Luminosity of young Jupiters revisited. Massive cores make hot planets

The intrinsic luminosity of young Jupiters is of high interest for planet formation theory. It is an observable quantity that is determined by important physical mechanisms during formation, namely the accretion shock structure, and even more fundamentally, the basic formation mechanism (core accretion or gravitational instability). We study the impact of the core mass on the post-formation entropy and luminosity of young giant planets forming via core accretion with a supercritical shock (cold accretion). For this, we conduct self-consistently coupled formation and evolution calculations of giant planets with masses between 1 and 12 Jovian masses and core masses between 20 and 120 Earth masses. We find that the post-formation luminosity of massive giant planets is very sensitive to the core mass. An increase of the core mass by a factor 6 results in an increase of the post-formation luminosity of a 10 Jovian mass planet by a factor 120. Due to this dependency, there is no single well defined post-formation luminosity for core accretion, but a wide range. For massive cores (~100 Earth masses), the post-formation luminosities of core accretion planets become so high that they approach those in the hot start scenario that is often associated with gravitational instability. For the mechanism to work, it is necessary that the solids are accreted before or during gas runaway accretion, and that they sink deep into the planet. We make no claims whether or not such massive cores can actually form in giant planets. But if yes, it becomes difficult to rule out core accretion as formation mechanism based solely on luminosity for directly imaged planets that are more luminous than predicted for low core masses. Instead of invoking gravitational instability as the consequently necessary formation mode, the high luminosity could also be caused simply by a more massive core.Comment: 11 pages, 6 figures. A&A accepte

Compositional imprints in density-distance-time: a rocky composition for close-in low-mass exoplanets from the location of the valley of evaporation

We use an end-to-end model of planet formation, thermodynamic evolution, and atmospheric escape to investigate how the statistical imprints of evaporation depend on the bulk composition of planetary cores (rocky vs. icy). We find that the population-wide imprints like the location of the "evaporation valley" in the distance-radius plane and the corresponding bimodal radius distribution clearly differ depending on the bulk composition of the cores. Comparison with the observed position of the valley (Fulton et al. 2017) suggests that close-in low-mass Kepler planets have a predominately Earth-like rocky composition. Combined with the excess of period ratios outside of MMR, this suggests that low-mass Kepler planets formed inside of the water iceline, but still undergoing orbital migration. The core radius becomes visible for planets losing all primordial H/He. For planets in this "triangle of evaporation" in the distance-radius plane, the degeneracy in compositions is reduced. In the observed diagram, we identify a trend to more volatile-rich compositions with increasing radius (R/R_Earth3: H/He). The mass-density diagram contains important information about formation and evolution. Its characteristic broken V-shape reveals the transitions from solid planets to low-mass core-dominated planets with H/He and finally to gas-dominated giants. Evaporation causes density and orbital distance to be anti-correlated for low-mass planets, in contrast to giants, where closer-in planets are less dense, likely due to inflation. The temporal evolution of the statistical properties reported here will be of interest for the PLATO 2.0 mission which will observe the temporal dimension.Comment: 24 pages, 12 figures. Accepted in ApJ. Minor changes relative to v

Deuterium burning in objects forming via the core accretion scenario - Brown dwarfs or planets?

Aims. Our aim is to study deuterium burning in objects forming according to the core accretion scenario in the hot and cold start assumption and what minimum deuterium burning mass limit is found for these objects. We also study how the burning process influences the structure and luminosity of the objects. Furthermore we want to test and verify our results by comparing them to already existing hot start simulations which did not consider, however, the formation process. Methods. We present a new method to calculate deuterium burning of objects in a self-consistently coupled model of planet formation and evolution. We discuss which theory is used to describe the process of deuterium burning and how it was implemented. Results. We find that the objects forming according to a hot start scenario behave approximately in the same way as found in previous works of evolutionary calculations, which did not consider the formation. However, for cold start objects one finds that the objects expand during deuterium burning instead of being partially stabilized against contraction. In both cases, hot and cold start, the mass of the solid core has an influence on the minimum mass limit of deuterium burning. The general position of the mass limit, 13 MJ, stays however approximately the same. None of the investigated parameters was able to change this mass limit by more than 0.8 MJ. Due to deuterium burning, the luminosity of hot and cold start objects becomes comparable after ~ 200 Myrs.Comment: Accepted to A&A. Identical as v1 except for corrected typos. 22 pages, 15 figure

