An Origin of Filamentary Structure in Molecular Clouds

The gravitational instability of a pressure-confined isothermal gas layer with uniform magnetic fields is investigated in the linear regime. We solve the eigenvalue problem for the growth rate of linear perturbations and obtain the dispersion relation and eigenfunctions. The result is compared with those of a magnetized incompressible layer. The unperturbed state is an isothermal equilibrium layer. The unperturbed magnetic field lines are parallel to the midplane of the layer. For the layer with a thickness much larger than pressure scale height H, perturbations parallel to the magnetic fields grow faster than those perpendicular to the fields. Therefore the layer fragments into filaments, and the direction of longitudinal axis of each filament is perpendicular to the magnetic field lines. On the other hand, the layer with a thickness much smaller than H becomes more unstable for perturbations perpendicular to the magnetic fields. In this case it fragments into filaments, and the direction of longitudinal axis of each filament is parallel to the magnetic field lines. We find that the critical half-thickness of the layer at which the most unstable mode changes its character is H/(2)1/2 regardless of the strength of magnetic fields. Hence the isothermal layer, which is confined by the external pressure that is larger than about 0.63 times the central pressure, fragments into filamentary gas clouds threaded by magnetic fields parallel to them.