Oscillation Waveforms and Amplitudes from Hot Spots on Neutron Stars

The discovery of high-amplitude brightness oscillations during type I X-ray bursts from six low-mass X-ray binaries has provided a powerful new tool to study the properties of matter at supranuclear densities, the effects of strong gravity, and the propagation of thermonuclear burning. There is substantial evidence that these brightness oscillations are produced by spin modulation of one or two localized hot spots confined to the stellar surface. It is therefore important to calculate the expected light curves produced by such hot spots under various physical assumptions, so that comparison with the observed light curves may most sensitively yield information about the underlying physical quantities. In this paper we make general relativistic calculations of the light curves and oscillation amplitudes produced by a rotating neutron star with one or two hot spots as a function of spot size, stellar compactness, rotational velocity at the stellar surface, spot location, orientation of the line of sight of the observer, and the angular dependence of the surface specific intensity. For the case of two emitting spots we also investigate the effects of having spot separations less than 180° and the effects of having asymmetries in the brightness of the two spots. We find that stellar rotation and beaming of the emission tend to increase the observed oscillation amplitudes whereas greater compactness and larger spot size tend to decrease them. We also show that when two emitting spots are either nonantipodal or asymmetric in brightness, significant power at the first harmonic is generated. By applying these results to 4U 1636-536, the two emitting spots of which produce power at the first harmonic, we place strong constraints on the neutron star's magnetic field geometry. We also show that the data on the phase lags between photons of different energies in the persistent pulsations in SAX J1808-58 can be fitted well with a model in which the observed hard leads are due to Doppler beaming.