Abstract
The convective Urca process of Paczynski (1972, 1973) as applied to carbon burning in degenerate carbon/oxygen cores is reexamined. On time scales long when compared with the convective circulation time but short compared with the evolutionary time scale, a quasi-steady exists in which the convective currents impose a mu dN term that precisely cancels the local heating described by Bruenn. The results is that the convective Urca process must lead to net cooling and to a control of degenerate carbon burning, at least temporarily. The subsequent evolution is complex. Stability arguments show that the evolution depends on the precise treatment of the recession of the boundary of the convective core and on the advance of the Urca shell due to the contraction of the whole core. The fundamental conclusion is that if carbon ignites quasi-statically at a density above the Na-23 threshold at rho = 1.714 x 10 to the 9th g/cu cm, the convective Urca process will be a major effect which cannot be ignored in discussions of degenerate carbon burning, specifically in models for Type Ia supernovae. The limitations of previous treatments are outlined, and possible evolutionary outcomes are discussed. 30 refs.
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