Embedded, Self-Gravitating Equilibria in Sheetlike and Filamentary Molecular Clouds

Numerical solutions of the isothermal Lane-Emden equation are presented, corresponding to self-gravitating gaseous cores embedded within a finite density envelope of overall cylindrical symmetry. These structures may be members of a fragmentation hierarchy proceeding from sheets, to filaments, to elongated, prolate clumps. The embedded solutions are the first of their kind, and as such represent a significant improvement upon the isolated cloud paradigm used almost exclusively by previous authors. The properties of the equilibria are in reasonable agreement with observations of dense molecular cores in star-forming clouds, despite the fact that there is only one free parameter in the models. We show that this parameter may be identified with the critical wavelength for instability in the parent filament. The implications of further fragmentation and the possible influence of magnetic fields are briefly discussed.