Sara Seager2014-03-17 4:52 PM

固体系外行星的质量-半径关系  Mass-radius Relationships For Solid Exoplanets 

论文摘要

考虑到行星主要是由铁,硅酸盐,水以及碳化合物组成,我们使用寒冷行星新内部模型来探索固体系外行星的质量-半径关系。实验发现我们所认为的寒冷类地质行星所有组成成分的质量-半径关系遵循非简单功率法则下的通用函数形式:[lnR(s)= K(1)+1 / 3ln(M(s))-K(2)M [K(3)s,M(p)〜= 20M(+)],其中M(s)和R(s)是可标度质量和半径值。这个函数形式的形成是因为所有固体行星的通用构建模块都具有能够用 þ的修正多项式得到极好近似的状态方程:þ= þ(0)+ cP(n)。我们发现包括温度结构和相位变化在内的极详细地球内部模型没有必要通过对质量和半径测量来推导固体系外行星的总组成成分。我们还发现那些没有实质大气的固体系外行星具有以下特征:对行星质量和半径组成中5%的不确定性使得我们能够区分主要构成行星成分的铁或硅酸盐或冰水,但无法获得更详细的组合物构成;拥有水成分占总重量约25%以上的水冰行星也因为这约5%的不确定性而可得到识别; 给定质量的情形下,符合常理的最小行星规模是纯铁行星;由于相似的零压密度和状态方程,碳行星的质量-半径关系与硅酸盐和水行星的质量-半径关系类似。基于具有和不具有气体层行星之间的显著半径差异,我们提出了'超级地球'的定义概念。


Abstract 

We use new interior models of cold planets to investigate the mass-radius relationships of solid exoplanets, considering planets made primarily of iron, silicates, water, and carbon compounds. We find that the mass-radius relationships for cold terrestrial mass planets of all compositions we considered follow a generic functional form that is not a simple power law: [lnR(s) =k(1)+1/3ln(M(s))-k(2)M[k(3) s] for up to M(p)~=20M(+)] , where M(s)and R(s) are scaled mass and radius values. This functional form arises because the common building blocks of solid planets all have equations of state that are well approximated by a modified polytrope of the form þ = þ(0)+cP(n). We find that highly detailed planet interior models, including temperature structure and phase changes, are not necessary to derive solid exoplanet bulk composition from mass and radius measurements. For solid exoplanets with no substantial atmosphere we have also found the following: with 5% fractional uncertainty in planet mass and radius it is possible to distinguish among planets composed predominantly of iron or silicates or water ice but not more detailed compositions; with~5% uncertainty water ice planets with ~>25% water by mass may be identified; the minimum plausible planet size for a given mass is that of a pure iron planet; and carbon planet mass-radius relationships overlap with those of silicate and water planets due to similar zero-pressure densities and equations of state. We propose a definition of “super-Earths” based on the clear distinction in radii between planets with significant gas envelopes and those without.

(摘要中的正确公式见原文)

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Sara Seager

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