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

Global Models of Planet Formation and Evolution

Despite the increase in observational data on exoplanets, the processes that lead to the formation of planets are still not well understood. But thanks to the high number of known exoplanets, it is now possible to look at them as a population that puts statistical constraints on theoretical models. A method that uses these constraints is planetary population synthesis. Its key element is a global model of planet formation and evolution that directly predicts observable planetary properties based on properties of the natal protoplanetary disk. To do so, global models build on many specialized models that address one specific physical process. We thoroughly review the physics of the sub-models included in global formation models. The sub-models can be classified as models describing the protoplanetary disk (gas and solids), the (proto)planet (solid core, gaseous envelope, and atmosphere), and finally the interactions (migration and N-body interaction). We compare the approaches in different global models and identify physical processes that require improved descriptions in future. We then address important results of population synthesis like the planetary mass function or the mass-radius relation. In these results, the global effects of physical mechanisms occurring during planet formation and evolution become apparent, and specialized models describing them can be put to the observational test. Due to their nature as meta models, global models depend on the development of the field of planet formation theory as a whole. Because there are important uncertainties in this theory, it is likely that global models will in future undergo significant modifications. Despite this, they can already now yield many testable predictions. With future global models addressing the geophysical characteristics, it should eventually become possible to make predictions about the habitability of planets.Comment: 30 pages, 16 figures. Accepted for publication in the International Journal of Astrobiology (Cambridge University Press

petitRADTRANS: a Python radiative transfer package for exoplanet characterization and retrieval

We present the easy-to-use, publicly available, Python package petitRADTRANS, built for the spectral characterization of exoplanet atmospheres. The code is fast, accurate, and versatile; it can calculate both transmission and emission spectra within a few seconds at low resolution ($\lambda/\Delta\lambda$ = 1000; correlated-k method) and high resolution ($\lambda/\Delta\lambda = 10^6$; line-by-line method), using only a few lines of input instruction. The somewhat slower correlated-k method is used at low resolution because it is more accurate than methods such as opacity sampling. Clouds can be included and treated using wavelength-dependent power law opacities, or by using optical constants of real condensates, specifying either the cloud particle size, or the atmospheric mixing and particle settling strength. Opacities of amorphous or crystalline, spherical or irregularly-shaped cloud particles are available. The line opacity database spans temperatures between 80 and 3000 K, allowing to model fluxes of objects such as terrestrial planets, super-Earths, Neptunes, or hot Jupiters, if their atmospheres are hydrogen-dominated. Higher temperature points and species will be added in the future, allowing to also model the class of ultra hot-Jupiters, with equilibrium temperatures $T_{\rm eq} \gtrsim 2000$ K. Radiative transfer results were tested by cross-verifying the low- and high-resolution implementation of petitRADTRANS, and benchmarked with the petitCODE, which itself is also benchmarked to the ATMO and Exo-REM codes. We successfully carried out test retrievals of synthetic JWST emission and transmission spectra (for the hot Jupiter TrES-4b, which has a $T_{\rm eq}$ of $\sim$ 1800 K). The code is publicly available at http://gitlab.com/mauricemolli/petitRADTRANS, and its documentation can be found at https://petitradtrans.readthedocs.io.Comment: 17 pages, 7 figures, published in A&

Detecting isotopologues in exoplanet atmospheres using ground-based high-dispersion spectroscopy

