We investigate the impact of rotation and magnetic fields on the dynamics and gravitational wave emission in 2D core-collapse supernova simulations with neutrino transport. We simulate 16 different models of $15,M_odot$ and $39,M_odot$ progenitor stars with various initial rotation profiles and initial magnetic fields strengths up to $10^{12}, mathrm{G}$, assuming a dipolar field geometry in the progenitor. Strong magnetic fields generally prove conducive to shock revival, though this trend is not without exceptions. The impact of rotation on the post-bounce dynamics is more variegated, in line with previous studies. A significant impact on the time-frequency structure of the gravitational wave signal is found only for rapid rotation or strong initial fields. For rapid rotation, the angular momentum gradient at the proto-neutron star surface can appreciably affect the frequency of the dominant mode, so that known analytic relations for the high-frequency emission band no longer hold. In case of two magnetorotational explosion models, the time-frequency structure of the post-bounce emission appears rather different from neutrino-driven explosions. In one of these two models, a new high-frequency emission component of significant amplitude emerges about $200, mathrm{ms}$ after the burst of gravitational wave emission around shock revival has subsided. This emission is characterised by broad-band power well into the kHz range. Its emission mechanism remains unclear and needs to be investigated further. We also estimate the maximum detection distances for our waveforms. The magnetorotational models do not stick out for higher detectability during the post-bounce and explosion phase.
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