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In this contribution, we summarize our recent studies on the chiral invariantmass and the chiral condensates in neutron star matter. We construct a unifiedequations of state assuming the crossover phase transition from hadronic matterdescribed by a parity doublet model to quark matter by an Nambu--Jona-Lasiniotype quark model. We first show that the chiral invariant mass is constrainedto be 600 MeV $\lesssim m_0 \lesssim$ 900 MeV from recent observations ofneutron stars. We then determine the density dependence of the chiralcondensate in the crossover description, and show that the chiral condensatesare actually smoothly connected from the hadronic matter where the change isdriven by the positive chiral scalar charge in a nucleon, to the quark matterwhere the change is by the modification of the quark Dirac sea, reflecting thehadron-quark crossover.

Chiral condensates for neutron stars in hadron-quark crossover; from a parity doublet nucleon model to an NJL quark model