MHD-Modeling of the molecular filament evolution with numerical FLASH code

We study numerically the gravitational fragmentation of a cylindrical molecular cloud with large-scale magnetic field. The simulations are performed with the help of the MHD code FLASH. We consider two cases: gravitational instability of the filament with initially deformed surface (model of Chandrasekhar and Fermi), and the instability of longitudinal compressible waves (model of Stodolkeiwicz). The simulations under typical parameters show that two types of the cores can be formed as a result of the fragmentation. Gravitational focusing leads to the formation of two massive clumps at the ends of filaments. Those cores move towards the cloud center with supersonic speeds. The instability of initial perturbations results in smaller evenly distributed cores inside the filament. The cores formed due to the instability of compressible waves have almost spherical shapes, while the cores resulted from the fragmentation of the filament with deformed surface are flattened. Typical sizes of the cores of 0.01–0.02 pc are in agreement with observations.