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Abstract

We study dynamics of circumstellar discs, with a focus on the $\beta$ Lyrae A binary system. This system with ongoing mass transfer has been extensively observed, using photometry, spectroscopy and interferometry. All these observations were recently interpreted using a radiation-transfer kinematic model. We modified the analytical Shakura-Sunyaev models for a general opacity prescription, and derived radial profiles of various quantities. These profiles were computed for the fixed accretion rate, $\dot M = 2\times 10^{-5}\,M_\odot\,{\rm yr}^{-1}$, inferred from the observed rate of change of the binary period. More general models were computed numerically, using 1-dimensional radiative hydrodynamics, accounting for viscous, radiative as well as irradiation terms. The initial conditions were taken from the analytical models. To achieve the accretion rate, the surface density~$\Sigma$ must be much higher (of the order of $10^4\,{\rm kg}\,{\rm m}^{-2}$ for the viscosity parameter $\alpha = 0.1$) than in the kinematic model. Viscous dissipation and radiative cooling in the optically thick regime lead to a high midplane temperature~$T$ (up to $10^5\,{\rm K}$). The accretion disc is still gas pressure dominated with the opacity close to Kramers one. To reconcile temperature profiles with observations, we had to distinguish three different temperatures: midplane, atmospheric and irradiation. The latter two are comparable to observations (30000 to 12000 $K$). We demonstrate that the aspect ratio~$H$ of 0.08 can be achieved in a hydrostatic equilibrium, as opposed to previous works considering the disc to be vertically unstable.