Planet Masses and Radiifrom

Physical Principles

Günther WuchterlCoRoT / 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 FormationAssumptions 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 modelIsothermal Planets

How to determine and classify all planets and protoplanets?

Pečnik 2005, Schönke 2007

The

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neta

ry p

hase

dia

gram

Characteristic mass: The Ω-point

natural planetary mass derived from microphysics , primary mass, and orbital period.

Compactification proto -> planet by self gravity

PLANET ESSENTIALSIsothermal planets: Pečnik 2005Analytical 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-->Teff

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*, Porb

1: 2006 Dec. 26th: CoRoT Launch Prediction: Planetary Masses from

Formation TheoryWuchterl et al.; 2006+n, Lammer et al. 2006+n

Dec. 26th: astro-ph/0701003 ;astro-ph/0701565

Planetary masses and distributionsM to A stars

orbital period up to 128 days

CoRoT - Mark 1: Dec 2005CoRoT - Mark 2: Sept 2007CoRoT - Mark 3: June 2008

At Chris Broegs webpagewww.space.unibe.ch/~broeg/

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: 1.308 (± 0.066) MJ Semi major axis: 0.051 (± 0.0031) AU Orbital period: 4.03519 (± 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

Age vs. evolving radius-distributions

Age vs. evolving radius-distributions

CoRoT-13b: density and theory

Outlook: Pop-Density in M-R-D

Outlook: Pop-Density in M-R-D

Outlook: Pop-Density in M-R-D

Outlook: Pop-Density in M-R-D

Outlook: Pop-Density in M-R-D

Outlook: Pop-Density in M-R-D

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

Outlook: Pop-Densitiy in M-R-D