Collapse and Fragmentation of Cylindrical Magnetized Clouds . II .

Fragmentation process in a cylindrical magnetized cloud is studied with the nested grid method. The nested grid scheme use 15 levels of grids with diierent spatial resolution overlaid subsequently, which enables us to trace the evolution from the molecular cloud density 100cm ?3 to that of the protostellar disk 10 10 cm ?3 or more. Fluctuation with small amplitude grows by the gravitational instability. It forms a disk perpendicular to the magnetic elds which runs in the direction parallel to the major axis of the cloud. Matter accrets on to the disk mainly owing along the magnetic elds and this makes the column density increase. The radial innow, whose velocity is slower than that perpendicular to the disk, is driven by the increase of the gravity. While the equation of state is isothermal and magnetic elds are perfectly coupled with the matter, which is realized in the density range of < 10 10 cm ?3 , never stops the contraction. The structure of the contracting disk reaches that of a singular solution as the density and the column density obey (r) / r ?2 and (r) / r ?1 , respectively. The magnetic eld strength on the mid-plane is proportional to (r) 1=2 and further that of the center (B c) evolves as proportional to the square root of the gas density (/ 1=2 c). It is shown that isothermal clouds experience \run-away" collapses. The evolution after the equation of state becomes hard is also discussed.