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

Thermodynamics of Giant Planet Formation: Shocking Hot Surfaces on Circumplanetary Disks

The luminosity of young giant planets can inform about their formation and accretion history. The directly imaged planets detected so far are consistent with the "hot-start" scenario of high entropy and luminosity. If nebular gas passes through a shock front before being accreted into a protoplanet, the entropy can be substantially altered. To investigate this, we present high resolution, 3D radiative hydrodynamic simulations of accreting giant planets. The accreted gas is found to fall with supersonic speed in the gap from the circumstellar disk's upper layers onto the surface of the circumplanetary disk and polar region of the protoplanet. There it shocks, creating an extended hot supercritical shock surface. This shock front is optically thick, therefore, it can conceal the planet's intrinsic luminosity beneath. The gas in the vertical influx has high entropy which when passing through the shock front decreases significantly while the gas becomes part of the disk and protoplanet. This shows that circumplanetary disks play a key role in regulating a planet's thermodynamic state. Our simulations furthermore indicate that around the shock surface extended regions of atomic - sometimes ionized - hydrogen develop. Therefore circumplanetary disk shock surfaces could influence significantly the observational appearance of forming gas-giants.Comment: 5 pages, 3 figures, 1 table, accepted for publication at MNRAS Letter

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

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

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&

Migration and giant planet formation

We extend the core-accretion model of giant gaseous planets by Pollack et al. (\cite{P96}) to include migration, disc evolution and gap formation. Starting with a core of a fraction of an Earth's mass located at 8 AU, we end our simulation with the onset of runaway gas accretion when the planet is at 5.5 AU 1 Myr later. This timescale is about a factor ten shorter than the one found by Pollack et al. (\cite{P96}) even though the disc was less massive initially and viscously evolving. Other initial conditions can lead to even shorter timescales. The reason for this speed-up is found to result from the fact that a moving planet does not deplete its feeding zone to the extend of a static planet. Thus, the uncomfortably long formation timescale associated with the core-accretion scenario can be considerably reduced and brought in much better agreement with the typical disc lifetimes inferred from observations of young circumstellar discs.Comment: 9 pages, 2 figures, published in A&A Letter

Characterization of exoplanets from their formation III: The statistics of planetary luminosities

This paper continues a series in which we predict the main observable characteristics of exoplanets based on their formation. In Paper I we described our global planet formation and evolution model. In Paper II we studied the planetary mass-radius relationship. Here we present an extensive study of the statistics of planetary luminosities during both formation and evolution. Our results can be compared with individual directly imaged (proto)planets as well as statistical results from surveys. We calculated three synthetic planet populations assuming different efficiencies of the accretional heating by gas and planetesimals. We describe the temporal evolution of the planetary mass-luminosity relation. We study the shock and internal luminosity during formation. We predict a statistical version of the post-formation mass versus entropy "tuning fork" diagram. We find high nominal post-formation luminosities for hot and cold gas accretion. Individual formation histories can still lead to a factor of a few spread in the post-formation luminosity at a given mass. However, if the gas and planetesimal accretional heating is unknown, the post-formation luminosity may exhibit a spread of as much as 2-3 orders of magnitude at a fixed mass covering cold, warm, and hot states. As a key result we predict a flat log-luminosity distribution for giant planets, and a steep increase towards lower luminosities due to the higher occurrence rate of low-mass planets. Future surveys may detect this upturn. During formation an estimate of the planet mass may be possible for cold gas accretion if the gas accretion rate can be estimated. Due to the "core-mass effect" planets that underwent cold gas accretion can still have high post-formation entropies. Once the number of directly imaged exoplanets with known ages and luminosities increases, the observed distributions may be compared with our predictions.Comment: 44 pages, 26 figures (journal format). A&A in print. Language correction only relative to V

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

Theory of planet formation and comparison with observation: Formation of the planetary mass-radius relationship

The planetary mass-radius diagram is an observational result of central importance to understand planet formation. We present an updated version of our planet formation model based on the core accretion paradigm which allows to calculate planetary radii and luminosities during the entire formation and evolution of the planets. We first study with it the formation of Jupiter, and compare with previous works. Then we conduct planetary population synthesis calculations to obtain a synthetic mass-radius diagram which we compare with the observed one. Except for bloated Hot Jupiters which can be explained only with additional mechanisms related to their proximity to the star, we find a good agreement of the general shape of the observed and the synthetic mass-radius diagram. This shape can be understood with basic concepts of the core accretion model.Comment: Proceedings Haute Provence Observatory Colloquium: Detection and Dynamics of Transiting Exoplanets (23-27 August 2010). Edited by F. Bouchy, R. F. Diaz & C. Moutou. Extended version: 17 pages, 8 figure