Modeling the albedo of magma ocean planets W. Pluriel 1, E. Marcq 1, M. Turbet 2, F. Forget 2, A. Salvador 3 1 LATMOS/IPSL/CNRS/UPMC/UVSQ, Guyancourt, France 2 LMD/IPSL/CNRS, Paris, France 3 GEOPS/IPSL/CNRS/UPSud, Orsay, France EPSC September 19 th 2017, Riga (Latvija)
Introduction Context Atmospheric submodel designed for coupling in order to study a generic telluric planet early evolution. Interior Atmosphere Escape Atmospheric module [Marcq, 2012; Marcq et al., 2017] is operational. Inputs Surface temperature Surface pressures (H 2 O, CO 2, N 2 ). Outputs Spectral reflectance how much energy is absorbed from the host star? OLR how fast does the magma ocean cool? Which thermal spectrum can be observed? TOA Z, T, ρ and composition at 0.1 Pa level: lower boundary condition for future escape submodel. T and ρ at TOA T surf P surf Escape Atmosphere Interior Net Radiative Flux Depletion or supply for volatiles
Introduction Context From Forget & Leconte (2013)
Introduction Context This model From Forget & Leconte (2013)
Introduction Summary Radiative convective 1D model Inspired from Abe & Matsui (1988) and Kasting (1988) Main difference no mandatory radiative balance (T eff T eq )! Surface temperature prescribed by interior submodel. Algorithm 1 Prescribed P grid up to 0.1 Pa. 2 Prescribed T (P) profile. 3 Computation of Z(P) et ρ i (P) according to equations of state and hydrostatic equilibrium. CO 2 and N 2 considered as ideal gases. H 2O is not! P > P c and/or T > T c common. 4 Computation of gaseous absorption (k-correlated LUT) and Rayleigh opacities from 0 to 3.5 10 5 cm 1 5 Computation of radiative properties of possible clouds. 6 Computation of IR and SW radiative fluxes with DISORT (4 streams).
Temperature profile Vertical Structure 3 layers from surface up to mesopause Dry Troposphere follows a dry adiabat. Moist Troposphere follows a moist adiabat. Clouds are located there. Mesosphere considered isothermal. Boundaries Dry/Moist where H 2 O reaches saturation (if already occuring at surface no dry troposphere and formation of a H 2 O ocean). Moist/Mesosphere where T < T 0 = TOA temperature, fixed here at 200 K. α v = ρ H2 O/(ρ CO2 + ρ N2 ) Vertically uniform within dry troposphere and mesosphere. Decreasing with increasing height within moist troposphere.
Radiative Fluxes Scattering Rayleigh Simple λ 4 dependency for CO 2, N 2 and H 2 O [Kopparapu et al., 2013; Sneep & Ubachs, 2005]. Clouds (optional) Present throughout the moist troposphere Mass loading from Kasting (1988) for Earth-like clouds. Optical properties (Q ext, ϖ 0, g) similar to present day Earth-like clouds. Henyey-Greenstein phase function 10 0 6 10 1 4 10 1 3 10 1 2 10 1 0 g Q ext 10 0 10 1 10 2 Wavelength [µm] Figure: Cloud optical properties
Radiative Fluxes Opacities Spectral Lines High-resolution spectra computed with KSPECTRUM [Eymet 2009]. Yields a (α v, T, P) grid of 16 k-coefficients [Wordsworth et al., 2010]. Reverting to grey opacities possible if approximate, fast computations are needed with no need for any spectral output. Continuum opacities CO 2 -CO 2 : derived from Venus measurements [Bézard, priv. comm.] H 2 O-H 2 O: from MT CKD v2.5 [Clough et al., 2005] CO 2 -H 2 O: not taken into account yet. Figure: Continua for H 2 O-H 2 O (solid) and H 2 O-CO 2 (dashed) from Ma & Tipping (1992)
