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

Properties and occurrence rates of KeplerKepler exoplanet candidates as a function of host star metallicity from the DR25 catalog

Correlations between the occurrence rate of exoplanets and their host star properties provide important clues about the planet formation processes. We studied the dependence of the observed properties of exoplanets (radius, mass, and orbital period) as a function of their host star metallicity. We analyzed the planetary radii and orbital periods of over 2800 $Kepler$ candidates from the latest $Kepler$ data release DR25 (Q1-Q17) with revised planetary radii based on $Gaia$~DR2 as a function of host star metallicity (from the Q1-Q17 (DR25) stellar and planet catalog). With a much larger sample and improved radius measurements, we are able to reconfirm previous results in the literature. We show that the average metallicity of the host star increases as the radius of the planet increases. We demonstrate this by first calculating the average host star metallicity for different radius bins and then supplementing these results by calculating the occurrence rate as a function of planetary radius and host star metallicity. We find a similar trend between host star metallicity and planet mass: the average host star metallicity increases with increasing planet mass. This trend, however, reverses for masses $> 4.0\, M_\mathrm{J}$: host star metallicity drops with increasing planetary mass. We further examined the correlation between the host star metallicity and the orbital period of the planet. We find that for planets with orbital periods less than 10 days, the average metallicity of the host star is higher than that for planets with periods greater than 10 days.Comment: 14 pages, 13 Figures, Accepted for publication in The Astronomical Journa

High signal-to-noise spectral characterization of the planetary-mass object HD 106906 b

We spectroscopically characterize the atmosphere of HD 106906b, a young low-mass companion near the deuterium burning limit. The wide separation from its host star of 7.1" makes it an ideal candidate for high S/N and high-resolution spectroscopy. We aim to derive new constraints on the spectral type, effective temperature, and luminosity of HD106906b and also to provide a high S/N template spectrum for future characterization of extrasolar planets. We obtained 1.1-2.5 $\mu$m integral field spectroscopy with the VLT/SINFONI instrument with a spectral resolution of R~2000-4000. New estimates of the parameters of HD 106906b are derived by analyzing spectral features, comparing the extracted spectra to spectral catalogs of other low-mass objects, and fitting with theoretical isochrones. We identify several spectral absorption lines that are consistent with a low mass for HD 106906b. We derive a new spectral type of L1.5$\pm$1.0, one subclass earlier than previous estimates. Through comparison with other young low-mass objects, this translates to a luminosity of log($L/L_\odot$)=$-3.65\pm0.08$ and an effective temperature of Teff=$1820\pm240$ K. Our new mass estimates range between $M=11.9^{+1.7}_{-0.8} M_{\rm Jup}$ (hot start) and $M=14.0^{+0.2}_{-0.5} M_{\rm Jup}$ (cold start). These limits take into account a possibly finite formation time, i.e., HD 106906b is allowed to be 0--3 Myr younger than its host star. We exclude accretion onto HD 106906b at rates $\dot{M}>4.8\times10^{-10} M_{\rm Jup}$yr$^{-1}$ based on the fact that we observe no hydrogen (Paschen-$\beta$, Brackett-$\gamma$) emission. This is indicative of little or no circumplanetary gas. With our new observations, HD 106906b is the planetary-mass object with one of the highest S/N spectra yet. We make the spectrum available for future comparison with data from existing and next-generation (e.g., ELT and JWST) spectrographs.Comment: 11 pages, 5 figures. Accepted for publication in Astronomy & Astrophysics. Fully reduced spectra will be made available for download on CD

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

Compliance of the L5-S1 spinal unit: a comparative study between an unconstrained and a partially constrained system

A comparison between an unconstrained and a partially constrained system for in vitro biomechanical testing of the L5-S1 spinal unit was conducted. The objective was to compare the compliance and the coupling of the L5-S1 unit measured with an unconstrained and a partially constrained test for the three major physiological motions of the human spine. Very few studies have compared unconstrained and partially constrained testing systems using the same cadaveric functional spinal units (FSUs). Seven human L5-S1 units were therefore tested on both a pneumatic, unconstrained, and a servohydraulic, partially constrained system. Each FSU was tested along three motions: flexion-extension (FE), lateral bending (LB) and axial rotation (AR). The obtained kinematics on both systems is not equivalent, except for the FE case, where both motions are similar. The directions of coupled motions were similar for both tests, but their magnitudes were smaller in the partially constrained configuration. The use of a partially constrained system to characterize LB and AR of the lumbosacral FSU decreased significantly the measured stiffness of the segment. The unconstrained system is today's "gold standard” for the characterization of FSUs. The selected partially constrained method seems also to be an appropriate way to characterize FSUs for specific applications. Care should be taken using the latter method when the coupled motions are importan

