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

Radiative Transfer for Exoplanet Atmospheres

Remote sensing of the atmospheres of distant worlds motivates a firm understanding of radiative transfer. In this review, we provide a pedagogical cookbook that describes the principal ingredients needed to perform a radiative transfer calculation and predict the spectrum of an exoplanet atmosphere, including solving the radiative transfer equation, calculating opacities (and chemistry), iterating for radiative equilibrium (or not), and adapting the output of the calculations to the astronomical observations. A review of the state of the art is performed, focusing on selected milestone papers. Outstanding issues, including the need to understand aerosols or clouds and elucidating the assumptions and caveats behind inversion methods, are discussed. A checklist is provided to assist referees/reviewers in their scrutiny of works involving radiative transfer. A table summarizing the methodology employed by past studies is provided.Comment: 7 pages, no figures, 1 table. Filled in missing information in references, main text unchange

Evidence of Three Mechanisms Explaining the Radius Anomaly of Hot Jupiters

The radii of hot Jupiters are still not fully understood and all of the proposed explanations are based on the idea that these close-in giant planets possess hot interiors. We approach the radius anomaly problem by adopting a statistical approach. We infer the internal luminosity for the sample of hot Jupiters, study its effect on the interior structure, and put constraints on which mechanism is the dominant one. We develop a flexible and robust hierarchical Bayesian model that couples the interior structure of exoplanets to their observed properties. We apply the model to 314 hot Jupiters and infer the internal luminosity distribution for each planet and study at the population level ({\it i}) the mass-luminosity-radius distribution and as a function of equilibrium temperature the distributions of the ({\it ii}) heating efficiency, ({\it iii}) internal temperature, and the ({\it iv}) pressure of the radiative-convective-boundary (RCB). We find that hot Jupiters tend to have high internal luminosity leading to hot interiors. This has important consequences on the cooling rate and we find that the RCB is located at low pressures. Assuming that the ultimate source of the extra heating is the irradiation from the host star, we illustrate that the heating efficiency follows a Gaussian distribution, in agreement with previous results. We discuss our findings in the context of the proposed heating mechanisms and illustrate that ohmic dissipation, advection of potential temperature, and thermal tides are in agreement with certain trends inferred from our analysis and thus all three models can explain aspects of the observations. We provide new insights on the interior structure of hot Jupiters and show that with our current knowledge it is still challenging to firmly identify the universal mechanism driving the inflated radii.Comment: 27 pages and 12 figures. Accepted in A&A. Source code can be found at https://github.com/psarkis/bloatedHJs and data at https://www.space.unibe.ch/research/research_groups/planets_in_time/numerical_data/index_eng.htm

First direct detection of an exoplanet by optical interferometry; Astrometry and K-band spectroscopy of HR8799 e

To date, infrared interferometry at best achieved contrast ratios of a few times $10^{-4}$ on bright targets. GRAVITY, with its dual-field mode, is now capable of high contrast observations, enabling the direct observation of exoplanets. We demonstrate the technique on HR8799, a young planetary system composed of four known giant exoplanets. We used the GRAVITY fringe tracker to lock the fringes on the central star, and integrated off-axis on the HR8799e planet situated at 390 mas from the star. Data reduction included post-processing to remove the flux leaking from the central star and to extract the coherent flux of the planet. The inferred K band spectrum of the planet has a spectral resolution of 500. We also derive the astrometric position of the planet relative to the star with a precision on the order of 100$\,\mu$as. The GRAVITY astrometric measurement disfavors perfectly coplanar stable orbital solutions. A small adjustment of a few degrees to the orbital inclination of HR 8799 e can resolve the tension, implying that the orbits are close to, but not strictly coplanar. The spectrum, with a signal-to-noise ratio of $\approx 5$ per spectral channel, is compatible with a late-type L brown dwarf. Using Exo-REM synthetic spectra, we derive a temperature of $1150\pm50$\,K and a surface gravity of $10^{4.3\pm0.3}\,$cm/s$^{2}$. This corresponds to a radius of $1.17^{+0.13}_{-0.11}\,R_{\rm Jup}$ and a mass of $10^{+7}_{-4}\,M_{\rm Jup}$, which is an independent confirmation of mass estimates from evolutionary models. Our results demonstrate the power of interferometry for the direct detection and spectroscopic study of exoplanets at close angular separations from their stars.Comment: published in A&

Planetary population synthesis

In stellar astrophysics, the technique of population synthesis has been successfully used for several decades. For planets, it is in contrast still a young method which only became important in recent years because of the rapid increase of the number of known extrasolar planets, and the associated growth of statistical observational constraints. With planetary population synthesis, the theory of planet formation and evolution can be put to the test against these constraints. In this review of planetary population synthesis, we first briefly list key observational constraints. Then, the work flow in the method and its two main components are presented, namely global end-to-end models that predict planetary system properties directly from protoplanetary disk properties and probability distributions for these initial conditions. An overview of various population synthesis models in the literature is given. The sub-models for the physical processes considered in global models are described: the evolution of the protoplanetary disk, the planets' accretion of solids and gas, orbital migration, and N-body interactions among concurrently growing protoplanets. Next, typical population synthesis results are illustrated in the form of new syntheses obtained with the latest generation of the Bern model. Planetary formation tracks, the distribution of planets in the mass-distance and radius-distance plane, the planetary mass function, and the distributions of planetary radii, semimajor axes, and luminosities are shown, linked to underlying physical processes, and compared with their observational counterparts. We finish by highlighting the most important predictions made by population synthesis models and discuss the lessons learned from these predictions - both those later observationally confirmed and those rejected.Comment: 47 pages, 12 figures. Invited review accepted for publication in the 'Handbook of Exoplanets', planet formation section, section editor: Ralph Pudritz, Springer reference works, Juan Antonio Belmonte and Hans Deeg, Ed

