Collapse and fragmentation of cylindrical magnetized clouds: Simulation with nested grid scheme

The fragmentation process in a cylindrical magnetized cloud has been studied using the nested grid method. The nested grid scheme uses 15 levels of grids with increasing spatial resolution, which enabled us to trace the evolution from molecular cloud densities similar to 100 cm(-3) to that of protostellar disks, similar to 10(10) cm(-3) or higher. Fluctuations with small. amplitude grow due to a gravitational instability. A disk is formed whose symmetric plane is perpendicular to magnetic field lines which run in the direction parallel to the major axis of the cloud. Matter accretes onto the disk, mainly flowing along the magnetic fields. This increases the column density. The radial inflow velocity is slower than the flow perpendicular to the disk, which is driven by an increase of the gravity. The contraction continues indefinitely for an isothermal equation of state and while the magnetic fields are perfectly coupled to matter. Both conditions are realized in the density range of rho less than or similar to < 10(10) cm(-3). The structure of the contracting disk reaches that of a singular solution as the density and column density obey rho(r) proportional to r(-2) and sigma(r) proportional to r(-1), respectively. The magnetic field strength in the mid-plane is proportional to rho(r)(1/2) and the field at the center (B-c,) evolves proportionally to the square root of the gas density (cc rho(c)(1/2). It is shown that isothermal clouds experience a ''run-away'' collapse. The evolution, including a hardening of the equation of state due to radiation trapping, is also discussed.