Resonant vibrational instabilities in magnetized stellar atmospheres

We perform linear stability analysis on stratified, plane-parallel atmospheres in uniform vertical magnetic fields. We assume perfect electrical conductivity and we model non-adiabatic effects with Newton's law of radiative cooling. Numerical computations of the dispersion diagrams in all cases result in patterns of avoided crossings and mergers in the real part of the frequency. We focus on the case of a polytrope with a prevalent, relatively weak, magnetic field with overstable modes. The growth rates reveal prominent features near avoided crossings in the diagnostic diagram, as has been seen in related problems (Banerjee, Hasan, and Christensen-Dalsgaard, 1997). These features arise in the presence of resonant oscillatory bifurcations in non-self adjoint eigenvalue problems. The onset of such bifurcations is signaled by the appearance of avoided crossings and mode mergers. We discuss the possible role of the linear stability results in understanding solar spicules.