Abstract Locally diffusive, radiative heat transport inside the earth is represented by an effective thermal conductivity ( k rad,dif ), calculated from spectra. Previous geophysical models assumed that emissivity ( ξ ) equals unity, which violates local radiative equilibrium in an internally heated, grainy medium. Our new formulation accounts for ξ depending on frequency, physical scattering depending on grain-size ( d ), and for light lost through back-reflections at interfaces. Mantle values of k rad,dif are estimated from recent visible spectra of olivine combined with new IR data. The following trends hold for k rad,dif calculated from olivine spectra, and should be equally valid for pyroxene and spinel: (1) pressure is unimportant, (2) radiative thermal conductivity depends non-linearly on d , temperature ( T ), and Fe 2+ content ( X ), (3) maxima occur in k rad,dif ( d ) when the grains are large enough to emit substantially, but not so large that light is strongly attenuated within a single-grain, (4) the dependence of k rad,dif on Fe 2+ content parallels that with d because absorption is controlled by the product dX (Beer's law), and (5) a local minimum occurs in k rad,dif near 2000 K for d > 2 mm because at that temperature the peak position of the blackbody curve coincides with that of the strongly absorbing Fe 2+ peak in the visible. Larger k rad,dif exists at lower and higher temperatures because mean free paths are long in the transmitting near-IR and UV spectral regions. As integration smooths over spectral details, the above representation based on olivine becomes increasingly accurate for other phases as grain-size decreases. For conditions expected in the transition zone, ∂ k rad,dif /∂ T is negative, which is destabilizing [Dubuffet, F., Yuen, D.A., Rainey, E.S.G., 2002. Controlling thermal chaos in the mantle by positive feedback from radiative thermal conductivity. Nonlinear Proc. Geophys. 9, 1–13]. In the lower mantle, photon transport dominates phonon, promoting stable, weak convection. That radiative transfer is linked to chemical composition and grain-size suggests that this process impacts planetary evolution through the non-linear feedback with rheology.
Read full abstract