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&

The Nuclear Power Plant Environment Monitoring System through Mobile Units

This article describes the information system for measuring and evaluating the dose rate in the environment of nuclear power plants Mochovce and Bohunice in Slovakia. The article presents the results achieved in the implementation of the EU project–Research of monitoring and evaluation of non-standard conditions in the area of nuclear power plants. The objectives included improving the system of acquisition, measuring and evaluating data with mobile and autonomous units applying new knowledge from research. The article provides basic and specific features of the system and compared to the previous version of the system, also new functions

On the Evolution and Survival of Protoplanets Embedded in a Protoplanetary Disk

We model the evolution of a Jupiter-mass protoplanet formed by the disk instability mechanism at various radial distances accounting for the presence of the disk. Using three different disk models, it is found that a newly-formed Jupiter-mass protoplanet at radial distance of $\lesssim$ 5-10 AU cannot undergo a dynamical collapse and evolve further to become a gravitational bound planet. We therefore conclude that {\it giant planets, if formed by the gravitational instability mechanism, must form and remain at large radial distances during the first $\sim$ 10$^5-10^6$ years of their evolution}. The minimum radial distances in which protoplanets of 1 Saturn-mass, 3 and 5 Jupiter-mass protoplanets can evolve using a disk model with $\dot{M}=10^{-6} M_{Sun}/yr$ and $\alpha=10^{-2}$ are found to be 12, 9, and 7 AU, respectively. The effect of gas accretion on the planetary evolution of a Jupiter-mass protoplanet is also investigated. It is shown that gas accretion can shorten the pre-collapse timescale substantially. Our study suggests that the timescale of the pre-collapse stage does not only depend on the planetary mass, but is greatly affected by the presence of the disk and efficient gas accretion.Comment: 26 pages, 2 tables, 10 figures. Accepted for publication in Ap