Fragmentation of elongated cylindrical clouds. I - Isothermal clouds

A numerical study is presented 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). Initial density perturbations are introduced on the axis of otherwise uniformly dense cylinders, and the maximum number of fragments Nf(max) that can form and grow for combinations of L/D and J0 is determined. The value of Nf(max) increases with J0 at small J0, then saturates at a finite value Nf(max) about 2L/D at large J0. That results contradicts analytical predictions based on a linear stability analysis for infinite cylinders or the ratio of the total mass to the Jeans mass. The results are directly applicable to observations of the cores of dark molecular clouds which are found to be mostly prolate. These cores are then expected to fragment and form stars in multiple systems or in small groups, as frequently observed in star-forming regions.