DOI: 10.1051/0004-6361:20054306

## Axisymmetric simulations of magneto-rotational core collapse: dynamics and gravitational wave signal

**M. Obergaulinger, M. A. Aloy and E. Müller**

Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching bei München, Germany

e-mail: mobergau@mpa-garching.mpg.de

(Received 5 October 2005 / Accepted 19 December 2005)

** Abstract ***Aims.*We have performed a comprehensive parameter study of the collapse of
rotating, strongly magnetized stellar cores in axisymmetry to
determine their gravitational wave signature based on the Einstein
quadrupole formula.
*Methods.*We use a Newtonian explicit magnetohydrodynamic Eulerian code based on
the relaxing-TVD method for the solution of the ideal MHD equations,
and apply the constraint-transport method to guarantee a divergence-free evolution of the magnetic field. We neglect effects
due to neutrino transport and employ a simplified equation of state.
The initial models are polytropes in rotational equilibrium with a prescribed degree of differential rotation and rotational energy. The
initial magnetic fields are purely poloidal the field strength ranging
from
to
. The evolution of
the core is followed until a few ten milliseconds past core bounce.
*Results.*The initial magnetic fields are amplified mainly by the differential
rotation of the core giving rise to a strong toroidal field component
with an energy comparable to the rotational energy. The poloidal field
component grows by compression during collapse, but does not change
significantly after core bounce. In large parts of the simulated
cores the growth time of the magneto-rotational instability (MRI) is
of the order of a few milliseconds. The saturation field strengths
that can be reached both via a pure dynamo or the MRI are of
the order of
at the surface of the core.
Sheet-like circulation flows which produce a strong poloidal field
component transporting angular momentum outwards develop due to MRI,
provided the initial field is not too weak. Weak initial magnetic
fields (
) have no significant effect on the
dynamics of the core and the gravitational wave signal. Strong
initial fields (
) cause considerable angular
momentum transport whereby rotational energy is extracted from the
collapsed core which loses centrifugal support and enters a phase of
secular contraction. The gravitational wave amplitude at bounce
changes by up to a few ten percent compared to the corresponding
non-magnetic model. If the angular momentum losses are large, the
post-bounce model. If the angular momentum losses are large the
post-bounce equilibrium state of the core changes from a centrifugally to a pressure supported one. This transition imprints in the gravitational wave signal a reduction of the amplitude of the
large-scale oscillations characteristic of cores bouncing due to
centrifugal forces.

In some models the quasi-periodic large-scale oscillations are
replaced by higher frequency irregular oscillations. This pattern
defines a new signal type which we call a type IV gravitational wave
signal. Collimated bipolar outflows give rise to a unique feature
that may allow their detection by means of gravitational wave
astronomy: a large positive quadrupole wave amplitude of similar
size as that of the bounce signal.

**Key words:**magnetohydrodynamics (MHD)

**--**gravitational waves

**--**supernovae: general

**©**

*ESO 2006*