White dwarfs with rapid rotation

Abstract

A new analytical approach for calculation of white dwarfs characteristics that accounts for two important competing factors — axial rotation and Coulomb interparticle interactions, is proposed. The feature of our approach is simultaneous usage of differential and integral forms of equilibrium equation. In dimensionless form the differential equilibrium equation is strongly nonlinear inhomogeneous equation of the second order in partial derivatives with two dimensionless parameters — the relativistic parameter in stellar center $x_0$ and dimensionless angular velocity $\Omega$. In inner stellar region, rotation is taken into account as perturbation in the linear approximation for $\Omega^2$. In stellar periphery rotation is considered as the main factor. Usage of the integral equation provides correct calculations of integration constants. Dwarf's mass, moment of inertia relative to the axis of rotation, equatorial and polar radii, equatorial gravity in the following parameter space $1\leq x_0\leq24$, $0\leq\Omega<\Omega_{\rm max}(x_0)$ have been calculated based on the solutions of equilibrium equation. For the first time it was calculated the total energy of dwarf as function of these parameters. By the extrapolation, it was calculated the maximal values $\Omega_{\rm max}(x_0)$, as well as the observed angular velocity $\omega_{\rm max}(x_0)$. The considered model is generalized by taking into account Coulomb interparticle interactions. Also, we provide the examples of application of obtained results. It was shown that the characteristics of observed massive dwarfs do not contradict the calculated values for the model with consideration of solid body rotation and Coulomb interparticle interactions.