Constraints on the existence of low-mass planets with supercritical hydrospheres
Authors: Vivien Hugo , Aguichine Artyom , Mousis Olivier , Deleuil Magali , Marcq Emmanuel 
Published: September 2022

&lt;p&gt;Short-period, low-mass planets have been found to often display inflated atmospheres [1]. Here, we investigate the interior structure of such planets with a moderate water budget using a fully self-consistent planet interior model [2, 3], where water can exist in supercritical state. This has been done by increasing the working range of an existing interior model, allowing us to explore the 0.2-2.3 Earth mass range. We consider planets with water mass fractions (WMF) ranging from 0.01% to 5% and irradiation temperatures between 500 and 2000K. Moreover, we consider three possible internal compositions; a pure rocky interior, an Earth-like core mass fraction (0.325) and a Mercury-like core mass fraction (0.7).&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Figure 1:&lt;/strong&gt; Computed planetary radii Rp at the transiting depth of 20mbar as a function of planetary mass and irradiation temperature. Columns correspond to different core mass fractions (0, 0.325, 0.7, from left to right) while rows correspond to different water mass fractions (5%, 1%, 0.01%, from top to bottom). Any missing data correspond to cases where the atmosphere is hydrostatically unstable.&lt;/p&gt;
&lt;p&gt;We find that at higher masses, the planet radius increases with the planet mass, and the radii for planets with supercritical water are greater than if water was in a condensed phase. An important mass of water can also result in a notable compression of the refractory layers (up to 0.1 Earth radius for a WMF of 5%). At lower masses, we find that the steam atmosphere inflates, and becomes gravitationally unstable when the scale height of the atmosphere exceeds ~0.1 times the planetary radius. We propose to use this H/Rp ratio as a stability criterion for steam atmospheres.&amp;#160;&lt;/p&gt;
&lt;p&gt;Our data can be used to estimate the maximum WMF that can be retained by a planet given its mass, irradiation temperature and interior composition. For a given mass and temperature, a large part of the planets considered here can be stable even if constituted of 100% water. As the temperature increases or as the mass decreases, the surface gravity of a 100% water planet becomes too weak to retain the steam atmosphere. It is then possible to estimate the maximum WMF under which the atmosphere is stable.&lt;/p&gt;
&lt;p&gt;Our results show that planets under 0.9 Earth masses should typically present unstable hydrospheres.&amp;#160; We also find that a sharp transition exists between a planet able to hold a 100% water atmosphere and an unstable one, as the H/Rp stability criterion exceeds 0.1. Additionally, we note that this class of planets is a viable explanation of the current Super-Puff category without invoking instrumental limitations, as the mass of water molecules induces a more inflated atmosphere than H/He planets.&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;References:&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;[1] Turbet, M., Bolmont, E., Ehrenreich, D., et al. 2020, A&amp;A, 638, A41&lt;/p&gt;
&lt;p&gt;[2] Aguichine, A., Mousis, O., Deleuil, M., et al. 2021, ApJ, 914, 84&lt;/p&gt;
&lt;p&gt;[3] Vivien, H.G., Aguichine, A., Mousis, O., et al. 2022, ApJ&lt;/p&gt;