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Probabilistic Mass-Radius Relationship(s)
Angie Wolfgang UCSC → Penn State
NSF Postdoctoral Fellow
Eric Ford, Leslie Rogers, SAMSI Bayesian Exoplanet Populations Group
for Sub-Neptune-sized Planets
Sub-Neptune Mass & Radius
Useful to constrain possible compositions. . . but not all can have masses measured
figure courtesy of Eric Lopez
Needed: Mass-Radius Relation
Comparing transit and RV detections
?
Burke et al. 2015Mayor et al. 2011 Dynamics of
non-TTV Kepler planets
Fabrycky et al. 2014
Schlichting 2014
Formation of Kepler planets and systems
Mass-Radius RelationshipHow exactly to incorporate
dispersion?Weiss & Marcy, 2014
PDF (probability density function)
Large M, R uncertainties;
C, !, "M are population-wide parameters . . .
Hierarchical Bayesian Modeling
What if there isn’t just one “true” value of # for all the data?i.e. # has its own intrinsic distribution?(Happens often for population studies)
“Regular” Bayes:p(!|x) ∝ p(x|!) p(!)posterior likelihood prior
Observables
Parameters
Example:Compositions
Hierarchical Bayesian Modeling“Regular” Bayes:p(!|x) ∝ p(x|!) p(!)posterior likelihood prior
Observables
Parameters
Hierarchical Bayes:p(!,"|x) ∝ p(x|!,") p(!|") p(")
posterior likelihood prior posterior likelihood prior
PopulationParameters
Observables
Individual Parameters
Can still use MCMC . . .“Just” adding another layer of
probabilistic structure
physics
data
HBM for Mass-Radius Relation
Observers, we need your likelihoods!!Please, publish your joint posterior samples *and* your priors!!
Mobs Robs
In practice . . .
Results
Wolfgang, Rogers, & Ford, in prep.
There is intrinsic scatter in the current set of R,M measurements, which an accurate M-R relation must reflect.
probabilistic M-R relation:deterministic M-R relation:
Changing the Data Set
Only the smallest (likely rocky) planets don’t require intrinsic dispersion to
accurately describe the M-R relation.
For Individual Planets:Case Study: Kepler-452 b
No mass measurement?Use probabilistic M-R relation to
constrain composition:github.com/dawolfgang/MRrelation
P(has gas) = 0.51
P(rocky) = 0.49
Jenkins et al. 2015
For Individual Planets:Case Study: Kepler-452 b
No mass measurement?Use probabilistic M-R relation to
constrain composition:github.com/dawolfgang/MRrelation
P(has gas) = 0.51
P(rocky) = 0.49
Jenkins et al. 2015
Rogers 2014:“Most 1.6 REarth Planets are Not
Rocky”
Consistent: 452b is NOT conclusively rocky: ~50% chance it is
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