Collapse and Fragmentation of Cylindrical Magnetized Clouds: Simulation with Nested Grid Scheme

Abstract

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 ∼ 100 cm−3 to that of protostellar disks, ∼ 1010 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 ρ ≲ 1010 cm−3. The structure of the contracting disk reaches that of a singular solution as the density and column density obey ρ(r) ∝ r−2 and σ(r) ∝ r−1, respectively. The magnetic field strength in the mid-plane is proportional to ρ(r)1/2 and the field at the center (Bc) evolves proportionally to the square root of the gas density (∝ ρc1/2). 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.