Sensitivity of pulsar light curves to spacetime geometry and efficacy of analytic approximations

Abstract

In order to examine the pulse profile from a pulsar, we derive the formula for describing the flux from antipodal hot spots with any static, spherically symmetric spacetime. We find that the pulse profiles are almost independent of the gravitational geometry outside the star when the compactness of neutron stars is low enough, e.g., the stellar mass and radius are $1.4M_\odot$ and 14 km, respectively. On the other hand, the pulse profiles depend strongly on the gravitational geometry when the compactness of neutron stars is so high, e.g., the stellar mass and radius are $1.8M_\odot$ and 10 km, respectively. Thus, one may probe the spacetime geometry outside the star and even distinguish gravitational theories via the observation of pulse profile with the help of another observations for the stellar compactness, if the compactness of central object is high enough. We also derive the 1st and 2nd order approximation of the flux with respect to a parameter defined by the radio of the gravitational radius of considered spacetime to the stellar radius. Then, we find that the relative error from full order numerical results in the bending angle becomes $\sim 20-30\%$ with the 1st order and $\sim 5-10\%$ with the 2nd order approximations for a typical neutron star, whose mass and radius are $1.4M_\odot$ and 12 km, respectively. Our results with the 1st order approximation for the Schwarzschild spacetime are different from those obtained in the literature, which suggests that the 1st order approximation has been misunderstood to yield highly accurate prediction.