Lithium Depletion Boundary in Brown Dwarfs

Cluster Evolution

Cluster age 10 Myr

Model Parameters

Li-ignition temperature 2.50 ×10⁶ K

Contraction rate κ 1.00×

Live Readouts

Lithium depletion boundary

—

Depleted objects

0 / 0

Core temp @ boundary mass

—

T_c vs Mass (this age)

core temperature ignition threshold

How it works

Lithium-7 burns via ⁽Li(p,α)⁴He once core temperature exceeds ≈2.5×10⁶ K — far below the ≈3×10⁶ K needed to sustain hydrogen fusion. Because low-mass stars and brown dwarfs are fully convective, the whole object is dredged through the burning core, so once ignition temperature is reached, primordial lithium is wiped out everywhere in a few Myr — fast compared to the contraction itself.

T_c(M,t) ≈ T_peak(M) · [1 − exp(−t / (0.3·τ(M)))]
T_peak(M) ∝ M^1.3          (higher mass → hotter core)
τ(M) ∝ κ·M^−2.5        (lower mass → slower Kelvin–Helmholtz contraction)

Below ≈0.06 M☉, an object never gets hot enough before electron degeneracy pressure halts further contraction — its lithium survives forever. Above that mass, contraction eventually pushes T_c past threshold and lithium is destroyed. In a coeval population (a real star cluster) this produces a sharp lithium depletion boundary mass, M_LDB: everything above it shows no Li 670.8 nm absorption line, everything below it does.

Cluster age — lower-mass objects need longer to contract and heat up, so M_LDB sweeps to lower mass as the cluster ages. Measuring M_LDB in a real young cluster (e.g. the Pleiades, NGC 2547) gives an age estimate independent of main-sequence isochrone fitting.
Ignition temperature & contraction rate κ — these encode the modelling uncertainty in published evolutionary tracks (opacity, metallicity, convection efficiency); nudging them shifts the boundary, showing why M_LDB-based ages carry systematic error bars.
This toy model recomputes T_c(M) directly from the current age slider rather than tracking a full burn history, so scrubbing the age backwards is a pedagogical simplification — in reality, once lithium is destroyed it cannot come back.

Lithium-rich (unburned) Lithium-depleted (burned)

mass increases → (0.02 M☉ left — 0.16 M☉ right)

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.