FRAGMENTATION OF ELONGATED CYLINDRICAL CLOUDS .1. ISOTHERMAL CLOUDS

We present a numerical study of fragmentation in its simplest possible form: that of elongated, isothermal, axially symmetric clouds. Results have been obtained for different ratios of length to diameter, L/D, and initial Jeans numbers, J0 (ratio of gravitational to thermal energies). We introduce initial density perturbations on the axis of otherwise uniformly dense cylinders and determine the maximum number of fragments N(fmax) that can form and grow for combinations of L/D and J0. The value of N(fmax) increases with J0 at small J0, then saturates at a finite value N(fmax) almost-equal-to 2L/D at large J0. That result contradicts analytical predictions based on (1) a linear stability analysis for infinite cylinders or (2) the ratio of the total mass to the Jeans mass. Our results are directly applicable to observations of the cores of dark molecular clouds which are found to be mostly prolate. One then expects these cores to fragment and form stars in multiple systems or in small groups, as frequently observed in star-forming regions.