2020ApJ...899..164H

Prospects of establishing the radii of massive neutron stars in PSR J1614 - 2230 and PSR J0740 + 6620 from Neutron Star Interior Composition ExploreR and Chandra observatories hold the potential to constrain the equation of state (EoS) of matter to densities well beyond those encountered in canonical stars of mass ∼1.4M_☉. In this work, we investigate the relation between the radii of very massive neutron stars up to the maximum mass, M_{max}, supported by dense matter EoSs. Results from models with hadronic matter are contrasted with those that include a first-order hadron-to-quark phase transition. We find that a lower bound on M_{max} with an upper bound on the radius of massive pulsars serves to rule out quark matter that is too soft, and an upper bound on M_{max} with a lower bound on the radius of massive pulsars strongly disfavors a transition into quark matter that is too stiff appearing at low densities. The complementary role played by radius inferences from future gravitational-wave events of inspiraling binary neutron stars is also briefly discussed.