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

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. 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 pre--collapse initial models are polytropes in rotational equilibrium with a prescribed degree of differential rotation and rotational energy (~ 1 % of the gravitational energy). The initial magnetic fields are purely poloidal the field strength ranging from 10^10 G to 10^13 G. The evolution of the core, whose collapse is initiated by reducing the gas pressure by a prescribed amount, is followed until a few ten milliseconds past core bounce. The initial magnetic fields are amplified mainly by the differential rotation of the core giving rise to a strong toroidal field component. The poloidal field component grows by compression during collapse, but does not change significantly after core bounce if (abbreviated)