Apparent radii of neutron stars and equation of state of dense matter

Apparent (radiation) radius of neutron star,R_\infty, depends on the star gravitational mass in quite a different way than the standard coordinate radius in the Schwarzschild metric, R. We show that, for a broad set of equations of state of dense matter, the lower bound on R_\infty at fixed M, R_\infty,min(M), resulting from the very definition of R_\infty, is very close to R_\infty(M_max) for the configurations with maximum allowable masses. Also, this absolute lower bound is only 0.6% lower than the value corresponding to the maximum compactness of neutron star consistent with general relativity and condition v_sound