Effect of Core Cooling on the Radius of Sub-Neptune Planets

Sub-Neptune planets are very common in our galaxy and show a large diversity in their mass-radius relation. In sub-Neptunes most of the planet mass is in the rocky part (hereafter core) which is surrounded by a modest hydrogen-helium envelope. As a result, the total initial heat content of such a planet is dominated by that of the core. Nonetheless, most studies contend that the core cooling will only have a minor effect on the radius evolution of the gaseous envelope, because the core's cooling is in sync with the envelope, i.e., most of the initial heat is released early on timescales of about 10-100 Myr. In this Letter we examine the importance of the core cooling rate for the thermal evolution of the envelope. Thus, we relax the early core cooling assumption and present a model where the core is characterized by two parameters: the initial temperature and the cooling time. We find that core cooling can significantly enhance the radius of the planet when it operates on a timescale similar to the observed age, i.e. several Gyr. Consequently, the interpretation of sub-Neptunes' mass-radius observations depends on the assumed core thermal properties and the uncertainty therein. The degeneracy of composition and core thermal properties can be reduced by obtaining better estimates of the planet ages (in addition to their radii and masses) as envisioned by future observations.Comment: Accepted for publication in A&A Letter

The Evolution and Internal Structure of Jupiter and Saturn with Compositional Gradients

The internal structure of gas giant planets may be more complex than the commonly assumed core-envelope structure with an adiabatic temperature profile. Different primordial internal structures as well as various physical processes can lead to non-homogenous compositional distributions. A non-homogenous internal structure has a significant impact on the thermal evolution and final structure of the planets. In this paper, we present alternative structure and evolution models for Jupiter and Saturn allowing for non-adiabatic primordial structures and the mixing of heavy elements by convection as these planets evolve. We present the evolution of the planets accounting for various initial composition gradients, and in the case of Saturn, include the formation of a helium-rich region as a result of helium rain. We investigate the stability of regions with composition gradients against convection, and find that the helium shell in Saturn remains stable and does not mix with the rest of the envelope. In other cases, convection mixes the planetary interior despite the existence of compositional gradients, leading to the enrichment of the envelope with heavy elements. We show that non-adiabatic structures (and cooling histories) for both Jupiter and Saturn are feasible. The interior temperatures in that case are much higher that for standard adiabatic models. We conclude that the internal structure is directly linked to the formation and evolution history of the planet. These alternative internal structures of Jupiter and Saturn should be considered when interpreting the upcoming Juno and Cassini data.Comment: accepted for publication in Ap

Explaining the low luminosity of Uranus: A self-consistent thermal and structural evolution

The low luminosity of Uranus is a long-standing challenge in planetary science. Simple adiabatic models are inconsistent with the measured luminosity, which indicates that Uranus is non-adiabatic because it has thermal boundary layers and/or conductive regions. A gradual composition distribution acts as a thermal boundary to suppress convection and slow down the internal cooling. Here we investigate whether composition gradients in the deep interior of Uranus can explain its low luminosity, the required composition gradient, and whether it is stable for convective mixing on a timescale of some billion years. We varied the primordial composition distribution and the initial energy budget of the planet, and chose the models that fit the currently measured properties (radius, luminosity, and moment of inertia) of Uranus. We present several alternative non-adiabatic internal structures that fit the Uranus measurements. We found that convective mixing is limited to the interior of Uranus, and a composition gradient is stable and sufficient to explain its current luminosity. As a result, the interior of Uranus might still be very hot, in spite of its low luminosity. The stable composition gradient also indicates that the current internal structure of Uranus is similar to its primordial structure. Moreover, we suggest that the initial energy content of Uranus cannot be greater than 20% of its formation (accretion) energy. We also find that an interior with a mixture of ice and rock, rather than separated ice and rock shells, is consistent with measurements, suggesting that Uranus might not be "differentiated". Our models can explain the luminosity of Uranus, and they are also consistent with its metal-rich atmosphere and with the predictions for the location where its magnetic field is generated.Comment: 10 pages, 7 figures, accepted for publication in A&

