A series of numerical simulations of magnetorotational core-collapse supernovae are carried out. Dipole-like configurations which are offset northward are assumed for the initially strong magnetic fields, along with rapid differential rotations. The aim of our study is to investigate the effects of the offset magnetic field on magnetar kicks and on supernova dynamics. Note that we study a regime where the proto-neutron star formed after collapse has a large magnetic field strength approaching that of a "magnetar," a highly magnetized slowly rotating neutron star. As a result, equatorially asymmetric explosions occur with the formation of the bipolar jets. We find that the jets are fast and light in the north and slow and heavy in the south for rapid cases, while they are fast and heavy in the north and slow and light in the south for slow-rotation cases. The resulting magnetar kick velocities are ∼300-1000 km s_1. We find that the acceleration is mainly due to the magnetic pressure, while the somewhat weaker magnetic tension works in the opposite direction, due to the stronger magnetic field in the northern hemisphere. Note that observations of magnetar proper motions are very scarce; our results supply a prediction for future observations. Namely, magnetars possibly have large kick velocities, several hundred km s-1, as ordinary neutron stars do, and in extreme cases they could have kick velocities up to 1000 km s_1. In each model, the formed protomagnetar is a slow rotator with a rotational period of more than 10 ms. It is also found that, in rapid-rotation models, the final configuration of the magnetic field in the protomagnetar is a collimated dipole-like field pinched by the torus of toroidal field lines, whereas in the protomagnetar produced in the slow-rotation model the poloidal field is totally dominant.
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