Static structure of chameleon dark Matter as an explanation of dwarf
  spheroidal galactic core
  We propose a novel mechanism which explains cored dark matter density profile
in recently observed dark matter rich dwarf spheroidal galaxies. In our
scenario, dark matter particle mass decreases gradually as function of distance
towards the center of a dwarf galaxy due to its interaction with a chameleon
scalar. At closer distance towards galactic center the strength of attractive
scalar fifth force becomes much stronger than gravity and is balanced by the
Fermi pressure of dark matter cloud, thus an equilibrium static configuration
of dark matter halo is obtained. Like the case of soliton star or fermion
Q-star, the stability of the dark matter halo is obtained as the scalar
achieves a static profile and reaches an asymptotic value away from the
galactic center. For simple scalar-dark matter interaction and quadratic scalar
self interaction potential, we show that dark matter behaves exactly like cold
dark matter (CDM) beyond few $\rm{kpc}$ away from galactic center but at closer
distance it becomes lighter and fermi pressure cannot be ignored anymore. Using
Thomas-Fermi approximation, we numerically solve the radial static profile of
the scalar field, fermion mass and dark matter energy density as a function of
distance. We find that for fifth force mediated by an ultra light scalar, it is
possible to obtain a flattened dark matter density profile towards galactic
center. In our scenario, the fifth force can be neglected at distance $ r \geq
1\, \rm{kpc}$ from galactic center and dark matter can be simply treated as
heavy non-relativistic particles beyond this distance, thus reproducing the
success of CDM at large scales.
