Stability of the Magnetopause of Disk-accreting Rotating Stars

We discuss three modes of oscillation of accretion disks around rotating magnetized neutron stars which may explain the separations of the kilo-Hertz -periodic oscillations (QPO) seen in low mass Xray binaries. The existence of these compressible, non-barotropic magnetohydrodynamic (MHD) modes requires that there be a maximum in the angular velocity Ωφ(r) of the accreting material larger than the angular velocity of the star Ω∗, and that the fluid is in approximately circular motion near this maximum rather than moving rapidly towards the star or out of the disk plane into funnel flows. Our MHD simulations show this type of flow and Ωφ(r) profile. The first mode is a Rossby wave instability (RWI) mode which is radially trapped in the vicinity of the maximum of a key function g(r)F(r) at rR. The real part of the angular frequency of the mode is ωr = mΩφ(rR), where m = 1, 2... is the azimuthal mode number. The second mode, is a mode driven by the rotating, non-axisymmetric component of the star’s magnetic field. It has an angular frequency equal to the star’s angular rotation rate Ω∗. This mode is strongly excited near the radius of the Lindblad resonance which is slightly outside of rR. The third mode arises naturally from the interaction of flow perturbation with the rotating non-axisymmetric component of the star’s magnetic field. It has an angular frequency Ω∗/2. We suggest that the first mode with m = 1 is associated with the upper QPO frequency, νu; that the nonlinear interaction of the first and second modes gives the lower QPO frequency, νl = νu − ν∗; and that the nonlinear interaction of the first and third modes gives the lower QPO frequency νl = νu − ν∗/2, where ν∗ = Ω∗/2π. Subject headings: keywords: accretion, accretion disks — stars: neutron — X-rays: binaries — magnetohydrodynamics — Instabilities — Waves