Modeling lithium-rich carbon stars in the Large Magellanic Cloud: An independent distance indicator?

We present the first quantitative computations explaining the presence in t he Large Magellanic Cloud of some asymptotic giant branch stars that are bo th lithium-rich stars and carbon stars (surface C/O > 1). A self-consistent description of time-dependent mixing, overshooting, and nuclear burning wa s required. The products of nucleosynthesis at the stellar surface turn out to be very sensitive to the temperature at the base of the outer convectiv e envelope (T-bce) during the quiescent phase of hydrogen burning. Lithium production is obtained for T-bce greater than or equal to 4 x 10(7) K (hot bottom burning), but T-bce greater than or equal to 6.5 x 107 K is necessar y in order to cycle into nitrogen the carbon that was previously convected to the stellar surface by the third dredge-up. Therefore, Li-rich C stars c an occur for T-bce's in this small range of temperatures. We then identify a possible (narrow) range of masses and luminosities for this peculiar evol utionary stage. Comparison of these models with the luminosities of the few Li-rich C stars in the LMC provides an independent distance indicator (wit hin similar to 0.25 mag) for the LMC. The present data and models are consi stent with (m - M)(o) similar to 18.7, but a better determination would be possible by refining the observations and the theoretical models.