Cross-correlation is a well-tested method for exoplanet characterization. A new, potentially powerful application is the measurement of atmospheric isotope ratios. In particular D/H can give unique insights into a planet's formation and evolution. Here we aim to study the detectability of isotopologues in the high-dispersion spectra of exoplanets, to identify the optimal wavelengths ranges, and to predict the required observational efforts with current and future ground-based instruments. High-dispersion (R=10$^5$) thermal emission (and sometimes reflection) spectra were simulated by self-consistently modeling exoplanet atmospheres over a wide range of temperatures. These were synthetically observed with telescopes equivalent to the VLT or ELT, and analyzed with cross-correlation, resulting in S/N predictions for the detection of $^{13}$CO, HDO, and CH$_3$D. For the best observable exoplanets, $^{13}$CO is in range of current telescopes. It will be most favorably detected at 2.4 microns, just longward of the spectral range probed by several high-dispersion observations in the literature. CH$_3$D can best be seen at 4.7 microns, using 40m-class telescopes for planets with $T_{\rm equ}$ below 600 K. In this case, sky emission is often dominating the noise. HDO can be targeted at 3.7 microns, where sky emission is smaller. 40m-class telescopes may detect it in planets with $T_{\rm equ}$ below 900~K, potentially even 8m-class telescopes in the case of methane quenching. If Proxima Cen b is water-rich, HDO could be detected with the ELT in 1 night in reflected light. Isotopologues will soon belong to the exoplanet characterisation tools. Measuring D/H, and ratios of other isotopes, could be a prime science case for the METIS instrument on the ELT, especially for nearby rocky and ice giant planets. This can give unique insights in their history of ice enrichment and atmospheric evaporation.Comment: 22 pages, 12 figures, updated version, accepted for publication in A &

Evolutionary models of cold and low-mass planets: Cooling curves, magnitudes, and detectability

Future instruments like NIRCam and MIRI on JWST or METIS at the ELT will be able to image exoplanets that are too faint for current direct imaging instruments. Evolutionary models predicting the planetary intrinsic luminosity as a function of time have traditionally concentrated on gas-dominated giant planets. We extend these cooling curves to Saturnian and Neptunian planets. We simulate the cooling of isolated core-dominated and gas giant planets with masses of 5 Earthmasses to 2 Jupitermasses. The luminosity includes the contribution from the cooling and contraction of the core and of the H/He envelope, as well as radiogenic decay. For the atmosphere we use grey, AMES-Cond, petitCODE, and HELIOS models. We consider solar and non-solar metallicities as well as cloud-free and cloudy atmospheres. The most important initial conditions, namely the core-to-envelope ratio and the initial luminosity are taken from planet formation simulations based on the core accretion paradigm. We first compare our cooling curves for Uranus, Neptune, Jupiter, Saturn, GJ 436b, and a 5 Earthmass-planet with a 1% H/He envelope with other evolutionary models. We then present the temporal evolution of planets with masses between 5 Earthmasses and 2 Jupitermasses in terms of their luminosity, effective temperature, radius, and entropy. We discuss the impact of different post formation entropies. For the different atmosphere types and initial conditions magnitudes in various filter bands between 0.9 and 30 micrometer wavelength are provided. Using black body fluxes and non-grey spectra, we estimate the detectability of such planets with JWST. It is found that a 20 (100) Earthmass-planet can be detected with JWST in the background limit up to an age of about 10 (100) Myr with NIRCam and MIRI, respectively.Comment: Language corrected version and improved arrangements of figures, online data at: http://www.space.unibe.ch/research/research_groups/planets_in_time/numerical_data/index_eng.htm

The 12CO/13CO isotopologue ratio of a young, isolated brown dwarf: possibly distinct formation pathways of super-Jupiters and brown dwarfs

Stars and planetary system

Search for gas from the disintegrating rocky exoplanet K2-22b

[Abridged] Aims. We searched for circumplanetary sodium and ionized calcium gas around the disintegrating rocky exoplanet K2-22 b to constrain its gas-loss and sublimation processes. Methods. We observed four transits of K2-22 b with X-shooter on ESO's Very Large Telescope to obtain time-series of intermediate-resolution (R $\sim$ 11400) spectra. Our analysis focused on the two sodium D lines (588.995 nm and 589.592 nm) and the Ca$^{+}$ triplet (849.802 nm, 854.209 nm and 866.214 nm). Planet-related absorption is searched for in the velocity rest frame of the planet, which changes from $\pm$66 kms$^{-1}$ during the transit. Results. Since K2-22 b exhibits highly variable transit depths, we analyzed the individual nights and their average. By injecting signals we reached 5$\sigma$ upper-limits on the individual nights that ranged from 11% - 13% and 1.7% - 2.0% for the tail's sodium and ionized calcium absorption, respectively. Night 1 was contaminated by its companion star so we considered weighted averages with and without Night 1 and quote conservative 5$\sigma$ limits without Night 1 of 9% and 1.4%, respectively. Assuming their mass fractions to be similar to those in the Earth's crust, these limits correspond to scenarios in which 0.04% and 35% of the transiting dust is sublimated and observed as absorbing gas. However, this assumes the gas to be co-moving with the planet. We show that for the high irradiation environment of K2-22 b, sodium and ionized calcium could be quickly accelerated to 100s of km s$^{-1}$ due to radiation pressure and entrainment by the stellar wind, making them much more difficult to detect. No evidence for such possibly broad and blue-shifted signals are seen in our data. Conclusions. Future observations aimed at observing circumplanetary gas should take into account the possible broad and blue-shifted velocity field of atomic and ionized species.Comment: Accepted on 7 June 2019 for publication in Astronomy and Astrophysics (A&A). 17 pages, 11 figures. Submission updated after language editing by A&

