Gravitational Instability of the Isothermal Gas Cylinder with an Axial magnetic Field

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Abstract
The gravitational instability is investigated for an isothermal gas cylinder with a uniform axial magnetic field. We treat the eigenvalue problem for the linear perturbations and obtain the dispersion relation numerically. It is found that the self-gravitating isothermal cylinder is unstable for axisymmetric perturbations of wavelength λ> λcr = 11.2H, where H is the radial scale height of gas distribution in the cylinder and that the fastest growing mode appears at the wavelength λm ∼2λcr. For the cylinder with the radius larger than H, the magnetic field reduces the growth rate but does not change the range of wavelength for unstable ones. The stabilizing effect saturates when the magnetic energy becomes comparable to the thermal energy. On the other hand, when the cylinder has a finite radius smaller than H, the dispersion relation approximates to that of incompressible fluid. The magnetic field is so effective to prevent the instability that both the critical wavelength and the most unstable growing time become longer exponentially as the strength of magnetic field increases.

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