On the pulsation of a star in which there is a prevalent magnetic field

Abstract

In this paper a simple approximate formula is obtained for the frequency (σ) of radial pulsation of a gaseous star in which there is a prevalent magnetic field. The formula is σ²I = - (3γ - 4) (Ω + B) , where γ is the ratio of the specific heats, I = ∫₀^Mr²dm (r) , and Ω and B denote the gravitational potential energy and the magnetic energy of the star, respectively. The formula is derived from the virial theorem in the form recently established by Chandrasekhar and Fermi; and it supports their conclusion that the period of pulsation can be made as long as one may desire by letting the magnetic energy approach the upper limit (namely, |Ω|) set by the virial theorem.