ELT-METIS: estimating the constraining power of high-resolution exoplanet spectra with Bayesian inference

Stars and planetary system

GRAVITY K-band spectroscopy of HD 206893 B

Context. Near-infrared interferometry has become a powerful tool for studying the orbital and atmospheric parameters of substellar companions. Aims. We aim to reveal the nature of the reddest known substellar companion HD 206893 B by studying its near-infrared colors and spectral morphology and by investigating its orbital motion. Methods. We fit atmospheric models for giant planets and brown dwarfs and perform spectral retrievals with petitRADTRANS and ATMO on the observed GRAVITY, SPHERE, and GPI spectra of HD 206893 B. To recover its unusual spectral features, first and foremost its extremely red near-infrared color, we include additional extinction by high-altitude dust clouds made of enstatite grains in the atmospheric model fits. However, forsterite, corundum, and iron grains predict similar extinction curves for the grain sizes considered here.We also infer the orbital parameters of HD 206893 B by combining the  100 μas precision astrometry from GRAVITY with data from the literature and constrain the mass and position of HD 206893 C based on the Gaia proper motion anomaly of the system. Results. The extremely red color and the very shallow 1:4 μm water absorption feature of HD 206893 B can be fit well with the adapted atmospheric models and spectral retrievals. By comparison with AMES-Cond evolutionary tracks, we find that only some atmospheric models predict physically plausible objects. Altogether, our analysis suggests an age of  3–300 Myr and a mass of  5–30 MJup for HD 206893 B, which is consistent with previous estimates but extends the parameter space to younger and lower-mass objects. The GRAVITY astrometry points to an eccentric orbit (e = 0:29+0:06 0:11) with a mutual inclination of \u3c34:4 deg with respect to the debris disk of the system. Conclusions. While HD 206893 B could in principle be a planetary-mass companion, this possibility hinges on the unknown influence of the inner companion on the mass estimate of 10+5 4 MJup from radial velocity and Gaia as well as a relatively small but significant Argus moving group membership probability of  61%. However, we find that if the mass of HD 206893 B is \u3c30 MJup, then the inner companion HD 206893 C should have a mass between  8–15 MJup. Finally, further spectroscopic or photometric observations at higher signal-to-noise and longer wavelengths are required to learn more about the composition and dust cloud properties of HD 206893 B

Observing Exoplanets with the James Webb Space Telescope

The census of exoplanets has revealed an enormous variety of planets or- biting stars of all ages and spectral types: planets in orbits of less than a day to frigid worlds in orbits over 100 AU; planets with masses 10 times that of Jupiter to planets with masses less than that of Earth; searingly hot planets to temperate planets in the Habitable Zone. The challenge of the coming decade is to move from demography to physical characterization. The James Webb Space Telescope (JWST) is poised to open a revolutionary new phase in our understanding of exoplanets with transit spectroscopy of relatively short period planets and coronagraphic imaging of ones with wide separations from their host stars. This article discusses the wide variety of exoplanet opportunities enabled by JWSTs sensitivity and stability, its high angular resolution, and its suite of powerful instruments. These capabilities will advance our understanding of planet formation, brown dwarfs, and the atmospheres of young to mature planets

LBT transmission spectroscopy of HAT-P-12b: confirmation of a cloudy atmosphere with no significant alkali features

The hot sub-Saturn-mass exoplanet HAT-P-12b is an ideal target for transmission spectroscopy because of its inflated radius. We observed one transit of the planet with the multi-object double spectrograph (MODS) on the Large Binocular Telescope (LBT) with the binocular mode and obtained an atmosphere transmission spectrum with a wavelength coverage of $\sim$ 0.4 -- 0.9 $\mathrm{\mu}$m. The spectrum is relatively flat and does not show any significant sodium or potassium absorption features. Our result is consistent with the revised Hubble Space Telescope (HST) transmission spectrum of a previous work, except that the HST result indicates a tentative detection of potassium. The potassium discrepancy could be the result of statistical fluctuation of the HST dataset. We fit the planetary transmission spectrum with an extensive grid of cloudy models and confirm the presence of high-altitude clouds in the planetary atmosphere. The fit was performed on the combined LBT and HST spectrum, which has an overall wavelength range of 0.4 -- 1.6 $\mathrm{\mu}$m. The LBT/MODS spectrograph has unique advantages in transmission spectroscopy observations because it can cover a wide wavelength range with a single exposure and acquire two sets of independent spectra simultaneously.Comment: 14 pages, 12 figures. Accepted for publication in Astronomy & Astrophysic