Abstract
We investigate the stability of a similarity solution for a gravitationally collapsing isothermal sphere by means of a normal-mode analysis. When the central density increases in proportion to ρc ∝ (t0 - t)-2, the bar mode grows in proportion to (t0 - t)-0.354. Here the symbol t denotes the time and the symbol t0 denotes an epoch. When the bar mode grows, the dense part of the collapsing cloud becomes either a thin filament or a disk. Since a thin filament is likely to fragment, the bar-mode instability will probably result in multiple stars at the center of the collapsing cloud.
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