Millisecond pulsars and the Galactic Center gamma-ray excess: the importance of luminosity function and secondary emission

Several groups of authors have analyzed Fermi LAT data in a region around the Galactic Center finding an unaccounted gamma-ray excess over diffuse backgrounds in the GeV energy range. It has been argued that it is difficult or even impossible to explain this diffuse emission by the leading astrophysical candidates - millisecond pulsars (MSPs). Here we provide a new estimate of the contribution to the excess by a population of yet unresolved MSP located in the bulge of the Milky Way. We simulate this population with the GALPLOT package by adopting a parametric approach, with the range of free parameters gauged on the MSP characteristics reported by the second pulsar catalogue (2PC). We find that the conclusions strongly depend on the details of the MSP luminosity function (in particular, its high luminosity end) and other explicit or tacit assumptions on the MSP statistical properties, which we discuss. Notably, for the first time we study the importance of the possible secondary emission of the MSPs in the Galactic Center, {i.e. the emission via inverse Compton losses of electrons injected in the interstellar medium. Differently from a majority of other authors, we find that within current uncertainties a large if not dominant contribution of MSPs to the excess cannot be excluded. We also show that the sensitivities of future instruments or possibly already of the latest LAT data analysis (Pass 8) provide good perspectives to test this scenario by resolving a significant number of MSPs.