A&A 439, 443-459 (2005)

DOI: 10.1051/0004-6361:20041511

## Forced oscillations in magnetized accretion disks and QPOs

**J. Pétri**

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 *m*=1 disturbance, which is
well studied for an inclined dipolar rotator; but our results are
general and easily extend to *m*>1. However, the radial location of
the resonances will be affected by this number *m*. For instance,
with an *m*=1 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 *m*=2 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.

**Key words:**accretion, accretion disks

**--**magnetohydrodynamics (MHD)

**--**instabilities

**--**methods: analytical

**--**methods: numerical

**--**stars: neutron

**©**

*ESO 2005*