Abstract: Prospects of establishing the radii of massive neutron stars in PSR
J1614-2230 and PSR J0740+6620 from NICER 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 ¡ 1.4
M¢Á. In this work, we investigate the relation between the radii of very
massive neutron stars up to the maximum mass, Mmax, 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 Mmax with an upper bound on the radius of massive
pulsars serves to rule out too soft quark matter, and an upper bound on
Mmax with a lower bound on the radius of massive pulsars strongly
disfavors a transition into too-stiff quark matter 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.