exoplanet mass and radius and the physics of planetary interiors · pdf fileexoplanet mass and...

TrentSchindler

TrentSchindler

Sara Seager Massachusetts

Institute of Technology

Exoplanet Mass and Radius and the Physics of Planetary Interiors

CaseyReid

Planet Interiors

The goal is to constrain the interior composition of exoplanets by their mass and radius measurements

Planet Mass-Radius 1995

Planet Mass-Radius 2000

Planet Mass-Radius 2005

Planet Mass-Radius 2010

Exoplanet Interiors Introduction Mass-Radius Relationships

Two Transiting Super Earths Kepler and Beyond

Exoplanet Mass-Radius Diagram Aimtoinferanexoplanet’sbulkcomposi<onfromitsMandR

Seager et al. 2007

Seager,Kuchner,Hier‐Majumder,Militzer2007ZapolskyandSalpeter1969Stevenson1982,Hubbard1984Valenciaetal.2006,2007So<netal.2007Selsisetal.2007…andothers

Weinferanexoplanet’sbulkcomposi<onfromitsMandR

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dP(r)dr

=−Gm(r)ρ(r)

r2

ρ(r) = F(P(r),T(r))€

dm(r )dr

= 4πr 2ρ(r )

Exoplanet Mass-Radius Diagram

Equation of State

Describesrela<onshipbetweendensity,temperatureandpressureforamaterialinthermodynamicequilibrium

1)  Idealgaslaw:P=nkT;ρ=PmHµ/kT2)  Polytrope:P=Kρ(n+1)/n3)  VinetEOS

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ρ(r) = f T(r),P(r)( )

High Pressure Physics Experiments

Wikipedia

Mass-radius relationships appear have a common functional form

Exoplanet Mass-Radius Diagram

Seager et al. 2007

Equation of State

Ms<~4

Ms<<1

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log10 Rs = −0.209 +1/3log10 Ms − 0.0804 ×Ms0.394

Seageretal.2007

Equation of State

Overall,theEOSsapproximatelyfollowρ=ρ0+cPnA“modifiedpolytrope”Ms<~4

Ms<<1

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log10 Rs = −0.209 +1/3log10 Ms − 0.0804 ×Ms0.394

Seageretal.2007

Thomas‐Fermi‐DiracEOS

VinetEOS

NosimpleEOSformula<onforpressuresbetweenVinetandTFD

Seager et al. 2007

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Ms =43πRs

3 1+ 1− 35n

23πRs

2

n

Ms<~4

Ms<<1

€

log10 Rs = −0.209 +1/3log10 Ms − 0.0804 ×Ms0.394

Seageretal.2007

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dm(r)dr

= 4πr2ρ(r)

€

dP(r)dr

=−Gm(r)ρ(r)

r2

ρ(r) = ρ0 + cP(r)n

The mass-radius relationships for cold terrestria lmass planets follow a generic functional form because the EOS are well approximated by a modified polytrope.

Generic Mass-Radius Relation

Seager et al. 2007

DiversityofsuperEarths?

Waterplanets?

Neptune‐sizebutnotnecessarilyicegiants

Currentground‐basedtransitsurveys.Someplanetsaretoobig!

Seager et al. 2007

Mass-Radius Relation Summary

Mass‐radiusrela<onshipsarewellunderstoodbutarenotadequatetostudy

individualobjects.

Exoplanet Interiors Introduction Mass-Radius Relationships

Two Transiting Super Earths

Kepler and Beyond

Planet Interiors

Exoplanets can be composed of three (or four) materials: rock (and iron), ice, and gas RogersandSeager2010b;Chambers2010

Ternary Diagrams

hgp://csmres.jmu.edu/geollab/fichter/SedRx/readternary.html

Ternary Diagrams

hgp://csmres.jmu.edu/geollab/fichter/SedRx/readternary.html

Ternary Diagrams

hgp://csmres.jmu.edu/geollab/fichter/SedRx/readternary.html

Ternary Diagrams

ZengandSeager2008

CoRoT‐7b

The first transiting super Earth R = 1.68±0.09 R M = 4.8±0.8 M P = 0.85 days a = 0.017 AU T ~ 2500 K

Leger et al. 2009 Queloz et al. 2009

RogersandSeager2010b

Degeneracy in internal composition is a permanent limitation no matter how small the observational uncertainties

