Constraining the interiors of exoplanets by measuring the Love number k2,f

This talk summarizes how the Love-numbers can be used to constrain the planetary interiors, how we can measure the exoplanetary Love-numbers and what precision can be reached

Bestimmung des inneren Aufbaus von Exoplaneten mit der Love-Zahl h2

The fascinating diversity in the properties of extrasolar planets and planetary systems, compared to those of the Solar System, has challenged our understanding of planetary formation and evolution. The interior of a planet holds traces of its history, and is thereby the present witness of the processes involved during its formation and evolution. The Love numbers, introduced by A.E.H. Love in 1911, are parameters holding precious information on a planetary structure and composition. While these parameters have been measured for several Solar System bodies, previous studies did not decidedly answer the question whether they can be estimated for extrasolar planets. To that end, I have developed a computer code which retrieves the Love number h2 from transit observations of planets undergoing strong tidal and rotational deformations. In the first study, I derive a photometric noise level above which the estimation of h2 becomes difficult. I show that the uncertainty in the stellar limb darkening coefficients and the non-unique relationships between Love number and planetary radius are the main limitations to the measurement of h2. The results show that the JWST and PLATO space telescope and the future very large ground-based facilities are the best suited observatories to measure h2. In the second study, I analyze one complete transit of the hot Jupiter WASP-121b observed by the Hubble Space Telescope. I perform a thorough noise analysis and limb darkening study, and derive the first tentative measurement of h2 for an exoplanet, whose central value confirms the inflated nature of WASP-121b. While measuring h2 for sub-Jovian bodies remains very difficult using this technique, I identify nine hot Jupiters where such measurement is feasible with current or future observatories. Finally, I show that h2 measurements of hot Jupiters could help us better understand the physics of planetary inflation, the mechanisms involved in the formation of these planets, and the architecture of planetary systems.Die faszinierende Vielfalt extrasolarer Planeten und Planetensysteme im Vergleich zu denen des Sonnensystems fordert unser Verständnis der Planetenentstehung und -entwicklung heraus. Das Innere eines Planeten zeigt die Spuren seiner Geschichte und ist somit Zeuge der Prozesse, die während seiner Entstehung und Entwicklung abgelaufen sind. Die Love-Zahlen—eingeführt 1911 von A.E.H. Love—sind Parameter, die wertvolle Informationen über Struktur und Zusammensetzung eines Planeten geben. Während diese Parameter für mehrere Körper des Sonnensystems gemessen wurden, haben bisherige Studien nicht definitiv klären können, ob man sie für extrasolare Planeten ebenfalls ermitteln kann. Aus diesem Grund habe ich einen Computercode entwickelt, der die Love-Zahl h2 für Planeten mit starken Gezeiten- und Rotationsdeformationen aus Transitbeobachtungen errechnet. Im ersten Teil meiner Arbeit leite ich einen photometrischen Rauschpegel ab, oberhalb dessen die Schätzung von h2 schwierig wird. Ich zeige, dass die Unsicherheit in den Koeffizienten, die die Mitte-Rand-Verdunklung eines Sterns beschreiben, und die nicht eindeutigen Beziehungen zwischen Love-Zahl und Planetenradius die wesentliche Beschränkung bei der Bestimmung von h2 sind. Die Ergebnisse zeigen, dass die Weltraumteleskope JWST und PLATO und die zukünftigen, sehr großen bodengestützten Anlagen die am besten geeigneten Observatorien für die Messung von h2 sind. Im zweiten Teil analysiere ich einen kompletten Transit des heißen Jupiters WASP-121b, der mit dem Weltraumteleskop Hubble beobachtet wurde. Ich führe eine gründliche Rauschanalyse und eine Studie zur Randverdunklung durch und leite die erste vorläufige Bestimmung von h2 für einen Exoplaneten ab, dessen Mittelwert bestätigt, dass WASP-121b ein aufgeblähter heißer Jupiter ist. Da die Bestimmung von h2 für Körper mit Massen kleiner als der Jupitermasse mit dieser Technik nach wie vor sehr schwierig ist, identifiziere ich neun heiße Jupiter, bei denen mit aktuellen oder zukünftigen Observatorien eine sinnvolle Messung möglich wäre. Schließlich zeige ich, dass h2-Messungen an heißen Jupitern uns helfen könnten, die Physik der des Aufblähens von Planeten, die Mechanismen in der Entstehung dieser Planeten und die Architektur von Planetensystemen besser zu verstehen.DFG, 280637173, Materie im Inneren von Planeten - Hochdruck-, Planeten- und Plasmaphysi

HST/STIS Capability for Love Number measurement of WASP-121b

Data from transit light curves, radial velocity, and transit timing observations can be used to probe the interiors of exoplanets beyond the mean density, by measuring the Love numbers h 2 and k 2. The first indirect estimate of k 2 for an exoplanet from radial velocity and transit timing variation observations has been performed by taking advantage of the years-spanning baseline. Not a single measurement of h 2 has been achieved from transit light curves, mostly because the photometric precision of current observing facilities is still too low. We show that the Imaging Spectrograph instrument onboard the Hubble Space Telescope (HST) could measure h 2 of the hot Jupiter WASP-121b if only a few more observations were gathered. We show that a careful treatment of the noise and stellar limb darkening (LD) must be carried out to achieve a measurement of h 2. In particular, we find that the impact of the noise modeling on the estimation of h 2 is stronger than that of the LD modeling. In addition, we emphasize that the wavelet method for correlated noise analysis can mask limb brightening. Finally, using currently available data, we briefly discuss the tentative measurement of ${h}_{2}={1.39}_{-0.81}^{+0.71}$ in terms of interior structure. Additional observations would further constrain the interior of WASP-121b and possibly provide insights on the physics of inflation. The possibility of using the approach presented here with the HST provides a bridge before the high-quality data to be returned by the James Webb Space Telescope and PLATO telescope in the coming decade

Retrieval of the fluid Love number k2 in transit light curves: a feasibility study

With about 4000 confirmed detected exoplanets, the characterization of their interior could potentially unveil information on their formation, migration, and habitability. The Love number k2, when hydrostatic equilibrium of the interior is assumed, is an indication of mass concentration towards the body's center. Hence, it helps to further constrain the interior when combined with planetary mass and mean radius. We first summarize the planetary shape model which allows the retrieval of k2 from transit light curves. Second, we apply our model to synthetic data of WASP-121b and show that a precision < 90 ppm/min is required to reliably retrieve k2 with present understanding of stellar limb darkening. Therefore we improve recent results based on ellipsoidal shape models

A method for direct testing of hydrostatic equilibrium in exopanet interiors

The characterization of the interior of exoplanets will unveil precious information on their formation, structure and evolution. The Love numbers h2 and k2, which describe the planet's response to external perturbations, contain information on the radial density distribution and other interior parameters (e.g. viscosity). In the case of hydrostatic equilibrium, we simply have h2=1+k2. We summarize how one can measure h2 from transit observations and k2 from periastron precession in eccentric orbits, hence providing a direct test for hydrostatic equilibrium in exoplanet interiors