Sonic-Point and Spin-Resonance Model of the Kilohertz QPO Pairs

Kilohertz quasi-periodic X-ray brightness oscillations (kilohertz QPOs) have now been detected in more than twenty accreting neutron stars in low-mass binary systems. Two kilohertz QPOs are usually detected in each star. Burst oscillations and two kilohertz QPOs have recently been detected in the 401 Hz accretion-powered X-ray pulsar SAX J1808.4−3658. In this star the frequency of the burst oscillation is approximately equal to the star’s spin frequency νspin whereas the frequency separation of the two kilohertz QPOs is approximately νspin/2. If as expected the frequency of the burst oscillations in other stars is also approximately νspin, the frequency separation is ≈ νspin in some stars but ≈ νspin/2 in others. A frequency separation approximately equal to νspin/2 is unexplained in all existing models of the kilohertz QPOs. Here we propose a modified version of the sonic-point beat-frequency model that can explain within a single framework why the frequency separation is close to νspin in some stars but close to νspin/2 in others. As in the original sonic-point model, the frequency νQPO2 of the upper kilohertz QPO is close to the orbital frequency νorb at the radius rsp of the sonic point in the disk flow. We show that magnetic and radiation fields rotating with the star will preferentially excite vertical motions in the disk at the “spin-resonance” radius rsr where νorb − νspin is equal to the vertical epicyclic frequency. If the flow at rsr is relatively smooth, the vertical motions excited at rsr modulate the X-ray flux at νQPO1 ≈ νQPO2 − νspin. If instead the gas at rsr is highly clumped, the vertical motions excited at rsr modulate the X-ray flux at ν ′ QPO1 ≈ νQPO2 − νspin/2. This sonic-point and spin-resonance model can also explain quantitatively the decrease of the kilohertz QPO frequency separation with increasing accretion rate that is observed in many sources. Subject headings: accretion — relativity — stars: neutron — X-rays: binaries — X-rays: bursts — X-rays: stars Also, Departments of Physics and Astronomy, University of Illinois at Urbana-Champaign.