Evolution and Spectral Response of a Steam Atmosphere for Early Earth with a coupled climate-interior model

The evolution of Earth's early atmosphere and the emergence of habitable conditions on our planet are intricately coupled with the development and duration of the magma ocean phase during the early Hadean period (4 to 4.5 Ga). In this paper, we deal with the evolution of the steam atmosphere during the magma ocean period. We obtain the outgoing longwave radiation using a line-by-line radiative transfer code GARLIC. Our study suggests that an atmosphere consisting of pure H$_{2}$O, built as a result of outgassing extends the magma ocean lifetime to several million years. The thermal emission as a function of solidification timescale of magma ocean is shown. We study the effect of thermal dissociation of H$_{2}$O at higher temperatures by applying atmospheric chemical equilibrium which results in the formation of H$_{2}$ and O$_{2}$ during the early phase of the magma ocean. A 1-6\% reduction in the OLR is seen. We also obtain the effective height of the atmosphere by calculating the transmission spectra for the whole duration of the magma ocean. An atmosphere of depth ~100 km is seen for pure water atmospheres. The effect of thermal dissociation on the effective height of the atmosphere is also shown. Due to the difference in the absorption behavior at different altitudes, the spectral features of H$_{2}$ and O$_{2}$ are seen at different altitudes of the atmosphere. Therefore, these species along with H$_{2}$O have a significant contribution to the transmission spectra and could be useful for placing observational constraints upon magma ocean exoplanets.Comment: 22 pages, 17 Figures, accepted for publication in ApJ on March

What factors affect the duration and outgassing of the terrestrial magma ocean?

The magma ocean (MO) is a crucial stage in the build-up of terrestrial planets. Its solidification and the accompanying outgassing of volatiles set the conditions for important processes occurring later or even simultaneously, such as solid-state mantle convection and atmospheric escape. To constrain the duration of a global-scale Earth MO we have built and applied a 1D interior model coupled alternatively with a grey H2O/CO2 atmosphere or with a pure H2O atmosphere treated with a line-by-line model described in a companion paper by Katyal et al. (2019). We study in detail the effects of several factors affecting the MO lifetime, such as the initial abundance of H2O and CO2, the convection regime, the viscosity, the mantle melting temperature, and the longwave radiation absorption from the atmosphere. In this specifically multi-variable system we assess the impact of each factor with respect to a reference setting commonly assumed in the literature. We find that the MO stage can last from a few thousand to several million years. By coupling the interior model with the line-by-line atmosphere model, we identify the conditions that determine whether the planet experiences a transient magma ocean or it ceases to cool and maintains a continuous magma ocean. We find a dependence of this distinction simultaneously on the mass of the outgassed H2O atmosphere and on the MO surface melting temperature. We discuss their combined impact on the MO's lifetime in addition to the known dependence on albedo, orbital distance and stellar luminosity and we note observational degeneracies that arise thereby for target exoplanets

Effect of mantle oxidation state and escape upon the evolution of Earth's magma ocean atmosphere

The magma ocean period was a critical phase determining how Earth atmosphere developed into habitability. However there are major uncertainties in the role of key processes such as outgassing from the planetary interior and escape of species to space that play a major role in determining the atmosphere of early Earth. We investigate the influence of outgassing of various species and escape of H$_2$ for different mantle redox states upon the composition and evolution of the atmosphere for the magma ocean period. We include an important new atmosphere-interior coupling mechanism namely the redox evolution of the mantle which strongly affects the outgassing of species. We simulate the volatile outgassing and chemical speciation at the surface for various redox states of the mantle by employing a C-H-O based chemical speciation model combined with an interior outgassing model. We then apply a line-by-line radiative transfer model to study the remote appearance of the planet in terms of the infrared emission and transmission. Finally, we use a parameterized diffusion-limited and XUV energy-driven atmospheric escape model to calculate the loss of H$_2$ to space. We have simulated the thermal emission and transmission spectra for reduced or oxidized atmospheres present during the magma ocean period of Earth. Reduced or thin atmospheres consisting of H$_2$ in abundance emit more radiation to space and have larger effective height as compared to oxidized or thick atmospheres which are abundant in H$_2$O and CO$_2$. We obtain the outgassing rates of H2 from the mantle into the atmosphere to be a factor of ten times larger than the rates of diffusion-limited escape to space. Our work presents useful insight into the development of Earth atmosphere during the magma ocean period as well as input to guide future studies discussing exoplanetary interior compositions.Comment: 26 pages, 15 figures, accepted for publicatio

Coarsening dynamics in the Vicsek model of active matter

We study the flocking model introduced by Vicsek et al. (Phys. Rev. Lett. 75, 1226 (1995)) in the “coarsening” regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as $L_{\rho}(t) \sim t^{\theta_\rho}$ (with $\theta_\rho \simeq 0.25$ , while the velocity length scale grows much faster, viz., $L_{v}(t) \sim t^{\theta_v}$ (with $\theta_v \simeq 0.83$ . The spatial fluctuations in the density and velocity fields are studied by calculating the two-point correlation function and the structure factor, which show deviations from the well-known Porod’s law. This is a natural consequence of scattering from irregular morphologies that dynamically arise in the system. At large values of the scaled wave vector, the scaled structure factors for the density and velocity fields decay with powers -2.6 and -1.52 , respectively