Structural Models for Beta Lyrae-Type Disks

Abstract

Equilibrium structural models are computed for a thick, self-gravitating disk in a binary system. Accretion onto the star is limited by the star’s rapid rotation (the system is a double-contact binary). The potential formulation is taken from a previous paper, and represents the gravitational potential as that of a massive wire. Corrections to the stellar structure differential equations for the distorted geometry are applied, and the equations are integrated and solved by the fitting point method. The energy is supplied by viscosity. Energy transfer is by convection, and is appreciably superadiabatic throughout the disk. A mass of 0.5 M⊙ is assumed. Representative results are: “central” temperature, 67000 K; “central” pressure, 5 × 10¹¹ dynes/cm²; “equal volume” radius, 17 R⊙; luminosity, 5 × 10³ L⊙. The model “radius” is in excellent agreement with the observational value for β Lyrae. The model luminosity is slightly higher than the available rate of expenditure of gravitational energy, indicating that a lower disk mass (perhaps 0.25 M⊙) should be tried.