Variability profiles of millisecond X-ray pulsars: Results of pseudo-Newtonian three-dimensional magnetohydrodynamic simulations

We model the variability profiles of millisecond-period X-ray pulsars. We performed three-dimensional magneto-hydrodynamic simulations of disk accretion to millisecond-period neutron stars with a misaligned magnetic dipole moment, using the pseudo-Newtonian Paczynski-Wiita potential to model general relativistic effects. We found that the shapes of the resulting funnel streams of accreting matter and the hot spots on the surface of the star are quite similar to those for more slowly rotating stars obtained from earlier simulations using the Newtonian potential. The funnel streams and hot spots rotate approximately with the same angular velocity as the star. The spots are bow-shaped (bar-shaped) for small (large) misalignment angles. We found that the matter falling on the star has a higher Mach number when we use the Paczynski-Wiita potential than in the Newtonian case. Having obtained the surface distribution of the emitted flux, we calculated the variability curves of the star, taking into account general relativistic, Doppler, and light-travel time effects. We found that general relativistic effects decrease the pulse fraction (flatten the light curve), while Doppler and light-travel time effects increase it and distort the light curve. We also found that the light curves from our hot spots are reproduced reasonably well by spots with a Gaussian flux distribution centered at the magnetic poles. We also calculated the observed image of the star in a few cases and saw that for certain orientations, both the antipodal hot spots are simultaneously visible, as noted by earlier authors.