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Context. The mass and radius of a planet directly provide its bulk density, which can be interpreted in terms of its overall composition. Any measure of the radial mass distribution provides a first step in constraining the interior structure. The fluid Love number $k_2$ provides such a measure, and estimates of $k_2$ for extrasolar planets are expected to be available in the coming years thanks to improved observational facilities and the ever-extending temporal baseline of extrasolar planet observations. Aims. We derive a method for calculating the Love numbers $k_n$ of any object given its density profile, which is routinely calculated from interior structure codes. Methods. We used the matrix-propagator technique, a method frequently used in the geophysical community. Results. We detail the calculation and apply it to the case of GJ 436b, a classical example of the degeneracy of mass-radius relationships, to illustrate how measurements of $k_2$ can improve our understanding of the interior structure of extrasolar planets. We implemented the method in a code that is fast, freely available, and easy to combine with preexisting interior structure codes. While the linear approach presented here for the calculation of the Love numbers cannot treat the presence of nonlinear effects that may arise under certain dynamical conditions, it is applicable to close-in gaseous extrasolar planets like hot Jupiters, likely the first targets for which $k_2$ will be measured., Comment: 10 pages, 9 figures

Plate tectonics is a fundamental component for the habitability of the Earth. Yet whether it is a recurrent feature of terrestrial bodies orbiting other stars or unique to the Earth is unknown. The stagnant lid may rather be the most common tectonic expression on such bodies. To understand whether a stagnant-lid planet can be habitable, i.e. host liquid water at its surface, we model the thermal evolution of the mantle, volcanic outgassing of H$_2$O and CO$_2$, and resulting climate of an Earth-like planet lacking plate tectonics. We used a 1D model of parameterized convection to simulate the evolution of melt generation and the build-up of an atmosphere of H$_2$O and CO$_2$ over 4.5 Gyr. We then employed a 1D radiative-convective atmosphere model to calculate the global mean atmospheric temperature and the boundaries of the habitable zone (HZ). The evolution of the interior is characterized by the initial production of a large amount of partial melt accompanied by a rapid outgassing of H$_2$O and CO$_2$. At 1 au, the obtained temperatures generally allow for liquid water on the surface nearly over the entire evolution. While the outer edge of the HZ is mostly influenced by the amount of outgassed CO$_2$, the inner edge presents a more complex behaviour that is dependent on the partial pressures of both gases. At 1 au, the stagnant-lid planet considered would be regarded as habitable. The width of the HZ at the end of the evolution, albeit influenced by the amount of outgassed CO$_2$, can vary in a non-monotonic way depending on the extent of the outgassed H$_2$O reservoir. Our results suggest that stagnant-lid planets can be habitable over geological timescales and that joint modelling of interior evolution, volcanic outgassing, and accompanying climate is necessary to robustly characterize planetary habitability.

The evolution and escape of the martian atmosphere and the planet's water inventory can be separated into an early and late evolutionary epoch. The first epoch started from the planet's origin and lasted $\sim$500 Myr. Because of the high EUV flux of the young Sun and Mars' low gravity it was accompanied by hydrodynamic blow-off of hydrogen and strong thermal escape rates of dragged heavier species such as O and C atoms. After the main part of the protoatmosphere was lost, impact-related volatiles and mantle outgassing may have resulted in accumulation of a secondary CO$_2$ atmosphere of a few tens to a few hundred mbar around $\sim$4--4.3 Gyr ago. The evolution of the atmospheric surface pressure and water inventory of such a secondary atmosphere during the second epoch which lasted from the end of the Noachian until today was most likely determined by a complex interplay of various nonthermal atmospheric escape processes, impacts, carbonate precipitation, and serpentinization during the Hesperian and Amazonian epochs which led to the present day surface pressure., Comment: 49 pages, 14 figures

