Attenuation of Beaming Oscillations Near Neutron Stars

Observations with the Rossi X-ray Timing Explorer have revealed kilohertz quasi-periodic brightness oscillations (QPOs) from nearly twenty different neutron-star low-mass X-ray binaries (LMXBs). These frequencies often appear as a pair of kilohertz QPOs in a given power density spectrum. It is extremely likely that the frequency of the higher-frequency of these QPOs is the orbital frequency of gas at some radius near the neutron star. It is also likely that the QPOs are caused by the movement of bright arcs or luminous clumps around the star, which produce a modulation in the observed X-ray intensity as they are periodically occulted by the star or as they present a different viewing aspect to the observer at infinity. If this picture is correct, it means that this type of QPO is a beaming oscillation. In such models it is expected that there will also be beaming oscillations at the stellar spin frequency and at overtones of the orbital frequency, but no strong QPOs have been detected at these frequencies. We therefore examine the processes that can attenuate beaming oscillations near neutron stars, and in doing so extend the work on this subject that was initiated by the discovery of lower-frequency QPOs from LMXBs. We consider attenuation by scattering, attenuation by light deflection, and the decrease in modulation caused by integration over the visible surface of the neutron star. Our main results are (1) in a spherical scattering cloud, all overtones of rotationally modulated beaming oscillations are attenuated strongly, not just the even harmonics, (2) the amount of attenuation is diminished, and hence the observed modulation amplitude is increased, by the presence of a central, finite-sized star, even if the scattering cloud is much larger than the star, and (3) if the specific intensity of radiating points on the star has a large angular width, then even with zero optical depth from the stellar surface to the observer, and even in the approximation of straight-line photon propagation, the modulation amplitude seen at infinity is decreased significantly by integration over the visible portion of the surface. We also compare the modulation of flux as seen at infinity with the modulation near the star, and show that (4) it is possible to have a relatively high-amplitude modulation near the star at, e.g., the stellar spin frequency, even if no peak at that frequency is detectable in a power density spectrum taken at infinity.