FRAGMENTATION OF ELONGATED CYLINDRICAL CLOUDS .2. POLYTROPIC CLOUDS

We present a numerical study of the fragmentation of elongated, polytropic, axially symmetric clouds. Results have been obtained for various ratios of length to diameter L/D, polytropic constant gamma, and initial Jeans number J0 (ratio of the absolute value 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(f max) that can form and grow for combinations of L/D, gamma, and J0. At fixed values of L/D and gamma, N(f max) increases with J0, then saturates at a finite value N(f max) = N(max) almost-equal-to 2L/D at large J0 for gamma greater-than-or-equal-to 1. At fixed values of L/D and J0, N(f max) decreases when gamma increases. Since the saturation value N(max) is independent of gamma, reaching saturation at high gamma requires a larger initial Jeans number. The number of fragments formed can exceed 2L/D for gamma < 1. We show that J(N), the initial Jeans number required for forming N fragments, scales approximately as gamma-2 for 0.9 less-than-or-equal-to gamma < 4/3 and N < N(max). This relation does not hold for gamma > 4/3. Implications of these results on the minimum stellar mass are discussed.