Results Thermal radiation NIR windows open up for T surf > T ε Detectability and magma ocean cooling rate decrease strongly for T surf < T ε T ε depends on H 2 O and CO 2 atmospheric inventory Surface Temperature [K] 2250 2000 1750 T 1500 1250 1000 Proxima Cen 10 0 10 1 Wavelength [µm] Figure: OLR Contrast for a 300 bar H 2 O, 100 bar CO 2 Earth-like planet around Proxima Centauri 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 Contrast 10 1 PCO2 [bar]102 1000 K 1200 K 1400 K 1600 K 1800 K 2000 K 2200 K 10 1 10 2 10 3 P H2O [bar] Figure: T ε contours wrt. H 2 O and CO 2 surface pressures
Results Vertical Structure Clouds become optically thinner with increasing T surf Vertical extent decreases. Integrated mass loading much more so. Altitude [km] 300 250 200 150 100 50 0 Mesosphere Moist Troposphere Unsaturated Troposphere 200 400 600 800 1000 1200 Temperature [K] Altitude [km] 700 600 500 400 300 200 100 0 Mesosphere Moist Troposphere Unsaturated Troposphere 500 1000 1500 2000 2500 3000 Temperature [K] Figure: T (z) profile for T surf = 1200 K, 300 bar H 2 O, 100 bar CO 2 Figure: T (z) profile for T surf = 2800 K, 300 bar H 2 O, 100 bar CO 2
Results Spectral Reflectance With clouds Overall visible/nir reflectance dominated by clouds. Loss of spectral constrast at higher T surf Without clouds Higher atmospheric temperatures lead to decrease in continuum opacity increasing reflectance with increasing T surf? Spectral Reflectance P H2O = 500 bar; P 10 0 CO2 = 100 bar 10 1 10 0 Wavelength [µm] Figure: With clouds 3000 2750 2500 2250 2000 1750 1500 1250 Tsurf Spectral Reflectance P H2O = 500 bar; P CO2 = 100 bar 10 0 10 2 10 4 10 6 10 0 Wavelength [µm] Figure: Without clouds 3000 2750 2500 2250 2000 1750 1500 1250 Tsurf
Results Albedo (with clouds) Spectral reflectance decreases with increasing wavelength Lower albedo around M-stars compared to G-stars Two regimes for albedo depending on T surf wrt. T A = T ε + 240 K T surf T A High albedo, dominated by cloud scattering T surf T A Low albedo, dominated by Rayleigh scattering Broadly speaking, albedo increases with CO 2 content, decreases with H 2 O content Albedo 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Transition albedo A A Atmospheric inventory: P(H 2 O) = 200 bar ; P(CO 2 ) = 100 bar A L T A 1000 1500 2000 2500 3000 Surface temperature [K] A H Modeled data Analytical fit Figure: Albedo wrt. T surf
Results Albedo (with clouds) Spectral reflectance decreases with increasing wavelength Lower albedo around M-stars compared to G-stars Two regimes for albedo depending on T surf wrt. T A = T ε + 240 K T surf T A High albedo, dominated by cloud scattering T surf T A Low albedo, dominated by Rayleigh scattering Broadly speaking, albedo increases with CO 2 content, decreases with H 2 O content Figure: Low T surf albedo around the Sun Figure: High T surf albedo around the Sun
Conclusion Summary Simple coupled atmospheric 1D model already operational [Lebrun et al., 2013; Salvador et al., 2017] Like Hamano et al. (2013,2015), can be made more complex than atmospheric parametrizations usually embedded in coupled magma ocean cooling studies [Elkins-Tanton 2008] Very high albedo until water ocean condenses unless very young (less than 10 5 yr) Albedo decreases with star temperature. To do Publish SW model results Marcq et al. (2017) already published for thermal IR. Smoothing the mesospheric temperature profile T (z) important for self-consistent TOA temperature. Implement corrections to plane-parallel geometry for small planets and very hot atmospheres. Longer simulations possible once coupled with an escape model.