Heat Transfer as a Key Process in Earth’s Mantle: New Measurements, New Theory

1. Heat Transfer as a Key Process in Earth’s Mantle: New Measurements, New Theory Anne M. Hofmeister

2. Janet Bowey (U. College London) Bob Criss (Washington U.) Paul Giesting (Notre Dame) Gabriel Gwanmesia (U. Delaware) Brad Jolliff (Washington U.) Andrew Locock (Notre Dame) Angela Speck (U. Missouri Columbia) Brigitte Wopenka (Washington U.) Tomo Yanagawa (Kyushu U.) Dave Yuen (U. Minnesota) Collaborators

3. Outline • Background • Heat transfer via vibrations • A model for klat • Laser – flash data on klat (T) • Implications for magma genesis, Transition Zone • Heat transfer via radiation • A model incorporating grain size • Does radiation or rheology have more impact? • Implications for the Lower Mantle • Merging Geological & Geophysical Constraints • Mantle convection is multiply layered. • The global power is low with no secular delay

4. Important Principles Heat = Light < 0 is destabilizing > 0 is stabilizing Dubuffett et al.(2002) Macedonio Melloni (1843) Photo Credit: www.Corbis.com

5. What drives convection? buoyancy heat diffusion viscous damping vs. & which is more important?

6. Baal Jehovah Rheology Thermal Conductivity Temperature Equation Quasi hyperbolic nonlinear Parabolic Equation Momentum Eq.Elliptic Eq. Credit: D. Yuen

7. Thermal conductivity is most important property because it controls the temperature, which then determines the other physical properties. k(T) temperature heat capacity thermal expansivity viscosity density

8. To model convection we need: k0 (ambient temperature and pressure)

9. Why is a model for k needed? because of crummy data!

10. Heat Transfer via Vibrations (phonons) Debye (1914) used Claussius’ kinetic theory of gases to relate the thermal conductivity of a solid to the collisions within its phonon gas: where ci is the heat capacity of the ith mode ui is the group velocity ti is the mean free lifetime between collisions

11. The formula was not very useful because the vibrations were treated as harmonic oscillators (i.e., non-interacting). Instead the vibrations interact through damping !

12. The Lorentz Model A damped harmonic oscillator has a lifetime: X = Ae(-t)cos (wt)

13. Examples of vibrations damped underdamped

14. Heat Transfer via Vibrations (phonons) + mean free gas theory damped harmonic oscillator model gives (Hofmeister, 1999; 2001) where Gis obtained from IR reflectivity data

15. IR Spectrometer

16. Lifetimes (t = 1/G) • are obtained from IR peak widths

17. Let’s test the model against reliable data

18. Compositional dependence of klat

19. Compositional dependence of klat

20. Pressure dependence of klat

21. To understand Earth processes, we need to make measurements at high T http://www.math.montana.edu

22. A laser-flash apparatus near-IR detector furnace Sample under cap cap support CO2 laser cabinet

23. How a laser flash apparatus works fayalite at 1000o C CO2 laser pulse fit detector Signal emissions t half detector output Sample in furnace CO2 laser Time, ms

24. Advantages of LFA Basalt • Rapid and accurate • Contact free: no power losses from cracks • Phonon component is separated from radiative transfer effects Heat transfer by phonons Signal 500oC Obsidian signal phonons photons 500oC time

25. Once Dlat/T = 0, Dlat no longer effects convection.

26. More laser-flash results: glass has low thermal diffusivity

27. Transient melting experiments Change upon melting

28. Results from laser-flash measurements • The thermal diffusivity of melts or glasses is lower than that of minerals or rocks • Thus, runaway melting is a possible mechanism for magma generation in the upper mantle • D and klat (of minerals, rocks, and glasses) are independent of T at high T • Thus, radiative transfer is the key process inside Earths’ mantle

29. Implications for Earth’s Mantle

30. Lower Mantle Upper Mantle Transition Zone Velocities in the Transition Zone cannot be explained by adiabatic gradients or by steep conductive temperature gradients (super-adiabatic). PREM (Anderson, 1989)

31. k0 for mantle minerals Low thermal conductivity is expected for the TZ, as it is rich in garnet (e.g., Vacher et al. 1998). But, low k suggests a super-adiabatic T gradient, which is not supported by seismic velocities.

32. Also, nearly constant temperatures suggest buoyancy/ instability of the Transition Zone: Mantle avalanche ??? Alternatively, a chemical gradient exists across the transition zone (Sinogeikin and Bass, 2002). Then, the temperature gradient is unconstrained. Layered mantle convection is implied.

33. Radiative Transfer Hot Gas Cool Dust Shells in the Egg Nebula Credit: R. Thompson (U. Arizona) et al., NICMOS, HST, NASA

34. The two types of radiative transfer diffusive cold direct hot Earth: diffusive Laboratory: direct 990 K ~1 km 1000 K recorder heater 298 K ~ 5 mm 800K

35. Diffusive Radiative Transfer • Earth’s mantle is internally heated and consists of grains which scatter and partially absorb light • Because the grains cannot be opaque, they cannot be blackbodies • The light emitted = the emissivity x the blackbody spectrum • Emissivity = absorptivity (Kirchhoff, ca. 1869). We measure absorption with a spectrometer. d

36. Diffusive radiative transfer is calculated fromspectra from the near-IR through the ultraviolet,accounting for scattering losses at grain boundaries: Visible region from Taran and Langer (2001) Ullrich et al. (2002) interface reflectivity

37. krad depends strongly and non-linearly on grain-size (d) due to competing effects: 1) small grains scatter light repeatedly, providing a short mean free path, which suppresses krad 2) small grains absorb light weakly, providing a large mean free path, which inhances krad 3) small grains emit weakly which suppresses krad

38. for ~0.1% interface reflectivity

39. Radiative transfer is large in the lower mantle, which promotes stability But in the transition zone, the negative T gradient of radiative transfer is destabilizing for large grain sizes

40. Does radiative transfer or viscosity affect convection more? work in progress by Tomo Yanagawa, Dave Yuen, and Masao Nakada

41. Vertical viscosity contrast is eg ~ 107 k=1 k = 1 + 4T3 represents upper mantle credit: Tomo Yanagawa

42. Vertical viscosity contrast is eg ~ 103 k contrast is 5 represents Lower Mantle credit: Tomo Yanagawa

43. Implications Radiative transport exerts greater control over convection than viscosity • Blob-like convection in Upper Mantle • An almost stagnant Lower Mantle Is there evidence ?

44. Tomography shows that the middle of the lower mantle is less heterogeneous than the rest Masters et al. (2000)

45. Possible stratigraphies for layered convection (categorized by different modes of heat transport) Upper Mantle Transition Zone slab Lower Mantle

46. Equatorial Section N Lower mantle L= 2 flow

47. Polar Section

48. Does the Earth’s engine lack sufficient vigor to produce whole mantle convection? The current model for the global heat flux assumed constant k and thus overestimated power: Strong radiative transfer in the lower mantle limits strong convection.

49. Global Power 31 TW at mid-ocean Half-space cooling model with constant k gives 44 TW. Analysis of the raw data gives 31 TW

50. Geologic evidence for weak convection • A global power of 31 TW is consistent with an enstatite chondrite model of the Earth, which also explains its O isotopes and huge Fe core (Lodders, Javoy). • The long-standing existence of basaltic volcanism of the oceanic crust implies near steady-state heat expulsion. • MORB and hot-spot melting is runaway, requires little excess heating. • Layered (weak) convection may address different styles of upper and lower mantle