Effect of the Kerr Metric on Photosperic Radius Expansion in X Ray Burst

Abstract

The main objective of this paper is to study general relativistic effects on the photospheric radius expansion during an X-ray burst. We examine how the Kerr metric causes a shift in the effective temperature and radiation flux with respect to the Schwarzschild values during mass accretion onto a neutron star or a black hole resulting in the X-ray burst. The spin of the compact object is used up to the maximal Kerr limit χ = 0.99 with different latitudes of accretion emission. The amplitude of temperature shift relative to the Schwarzschild case is found to be δT/T ≈ − (10−3 − 10−4) for the range χ = 0.1 − 0.99 at latitudes θ = 0o , 30o, 45o and 88o. The ratio of emission flux in the Kerr metric to that in the Schwarzschild metric, F(K)/F(S), is found to be less than unity. It goes up to a maximum of 0.9 for the lowest nonzero value of the spin parameter (i.e., 0.1). For the maximal Kerr limit, χ = 0.99 , it saturates near 0.8. This effect is more prominent towards the pole. This reduction in temperature and flux is found to be consistent with the absence of photospheric radius expansion in the X Ray burst LMXB 4U 1608-52, observed by NuSTAR. Although this is not uniquely ascribed to the metric, it is believed that the spacetime metric effect in the burst phenomena can be used as a probe for testing general relativity. Also, the shift in temperature or the radiation flux might have an observable signature in the element synthesis processes in such environments.