From stellar to planetary composition: Galactic chemical evolution of Mg/Si mineralogical ratio

The main goal of this work is to study element ratios that are important for the formation of planets of different masses. We study potential correlations between the existence of planetary companions and the relative elemental abundances of their host stars. We use a large sample of FGK-type dwarf stars for which precise Mg, Si, and Fe abundances have been derived using HARPS high-resolution and high-quality data. A first analysis of the data suggests that low-mass planet host stars show higher [Mg/Si] ratios, while giant planet hosts present [Mg/Si] that is lower than field stars. However, we found that the [Mg/Si] ratio significantly depends on metallicity through Galactic chemical evolution. After removing the Galactic evolution trend only the difference in the [Mg/Si] elemental ratio between low-mass planet hosts and non-hosts was present in a significant way. These results suggests that low-mass planets are more prevalent around stars with high [Mg/Si]. Our results demonstrate the importance of Galactic chemical evolution and indicate that it may play an important role in the planetary internal structure and composition.Comment: Accepted by A&A (Letter to the Editor

Detection of Neptune-size planetary candidates with CoRoT data. Comparison with the planet occurrence rate derived from Kepler

[Abridged] Context. The CoRoT space mission has been searching for transiting planets since the end of December 2006. Aims. We aim to investigate the capability of CoRoT to detect small-size transiting planets in short-period orbits, and to compare the number of CoRoT planets with 2 \leq R_p \leq 4 Rearth with the occurrence rate of small-size planets provided by the distribution of Kepler planetary candidates (Howard et al. 2012). Methods. We performed a test that simulates transits of super-Earths and Neptunes in real CoRoT light curves and searches for them blindly by using the LAM transit detection pipeline. Results. The CoRoT detection rate of planets with radius between 2 and 4 Rearth and orbital period P \leq 20 days is 59% (31%) around stars brighter than r'=14.0 (15.5). By properly taking the CoRoT detection rate for Neptune-size planets and the transit probability into account, we found that according to the Kepler planet occurrence rate, CoRoT should have discovered 12 \pm 2 Neptunes orbiting G and K dwarfs with P \leq 17 days in six observational runs. This estimate must be compared with the validated Neptune CoRoT-24b and five CoRoT planetary candidates in the considered range of planetary radii. We thus found a disagreement with expectations from Kepler at 3 \sigma or 5 \sigma, assuming a blend fraction of 0% (six Neptunes) and 100% (one Neptune) for these candidates. Conclusions. This underabundance of CoRoT Neptunes with respect to Kepler may be due to several reasons. Regardless of the origin of the disagreement, which needs to be investigated in more detail, the noticeable deficiency of CoRoT Neptunes at short orbital periods seems to indirectly support the general trend found in Kepler data, i.e. that the frequency of small-size planets increases with increasing orbital periods and decreasing planet radii.Comment: 10 pages, 7 figures. Accepted for publication in A&

The formation of Jupiter by hybrid pebble-planetesimal accretion

The standard model for giant planet formation is based on the accretion of solids by a growing planetary embryo, followed by rapid gas accretion once the planet exceeds a so-called critical mass. The dominant size of the accreted solids (cm-size particles named pebbles or km to hundred km-size bodies named planetesimals) is, however, unknown. Recently, high-precision measurements of isotopes in meteorites provided evidence for the existence of two reservoirs in the early Solar System. These reservoirs remained separated from ~1 until ~ 3 Myr after the beginning of the Solar System's formation. This separation is interpreted as resulting from Jupiter growing and becoming a barrier for material transport. In this framework, Jupiter reached ~20 Earth masses within ~1 Myr and slowly grew to ~50 Earth masses in the subsequent 2 Myr before reaching its present-day mass. The evidence that Jupiter slowed down its growth after reaching 20 Earth masses for at least 2 Myr is puzzling because a planet of this mass is expected to trigger fast runaway gas accretion. Here, we use theoretical models to describe the conditions allowing for such a slow accretion and show that Jupiter grew in three distinct phases. First, rapid pebble accretion brought the major part of Jupiter's core mass. Second, slow planetesimal accretion provided the energy required to hinder runaway gas accretion during 2 Myr. Third, runaway gas accretion proceeded. Both pebbles and planetesimals therefore have an important role in Jupiter's formation.Comment: Published in Nature Astronomy on August 27, 201