DIFFUSION AND MIXING IN ACCRETING WHITE-DWARFS

Numerical experiments have been conducted to determine the degree of enhancement of CNO elements in the envelope of a 1 M. carbon-oxygen white dwarf accreting hydrogen-rich material at rates of 10(-10), 10(-9), and 10(-8) M. yr-1. Three initial configurations have been adopted: (1) no initial surface helium layer, 10(9) yr of cooling prior to start of accretion; (2) no initial surface helium layer, a steady state interior thermal structure that is expected after many thermonuclear outbursts; and (3) an initial layer of 10(-3) M. of helium, 10(9) yr of cooling, with diffusion, before the start of accretion at the rate 10(-10) M. yr-1. Only ordinary particle diffusion and convective mixing are taken into account. Prior to hydrogen ignition in the initially cold cases, only diffusion contributes to the intermixing of hydrogen with carbon and oxygen; at maximum extent, the convective shell formed in consequence of the thermonuclear runaway is more massive than the mass of material accreted prior to the runaway by 24% at dM/dt = 10(-10) M. yr-1 and 9% at dM/dt = 10(-8) M. yr-1; the surface enhancement of CNO elements varies (by number relative to solar) from a factor of 27 at dM/dt = 10(-10) M. yr-1 to a factor of 11 at dM/dt = 10(-8) M. yr-1. In the steady state cases for which dM/dt greater-than-or-equal-to 10(-9) M. yr-1, both ordinary convection and diffusion contribute to the intermixing of hydrogen with carbon and oxygen prior to hydrogen ignition. The large contrast in radiative opacity near the interface between carbon-rich material and hydrogen-rich material is responsible for the establishment of a pre-runaway convective zone. At maximum extent, the convective shell formed subsequently in consequence of a thermonuclear runaway is more massive than the mass of material accreted prior to the runaway by 19% at dM/dt = 10(-10) M. yr-1 and by 35% at dM/dt = 10(-8) M. yr-1; the surface enhancement of CNO elements varies from a factor of 22 at dM/dt = 10(-10) M. yr-1 to a factor of 30 at dM/dt = 10(-8) M. yr-1. In the case of a helium buffer layer of mass 10(-3) M., approximately 3% of the mass of the helium layer is incorporated into the convective shell during the runaway, and negligible surface enhancements of heavy elements are found. However, estimating the amount of mass lost in a nova explosion, we argue that, if dM/dt less-than-or-equal-to 2 x 10(-10) M. yr-1, the helium layer can be eroded, and, after 60 or so nova explosions, the mass which is dredged into the convective layer during a thermonuclear runaway is larger than the mass of the helium zone produced by continued hydrogen burning in the remnant. Hence, for a small enough mass accretion rate, mixing due to particle diffusion and convection alone is sufficient to produce a large enhancement of heavy elements in the nova ejectum, and the mass of the white dwarf decreases with time. This does not prove, however, that these mechanisms are acutally responsible for observed enhancements. For dM/dt greater-than-or-equal-to 10(-9) M. yr-1 (and thus for the majority of classical nova precursors), the dredge-up mass is smaller than the mass of the remnant helium layer, and we conclude that more efficient mixing (possibly induced by differential rotation) is required to achieve order-of-magnitude enhancement of heavy elements. To discover the contribution of particle diffusion and pre-runaway convective mixing relative to the contribution of mixing induced by differential rotation requires numerical modeling.