Ternary diagrams: see Valencia et al. 2007 Zeng & Seager 2008

CoRoT‐7b

RogersandSeager2010b

R = 1.68±0.09 REarth M = 4.8±0.8 MEarth

CoRoT-7b is likely made of material less dense than Earthʼs, assuming no water content

GJ 1214b

GJ 1214b by Charbonneau et al. 2009 Interpretation by Rogers and Seager 2010a

The second transiting super Earth R = 2.68±0.13 R M = 6.6±0.8 M P = 1.58 days a = 0.014 AU T ~ 550 K

Quaternary Diagrams

Most super Earths or exo-Neptunes found in the near future are likely to have gas envelopes.

This adds a further degeneracy to the interior composition interpretation.

Adds more complexity t the models because of the free parameters in the gas layer.

RogersandSeager2010b

GJ 1214b

GJ 1214b by Charbonneau et al. 2009 Interpretation by Rogers and Seager 2010a

The second transiting super Earth R = 2.68±0.13 R M = 6.6±0.8 M P = 1.58 days a = 0.014 AU T <~ 550 K

Water Phase Diagram 1012

106

103

1

109

Pressure(P

a)

Temperature(K)0 200 400 800600

Super Earth Interiors Summary Interiorcomposi<oninterpreta<onishighly

degeneratebasedonmassandradiusmeasurements

Parameterspacecanbequan<ta<velyconstrained,andcri<calinterpreta<oncans<llbemade,e.g.,the

likelyabsenceofliquidwateronGJ1214b

Exoplanet Interiors Introduction Mass-Radius Relationships

Two Transiting Super Earths Kepler and Beyond

NASAʼs Kepler Space Telescope

Telescope Summary 0.95 m 105 sq-degree FOV Centered in the Cygnus-Lyra region No moving parts in science payload Heliocentric Earth-trailing orbit Telemetry limited Bandpass 423-897 nm

Goal: to determine the frequency of Earth-size planets in Earth-like orbits about sun-sized stars

Boruckietal.2010

Planets 2000

Planets 2005

Planets June 14 2010

Planet Candidates June 15 2010

Planet Candidates June 15 2010

Too faint for RV followup About ½ false positives

See Borucki et al. 2010, astroph yesterday

Astrophysical False Positives

•  Eclipsing binary with grazing orientation

•  Small star crossing in front of another star

•  Eclipsing binary diluted by the light of a third star (“blend”): the trickiest case

AdaptedfromG.Torres

Number of Planet Candidates

Boruckietal.2010

Planet Candidates vs. Semi-Major Axis

Boruckietal.2010

Kepler Multi-Planet Transits

Five multi-planet candidate systems were announced yesterday Steffen et al. astroph yesterday

Multi-Planet Transits Harbinger for huge advancements in exoplanet science Planet formation -why so coplanar? -frequency of coplanar systems?

Orbital evolution -orbital resonances

Planet characterization -masses (from transit timing variations) and radii for planets in the same system

V = 13.9 R = 0.58 RJ P > 27 d

R = 0.3 RJ P = 27.406 d

R = 0.3 RJ P = 13.478 d

KeplerSummaryKeplerwillmorethandoublethenumberofexoplanets,extendingtheorbitalsepara<onoftransi<ngplanetsout

to1AU.Thedatareleaseisagame‐changerforexoplanetscience

intermsofquan<tyvs.detailedphysicalproper<es

Theplanistoconnectradiivs.periodwithplanetinteriorsandpopula<onsynthesismodelstoconstrain

planetforma<onmodels

Ultimately we want to connect planet atmosphere and interior models with planet formation and population synthesis models and large observational data sets like Kepler.

Summary •  Mass-Radius Measurements

–  For almost 100 exoplanets –  Mass-radius relationships are well understood

•  Characterization of Individual Super Earths –  Only two data points (mass and radius) translates to a

permanent degeneracy in interior composition –  Quantitative constraints are possible

•  Kepler Data –  Historic announcement of 5 multi-planet transiting candidates –  Hundreds of new planet candidates

•  The Way Forward –  connect mass, radius, and/or period data, planet population

synthesis models, and planet interior and atmosphere models –  With the aim of understanding planet formation, migration, and

evolution