  We obtain the space time of the galactic core in the framework of general
relativity by taking the flat rotational curve as input and considering the
matter content in the galactic core region as strange quark matter. We also
obtain the energy density, radial and tangential pressures of the core strange
quark matter. Significantly we have shown that Bag Constant takes an important
role to stabilize the circular orbit of the test particles. We also give a
limit of the Bag Constant for the existence of quark matter in the galactic
halo region.
