Transonic magnetic slim accretion disks and kilohertz quasi-periodic oscillations in low-mass X-ray binaries

The inner regions of accretion disks of weakly magnetized neutron stars are affected by general relativistic gravity and stellar magnetic fields. Even for field strengths sufficiently small so that there is no well-defined magnetosphere surrounding the neutron star, there is still a region in the disk where magnetic field stress plays an important dynamical role. We construct magnetic slim disk models appropriate for neutron stars in low-mass X-ray binaries (LMXBs), which incorporate the effects of both magnetic fields and general relativity (GR). The magnetic field-disk interaction is treated in a phenomenological manner, allowing for both closed- and open-field configurations. We show that even for surface magnetic fields as weak as 10(7)-10(8) G, the sonic point of the accretion flow can be significantly modified from the pure GR value (near r(GR) = 6GM/c(2) for slowly rotating neutron stars). We derive an analytical expression for the sonic radius in the limit of small disk viscosity and pressure. We show that the sonic radius mainly depends on the stellar surface field strength B-0 and mass accretion rate (M) over dot through the ratio b(2) proportional to beta B-0(2)/(M) over dot, where beta similar or equal to \B-phi/B-z\ measures the azimuthal pitch angle of the magnetic field threading the disk. The sonic radius thus obtained approaches the usual Alfven radius for high b(2) (for which a genuine magnetosphere is expected to form) and asymptotes to 6GM/c(2) as b(2) --> 0. We therefore suggest that for neutron stars in LMXBs, the distinction between the disk sonic radius and the magnetosphere radius may not exist; there is only one "generalized" sonic radius, which is determined by both the GR effect and the magnetic effect. We apply our theoretical results to the kilohertz (kHz) quasi-periodic oscillations (QPOs) observed in the X-ray fluxes of LMXBs. If these QPOs are associated with the orbital frequency at the inner radius of the disk, then the QPO frequencies and their correlation with mass accretion rate can provide useful diagnostics on the (highly uncertain) nature of the magnetic field-disk interactions. In particular, a tight upper limit to the surface magnetic field B-0 can be obtained, i.e., B-0 less than or similar to 3 x 10(7) ((M) over dot(17)/beta)(1/2) G, where (M) over dot(17) = (M) over dot/(10(17) g s(-1)), in order to produce kHz orbital frequency at the sonic radius. Current observational data may suggest that the magnetic fields in LMXBs have complex topology.