Resonant vibrational instabilities in magnetized stellar atmospheres

We perform linear stability analysis on stratified, plane-parallel atmosphe res in uniform vertical magnetic fields. We assume perfect electrical condu ctivity and we model non-adiabatic effects with Newton's law of radiative c ooling. Numerical computations of the dispersion diagrams in all cases resu lt in patterns of avoided crossings and mergers in the real part of the fre quency. We focus on the case of a polytrope with a prevalent, relatively we ak, magnetic field with overstable modes. The growth rates reveal prominent features near avoided crossings in the diagnostic diagram, as has been see n in related problems (Banerjee, Hasan, and Christensen-Dalsgaard, 1997). T hese features arise in the presence of resonant oscillatory bifurcations in non-self adjoint eigenvalue problems. The onset of such bifurcations is si gnaled by the appearance of avoided crossings and mode mergers. We discuss the possible role of the linear stability results in understanding solar sp icules.