U. Kramm

Interior structure models of GJ 436b

Context. GJ436b is the first extrasolar planet discovered that resembles Neptune in mass and radius. Two more are known (HAT-P-11b and Kepler-4b), and many more are expected to be found in the upcoming years. The particularly interesting property of Neptune-sized planets is that their mass Mp and radius Rp are close to theoretical M − R relations of water planets. Given Mp, Rp, and equilibrium temperature, however, various internal compositions are possible. Aims. A broad set of interior structure models is presented here that illustrates the dependence of internal composition and possible phases of water occurring in presumably water-rich planets, such as GJ 436b on the uncertainty in atmospheric temperature profile and mean density. We show how the set of solutions can be narrowed down if theoretical constraints from formation and model atmospheres are applied or potentially observational constraints for the atmospheric metallicity Z1 and the tidal Love number k2. Methods. We model the interior by assuming either three layers (hydrogen-helium envelope, water layer, rock core) or two layers (H/He/H2O envelope, rocky core). For water, we use the equation of state H2O-REOS based on finite temperature – density functional theory – molecular dynamics (FT-DFT-MD) simulations. Results. Some admixture of H/He appears mandatory for explaining the measured radius. For the warmest considered models, the H/He mass fraction can reduce to 10 −3 , still extending over ∼0.7R⊕. If water occurs, it will be essentially in the plasma phase or in the superionic phase, but not in an ice phase. Metal-free envelope models have 0.02 < k2 < 0.2, and the core mass cannot be determined from a measurement of k2. In contrast, models with 0.3 < k2 < 0.82 require high metallicities Z1 < 0.89 in the outer envelope. The uncertainty in core mass decreases to 0.4Mp ,i fk2 ≥ 0.3, and further to 0.2Mp ,i fk2 ≥ 0.5, and core mass and Z1 become sensitive functions of k2. Conclusions. To further narrow the set of solutions, a proper treatment of the atmosphere and the evolution is necessary. We encourage efforts to observationally determine the atmospheric metallicity and the Love number k2.

The Young Exoplanet Transit Initiative (YETI)

We present the Young Exoplanet Transit Initiative (YETI), in which we use several 0.2 to 2.6-m telescopes around the world to monitor continuously young (≤100 Myr), nearby (≤1 kpc) stellar clusters mainly to detect young transiting planets (and to study other variability phenomena on time-scales from minutes to years). The telescope network enables us to observe the targets continuously for several days in order not to miss any transit. The runs are typically one to two weeks long, about three runs per year per cluster in two or three subsequent years for about ten clusters. There are thousands of stars detectable in each field with several hundred known cluster members, e.g. in the first cluster observed, Tr-37, a typical cluster for the YETI survey, there are at least 469 known young stars detected in YETI data down to R = 16.5 mag with sufficient precision of 50 millimag rms (5 mmag rms down to R = 14.5 mag) to detect transits, so that we can expect at least about one young transiting object in this cluster. If we observe ∼10 similar clusters, we can expect to detect ∼10 young transiting planets with radius determinations. The precision given above is for a typical telescope of the YETI network, namely the 60/90-cm Jena telescope (similar brightness limit, namely within ±1 mag, for the others) so that planetary transits can be detected. For targets with a periodic transit-like light curve, we obtain spectroscopy to ensure that the star is young and that the transiting object can be sub-stellar; then, we obtain Adaptive Optics infrared images and spectra, to exclude other bright eclipsing stars in the (larger) optical PSF; we carry out other observations as needed to rule out other false positive scenarios; finally, we also perform spectroscopy to determine the mass of the transiting companion. For planets with mass and radius determinations, we can calculate the mean density and probe the internal structure. We aim to constrain planet formation models and their time-scales by discovering planets younger than ∼100 Myr and determining not only their orbital parameters, but also measuring their true masses and radii, which is possible so far only by the transit method. Here, we present an overview and first results (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

CONSTRAINTS ON A SECOND PLANET IN THE WASP-3 SYSTEM*

There have been previous hints that the transiting planet WASP-3b is accompanied by a second planet in a nearby orbit, based on small deviations from strict periodicity of the observed transits. Here we present 17 precise radial velocity (RV) measurements and 32 transit light curves that were acquired between 2009 and 2011. These data were used to refine the parameters of the host star and transiting planet. This has resulted in reduced uncertainties for the radii and masses of the star and planet. The RV data and the transit times show no evidence for an additional planet in the system. Therefore, we have determined the upper limit on the mass of any hypothetical second planet, as a function of its orbital period.

