Cumulative theoretical uncertainties in lithium depletion boundary age

Abstract

We performed a detailed analysis of the main theoretical uncertainties affecting the age at the lithium depletion boundary (LDB). To do that we computed almost 12 000 premain sequence models with mass in the range [0.06, 0.4] M ⊙ by varying input physics (nuclear reaction cross-sections, plasma electron screening, outer boundary conditions, equation of state, and radiative opacity), initial chemical elements abundances (total metallicity, helium and deuterium abundances, and heavy elements mixture), and convection efficiency (mixing length parameter, α ML ). As a first step, we studied the effect of varying these quantities individually within their extreme values. Then, we analysed the impact of simultaneously perturbing the main input/parameters without an a priori assumption of independence. Such an approach allowed us to build for the first time the cumulative error stripe, which defines the edges of the maximum uncertainty region in the theoretical LDB age.We found that the cumulative error stripe is asymmetric and dependent on the adopted mixing length value. For α ML = 1.00, the positive relative age error ranges from 5 to 15%, while for solar-calibrated mixing length, the uncertainty reduces to 5 − 10%. A large fraction of such an error (≈ 40%) is due to the uncertainty in the adopted initial chemical elements abundances.