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Effects of magnetic field orientations in dense cores on gas kinematics in protostellar envelopes

Theoretically, misalignment between the magnetic field and rotational axis in a dense core is considered to be dynamically important in the star formation process, however, extent of this influence remains observationally unclear. For a sample of 32 Class 0 and I protostars in the Perseus Molecular Cloud, we analyzed gas motions using C$^{18}$O data from the SMA MASSES survey and the magnetic field structures using 850 $μ$m polarimetric data from the JCMT BISTRO-1 survey and archive. We do not find any significant correlation between the velocity gradients in the C$^{18}$O emission in the protostellar envelopes at a 1,000 au scale and the misalignment between the outflows and magnetic field orientations in the dense cores at a 4,000 au scale, and there is also no correlation between the velocity gradients and the angular dispersions of the magnetic fields. However, a significant dependence on the misalignment angles emerges after we normalize the rotational motion by the infalling motion, where the ratios increase from $\lesssim1$ to $\gtrsim1$ with increasing misalignment angles. This suggests that the misalignment could prompt angular momentum transportation to the envelope scale but is not a dominant factor in determining the envelope rotation, and other parameters, like mass accretion in protostellar sources, also play an important role. These results remain valid after taking into account projection effects. The comparison between our estimated angular momentum in the protostellar envelopes and the sizes of the known protostellar disks suggests that significant angular momentum is likely lost between radii of $\sim$1,000-100 au in protostellar envelopes.