Interior and Evolution of the Giant Planets

The giant planets were the first to form and hold the key to unveiling the solar system's formation history in their interiors and atmospheres. Furthermore, the unique conditions present in the interiors of the giant planets make them natural laboratories for exploring different elements under extreme conditions. We are at a unique time to study these planets. The missions Juno to Jupiter and Cassini to Saturn have provided invaluable information to reveal their interiors like never before, including extremely accurate gravity data, atmospheric abundances and magnetic field measurements that revolutionised our knowledge of their interior structures. At the same time, new laboratory experiments and modelling efforts also improved, and statistical analysis of these planets is now possible to explore all the different conditions that shape their interiors. We review the interior structure of Jupiter, Saturn, Uranus and Neptune, including the need for inhomogeneous structures to explain the data, the problems unsolved and the effect that advances in our understanding of their internal structure have on their formation and evolution.Comment: Review paper published in the special issue "Remote Sensing Observations of the Giant Planets

Rocky sub-Neptunes formed by pebble accretion: Rain of rocks from polluted envelopes

Sub-Neptune planets formed in the protoplanetary disk accreted hydrogen-helium (H,He) envelopes. Planet formation models of sub-Neptunes formed by pebble accretion result in small rocky cores surrounded by polluted H,He envelopes where most of the rock (silicate) is in vapor form at the end of the formation phase. This vapor is expected to condense and rain-out as the planet cools. In this Letter we examine the timescale for the rainout and its effect on the thermal evolution. We calculate the thermal and structural evolution of a 10 Earth masses planet formed by pebble accretion, taking into account material redistribution from silicate rainout (condensation and settling) and from convective mixing. We find that the duration of the rainout in sub-Neptunes is on Gyr timescale and varies with envelope mass: planets with envelopes below 0.75 Earth mass rainout into a core-envelope structure in less than 1 Gyr, while planets in excess of 0.75 Earth mass of H,He preserve some of their envelope pollution for billions of years. The energy released by the rainout inflates the radius with respect to planets that start out from a plain core-envelope structure. This inflation would result in estimates of the H,He contents of observed exoplanets based on the standard core-envelope structure to be too high.We identify a number of planets in the exoplanet census where rainout may operate, which would result in their H,He contents to be overestimated by up to a factor two. Future accurate age measurements by the PLATO mission may allow the identification of planets formed with polluted envelopes.Comment: accepted to A&A Letter

How planets grow by pebble accretion. III. Emergence of an interior composition gradient

During their formation, planets form large, hot atmospheres due to the ongoing accretion of solids. It has been customary to assume that all solids end up at the center constituting a "core" of refractory materials, whereas the envelope remains metal-free. Recent work, as well as observations by the JUNO mission, indicate however that the distinction may not be so clear cut. Indeed, small silicate, pebble-sized particles will sublimate in the atmosphere when they hit the sublimation temperature (T ~ 2,000 K). In this paper we extend previous analytical work to compute the properties of planets under such a pebble accretion scenario. We conduct 1D numerical calculations of the atmosphere of an accreting planet, solving the stellar structure equations, augmented by a non-ideal equation of state that describes a hydrogen/helium-silicate vapor mixture. Calculations terminate at the point where the total mass in metal equals that of the H/He gas, which we numerically confirm as the onset of runaway gas accretion. When pebbles sublimate before reaching the core, insufficient (accretion) energy is available to mix dense, vapor-rich lower layers with the higher layers of lower metallicity. A gradual structure in which Z decreases with radius is therefore a natural outcome of planet formation by pebble accretion. We highlight, furthermore, that (small) pebbles can act as the dominant source of opacity, preventing rapid cooling and presenting a channel for (mini-)Neptunes to survive in gas-rich disks. Nevertheless, once pebble accretion subsides, the atmosphere rapidly clears followed by runaway gas accretion. We consider atmospheric recycling to be the more probable mechanisms that have stalled the growth of these planets' envelopes.Comment: Accepted for publication in A&