|Internal structure modeling of the super-Earths|
|Written by Benoit LANGLAIS|
Abstract - Un modèle théorique qui décrit la structure interne des planètes depuis 1 jusqu’à 100 masses terrestres a été mis au point. Avec ce modèle, le rayon et le moment d’inertie d’une planète se déduisent de la masse du corps concerné, en supposant que sa composition globale en éléments lourds est similaire à celle de son étoile. Ce modèle calcule la position, les proﬁls de pression et de densité des différentes couches qui composent ce corps. Il permet de décrire les relations Masse-Rayon des différentes familles de planètes, outil indispensable au traitement des données de la sonde CoroT
Observing other planetary systems opens the perspective of discovering new types of planets, unknown in our Solar System. The recent discoveries of exoplanets with masses below 20 ME (Earth masses) conﬁrms the existence of Super-Earths [Léger et al., 2009, Selsis et al., 2007]. This family ncludes terrestrial planets such as Mars, Venus and Earth, water-rich planets like our giant icy moons, iron-rich planets similar to Mercury, but also mini-Neptunes (Fig.1). The abundance of low mass planets is not yet known. So far, over the 350 exoplanets which have been discovered, but only 34 are below 30 ME . This observed distribution is biased by observational limitations and is evolving very rapidly.
So far, over the 350 exoplanets which have been discovered, more than 90 % are giant planets, and only 34 are below 30 ME . But this observed distribution, which is biased by observational limitations, is evolving very rapidly. By analogy with the solar system, a metallic iron core is expected if the amount of iron is sufﬁcient. One important aspect of these planets is that they are potentially habitable, in the sense of bearing a sufﬁcient amount of liquid water at the surface (if permitted by the planetary surface temperature). It is anticipated that terrestrial concepts such as oceans and continents, volcanic and tectonic activity and even vegetal cover ("forests") are applicable to these planets.
It is assumed that the structure of a super-Earth is similar to that of Earth-like planets of the solar system: a metallic core, overlaid by a silicate mantle, and a water-rich outer layer. The bulk composition is then ﬁxed by the amount of water Xw , and the atomic ratios Fe/Si and Mg/Si [Léger et al., 2009; Selsis et al., 2007]. Stars which host exoplanets, have Fe/Si and Mg/Si ratios which can differ signiﬁcantly from solar ones. It is shown that our model is compatible with all these compositions, meaning that the presence of silicate-rich planets with or without water is very likely around these stars. Planetary radii have been calculated for a range of M and Xw . The ﬁrst result is that R is only multiplied by 3 (Fig. 2) for M increasing from 1 to 100 ME , whereas it should be 1001/3 = 4.6 if the sphere was homogeneous and incompressible. The exponent decreases as mass increases resulting in a signiﬁcant ﬂattening of the curves above 20 ME . For a given M , the transition from a dry silicate-rich planet to an icy world induces an increase of the radius between 30 % (100 ME ) and 40 % (1 ME ). All this information can be gathered into one empirical equation [Grasset et al., 2009] describing M − R relationships in the range 1-100 ME using α, β, γ and ε parameters depending on Xw :
with RE =6430 km is the radius of a 1ME planet in the reference case (not the Earth’s radius).
This internal structure model is applied to CoroT measurements, and in particular to the special case of recently detected CoroT-7b Super Earth planet.
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