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, R_\infty(M_max) for the configurations with maximum allowable masses is very close to the absolute lower bound on R_\infty at fixed M, resulting from the very definition of R_\infty. Also, the value of R_infty at given M, corresponding to the maximum compactness (minimum R) of neutron star consistent with general relativity and condition v_sound<c, is only 0.6% higher than this absolute lower bound. Theoretical predictions for R_\infty are compared with existing observational estimates of the apparent radii of neutron stars.