Pre-main sequence lithium burning. I. Weak T Tauri stars.

We derive lithium abundances in 53 T Tauri stars (TTS), concentrating on weak-line TTS. Our study gives the following results: 1)At luminosities $\ge 0.9 L\sun$ the Li abundances are remarkably uniform, with a mean value, log~N(Li)=3.1, equal to the "cosmic" lithium abundance. 2)Significant Li depletion appears below 0.5~L$\sun$ in the mass range 0.9-0.2 M$\sun$ and increases towards lower luminosities. At the lower mass end (0.4-0.2 M$\sun$), the observed luminosity of the Li burning turning point is about a factor 4 higher than predicted by the models. At masses 1.2-1.0 M$\sun$ the observations imply less PMS Li burning than theoretically expected. Moreover we show that: 1)Low Li abundances appear only among stars with low $v\sin{i}$. Fast rotators with masses around 0.8~M$\sun$ do not show evidence for strong Li depletion towards lower luminosities as slow rotators do. 2)In a sample restricted to only K5-K7 stars we find that the angular momentum spread before Li burning begins is larger than a factor 10. Lithium depletion associated to angular momentum loss during PMS evolution is not required to explain the observed abundances. The efficiency of PMS Li burning in the mass range 0.9-0.7~M$\sun$ is reduced in the presence of rapid rotation.