Estimating the GeV Emission of Millisecond Pulsars in Dwarf Spheroidal Galaxies

We estimate the conventional astrophysical emission from dwarf spheroidal satellite galaxies (dSphs) of the Milky Way, focusing on millisecond pulsars (MSPs), and evaluate the potential for confusion with dark matter (DM) annihilation signatures at GeV energies. In low-density stellar environments, such as dSphs, the abundance of MSPs is expected to be proportional to stellar mass. Accordingly, we construct the $\gamma$-ray luminosity function of MSPs in the Milky Way disk, where $>90$ individual MSPs have been detected with the $\textit{Fermi}$ Large Area Telescope (LAT), and scale this luminosity function to the stellar masses of 30 dSphs to estimate the cumulative emission from their MSP populations. We predict that MSPs within the highest stellar mass dSphs, Fornax and Sculptor, produce a $\gamma$-ray flux $>500$~MeV of $\sim10^{-11}$~ph~cm$^{-2}$~s$^{-1}$, which is a factor $\sim10$ below the current LAT sensitivity at high Galactic latitudes. The MSP emission in ultra-faint dSphs, including targets with the largest J-factors, is typically several orders of magnitude lower, suggesting that these targets will remain clean targets for indirect DM searches in the foreseeable future. For a DM particle of mass 25~GeV annihilating to $b$ quarks at the thermal relic cross section (consistent with DM interpretations of the Galactic Center excess), we find that the expected $\gamma$-ray emission due to DM exceeds that of MSPs in all of the target dSphs. Using the same Milky Way MSP population model, we also estimate the Galactic foreground MSP coincidence probability along the same sightlines to the dSphs.