Lithium Production in Hot Advection-Dominated Accretion Flows in Soft X-Ray Transients

High Li abundances have been reported in the late type secondaries of five soft X-ray transients (SXTs), V404 Cyg, A0620-00, GS2000+25, Nova Mus 1991, and Cen X-4. Since Li is likely to be depleted in stars of this type, the origin of the Li is puzzling. Li has not been seen in similar secondaries of cataclysmic variables, which suggests that the high Li abundance is not due to an anomalous suppression of Li depletion in close binaries. SXTs in the quiescent state have hot advection-dominated accretion flows (ADAFs) in which the ions are essentially at virial temperature. At such temperatures, Li production via $\alpha-\alpha$ spallation is possible. We show that quiescent SXTs can produce sufficient Li via spallation to explain the observations in V404 Cyg, A0620-00, GS2000+25, and Nova Mus 1991. Depending on the Li depletion time scale in the secondary, which may range between $10^7-10^9$ yr, the model requires $\sim 10^{-4}-10^{-6}$ of the accreted mass to be intercepted by the secondary after undergoing Li production and being ejected. In the case of Cen X-4, we can explain the observed Li only if the mass accretion rate is $\sim 10^{-3}$ times the Eddington rate and if there is enhanced ejection due to a propeller effect. We discuss possible observational tests of this proposal. Li production during outbursts could be quite important and may even dominate over the production during quiescence, but the estimate of the Li yield is uncertain. We calculate the expected luminosity in gamma-ray lines due to the production of excited Li and Be nuclei, but conclude that the line cannot be detected with current instruments.