固态系外行星的质量-半径关系
Mass-Radius Relationships for Solid Exoplanets
摘要：
我们使用新的冷行星内部模型来研究固体系外行星的质量-半径关系，考虑主要由铁，硅酸盐，水和碳化合物组成的行星。我们发现，我们考虑的所有成分的冷的陆地质量的行星的质量-半径关系遵循一个通用的函数形式，这不是一个简单的幂律：$\log_{10} R_s = k_1 + 1/3 \log_{10}(M_s) - k_2 M_s^{k_3}$为高达$M_p \approx 20 M_{\oplus}$，其中$M_s$和$R_s$是缩放的质量和半径值。这种函数形式的出现是因为固体行星的常见组成部分都具有状态方程，这些状态方程可以很好地近似为$ρ= ρ_0 + c P^n$形式的修改后的多面体。我们发现，非常详细的行星内部模型，包括温度结构和相变，是没有必要的固体系外行星的质量和半径测量散装组成。对于没有实质性大气层的固态系外行星，我们还发现：行星质量和半径的分数不确定性为5%时，可以区分主要由铁或硅酸盐或水冰组成的行星，但不能区分更详细的成分; $\sim$的不确定性为5%时，可以识别质量为$\gtrsim 25%$水的水冰行星;对于一个给定的质量来说，最小的行星尺寸是一个纯铁行星;碳行星的质量-半径关系与硅酸盐和水行星的质量-半径关系重叠，因为它们具有相似的零压密度和状态方程。我们提出了一个“超级地球”的定义，其基础是具有显著气体包层的行星和没有气体包层的行星之间的半径的明显区别。
英文摘要：
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: $\log_{10} R_s = k_1 + 1/3 \log_{10}(M_s) - k_2 M_s^{k_3}$ for up to $M_p \approx 20 M_{\oplus}$, 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 $ρ= ρ_0 + c P^n$. 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 that: 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 $\sim$~5% uncertainty water ice planets with $\gtrsim 25%$ 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.
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