Core temperature is modelled with the same Kelvin–Helmholtz contraction law used across the site's brown-dwarf sims:
T_c(M,t) = T_peak(M)·[1 − exp(−t / (0.3·τ(M,κ)))]
T_peak(M) = 8.74×10⁶·M^1.3 K (M in M☉)
τ(M,κ) = κ·100·(M/0.06)^−2.5 Myr
Unlike the toy 3D version (instant on/off at threshold), this engine integrates a real depletion ODE. Lithium-7 destruction via ⁽Li(p,α)⁴He is a nuclear reaction, so its rate rises exponentially with temperature (Arrhenius form):
dN/dt = −N / τburn(T)
τburn(T) = τref·exp[ Ea·(1/T − 1/Tign) ]
with τref = 3 Myr at the ignition temperature Tign, so once the core is a few percent hotter than Tign the burn timescale collapses to <1 Myr (lithium vanishes almost instantly, matching real fully-convective mixing), while a core a few percent cooler has a burn timescale of billions of years — effectively never depletes within the age of the universe.
Because Tpeak(M) ∝ M1.3 saturates as t→∞, any mass below a sharp critical mass Mcrit = (Tign/8.74×10⁶)1/1.3 never reaches ignition temperature at all — its lithium survives forever, exactly like electron-degenerate brown dwarfs in nature. At the default Tign = 2.5×10⁶ K this evaluates to ≈0.065 M☉, the real observed lithium depletion boundary mass.
- The Li abundance vs age chart integrates the ODE above for the currently selected mass across the full age range (1 Myr–3 Gyr), so you can watch N(Li) collapse once the core crosses ignition.
- The mass vs depletion-age chart repeats that integration for ~70 masses spanning 0.02–0.16 M☉ and records the age at which each one first reaches 99% depletion — the curve diverges to "never" as mass approaches Mcrit from above, which is exactly the astronomical lithium test: everything above the boundary mass in a coeval cluster shows no Li 670.8 nm line, everything below it still does.
- Nudging the ignition temperature or contraction rate κ shifts Mcrit and the whole boundary curve, illustrating the modelling uncertainty behind published lithium-test cluster ages.