  We present a systematic study of the properties of pure hadronic and hybrid
compact stars. The nuclear equation of state (EoS) for beta-equilibrated
neutron star matter was obtained using density dependent effective
nucleon-nucleon interaction which satisfies the constraints from the observed
flow data from heavy-ion collisions. The energy density of quark matter is
lower than that of this nuclear EoS at higher densities implying the
possibility of transition to quark matter inside the core. We solve the
Einstein's equations for rotating stars using pure nuclear matter and quark
core. The beta- equilibrated neutron star matter with a thin crust is able to
describe highly massive compact stars but find that the nuclear to quark matter
deconfinement transition inside neutron stars causes reduction in their masses.
Recent observations of the binary millisecond pulsar J1614-2230 by P. B.
Demorest et al. [1] suggest that the masses lie within 1.97\pm0.04 M\odot where
M\odot is the solar mass. In conformity with recent observations, pure
nucleonic EoS determines that the maximum mass of NS rotating with frequency
below r-mode instability is ~1.95 M\odot with radius ~10 kilometers. Although
compact stars with quark cores rotating with Kepler's frequency have masses up
to ~2 M\odot, but if the maximum frequency is limited by the r-mode
instability, the maximum mass ~1.7 M\odot turns out to be lower than the
observed mass of 1.97\pm0.04 M\odot, by far the highest yet measured with such
certainty, implying exclusion of quark cores for such massive pulsars.
