  The angular momentum of molecular cloud cores plays a key role in the star
formation process. However, the evolution of the angular momentum of molecular
cloud cores formed in magnetized molecular filaments is still unclear. In this
paper, we perform three-dimensional magnetohydrodynamics simulations to reveal
the effect of the magnetic field on the evolution of the angular momentum of
molecular cloud cores formed through filament fragmentation. As a result, we
find that the angular momentum decreases by 30% and 50% at the mass scale of
1Msun in the case of weak and strong magnetic field, respectively. By analyzing
the torques exerted on fluid elements, we identify the magnetic tension as the
dominant process for angular momentum transfer for mass scales < 3Msun for the
strong magnetic field case. This critical mass scale can be understood
semi-analytically as the timescale of magnetic braking. We show that the
anisotropy of the angular momentum transfer due to the presence of strong
magnetic field changes the resultant angular momentum of the core only by a
factor of two. We also find that the distribution of the angle between the
rotation axis and the magnetic field does not show strong alignment even just
before the first core formation. Our results also indicate that the variety of
the angular momentum of the cores are inherited from the difference of the
phase of the initial turbulent velocity field. The variety could contribute to
the diversity in size and other properties of protoplanetary disks recently
reported by observations.
