COLLAPSE AND FRAGMENTATION OF CYLINDRICAL MAGNETIZED CLOUDS - SIMULATION WITH NESTED GRID SCHEME

The fragmentation process in a cylindrical magnetized cloud has been s tudied using the nested grid method. The nested grid scheme uses 15 le vels 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 instabi lity. A disk is formed whose symmetric plane is perpendicular to magne tic 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 d riven by an increase of the gravity. The contraction continues indefin itely for an isothermal equation of state and while the magnetic field s 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 str ucture of the contracting disk reaches that of a singular solution as the density and column density obey rho(r) proportional to r(-2) and s igma(r) proportional to r(-1), respectively. The magnetic field streng th in the mid-plane is proportional to rho(r)(1/2) and the field at th e center (B-c,) evolves proportionally to the square root of the gas d ensity (cc rho(c)(1/2). It is shown that isothermal clouds experience a ''run-away'' collapse. The evolution, including a hardening of the e quation of state due to radiation trapping, is also discussed.