Constraining the Galactic millisecond pulsar population using Fermi
  Large Area Telescope
  The Fermi Large Area Telescope (Fermi-LAT) 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 samples 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. 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 gamma-ray sources that show characteristics reminiscent of
MSPs. 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.
