Formation and Evolution of Filamentary Structure in Molecular Clouds

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The gravitational instability of a pressure-confined isothermal gas layer with uniform and nonuniform 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 unperturbed magnetic fields are parallel to the mid-plane 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 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 of which the most unstable mode changes its character is H/sqrt{2} regardless of the strength of magnetic fields in the case that magnetic fields are uniform. Hence the isothermal layer 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.

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