The Contour Method: a New Approach to Finding Modes of Nonadiabatic Stellar Pulsations

The contour method is a new approach to calculating the nonadiabatic pulsation frequencies of stars. These frequencies can be found by solving for the complex roots of a characteristic equation constructed from the linear nonadiabatic stellar pulsation equations. A complex-root solver requires an initial trial frequency for each nonadiabatic root. A standard method for obtaining initial trial frequencies is to use a star's adiabatic pulsation frequencies, but this method can fail to converge to nonadiabatic roots, especially as the growth and/or damping rate of the pulsations becomes large. The contour method provides an alternative way to obtain initial trial frequencies that robustly converges to nonadiabatic roots, even for stellar models with extremely nonadiabatic pulsations and thus high growth/damping rates. We describe the contour method implemented in the gyre stellar pulsation code and use it to calculate the nonadiabatic pulsation frequencies of and β Cephei star models, and of a extreme helium star model.