The Effects of Rotation on Thermal X-Ray Afterglows Resulting from Pulsar Glitches

We derive the anisotropic heat transport equation for rotating neutron stars and the thermal equilibrium condition in a relativistic rotating axisymmetric star is also derived through a simple variational argument. With a simple model of neutron star, we model the propagation of heat pulses resulting from transient energy releases inside the star. {\bf Such sudden energy release can occur in pulsars during glitches.} Even in slow rotation limit ($\Omega\leq 1\times 10^{3}{s}^{-1}$), the results with rotational effects involved could be noticeably different from those obtained with a spherically symmetric metric in terms of the time scales and magnitudes of thermal afterglow. The effects of gravitational lensing and frame dragging on the X-ray light curve pulsations are also studied. The results we obtain indicate that the effect of rotation on the light curve modulation is small, and the spacetime curvature effect predominates. The metric components and rotational deformation on the stellar structure are calculated by using Hartle-Thorne formalism. {\bf We have applied our model to study the thermal response time scales of pulsars after glitches and find that the centrifugal force produced by rotation can substantially reduce the response time by a factor of three between non-rotating star and rotating star with $\Omega \sim 900 s^{-1}$. The equation of state can also affect the duration of response.