$J$-factor estimation of Draco, Sculptor and Ursa Minor dwarf spheroidal
  galaxies with the member/foreground mixture model
  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.