Atmospheric retrievals for LIFE and other future space missions: the importance of mitigating systematic effects

Atmospheric retrieval studies are essential to determine the science requirements for future generation missions, such as the Large Interferometer for Exoplanets (LIFE). The use of heterogeneous absorption cross-sections might be the cause of systematic effects in retrievals, which could bias a correct characterization of the atmosphere. In this contribution we quantified the impact of differences in line list provenance, broadening coefficients, and line wing cut-offs in the retrieval of an Earth twin exoplanet orbiting a Sun-like star at 10 pc from the observer, as it would be observed with LIFE. We ran four different retrievals on the same input spectrum, by varying the opacity tables that the Bayesian retrieval framework was allowed to use. We found that the systematics introduced by the opacity tables could bias the correct estimation of the atmospheric pressure at the surface level, as well as an accurate retrieval of the abundance of some species in the atmosphere (such as CO$_2$ and N$_2$O). We argue that differences in the line wing cut-off might be the major source of errors. We highlight the need for more laboratory and modeling efforts, as well as inter-model comparisons of the main radiative transfer models and Bayesian retrieval frameworks. This is especially relevant in the context of LIFE and future generation missions, to identify issues and critical points for the community to jointly work together to prepare for the analysis of the upcoming observations.Comment: 24 pages, 12 figures. Proceedings SPIE Volume 12180, Space Telescopes and Instrumentation 2022: Optical, Infrared, and Millimeter Wave; 121803L (2022

MIRACLES: atmospheric characterization of directly imaged planets and substellar companions at 4-5 μ\mum. II. Constraints on the mass and radius of the enshrouded planet PDS 70 b

The circumstellar disk of PDS 70 hosts two forming planets, which are actively accreting gas from their environment. In this work, we report the first detection of PDS 70 b in the Br$\alpha$ and $M'$ filters with VLT/NACO, a tentative detection of PDS 70 c in Br$\alpha$, and a reanalysis of archival NACO $L'$ and SPHERE $H23$ and $K12$ imaging data. The near side of the disk is also resolved with the Br$\alpha$ and $M'$ filters, indicating that scattered light is non-negligible at these wavelengths. The spectral energy distribution of PDS 70 b is well described by blackbody emission, for which we constrain the photospheric temperature and photospheric radius to $T_\mathrm{eff}=1193 \pm 20$ K and $R=3.0 \pm 0.2$ $R_\mathrm{J}$. The relatively low bolometric luminosity, $\log(L/L_\odot) = -3.79 \pm 0.02$, in combination with the large radius, is not compatible with standard structure models of fully convective objects. With predictions from such models, and adopting a recent estimate of the accretion rate, we derive a planetary mass and radius in the range of $M_\mathrm{p}\approx 0.5-1.5$ $M_\mathrm{J}$ and $R_\mathrm{p}\approx 1-2.5$ $R_\mathrm{J}$, independently of the age and post-formation entropy of the planet. The blackbody emission, large photospheric radius, and the discrepancy between the photospheric and planetary radius suggests that infrared observations probe an extended, dusty environment around the planet, which obscures the view on its molecular composition. Finally, we derive a rough upper limit on the temperature and radius of potential excess emission from a circumplanetary disk, $T_\mathrm{eff}\lesssim256$ K and $R\lesssim245$ $R_\mathrm{J}$, but we do find weak evidence that the current data favors a model with a single blackbody component.Comment: 19 pages, 7 figures, accepted for publication in A&

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

Stars and planetary system