Sonic-Point and Spin-Resonance Model for Kilohertz QPO Pairs

ABSTRACT

KHz QPOs have now been detected in more than twenty accreting neutron stars in low-mass binary systems. Two kHz QPOs are usually detected in each star. Burst oscillations and two kHz 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 ν_spin whereas the frequency separation of the two kHz QPOs is approximately ν_spin/2. If as expected the frequency of the burst oscillations in other stars is also approximately ν_spin, the frequency separation is approximately ν_spin in some stars but approximately ν_spin/2 in others. A frequency separation approximately equal to ν_spin/2 is unexplained in all existing models of the kHz 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 ν_spin in some stars but close to ν_spin/2 in others. As in the original sonic-point model, the frequency ν_QPO2 of the upper kHz QPO is close to the orbital frequency ν_orb at the radius r_{sp} 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 r_{sr} where ν_orb - ν_spin is equal to the vertical epicyclic frequency, producing vertical motions in the disk that modulate the X-ray flux at approximately ν_QPO2 - ν_spin or approximately ν_QPO2 - ν_spin/2, depending on whether the disk flow at r_{sr} is smooth or clumped. This sonic-point and spin-resonance model can also explain quantitatively the decrease of the kHz QPO frequency separation with increasing accretion rate that is observed in many sources.

ApJ, astro-ph/0308179