Attenuation of Beaming Oscillations near Neutron Stars

Abstract

Observations made with the Rossi X-Ray T iming Explorer have revealed kilohertz quasi-periodic brightness oscillations (QPOs) from nearly twenty di †erent 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 di †erent viewing aspect to the observer at inÐnity. 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 we 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 deÑection, 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, Ðnite-sized star, even if the scattering cloud is much larger than the star, and (3) if the speciÐc 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 inÐnity is decreased signiÐcantly by integration over the visible portion of the surface. We also compare the modulation of Ñux as seen at inÐnity 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 inÐnity.

A Model for the Waveform Behavior of Accreting Millisecond X-Ray Pulsars: Nearly Aligned Magnetic Fields and Moving Emission Regions

“…As discussed in Section 4, rapid fluctuations in the amplitude and phase of the oscillations would not be directly detectable in time-averaged observations, but would raise the background noise level and further reduce the detectability of the oscillations. These effects, possibly in combination with others, such as reduction of the modulation fraction by scattering in circumstellar gas (Lamb et al 1985;Miller 2000), may explain the nondetection of accretion-powered oscillations in accreting neutron stars in which nuclear-powered oscillations have been detected.…”

“…If they are very close to the spin axis and remain there, the amplitudes of the oscillations they produce can be ∼ 0.5% or less. Thus, emission from very close to the spin axis, in combination with other effects, such as rapid phase and amplitude fluctuations and suppression of Xray modulation by scattering of photons in circumstellar gas (see Lamb et al 1985;Miller 2000), may explain the nondetection of accretion-powered oscillations in accreting neutron stars in which nuclear-powered oscillations have been detected.…”

The Amplitude Evolution and Harmonic Content of Millisecond Oscillations in Thermonuclear X‐Ray Bursts

“…On the other hand, scattering in an accretion disk (Sazonov & Sunyaev 2001) or in a spherical corona around the neutron star (e.g. Brainerd & Lamb 1987;Bussard et al 1988;Miller 2000) could explain the lack of harmonic content in the oscillations. The scattering both damps the peak amplitude of the signal from the bright regions, and allows the observer to receive flux from the bright spots over a larger fraction of the neutron star's rotational period.…”

“…On the other hand, the harmonic content of the pulsations can also be suppressed if the signal from the neutron star scatters in the accretion flow before it reaches the observer (Sazonov & Sunyaev 2001;Brainerd & Lamb 1987;Bussard et al 1988;Miller 2000). Further signatures of scattering should be sought in the energy dependence of the profiles of burst oscillations.…”

High-Frequency Variability in Neutron-Star Low-Mass X-ray Binaries

“…The 95% confidence upper limits of a peak at 2ν low and 2ν upp − ν low are, respectively, 0.12 and 0.26 times the amplitude of the upper kHz QPO in this source (the amplitude of the upper kHz QPO in Sco X-1 is between 0.6% and 2.5%; see table 1 in [106], for the upper limits at other frequencies). The signal of these other peaks could be attenuated in the corona [29,84,112,115] depending on the frequency of the peak, and the radius and optical depth of the corona. Considering this effect, the upper limits of an unattenuated signal at those two frequencies would be a factor between 0.15 and 0.30 of the unattenuated amplitude of the upper kHz QPO in Sco X-1 (see table 2 in [106], for the unattenuated upper limits at other frequencies).…”