Earth’s Energy Equation, simplified

1. Earth’s Energy Equation, simplified Qsurface≈ Hradioactive + Hmantle secular cooling + Qcore Qsurface≈ 44 TW (surface heat flow measurements) Hradioactive≈ 20 TW (chondrite-based composition models) Hsecular cooling≈ 9-18 TW (50-100 K/Ga, based on petrologic studies and rates of continental uplift) Qcore≈ 2-15 TW (geodynamo requirements, age of inner core, conductive heat flow across core/mantle boundary layer, heat transport by plumes)

2. Generally accepted global value is ~44±1 TW (c.f., Pollack et al., 1993) • Hofmeister and Criss (2005) argue for much lower surface heat flow (~31 TW). • Difference reflects debate over the importance of hydrothermal circulation in transporting heat near mid-ocean ridges How much heat are we loosing? Modified from Pollack et al. (1993)

3. Was mantle heat flow higher or lower in the past? Standard view: Higher mantle temperatures in the early Earth result in lower mantle viscosity, more rapid convection, and higher surface heat flow. Alternate view: Higher mantle temperatures in the early Earth result in deeper initiation of mantle melting and extraction of water and other volatile species. This increases viscosity of the melt-depleted region, resulting in thicker, stiffer tectosphere, more sluggish plate tectonics, and lower surface heat flow.

4. How much radiogenic heat production? Major element trends in chondrite meteorites and mantle xenoliths

6. How much potassium? (McDonough & Sun, 1995; Allegre et al., 2001)

8. Is the chondritic model valid? 146Sm => 142Nd T1/2 = 103 Ma Possible explanations for the difference in 142Nd/144Nd in terrestrial and chondritic samples include: Earth has non-chondritic relative abundances of Sm and Nd, possibly due to early impact erosion of proto-crust. There is an enriched “hidden” reservoir with low 142Nd/144Nd somewhere in the mantle.

9. Could a giant impact such as the moon-forming impact have ejected an early proto-crust rich in incompatible heat-producing elements? This scenario could account for the 142Nd depletion in terrestrial samples relative to chondrites but would suggest significantly less than 20 TW present-day radiogenic heat production in the Earth.

10. Hmantle secular cooling≈ Mmantle*Cp*dT/dt How can we estimate rates of mantle cooling? Rates of continental uplift (constant freeboard argument) (c.f., Galer & Metzger,1996) FeO-MgO or REE fractionation trends in Archaean basalts or komatiites (adiabatic melting models) (c.f., Mayborn & Lesher, 2004) “Lock-in” ages of lithospheric mantle xenoliths (coupling between lithospheric and asthenospheric cooling) (c.f., Bedini et al., 2004) All of these methods suggest mantle secular cooling of ~50-120 K/Ga, and most suggest 50-60 K/Ga since the archaean, but all are highly model-dependant.

11. How do we measure mantle cooling rates? Mantle cooling causes uplift of continental crust as the underlying mantle becomes denser. Average metamorphic pressures of exposed Archean terranes suggest mantle cooling rates of ~50-60 Ga since 3 Ga. From Galer & Metzger, 1996

12. Constraints on heat flow across the core/mantle boundary Power requirements of the geodynamo: ??? Conduction along outer core adiabat: ~7 TW (c.f., Anderson, 2002) Conduction across CMB: ~7-14 TW (c.f., Buffett, 2003) Heat transport by mantle plumes: ~2-13 TW (c.f., Davies, 1988; Zhong, 2006)

13. Qcond = A(dT/dZ) Qcond, CMB = ~8-14 TW T = ~1000-1800 K  = 9.5 Wm-1K-1 h = 200 km (dT/dZ)oc = ~0.94 K/km 46 Wm-1K-1 Qcond, oc = ~7 TW c.f., Anderson, 2002; Buffett, 2003

14. Thermal consequences of inner core crystallization Egrav = 4.1x1028 J Elatent = 7x1028 J Ecooling = 18.2x1028 J Etotal = 29.3x1028 J (+/- 18x1028J) (Labrosse et al., 2003) For CMB heat flow of 6-15 TW, age of onset of inner core crystallization is less than ~1.5 Ga. Largest sources of uncertainty are core Cp, slope of melting curve.

15. Segregation of crust, either early in Earth history or continuously through plate subduction, could store large amounts of U, Th, and K at base of mantle CMB

16. Core-mantle heat flow decreases with increasing CMB radiogenic heat production

18. Heat production within the core? • Experimental and theoretical studies suggest potassium could partition into the core under the right circumstances. • Potassium can enter sulfide liquids at low pressure • At high pressure (>25 GPa) potassium acts like a transition metal, can enter metal phases directly • Low-pressure segregation of sulfides or high-pressure core/mantle equilibration could result in significant quantities of potassium in the Earth’s core. Were the conditions necessary for potassium to enter the Earth’s core present during core formation?

19. Effect of sulfide fractionation during core formation on Cu concentrations in the mantle 2% S 10% S (McDonough & Sun, 1995; Allegre et al., 2001)

20. Alkali metal depletion trend-volatile loss or core segregation? s-d transition pressures from Young (1991) and other literature sources Condensation temperatures from Allegre et al. (2001) after Wasson (1985)

21. Silicate Earth K/Rb fractionation from high-P core formation Estimated BSE value

22. Questions an anti-neutrino observatory could help answer: What is the total radiogenic heat budget of the Earth? What is the composition of the Earth? Are heat-producing elements concentrated in the lower mantle or at the core/mantle boundary? Does the core contain heat-producing elements? What is really needed: Detection of neutrinos or anti-neutrinos produced from decay of 40K Directional detectors