Dwarf spheroidal galaxies (dSphs) are promising targets of indirect detection experiments searching for dark matter (DM) at present universe. Toward robust prediction for the amount of signal flux originating in DM annihilation inside dSphs, a precise determination of DM distributions as well as $J$-factors of the dSphs is particularly important. In this work, we estimate those of Draco, Sculptor, and Ursa Minor dSphs by an improved statistical method in which both foreground stars and dSph member stars are simultaneously taken into account. We define the likelihood function of the method as the so-called conditional one to remove sampling bias of observed stellar data. This improved method enables us to estimate DM distributions and $J$-factors of the dSphs directly from observed stellar data contaminated by foreground stars without imposing stringent membership criteria on the measured quantities.

中文翻译：

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使用成员/前景混合模型对 Draco、Sculptor 和 Ursa Minor 矮椭球星系进行 J 因子估计

矮椭球星系 (dSphs) 是目前宇宙中寻找暗物质 (DM) 的间接探测实验的有希望的目标。为了对源自 dSph 内部 DM 湮灭的信号通量量进行稳健预测，精确确定 DM 分布以及 dSph 的 $J$ 因子尤为重要。在这项工作中，我们通过改进的统计方法估计了 Draco、Sculptor 和 Ursa Minor dSphs，其中前景星和 dSph 成员星同时被考虑在内。我们将该方法的似然函数定义为所谓的条件函数，以消除观测到的恒星数据的采样偏差。