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The gamma-ray observation of the dwarf spheroidal galaxies (dSphs) is apromising approach to search for the dark matter annihilation (or decay)signal. The dSphs are the nearby satellite galaxies with a clean environmentand dense dark matter halo so that they give stringent constraints on the 1 TeVdark matter. However, recent studies have revealed that current estimation ofastrophysical factors relevant for the dark matter searches are notconservative, where the various non-negligible systematic uncertainties are nottaken into account. Among them, the effect of foreground stars on theastrophysical factors has not been paid much attention, which becomes moreimportant for deeper and wider stellar surveys in the future. In this article,we assess the effects of the foreground contamination by generating the mocksamples of stars and using a model of future spectrographs. We investigatevarious data cuts to optimize the quality of the data and find that the cuts onthe velocity and surface gravity can efficiently eliminate the contamination.We also propose a new likelihood function which includes the foregrounddistribution function. We apply this likelihood function to the fit of thethree types of the mock data (Ursa Minor, Draco with large dark matter halo,and Draco with small halo) and three cases of the observation. The likelihoodsuccessfully reproduces the input $J$-factor value while the fit withoutconsidering the foreground distribution gives large deviation from the inputvalue by a factor of three.

Foreground effect on the $J$-factor estimation of classical dwarf spheroidal galaxies