Evolution and Magnitudes of Candidate Planet Nine

The recently renewed interest in a possible additional major body in the outer solar system prompted us to study the thermodynamic evolution of such an object. We assumed that it is a smaller version of Uranus and Neptune. We modeled the temporal evolution of the radius, temperature, intrinsic luminosity, and the blackbody spectrum of distant ice giant planets. The aim is also to provide estimates of the magnitudes in different bands to assess whether the object might be detectable. Simulations of the cooling and contraction were conducted for ice giants with masses of 5, 10, 20, and 50 Mearth that are located at 280, 700, and 1120 AU from the Sun. The core composition, the fraction of H/He, the efficiency of energy transport, and the initial luminosity were varied. The atmospheric opacity was set to 1, 50, and 100 times solar metallicity. We find for a nominal 10 Mearth planet at 700 AU at the current age of the solar system an effective temperature of 47 K, much higher than the equilibrium temperature of about 10 K, a radius of 3.7 Rearth, and an intrinsic luminosity of 0.006 Ljupiter. It has estimated apparent magnitudes of Johnson V, R, I, L, N, Q of 21.7, 21.4, 21.0, 20.1, 19.9, and 10.7, and WISE W1-W4 magnitudes of 20.1, 20.1, 18.6, and 10.2. The Q and W4 band and other observations longward of about 13 microns pick up the intrinsic flux. If candidate Planet 9 has a significant H/He layer and an efficient energy transport in the interior, then its luminosity is dominated by the intrinsic contribution, making it a self-luminous planet. At a likely position on its orbit near aphelion, we estimate for a mass of 5, 10, 20, and 50 Mearth a V magnitude from the reflected light of 24.3, 23.7, 23.3, and 22.6 and a Q magnitude from the intrinsic radiation of 14.6, 11.7, 9.2, and 5.8. The latter would probably have been detected by past surveys.Comment: 6 pages, 3 figures, accepted to A&

Planetary evolution with atmospheric photoevaporation I. Analytical derivation and numerical study of the evaporation valley and transition from super-Earths to sub-Neptunes

Observations have revealed in the Kepler data a depleted region separating smaller super-Earths from larger sub-Neptunes. This can be explained as an evaporation valley between planets with and without H/He that is caused by atmospheric escape. First, we conduct numerical simulations of the evolution of close-in low-mass planets with H/He undergoing escape. Second, we develop an analytical model for the valley locus. We find that the bottom of the valley quantified by the radius of the largest stripped core $R_{\rm b}$ at a given orbital distance depends only weakly on post-formation H/He mass. The reason is that a high initial H/He mass means that there is more gas to evaporate, but also that the planet density is lower, increasing loss. Regarding stellar $L_{\rm XUV}$, $R_{\rm b}$ scales as $L_{\rm XUV}^{0.135}$. The same weak dependency applies to the efficiency factor $\varepsilon$ of energy-limited evaporation. As found numerically and analytically, $R_{\rm b}$ varies as function of orbital period $P$ for a constant $\varepsilon$ as $P^{-2 p_{\rm c}/3}\approx P^{-0.18}$ where $M \propto R^{p_{\rm c}}$ is the mass-radius relation of solid cores. $R_{\rm b}$ is about 1.7 $R_{\oplus}$ at a 10-day orbit for an Earth-like composition, increasing linearly with ice mass fraction. The numerical results are explained very well with the analytical model where complete evaporation occurs if the temporal integral over the stellar XUV irradiation absorbed by the planet is larger than binding energy of the envelope in the gravitational potential of the core. The weak dependency on primordial H/He mass, $L_{\rm XUV}$ and $\varepsilon$ explains why observationally the valley is visible, and why theoretically models find similar results. At the same time, given the large observed spread of $L_{\rm XUV}$, the dependency on it is still strong enough to explain why the valley is not completely empty.Comment: 32 pages, 16 figures. Accepted to A&

Two Empirical Regimes of the Planetary Mass-Radius Relation

Today, with the large number of detected exoplanets and improved measurements, we can reach the next step of planetary characterization. Classifying different populations of planets is not only important for our understanding of the demographics of various planetary types in the galaxy, but also for our understanding of planet formation. We explore the nature of two regimes in the planetary mass-radius (M-R) relation. We suggest that the transition between the two regimes of "small" and "large" planets, occurs at a mass of 124 \pm 7, M_Earth and a radius of 12.1 \pm 0.5, R_Earth. Furthermore, the M-R relation is R \propto M^{0.55\pm 0.02} and R \propto M^{0.01\pm0.02} for small and large planets, respectively. We suggest that the location of the breakpoint is linked to the onset of electron degeneracy in hydrogen, and therefore, to the planetary bulk composition. Specifically, it is the characteristic minimal mass of a planet which consists of mostly hydrogen and helium, and therefore its M-R relation is determined by the equation of state of these materials. We compare the M-R relation from observational data with the one derived by population synthesis calculations and show that there is a good qualitative agreement between the two samples.Comment: accepted for publication in A&

Giant Planet Formation by Core Accretion

We present a review of the standard paradigm for giant planet formation, the core accretion theory. After an overview of the basic concepts of this model, results of the original implementation are discussed. Then, recent improvements and extensions, like the inclusion of planetary migration and the resulting effects are discussed. It is shown that these improvement solve the timescale problem. Finally, it is shown that by means of generating synthetic populations of (extrasolar) planets, core accretion models are able to reproduce in a statistically significant way the actually observed planetary population.Comment: 8 pages, 3 figures, invited review, to appear in "Extreme Solar Systems" ASP Conference Series, eds. Debra Fischer, Fred Rasio, Steve Thorsett and Alex Wolszcza

