  In this contribution, we summarize our recent studies on the chiral invariant
mass and the chiral condensates in neutron star matter. We construct a unified
equations of state assuming the crossover phase transition from hadronic matter
described by a parity doublet model to quark matter by an Nambu--Jona-Lasinio
type quark model. We first show that the chiral invariant mass is constrained
to be 600 MeV $\lesssim m_0 \lesssim$ 900 MeV from recent observations of
neutron stars. We then determine the density dependence of the chiral
condensate in the crossover description, and show that the chiral condensates
are actually smoothly connected from the hadronic matter where the change is
driven by the positive chiral scalar charge in a nucleon, to the quark matter
where the change is by the modification of the quark Dirac sea, reflecting the
hadron-quark crossover.
