# From Theory to Characterisation and Observation

The combined non-linear actions of numerous physical processes intervening during the formation and evolution of planets mean that it is difficult to understand the origins of planets solely from theoretical models built on first principles. Confronting theoretical models with observational data is therefore a key vector necessary to improve the understanding of planet formation where observations are acting as a guidance for the theoretical models. The comparison of theory and observations applies to observational data both from the Solar System where detailed observational constraints are available, as well as to the extrasolar planets which provide statistical constraints. For this comparison the characterization of planets in terms of observable astronominal and geophysical quantities provides the necessary link between theory and observations. The TAPS group uses multiple approaches to link theory via characterization with observations. This includes detailed studies of individual planets and minor bodies like comets in terms of their formation history, internal structure, composition, and spectrum as well as statistical comparisons with planetary populations, taking for the latter into account also the effects of selection biases.

## Comparison with Solar System objects

The best studied planets are those of the Solar System. Various geophysical data types provide us with well-constrained interior models of the Solar System planets. These represent perfect benchmark cases to test our assumptions and models that we use for exoplanets, for example when characterizing exoplanet interiors.

How did the Moon form and how did Mars evolve? How did asteroids and comets obtain their particular shapes and structures?

We study how the final properties of Solar System bodies were determined by the last major impacts occurring at the end stages of planet formation.

Does planet nine exist?

If it would exist it would lead to many new questions concerning the formation and evolution of Solar System planets. We studied if this planet could be observable and find that this depends on various parameters.

- Linder, Esther; Mordasini, Christoph (2016):

Evolution and magnitudes of candidate Planet Nine.*A&A*,**589**, A134

## Comparison with extrasolar planets

#### Composition of exoplanets

What are exoplanets made of? What is the probability of an exoplanet to be Earth-like? What are the controlling parameters for the diversity in planet structure?

In order to tackle these and other questions, we use Bayesian inference analysis to quantify confidence regions of interior parameters.

The data are few and dat errors are large. In addition, there are different interior structures that cannot be distinguished by observable data. Thus, interior parameters are highly degenerate. In order to make a meaningful statement about interiors of exoplanets, we quantify parameter degeneracy.

- Dorn, Caroline; Venturini, Julia; Khan, Amir; Heng, Kevin; Alibert, Yann; Helled, Ravit; Rivoldini, Attilio; Benz, Willy (2016):

A Generalized Bayesian Inference Method for Constraining the Interiors of Super Earths and Sub-Neptunes.*A&A*,**597**, A37 - Dorn, Caroline; Hinkel, Natalie R.; Venturini, Julia (2016):

Bayesian analysis of interiors of HD 219134b, Kepler-10b, Kepler-93b, CoRoT-7b, 55 Cnc e, and HD 97658b using stellar abundance proxies.*A&A*,**597**, A38 - Dorn, Caroline; Khan, Amir; Heng, Kevin; Connolly, James A. D.; Alibert, Yann; Benz, Willy; Tackley, Paul (2015):

Can we constrain the interior structure of rocky exoplanets from mass and radius measurements?.*A&A*,**577**, A83

#### Statistical comparison with population synthesis

The steadily growing population of exoplanets yields numerous statistical constraints that are of high importance for theoretical planet formation models. This includes distributions of the mass, the semi-major axis, the eccentricity, the radius and the luminosity, their mutual dependencies, as well as correlations with stellar properties like the metallicity. Particularly strong observational constraints can be obtained when the theoretical predictions of planetary population syntheses are compared with many different observational techniques. The planetary mass function can for example be compared with the results of radial velocity surveys, while the plot below shows for a synthetic population around solar-like stars the predicted contrasts in the H-band that can be compared with direct imaging surveys like NACO, GPI, or SPHERE. The plot also shows the C/O ratio predicted by our chemistry model. The C/O strongly affects the abundances of spectroscopically active molecules like CO, H2O, CH4 or CO2 and bears an imprint of the formation history and location of an exoplanet, at least if the atmospheric composition is representative of the bulk composition. This is shown in the plot by the size of a point that represents the distance from the star where the planet reaches the cross-over mass. Such combined constrains are important observational checks for the internal coherence of theoretical formation models.

- Benz, Willy; Ida, Shigeru; Alibert, Yann; Lin, Douglas; Mordasini, Christoph (2014):

Planet Population Synthesis.*Protostars and Planets VI*, 691 - Mordasini, Christoph; Alibert, Yann; Benz, Willy; Naef, Dominique (2009):

Extrasolar planet population synthesis. II. Statistical comparison with observations.*A&A*,**vol. 501**, pp. 1161