Oscillations in clusters of galaxies

Oscillations of the intracluster medium in clusters of galaxies are studied by means of linear perturbations. An Eulerian analysis is given and its limitations discussed. The problem is then reformulated in terms of Lagrangian perturbations and an expression for the stability coefficient is given. The effect of a flow, such as occurs in cooling flow clusters, is included. The stability coefficient is formally the same whether or not a flow is present. Mass dropping out of or joining the flow can lead to instability. A time dependent flow leads to the modes evolving adiabatically if the period of oscillation is much shorter than the time-scale of evolution of the background. No assumptions of isobaricity, locality or high wavenumber perturbations are made. (author)