On the degeneracy of the tidal Love number k2 in multi-layer planetary models: application to Saturn and GJ 436b

Context. In order to accurately model giant planets, a whole set of observational constraints is needed. As the conventional constraints for extrasolar planets like mass, radius, and temperature allow for a large number of acceptable models, a new planetary parameter is desirable in order to further constrain planetary models. Such a parameter may be the tidal Love number k2. Aims. In this paper we aim to study the capability of k2 to reveal further information about the interior structure of a planet. Methods. With theoretical planetary models we investigate how the tidal Love number k2 responds to the internal density distribution of a planet. In particular, we demonstrate the effect of the degeneracy of k2 due to a density discontinuity in the envelope of a threelayer planetary model. Results. The effect of a possible outer density discontinuity masks the effect of the core mass on the Love number k2. Hence, there is no unique relationship between the Love number k2 and the core mass of a planet. We show that the degeneracy of k2 with respect to a layer boundary in the envelope also occurs in existing planets, e.g. Saturn and the Hot Neptune GJ 436b. As a result of the degeneracy, the planetary parameter k2 cannot be used to further constrain the core mass of state-of-the-art Saturn models and for GJ 436b only a maximum possible core mass can be derived from a given k2. To significantly narrow the uncertainty about the core mass of GJ 436b the combined knowledge of k2 and atmospheric metallicity and temperature profile is necessary.

Constraining the interior of extrasolar giant planets with the tidal Love number k_2 using the example of HAT-P-13b

Context. Transit and radial velocity observations continuously discover an increasing number of exoplanets. However, when it comes to the composition of the observed planets the data are compatible with several interior structure models. Thus, a planetary parameter sensitive to the planet’s density distribution could help constrain this large number of possible models even further. Aims. We aim to investigate to what extent an exoplanet’s interior can be constrained in terms of core mass and envelope metallicity by taking the tidal Love number k2 into account as an additional, possibly observable parameter. Methods. Because it is the only planet with an observationally determined k2, we constructed interior models for the Hot Jupiter exoplanet HAT-P-13b by solving the equations of hydrostatic equilibrium and mass conservation for different boundary conditions. In particular, we varied the surface temperature and the outer temperature profile, as well as the envelope metallicity within the widest possible parameter range. We also considered atmospheric conditions that are consistent with nongray atmosphere models. For all these models we calculated the Love number k2 and compared it to the allowed range of k2 values that could be obtained from eccentricity measurements of HAT-P-13b. Results. We use the example of HAT-P-13b to show the general relationships between the quantities temperature, envelope metallicity, core mass, and Love number of a planet. For any given k2 value a maximum possible core mass can be determined. For HAT-P-13b we find Mcore < 27 M⊕, based on the latest eccentricity measurement. We favor models that are consistent with our model atmosphere, which gives us the temperature of the isothermal region as ∼2100 K. With this external boundary condition and our new k2-interval we are able to constrain both the envelope and bulk metallicity of HAT-P-13b to 1−11 times stellar metallicity and the extension of the isothermal layer in the planet’s atmosphere to 3−44 bar. Assuming equilibrium tidal theory, we find lower limits on the tidal Q consistent with 10 3 −10 5 . Conclusions. Our analysis shows that the tidal Love number k2 is a very useful parameter for studying the interior of exoplanets. It allows one to place limits on the core mass and estimate the metallicity of a planet’s envelope.

INTERIOR OF SOLAR AND EXTRASOLAR GIANT PLANETS

We present new results for the interior of solar as well as extrasolar giant planets based on ab initio molecular dynamics simulations for the most abundant planetary materials hydrogen, helium, and water. The equation of state, the electrical conductivity and reflectivity can be calculated up to high pressures; very good agreement with shock‐wave experimental results is found. The nonmetal‐to‐metal transition in hydrogen and the subsequent demixing of hydrogen from helium is of great importance for the interior of Jovian planets. The superionic phase predicted for water at high pressures is relevant for Neptune‐like giant planets. Advanced planetary models can be constructed based on the new ab initio data.