The paper analyzes the results of numerical magnetohydrodynamic (MHD) modeling of the gravitational fragmentation of molecular filaments with a longitudinal magnetic field. Based on the simulations, we study the evolution of the magnetic field of the cores formed as a result of the fragmentation at the filament edges and inside the filament. The simulations show that, during the evolution of the filament, its magnetic field bends towards the boundaries of the gravitationally bound cores. Inside the cores, the magnetic field retains its initial geometry, and its strength anisotropically increases towards the core center. The magnetic field of the cores ranges from 0. 18 to 6. 3 mG, which agrees with the observed values in the Orion A filament. In the supercritical clouds with a weak magnetic field, the initial stage of core collapse is characterized by a “kinematic” compression across the magnetic field lines and an increase in magnetic field strength proportional to the gas density. In the subcritical clouds with a strong magnetic field, the cores collapse along the filament axis with virtually no increase in the magnetic field strength. In both cases, further increase in gas density and the formation of gravitationally bound cores is accompanied by an anisotropic radial compression of the cores, such that the magnetic flux density depends on the gas density as B { ^{1/3}}. The magnetic field distributions in the cores at the filament edges and inside the filament have different degrees of anisotropy, which points to different pathways for the formation of stars in the corresponding parts of the observed filaments.
Khaibrakhmanov et al. (Thu,) studied this question.