Forced oscillations in magnetized accretion disks and QPOs

Astronomical Institute, University of Utrecht, PO Box 80000, 3508 TA Utrecht, The Netherlands e-mail: Jerome.Petri@mpi-hd.mpg.de

Received: 22 June 2004
Accepted: 12 April 2005

Abstract

Quasi-periodic oscillations (QPOs) have been observed in accretion disks around neutron star, black hole, and white dwarf binaries with frequencies ranging from a few 0.1 Hz up to 1300 Hz. Recently, a correlation between their low- and high-frequency components was discovered and fitted with a single law, irrespective of the nature of the compact object. That such a relation holds over 6 orders of magnitude strongly supports the idea that the physical mechanism responsible for these oscillations should be the same in all binary systems.
We propose a new model for these QPOs based on forced oscillations induced in the accretion disk due to the stellar magnetic field. First, it is shown that a magnetized accretion disk evolving in a rotating nonaxisymmetric magnetic field anchored to a neutron star will be subject to three kinds of resonances: a corotation resonance, a Lindblad resonance due to a driving force, and a parametric resonance due to the time varying epicyclic frequencies. The asymmetric part of the field is assumed to contain only one azimuthal mode . We focus on the  disturbance, which is well studied for an inclined dipolar rotator; but our results are general and easily extend to . However, the radial location of the resonances will be affected by this number m. For instance, with an  asymmetric structure, the resonances reach regions very close to the innermost stable circular orbit (ISCO) and can account for observations of kHz-QPOs at frequencies as high as 1200–1300 Hz. If we replace the dipolar by a higher order multipolar component, the resonance location is shifted to larger radius, implying lower QPO frequencies. To compare the MHD situation with the hydrodynamical case, we also consider an  component in the magnetic perturbation in order to prove that, at least in the linear regime, the conclusions in both cases are the same. In the second part of the paper, we focus on the linear response of a thin accretion disk, developing the density perturbation as the sum of free wave solutions and non-wavelike disturbances. In the last part, we show results of 2D numerical simulations of a simplified version of the accretion disk consisting of a column of plasma threaded by a vertical magnetic field. These simulations are performed for the Newtonian gravitational potential, as well as for a pseudo-general relativistic potential, which enables us to explore the behavior of the resonances around both rotating neutron stars and black holes. We found that the density perturbations are only significant in the region located close to the inner edge of the disk near the ISCO where the magnetic perturbation is maximal. They induce fluctuations in the density which persist over the whole time of the simulations and are closely related to the spin of the magnetic perturbation. It is argued that the nearly periodic motion induced in the disk will produce high quality factor QPOs.