Critical equipotential surfaces in close binary systems

Abstract

The well-known problem of reckoning the critical surfaces (equipotential zero-velocity surfaces) in the close binary systems is approached by an independent method. The formulation of the problem is based on the assumptions of the binary's matter consisting of ionized hydrogen, the system possessing black-body radiation, a potential magnetic field, being in adiabatic equilibrium. Total pressure and total internal energy are examined. The model, implying synchronous rotation of the components, is described by hydromagnetic equations. For a statical case, however, it is representable by the equation of motion alone. Next, the temperature field is reproduced whereby the ratioPr/Pg=α is playing part of a free parameter. The resulting potential functions, applied to particular binaries, furnish the Lagrangian collinear points, critical surfaces and potentials over them in terms of α. The families of surfaces thus obtained, compared with those springing from the Roche model, differ qualitatively in their geometry, position of the collinear equilibrium points, number of possible equilibrium states and the values of critical potentials. At identifying the allowed and forbidden regions of the gas motion new areas have been disclosed across which the gas outflow can take place and more possibilities of shell forming both around the individual components and the system as a whole. As the gas enthalpy and radiation are increased, the surfaces' geometry is undergoing changes. The method enables the intensity of gas velocity to be ascertained at any point in the system.