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

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 $10^{10}~{\rm G}$ to $10^{13}~{\rm G}$. 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 Ω dynamo or the MRI are of the order of $10^{15}~{\rm G}$ 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 ($\la$$10^{11}~{\rm G}$) have no significant effect on the dynamics of the core and the gravitational wave signal. Strong initial fields ($\ga$$10^{12}~{\rm G}$) 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 l