Formation, Orbital and Internal Evolutions of Young Planetary Systems

The growing body of observational data on extrasolar planets and protoplanetary disks has stimulated intense research on planet formation and evolution in the past few years. The extremely diverse, sometimes unexpected physical and orbital characteristics of exoplanets lead to frequent updates on the mainstream scenarios for planet formation and evolution, but also to the exploration of alternative avenues. The aim of this review is to bring together classical pictures and new ideas on the formation, orbital and internal evolutions of planets, highlighting the key role of the protoplanetary disk in the various parts of the theory. We begin by briefly reviewing the conventional mechanism of core accretion by the growth of planetesimals, and discuss a relatively recent model of core growth through the accretion of pebbles. We review the basic physics of planet-disk interactions, recent progress in this area, and discuss their role in observed planetary systems. We address the most important effects of planets internal evolution, like cooling and contraction, the mass-luminosity relation, and the bulk composition expressed in the mass-radius and mass-mean density relations.Comment: 49 pages, 12 figures, accepted for publication in Space Science Reviews. Chapter in International Space Science Institute (ISSI) Book on "The Disk in Relation to the Formation of Planets and their Proto-atmospheres" to be published in Space Science Reviews by Springe

Exploring the formation by core accretion and the luminosity evolution of directly imaged planets: The case of HIP 65426 b

A low-mass companion to the two-solar mass star HIP65426 has recently been detected by SPHERE at around 100 au from its host. Explaining the presence of super-Jovian planets at large separations, as revealed by direct imaging, is currently an open question. We want to derive statistical constraints on the mass and initial entropy of HIP65426b and to explore possible formation pathways of directly imaged objects within the core-accretion paradigm, focusing on HIP65426b. Constraints on the planet's mass and post-formation entropy are derived from its age and luminosity combined with cooling models. For the first time, the results of population synthesis are also used to inform the results. Then, a formation model that includes N-body dynamics with several embryos per disc is used to study possible formation histories and the properties of possible additional companions. Finally, the outcomes of two- and three-planet scattering in the post-disc phase are analysed, taking tides into account. The mass of HIP65426b is found to be Mp = 9.9 +1.1 -1.8 MJ using the hot population and Mp = 10.9 +1.4 -2.0 MJ with the cold-nominal population. Core formation at small separations from the star followed by outward scattering and runaway accretion at a few hundred AU succeeds in reproducing the mass and separation of HIP65426b. Alternatively, systems having two or more giant planets close enough to be on an unstable orbit at disc dispersal are likely to end up with one planet on a wide HIP65426b-like orbit with a relatively high eccentricity (>~ 0.5). If this scattering scenario explains its formation, HIP65426b is predicted to have a high eccentricity and to be accompanied by one or several roughly Jovian-mass planets at smaller semi-major axes, which also could have a high eccentricity. This could be tested by further direct-imaging as well as radial-velocity observations.Comment: 17 pages, 11 figures. A&A in press. Bern EXoplanet cooling curves (BEX) available upon request. v2: Language and other minor changes; Fig. 4 now has labels summarising a possible formation pathway discussed in the tex

Model atmospheres of irradiated exoplanets: The influence of stellar parameters, metallicity, and the C/O ratio

Many parameters constraining the spectral appearance of exoplanets are still poorly understood. We therefore study the properties of irradiated exoplanet atmospheres over a wide parameter range including metallicity, C/O ratio and host spectral type. We calculate a grid of 1-d radiative-convective atmospheres and emission spectra. We perform the calculations with our new Pressure-Temperature Iterator and Spectral Emission Calculator for Planetary Atmospheres (PETIT) code, assuming chemical equilibrium. The atmospheric structures and spectra are made available online. We find that atmospheres of planets with C/O ratios $\sim$ 1 and $T_{\rm eff}$ $\gtrsim$ 1500 K can exhibit inversions due to heating by the alkalis because the main coolants CH$_4$, H$_2$O and HCN are depleted. Therefore, temperature inversions possibly occur without the presence of additional absorbers like TiO and VO. At low temperatures we find that the pressure level of the photosphere strongly influences whether the atmospheric opacity is dominated by either water (for low C/O) or methane (for high C/O), or both (regardless of the C/O). For hot, carbon-rich objects this pressure level governs whether the atmosphere is dominated by methane or HCN. Further we find that host stars of late spectral type lead to planetary atmospheres which have shallower, more isothermal temperature profiles. In agreement with prior work we find that for planets with $T_{\rm eff}$ $<$ 1750 K the transition between water or methane dominated spectra occurs at C/O $\sim$ 0.7, instead of $\sim$ 1, because condensation preferentially removes oxygen.Comment: 30 pages, 20 figures. Accepted for publication in Ap