Dependence of accessible dark matter annihilation cross-sections on the
  density profiles of dwarf spheroidal galaxies with the Cherenkov Telescope
  Array
  Dwarf spheroidal galaxies are excellent targets in gamma-ray searches for
dark matter. We consider dark matter searches in dwarf spheroidal galaxies
(dSphs) with the Cherenkov Telescope Array (CTA). The aim of this work is to
reveal a quantitative and precise dependence of the accessible dark matter
annihilation cross-sections on the dark matter density profiles of dSphs and on
the distance to them. In most data analyses, researchers have assumed
point-like signals from dSphs because it is difficult to resolve the expected
emission profiles with current gamma-ray observatories. In future however, CTA
will be able to resolve the peak emission profiles in dSphs. We take several
variations of the dark matter density profile of Draco dSph as examples and
analyze the simulated observations of with CTA. We derive the accessible region
of the dark matter annihilation cross-section with each dark matter density
profile. The accessible region of the annihilation cross-section can differ by
a factor of 10 among plausible profiles. We also examine the dependence on the
distance to the target dSphs by assuming the same profiles of dSphs at
different distances. Closer targets are better due to the higher J-factor,
while their spatial extension significantly degrades our reach to the
annihilation cross-section compared to the value expected from a simple
distance-scaling of the J-factor. Spatial extension of the source affects the
probable parameter region in energy-dependent ways. In some gamma-ray energy
ranges, this behaviour becomes moderately dependent on the properties of the
observation facility.
