exoplanet mass and radius and the physics of planetary interiors sara … · 2010-06-28 · sara...
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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
€
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
€
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
€
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
€
log10 Rs = −0.209 +1/3log10 Ms − 0.0804 ×Ms0.394
Seageretal.2007
Thomas‐Fermi‐DiracEOS
VinetEOS
NosimpleEOSformula<onforpressuresbetweenVinetandTFD
Seager et al. 2007
€
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
€
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