Planetary internal structures

This chapter reviews the most recent advancements on the topic of terrestrial and giant planet interiors, including Solar System and extrasolar objects. Starting from an observed mass-radius diagram for known planets in the Universe, we will discuss the various types of planets appearing in this diagram and describe internal structures for each type. The review will summarize the status of theoretical and experimental works performed in the field of equation of states (EOS) for materials relevant to planetary interiors and will address the main theoretical and experimental uncertainties and challenges. It will discuss the impact of new EOS on interior structures and bulk composition determination. We will discuss important dynamical processes which strongly impact the interior and evolutionary properties of planets (e.g plate tectonics, semiconvection) and describe non standard models recently suggested for our giant planets. We will address the case of short-period, strongly irradiated exoplanets and critically analyse some of the physical mechanisms which have been suggested to explain their anomalously large radius.Comment: 24 pages, 8 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.

Equilibrium composition between liquid and clathrate reservoirs on Titan

Hundreds of lakes and a few seas of liquid hydrocarbons have been observed by the Cassini spacecraft to cover the polar regions of Titan. A significant fraction of these lakes or seas could possibly be interconnected with subsurface liquid reservoirs of alkanes. In this paper, we investigate the interplay that would happen between a reservoir of liquid hydrocarbons located in Titan's subsurface and a hypothetical clathrate reservoir that progressively forms if the liquid mixture diffuses throughout a preexisting porous icy layer. To do so, we use a statistical-thermodynamic model in order to compute the composition of the clathrate reservoir that forms as a result of the progressive entrapping of the liquid mixture. This study shows that clathrate formation strongly fractionates the molecules between the liquid and the solid phases. Depending on whether the structure I or structure II clathrate forms, the present model predicts that the liquid reservoirs would be mainly composed of either propane or ethane, respectively. The other molecules present in the liquid are trapped in clathrates. Any river or lake emanating from subsurface liquid reservoirs that significantly interacted with clathrate reservoirs should present such composition. On the other hand, lakes and rivers sourced by precipitation should contain higher fractions of methane and nitrogen, as well as minor traces of argon and carbon monoxide.Comment: Accepted for publication in Icaru

Titan's past and future: 3D modeling of a pure nitrogen atmosphere and geological implications

Several clues indicate that Titan's atmosphere has been depleted in methane during some period of its history, possibly as recently as 0.5-1 billion years ago. It could also happen in the future. Under these conditions, the atmosphere becomes only composed of nitrogen with a range of temperature and pressure allowing liquid or solid nitrogen to condense. Here, we explore these exotic climates throughout Titan's history with a 3D Global Climate Model (GCM) including the nitrogen cycle and the radiative effect of nitrogen clouds. We show that for the last billion years, only small polar nitrogen lakes should have formed. Yet, before 1 Ga, a significant part of the atmosphere could have condensed, forming deep nitrogen polar seas, which could have flowed and flooded the equatorial regions. Alternatively, nitrogen could be frozen on the surface like on Triton, but this would require an initial surface albedo higher than 0.65 at 4 Ga. Such a state could be stable even today if nitrogen ice albedo is higher than this value. According to our model, nitrogen flows and rain may have been efficient to erode the surface. Thus, we can speculate that a paleo-nitrogen cycle may explain the erosion and the age of Titan's surface, and may have produced some of the present valley networks and shorelines. Moreover, by diffusion of liquid nitrogen in the crust, a paleo-nitrogen cycle could be responsible of the flattening of the polar regions and be at the origin of the methane outgassing on Titan.Comment: Accepted for publication in Icarus on July 7, 201

Improving WCET Analysis Precision through Automata Product

Real-time scheduling of application requires sound estimation of the Worst-Case Execution Time (WCET) of each task. Part of the over-approximation introduced by the WCET analysis of a task comes from not taking into account the fact that the (implicit) worst-case execution path may be infeasible. This article does not address the question of finding infeasible paths but provides a new formalism of automata to describe sets of infeasible paths. This formalism combines the possibilities to express state-based path acceptance (like in regular automata), constraints on counters (in the Implicit Path Enumeration Technique fashion) and contexts of validity (like in State charts). We show the applicability of our proposal by performing infeasible paths aware WCET analyses within the OTAWA framework. We provide algorithms that transform the control flow graph and/or the constraints system supporting the WCET analysis in order to exclude the specified paths

Quantitative Static Analysis Over Semirings: Analysing Cache Behaviour for Java Card

AbstractWe present a semantics-based technique for modeling and analysing resource usage behaviour of programs written in a simple object oriented language like Java Card byte code. The approach is based on the quantitative abstract interpretation framework of Di Pierro and Wiklicky where programs are represented as linear operators. We consider in particular linear operators over semi-rings (such as max-plus) that have proven useful for analysing cost properties of discrete event systems. We illustrate our technique through a cache behaviour analysis for Java Card

Thermal evolution and lifetime of intrinsic magnetic fields of Super Earths in habitable zones

We have numerically studied the thermal evolution of various-mass terrestrial planets in habitable zones, focusing on duration of dynamo activity to generate their intrinsic magnetic fields, which may be one of key factors in habitability on the planets. In particular, we are concerned with super-Earths, observations of which are rapidly developing. We calculated evolution of temperature distributions in planetary interior, using Vinet equations of state, Arrhenius-type formula for mantle viscosity, and the astrophysical mixing length theory for convective heat transfer modified for mantle convection. After calibrating the model with terrestrial planets in the Solar system, we apply it for 0.1--$10M_{\oplus}$ rocky planets with surface temperature of 300~\mbox{K} (in habitable zones) and the Earth-like compositions. With the criterion for heat flux at the CMB (core-mantle boundary), the lifetime of the magnetic fields is evaluated from the calculated thermal evolution. We found that the lifetime slowly increases with the planetary mass ($M_p$) independent of initial temperature gap at the core-mantle boundary ($\Delta T_{\rm CMB}$) but beyond a critical value $M_{c,p}$ ($\sim O(1)M_{\oplus}$) it abruptly declines by the mantle viscosity enhancement due to the pressure effect. We derived $M_{c,p}$ as a function of $\Delta T_{\rm CMB}$ and a rheological parameter (activation volume, $V^*$). Thus, the magnetic field lifetime of super-Earths with $M_p > M_{p,c}$ sensitively depends on $\Delta T_{\rm CMB}$, which reflects planetary accretion, and $V^*$, which has uncertainty at very high pressure. More advanced high-pressure experiments and first-principle simulation as well as planetary accretion simulation are needed to discuss habitability of super-Earths.Comment: 19pages, 15 figures, accepted for publication in Ap

A New Family of Planets ? "Ocean Planets"

A new family of planets is considered which is between rochy terrestrial planets and gaseous giant ones: "Ocean-Planets". We present the possible formation, composition and internal models of these putative planets, including that of their ocean, as well as their possible Exobiology interest. These planets should be detectable by planet detection missions such as Eddington and Kepler, and possibly COROT (lauch scheduled in 2006). They would be ideal targets for spectroscopic missions such as Darwin/TPF.Comment: 15 pages, 3 figures submitted to Icarus notes (10 july 2003