Note on Equilibrium Configurations for Rotating White Dwarfs

The properties of non-rotating white dwarfs have been considered in detail by Chandrasekhar ⋆ , who finds that no degenerate equilibrium configuration exists if the mass of a star exceeds 5.75 $$M\odot/\mu^2_e$$ where $$M\odot$$ is the solar mass and $$\mu_e$$ is defined by the equation $$\mu_e = \rho/nm_H,$$ where ρ is the density, n is the number of electrons per cm. ³ , and m _H is the mass of the hydrogen atom. The main purpose of the present paper is to show that this result does not remain valid if the star possesses rotation. It will be shown that a degenerate equilibrium configuration always exists for a star with rotation, no matter how large a value is taken for the mass. The existence of a degenerate equilibrium configuration (in which the temperature of the material is zero) does not necessarily mean that a collapsing star can attain such a configuration. Indeed it is shown below that when the mass appreciably exceeds 5.75 $$M\odot/\mu^2_e$$ the equilibrium configuration could not be attained without a collapsing star passing through rotationally unstable states. It is suggested therefore that collapsing stars of large mass must become rotationally unstable. The observed result that white dwarfs of large mass do not occur is attributed to this process. In the writer's opinion this conclusion can be stated in a stronger form: That rotational instability is the only process capable of explaining the observational data, for it seems that if rotational instability did not occur there would be no process that could intervene to prevent collapsing stars of large mass from attaining their equilibrium configurations.