Planet Masses and Radii from Physical Principles Günther Wuchterl CoRoT / DLR Thüringer Landessternwarte Tautenburg

A theory for the discovery era General – all stars, all orbital periods, core: y/n Simple – direct relation to physics Robust – no a-priori selection of mechanisms Predictive - no free parameters Fast – evaluation feasible to better than observed accuracy in entire discovery space

General Theory of Planet Formation Assumptions and Principles Diversity of nebulae: study planet formation in any gravitationally stable nebula for all stellar masses, Strong planetesimal hypothesis: there are always enough planetesimals, Study all planets with cores of all masses including zero - do not separate into nucleated instability or disk instability; ADS: see Pečnik, Broeg, Schönke, Wuchterl

I: Full study of a simple model Isothermal Planets How to determine and classify all planets and protoplanets?

Pečnik 2005, Schönke 2007 The planetary phase diagram

Characteristic mass: The Ω-point natural planetary mass derived from microphysics, primary mass, and orbital period. Compactification proto -> planet by self gravity

PLANET ESSENTIALS Isothermal planets: Pečnik 2005 Analytical Theory: Schönke 2007 Envelope self-gravity Gravity and tides of primary (Hill-sphere) Compacting by core-gravity and self-gravity \Star (luminosity+tides) + nebula = planets

Why does this work? Think of planet formation as analogy to the van der Waals gas with gravity as the long-range force, Take planets as analogy to the liquid-phase in coexistence with a gas-phase, the nebula. Find out more at  Pečnik and Pečnik+W for the isothermal case  Schönke 2007 etc., for stability and analytics  Broeg and Broeg+W for realistic planets  Wuchterl et al. for the CoRoT-stellar-mixture  Broeg, Icarus 2009

II: Planets with Energy Transfer Detailed non-ideal equations of state, Energy transfer by radiation and convection, Detailed opacity: “stellar”, molecular, dust, Energy-input by planetesimal accretion.

Main sequences: stars and planets Stars Mostly hydrostatic Energy balance on main sequence Complete equilibria on main sequence Mostly constant mass Determine: L,R-->T eff Planets Mostly hydrostatic Energy balance when young Complete equilibria in the nebulae Mass exchange with the nebulae Determine: M, R

Step 1: Masses Consider host star and orbital period Planetary equilibria with all core masses:  hydrostatic equilibrium (P vs. core and gas)  thermal equilibrium (L vs. planetesimal accr.) Balance:  force: planet with nebula pressure, and  Thermal: planetesimal heat with radiation into equilibrium temperature nebulae Count all possible planets in any stable nebula \Get planetary initial mass function, for M*, P orb

1: 2006 Dec. 26 th : CoRoT Launch Prediction: Planetary Masses from Formation Theory Wuchterl et al.; 2006+n, Lammer et al n Dec. 26th: astro-ph/ ;astro-ph/

Planetary masses and distributions M to A stars orbital period up to 128 days CoRoT - Mark 1: Dec 2005 CoRoT - Mark 2: Sept 2007 CoRoT - Mark 3: June 2008 At Chris Broegs webpage Or search “CoRoT survey Mark3”

Step 2: Radii Initial masses and initial interior structures for the “IMF”-ensemble of planets found in step 1 Evolution of planetary populations:  switch-off planetesimal accretion  nebula decompression (if any)  follow contraction/expansion to determine R

Radius(time) for planet-population

Planet radii for A,F,G,K stellar pop.

Planet radii – Oct 2010

Transit depth - A,F,G,K stellar pop.

Case-study: CoRoT-13b A Jupiter with monster core Host star: G0V, 1.1 M_Sun, 5945 (± 90) K Mass: (± 0.066) MJ Semi major axis:0.051 (± ) AU Orbital period: (± 3e-05) days Radius:0.885 (± 0.014) RJ → density is almost twice Jupiter's 150 – 300 Earth masses of heavy elements! #CoRoT-13b 4.04d,G0V,0.12−3.15Ga lg:-0.92,0.50=-0.21+/-0.71;1.308±0.066 MJ,0.885±0.014,lg=(27.37,27.42),RJ,2.34±0.23g/cm3

Mass function and CoRoT-13b #CoRoT-13b 4.04d,G0V,0.12−3.15Ga lg:-0.92,0.50=-0.21+/-0.71;1.308±0.066 MJ,0.885±0.014,lg=(27.37,27.42),RJ,2.34±0.23g/cm3

Radius-Function and CoRoT-13b

Age vs. evolving radius-distributions

CoRoT-13b: density and theory

Outlook: Pop-Density in M-R-D

Conclusion – General Theory Predicts high resolution mass and radius distributions from basic physics for planets of  M to A stars and;  orbital periods up to 120d; Bimodal mass and radius distributions; Large gaps between “Jupiters” and “Neptunes”; Explains M,R,t of extreme planets as the ~200 M ⊕ monster core of CoRoT-13b (and others).

CoRoT.TLS-Tautenburg.de/CoRoT-7

Src01 mosaic, Alfred Jensch 2m TLS Tautenburg, Bringfried Stecklum

Outlook: Pop-Densitiy in M-R-D