100 MeV, which corresponds to 0.2% of the high-latitude background intensity. Using the extended sample increases the estimated number of gamma-ray emitting MSPs in the Galaxy to similar to 22 000 and slightly reduces the scale parameters of the spatial distribution. The results are robust with respect to systematic uncertainties in the estimated Fermi-LAT detection sensitivity. Conclusions. For the first time our analysis provides gamma-ray based constraints on the Galactic population of MSPs. The radial scale length and vertical scale height of the population is consistent with estimates based on radio data. Our analysis suggests that MSPs do not provide any significant contribution to the isotropic diffuse gamma-ray background emission.