Population study for $\gamma$-ray emitting Millisecond Pulsars and $Fermi$ unidentified sources

The $Fermi$-LAT has revealed that rotation powered millisecond pulsars (MSPs) are a major contributor to the Galactic $\gamma$-ray source population. We discuss the $\gamma$-ray emission process within the context of the outer gap accelerator model, and use a Monte-Calro method to simulate the Galactic population of the $\gamma$-ray emitting MSPs. We find that the outer gap accelerator controlled by the magnetic pair-creation process is preferable in explaining the possible correlation between the $\gamma$-ray luminosity and the spin down power. Our Monte-Calro simulation implies that most of the $\gamma$-ray emitting MSPs are radio quiet in the present sensitivity of the radio survey, indicating that most of the $\gamma$-ray MSPs have been unidentified. We argue that the Galactic $Fermi$ unidentified sources located at high latitudes should be dominated by MSPs, whereas the sources in the galactic plane are dominated by radio-quiet canonical pulsars.