The effects of rotation on thermal X-ray afterglows resulting from pulsar glitches

Abstract

We derive the anisotropic heat transport equation for rotating neutron stars, and we also derive the thermal equilibrium condition in a relativistic rotating axisymmetric star through a simple variational argument. With a simple model of a neutron star, we model the propagation of heat pulses resulting from transient energy releases inside the star. Such sudden energy release can occur in pulsars during glitches. Even in a slow rotation limit (Ω ≤ 1 × 103 s-1), the results with rotational effects involved could be noticeably different from those obtained with a spherically symmetric metric in terms of the timescales and magnitudes of thermal afterglow. We also study the effects of gravitational lensing and frame dragging on the X-ray light curve pulsations. Our results indicate that the effect of rotation on the light-curve modulation is small and that the spacetime-curvature effect predominates. The metric components and rotational deformation of the stellar structure are calculated using Hartle-Thorne formalism. We have applied our model to study the thermal response timescales of pulsars after glitches and find that the centrifugal force produced by rotation can substantially reduce the response time by a factor of 3 between a nonrotating star and a rotating star with Ω ∼ 900 s-1. The equation of state can also affect the duration of the response.