Self lensing effects for compact stars and their mass-radius relation

Abstract

During the last couple of years astronomers and astrophysicists have been debating on the fact whether the so called `strange stars' - stars made up of strange quark matter, have been discovered with the candidates like SAX J1808.4-3658, 4U 1728-34, RX J1856.5-3754, etc. The main contention has been the estimation of radius of the star for an assumed mass of ~ 1.4 M_sun and to see whether the point overlaps with the graphs for the neutron star equation of state or whether it goes to the region of stars made of strange matter equation of state. Using the well established formulae from general relativity for the gravitational redshift and the `lensing effect' due to bending of photon trajectories, we, in this letter, relate the parameters M and R with the observable parameters, the redshift z and the radiation radius R_\infty, thus constraining both M and R for specific ranges, without any other arbitrariness. With the required inputs from observations, one ought to incorporate the effects of self lensing of the compact stars which has been otherwise ignored in all of the estimations done so far. Nonetheless, these effect of self lensing makes a marked difference and constraints on the M-R relation.