We compare estimates of atmospheric precipitation during the Martian Noachian-Hesperian boundary 3.8 Gyr ago as calculated in a radiative-convective column model of the atmosphere with runoff values estimated from a geomorphological analysis of dendritic valley network discharge rates. In the atmospheric model, we assume CO2-H2O-N2 atmospheres with surface pressures varying from 20 mb to 3 bar with input solar luminosity reduced to 75% the modern value. Results from the valley network analysis are of the order of a few mm d-1 liquid water precipitation (1.5-10.6 mm d-1, with a median of 3.1 mm d-1). Atmospheric model results are much lower, from about 0.001-1 mm d-1 of snowfall (depending on CO2 partial pressure). Hence, the atmospheric model predicts a significantly lower amount of precipitated water than estimated from the geomorphological analysis. Furthermore, global mean surface temperatures are below freezing, i.e. runoff is most likely not directly linked to precipitation. Therefore, our results strongly favor a cold early Mars with episodic snowmelt as a source for runoff. Our approach is challenged by mostly unconstrained parameters, e.g. greenhouse gas abundance, global meteorology (for example, clouds) and planetary parameters such as obliquity- which affect the atmospheric result - as as well as by inherent problems in estimating discharge and runoff on ancient Mars, such as a lack of knowledge on infiltration and evaporation rates and on flooding timescales, which affect the geomorphological data. Nevertheless, our work represents a first step in combining and interpreting quantitative tools applied in early Mars atmospheric and geomorphological studies., Comment: accepted in Planetary and Space Science, 37 pages, 14 figures, 2 tables

The impact heat accumulated during the late stage of planetary accretion can melt a significant part or even the entire mantle of a terrestrial body, giving rise to a global magma ocean. [...] Assuming fractional crystallization of the magma ocean, dense cumulates are produced close to the surface, largely due to iron enrichment in the evolving magma ocean liquid (Elkins-Tanton et al., 2003). A gravitationally unstable mantle thus forms, which is prone to overturn. We investigate the cumulate overturn and its influence on the thermal evolution of Mars using mantle convection simulations in 2D cylindrical geometry. We present a suite of simulations using different initial conditions and a strongly temperature-dependent viscosity. We assume that all radiogenic heat sources have been enriched during the freezing-phase of the magma ocean in the uppermost 50 km and that the initial steam-atmosphere created by the degassing of the freezing magma ocean was rapidly lost, implying that the surface temperature is set to present-day values. In this case, a stagnant lid forms rapidly on top of the convective interior preventing the uppermost dense cumulates to sink, even when allowing for a plastic yielding mechanism. Below this dense stagnant lid, the mantle chemical gradient settles to a stable configuration. The convection pattern is dominated by small-scale structures, which are difficult to reconcile with the large-scale volcanic features observed over Mars' surface and partial melting ceases in less than 900 Ma. Assuming that the stagnant lid can break because of additional mechanisms and allowing the uppermost dense layer to overturn, a stable density gradient is obtained, with the densest material and the entire amount of heat sources lying above the CMB. This stratification leads to a strong overheating of the lowermost mantle [...], Comment: 30 pages, 5 figures, 1 table, submitted to EPSL

Radioisotopic ages for meteorites and their components provide constraints on the evolution of small bodies: timescales of accretion, thermal and aqueous metamorphism, differentiation, cooling and impact metamorphism. Realising that the decay heat of short-lived nuclides (e.g. 26Al, 60Fe), was the main heat source driving differentiation and metamorphism, thermal modeling of small bodies is of utmost importance to set individual meteorite age data into the general context of the thermal evolution of their parent bodies, and to derive general conclusions about the nature of planetary building blocks in the early solar system. As a general result, modelling easily explains that iron meteorites are older than chondrites, as early formed planetesimals experienced a higher concentration of short-lived nuclides and more severe heating. However, core formation processes may also extend to 10 Ma after formation of Calcium-Aluminum-rich inclusions (CAIs). A general effect of the porous nature of the starting material is that relatively small bodies (< few km) will also differentiate if they form within 2 Ma after CAIs. A particular interesting feature to be explored is the possibility that some chondrites may derive from the outer undifferentiated layers of asteroids that are differentiated in their interiors. This could explain the presence of remnant magnetization in some chondrites due to a planetary magnetic field., Comment: 24 pages, 9 figures, Accepted for publication as a chapter in Protostars and Planets VI, University of Arizona Press (2014), eds. H. Beuther, R. Klessen, C. Dullemond, Th. Henning