The Effect of Cosmic‐Ray Diffusion on the Parker Instability

The Parker instability, which has been considered as a process governing thestructure of the interstellar medium, is induced by the buoyancy of magneticfield and cosmic rays. In previous studies, while the magnetic field has beenfully incorporated in the context of isothermal magnetohydrodynamics, cosmicrays have been normally treated with the simplifying assumption of infinitediffusion along magnetic field lines but no diffusion across them. The cosmicray diffusion is, however, finite. In this work, we take into account fully thediffusion process of cosmic rays in a linear stability analysis of the Parkerinstability. Cosmic rays are described with the diffusion-convection equation.With realistic values of cosmic ray diffusion coefficients expected in theinterstellar medium, we show that the result of previous studies with thesimplifying assumption on cosmic ray diffusion applies well. Finiteness ofparallel diffusion decreases the growth rate of the Parker instability, whilethe relatively smaller perpendicular diffusion has no significant effect. Wediscuss the implication of our result on the role of the Parker instability inthe interstellar medium.Comment: 19 pages including 3 figures, to appear in The Astrophysical Journal (v589 n1 May 20, 2003 issue