Fragmentation of collapsing gas disks in external potentials

The star-formation activity in protogalactic disks is regulated by the frag mentation process of self-gravitating gas disks formed by the collapse in d ark halo potentials. In order to study this process, we numerically simulat ed the dynamical evolution of rotating gas clouds in external potentials. T he fragmentation was found to occur only in the limited area of the paramet er space defined by the initial ratios of the thermal and rotational energi es to the gravitational energy. A linear instability analysis has been appl ied to rotating equilibrium disks resulting from the initial clouds. We fou nd that the critical condition for the growth of axisymmetric perturbations nicely explains the fragmentation boundary found in the simulation results . The generalized fragmentation condition derived by the linear instability analysis consists of two criteria: the "Q-value" criterion, which requires existence of at least one unstable perturbation, and the "wavelength" crit erion, which states that the wavelength of the most unstable perturbation i s less than the radial scale length of the disk. The second criterion inclu des the first one automatically when the external gravitational field is ab sent, whereas the two criteria combine to control fragmentation process in the external potential.