THE HEAT LOSS OF THE EARTH Claude Jaupart Jean-Claude Mareschal Stéphane Labrosse Institut de Physique du Globe de Paris

SECULAR COOLING EQUATION M C p = - ∫ q r dA + ∫ H dV + ∫  dV = - heat loss + internal heat production + external energy tranfers (ex: tidal interaction) Note (1) : negligible contribution of contraction, zero contribution of dissipation Note (2) : external energy transfers are negligible dT dt

Core Mantle Core has no U, Th, K?

AIMS (1)Evaluate heat loss and uncertainty (2)Constraints on secular cooling (3)Breakdown between core and mantle

Heat flux ~ (age) -1/2 (Cooling by conduction in upper boundary layer)

OCEANIC HEAT FLUX

k T m Q = √   t Cooling model (based on boundary layer theory, consistent with laboratory experiments and numerical simulations) T m = mid-ocean ridge temperature k,  = thermal conductivity, diffusivity t = age

t -1/2 model

Juan de Fuca ridge

Well-sedimented areas worldwide

Check no.1 = depth variations of the ocean floor (contraction due to cooling) Check no.2 = temperature at mid-ocean ridges T m = 1350 ± 50 °C consistent with basalt composition k T m Q = √   t

Heat flux through old sea floor

OCEANIC HEAT LOSS = 32 ± 2 TW (includes contributions from “hot spots” (mantle plumes) Main uncertainty : time-variations of age distribution

CONTINENTAL HEAT FLUX

CRUST Enriched in U, Th and K Lithospheric mantle (rigid root) Radiogenic heat production in continental lithosphere Q s =  Q c +  Q LM + Q b QcQc  Q LM Basal heat flux Q b

 (Q)  (Q) N WORLD All values Continental Heat Flow

Scale  (Q)  (Q) N CANADIAN SHIELD All values km km km Continental Heat Flow Averaging over different scales (windows)

Scale  (Q)  (Q) N CANADIAN SHIELD All values km km km WORLD All values °x 1° (≈100 km) °x 2° °x 5° Continental Heat Flow Averaging over different scales (windows)

From Abbott et al. (1994) Earth’s secular cooling rate From the composition of mid-ocean ridge basalts and similar magmas

50 K Gy - 1 ≈ 50 ± 25 K Gy -1

Sub-solidus convection. Constraints from phase-diagram

Solid fraction ≈ 1800 ± 100 K

(1)Assume same secular cooling rate than the mantle. Accounting for latent heat release and potential energy change due to crystallization: TW (2) Use magnetic field intensity and dynamo efficiency TW CORE HEAT LOSS 2 methods (Upper bound preferred because of constraints on boundary layer at the core-mantle boundary)

M C p = - ∫ q r dA + ∫ H dV Secular cooling rate ≈ K Gy -1 ≈ TW (for mantle + crust) Present-day crust + mantle heat loss = surface heat loss - heating from the core ≈ TW Bulk Silicate Earth (BSE) radiogenic heat production ≈ TW dT dt

Bulk Silicate Earth (BSE) radiogenic heat production ≈ TW Mean Uranium concentration (assuming chondritic Th/U and K/U) ≈ ppm

CRUST Enriched in U, Th and K Lithospheric mantle (rigid root) Radiogenic heat production in continental lithosphere Q s =  Q c +  Q LM + Q b QcQc  Q LM Basal heat flux Q b

BSE radiogenic heat production ≈ TW Heat production in continental crust (+ lithos. mantle) ≈ TW Internal heat generation for mantle convection ≈ TW