Apparent radii of neutron stars, observations of Geminga and RX J185635-3754, and equation of state of dense matter

Apparent (radiation) radius of neutron star, R∞, 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∞ at fixed M , R∞,min(M), resulting from the very definition of R∞, is very close to R∞(Mmax) 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 vsound < c. Estimates of R∞ for Geminga and RX J1856353754 are consistent, within 2σ, with all considered equations of state, provided the detected photon spectra are fitted using the atmosphere models, and neutron star mass is above 0.2M⊙. If one fitted the RX J185635-3754 photon spectrum with black body one, the resulting upper bound on R∞ would imply that this compact object is a low-mass strange star covered with a normal matter envelope; such a possibility, however, seems to be excluded by the optical part of the detected spectrum.