THE EVOLUTION OF ACCRETING STARS WITH TURBULENT MIXING

Under the assumption that, in differentially rotating stars, turbulence prevails due to the hydrodynamical instability of nonaxisymmetric, adiabatic modes, the equations of stellar evolution are formulated in such a way as to include the material mixing and heat transport associated with turbulent motions consistently. Applying these equations, the influence of accreted angular momentum is discussed for neutron stars and white dwarfs, accreting in close binary systems. With the turbulent viscosity estimated from the growth rates of the instability and the characteristic lengths, it is shown that nonaxisymmetric, adiabatic instabilities, in particular, the baroclinic instability, can provide turbulent viscosity efficient enough to smooth out differential rotation to such an extent that nearly uniform rotation prevails over most of the interior. It is also shown that the turbulent mixing of material, concomitant with the redistribution of angular momentum, possibly occurs deep enough to affect the progress of thermonuclear runaways for high accretion rates. The degree of material mixing increases if a smaller strength is assumed for the turbulent viscosity. The more compact the star, the more conspicuous is the influence of the accreted angular momentum. The results are compared with the observed properties of X-ray bursts and nova explosions to evaluate the strength of turbulent viscosity actually operating in these systems.