The treatment of highly non-adiabatic, non-radial pulsations by application of the Riccati method to the example of hydrogen-deficient carbon stars

Astronomy and Astrophysics – Astronomy

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B Stars, Carbon Stars, Stellar Interiors, Stellar Oscillations, Approximation, Boundary Value Problems, Riccati Equation

Scientific paper

The Riccati method, developed to solve the linear boundary-value problem of radial stellar pulsations, is generalized and shown to be applicable to the calculation of non-radial, nonadiabatic oscillations. Its advantages are demonstrated for the extreme example of a highly nonadiabatic helium star. The acoustic spectrum of helium stars is studied in detail. Mode-coupling instabilities occur in the nonradial spectrum for a wide range of the harmonic degree l, their appearance being similar to the radial case studied previously. With increasing l, the width of the instability strip in the HRD - extending up to log Teff of approximately 4.3 for low l - shrinks, and the growth rates of the instabilities decrease. Stabilization is reached between l = 10 and 100.

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