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.