Protostellar accretion in low mass metal poor stars and the cosmological lithium problem

Context.The cosmological lithium problem, that is, the discrepancy between the lithium abundance predicted by the Big Bang nucleosynthesis and the one observed for the stars of the "Spite plateau", is one of the long standing problems of modern astrophysics. Recent hints for a possible solution involve lithium burning induced by protostellar mass accretion on Spite plateau stars. However, to date, most of the protostellar and pre-main sequence stellar models that take mass accretion into account have been computed at solar metallicity, and a detailed analysis on the impact of protostellar accretion on the lithium evolution in the metal-poor regime, which is relevant for stars in the Spite plateau, is completely missing. Aims.The purpose of this paper is to fill this gap, analysing, in detail, for the first time the effect of protostellar accretion on low metallicity low-mass stars with a focus on pre-main sequence lithium evolution. Methods.We computed the evolution from the protostar to the main-sequence phase of accreting models with final masses equal to 0.7 and 0.8M(circle dot), and three metallicities Z = 0.0001, Z = 0.0010, and Z = 0.0050, corresponding to [Fe/H] similar to -2.1, -1.1 (typical of Spite plateau stars), and [Fe/H] similar to -0.42, respectively. We followed the temporal evolution of the chemical composition by considering nuclear burning, convective mixing, and diffusion. The effects of changing some of the main parameters affecting accreting models, that is the accretion energy (i.e. cold versus hot accretion), the initial seed mass M-seed and radius R-seed, and the mass accretion ratem(also considering episodic accretion), have been investigated in detail. Results.As for the main stellar properties and in particular the surface Li-7 abundance, hot accretion models converge to standard non-accreting ones within 1 Myr, regardless of the actual value of M-seed, R-seed, and m. Also, cold accretion models with a relatively large M-seed (greater than or similar to 10 M-J) or R-seed (greater than or similar to 1 R-circle dot) converge to standard non-accreting ones in less than about 10-20 Myr. However, a drastically different evolution occurs whenever a cold protostellar accretion process starts from small values of M-seed and R-seed (M-seed similar to 1M(J), R-seed less than or similar to 1 R-circle dot). These models almost entirely skip the standard Hayashi track evolution and deplete lithium before the end of the accretion phase. The e