Three-dimensional hydrodynamic simulations of collapsing prolate clouds

We present the results of collapse calculations for elongated clouds performed using the numerical method of smoothed particle hydrodynamics (SPH). The clouds considered are isothermal, prolate spheroids with different axial ratios (a/b). Results are obtained for different values of a/b and , the mean mass per unit length. It is found that initially uniform clouds undergo fragmentation when the collapse is preferentially down on to the major axis, due to the intrinsic instability of a linear configuration. This occurs when the value of is sufficiently large. A criterion for elongated clouds to undergo linear collapse is derived using the tensor virial theorem, and it is found that the numerically obtained value of for which fragmentation occurs corresponds closely to that expected from analytical considerations