Theory of stellar pulsation

Important time scales considered include the pulsation period, the 'free-fall' time, the Kelvin time, and the 'nuclear' time. Some observational and basic theoretical considerations are discussed, taking into account classical Cepheids and the period-luminosity relation, more recently recognized types of variable stars, the empirical determination of radii of pulsating stars, limb darkening and radial velocity, Eulerian and Lagrangian descriptions, the gravitational field, and the energy conservation theorem for a self-gravitating system. Radial oscillations of stars are described, giving attention to spherically symmetric radial motion, linearized equations, linear adiabatic radial oscillations, the pulsational stability of actual stars, the phase lag, and simple models of stellar pulsation. Nonradial oscillations of stars are studied, taking into account the general nonlinear partial differential equation, the hermiticity of the linear adiabatic wave equation, the growth or decay of small nonradial oscillations, and linear nonradial oscillations of spherical stars