CyberScience and Hunting for Planets Beyond our Solar System · “Super-Earth” Jupiter Analog...

CyberScience and Hunting for

Planets Beyond our Solar System

Eric B. Ford, ICS Co-Hire, 2013

Astronomy & Astrophysics

Center for Astrostatistics

Center for Exoplanets & Habitable Worlds

Penn State Astrobiology Research Center

From the Solar System to Exoplanets

Hunting for Exoplanets

Credit: Frank Cianciolo/McDonald Observatory Credit: NOAO/WIYN

Hobby-Eberly Telescope (10m)

Habitable Zone Planet Finder

WIYN Telescope (3.5m)

NEID Spectrograph

Next-Generation Spectrographs being led by Penn

State’s Center for Exoplanets & Habitable Worlds

Echelle Spectrometer

CCD

Echelle

Grating

Collimator

Starlight

From TelescopeEchelle Spectrograph

Measure Shift of Absorption Lines to

Determine the Radial Velocity of Star

Image of Star’s Spectrum

55 Cnc: An RV ClassicApsidal AlignmentApsidal Alignment

Butler+ 1996; Marcy+ 2002; McArthur+ 2004; Endl et al 2012; Nelson et al. 2014

55 Cnc: Astroinformatics in Action

Near

1:3 MMR“Super-Earth”

Jupiter

Analog

• 1,418 RVs from 4 observatories, spanning over 23 years

• Self-consistent Bayesian Analysis w/ full N-body treatment

• ~40 model parameters

• Differential Evolution MCMC (ter Braak 2006; Nelson+ 2014)

• >6.4M models in Markov chains

N-body integration using Swarm-NG GPU (Dindar+ 2012)

Apsidal AlignmentApsidal Alignment

B. Nelson et al. 2014

Candidate for update

i

Differential Evolution MCMC

x

y

ter Braak 2008; Veras & Ford 2009; Wright et al. 2010; Johnson et al. 2011; Carter et al. 2012; Nelson et al. 2014


i

j

k


x

y


Proposed displacement ( )scaled


i

j

k


x

y


Proposed displacement ( )scaled


Proposal

i

j

k


x

y


i

j

k

Proposal


(correlated posterior)

x

y


DEMCMC in Action (resonant case)

Johnson et al. 2011Nelson et al. 2014

55 Cnc e: Mass of a Super-Earth

“Super-Earth”

1,086 RVs over 23 years

Self-consistent Bayesian Analysis

>6.4M models in Markov chain

N-body integration using

Swarm-NG GPU (Dindar+ 2012)


Orbital Phase

Radia

l V

elo

city

Density (g/cm3)

Pro

bab

ility

Near

1:3 MMR

Jupiter

Analog Endl et al. 2012


55 Cnc d: A Jupiter Analog

Near

1:3 MMR“Super-Earth”

Jupiter

Analog

• 13.4 year orbital period

• Small, but non-zero eccentricity

• Very different inner planetary

system than our solar system



What does it mean to “Discover a Planet”?

• Old Frequentist approach:

Reject the null hypothesis that a

simpler model without the planet could

reasonably explain your data

• Modern Bayesian approach:

The Evidence for a model with the

planet is significantly greater than the

alternative models.

How Many Planets?

Bayesian Model Comparison

Evidence or Fully

marginalized

likelihood (FML)

Prior Likelihood

The probability of a radial velocity dataset {d} being

generated from some model M parameterized by {θ} is

given by…

To choose between two competing models M1 and M2,

take the ratio of the evidences for the two models

Bayes Factor

How many planets?

• Bayesian Evidence

• Importance Sampling

• Importance Sampling with Finite Sample Size

• Truncate Importance Sampling Density

Nelson et al. 2015; see also Ford & Gregory 2007

How many planets?

Comparing, can see this is a special case:

• Truncated Importance Sampling Density

• Ratio Estimator (J. Berger; Ford & Gregory 2007)

Nelson et al. 2015; Ford & Gregory 2007

Next Generation of Spectrographs for

Characterizing Earth-mass Planets

Credit: NEID.psu.edu

Hobby-Eberly Telescope (10m)

Habitable Zone Planet Finder

WIYN Telescope (3.5m)

NEID Spectrograph

HPF & NEID Spectrographs being built by Penn


Next Generation of Spectrographs for

Characterizing Earth-mass Planets

HPF & NEID Spectrographs being built by Penn


How to Separate Signals of

Planets & Stellar Activity?

X. DumusqueS. Berdyugina

Principal Components Analysis to

Distinguish Stellar Activity & Planets

Results of PCA applied to ensembles of simulated spectra with

different types of stellar activity (plage or spots) or just kinematic

Doppler shifts.

Davis, Cisewski, Dumusque, Fischer, Ford, Robertson, Valenti in prep.

Algorithmic Regression Path for

Sparse Principal Components Analysis

Red spectra from Dumusque 2014’s SOAP 2.0 model

Measuring Planet Sizes

TESS (launch 2018)

Small Planets around Bright Stars

Kepler/K2 (launched 2009)

Frequency of Small Planets

ESANASA NASA/MIT

NASA/Ames/JPL-Caltech

Detecting a Transiting Planet

NASA/Kepler/Dana Berry

Correlated noise afflicts Kepler light curves

Kepler lightcurve segment of Sun-like star

correlated noise even

on short timescales

R. Dawson, IAU 2015

Accuracy & precision of transit times

improves by modeling correlated noise

Short timescale correlated noise accounted for by GP likelihood using Matern 5/2 radial kernel

(One of sixteen transits)

recovered - injected (minutes)

Model 1: Joint modeling of transits +

polynomials with white noise likelihood

Model 2: Joint modeling of transits +

polynomials with Gaussian process likelihood

Model 1

Model 2

Example

R. Dawson, IAU 2015

Measuring the Day Side Properties of Exoplanets Using Gaussian-Process Regression

We use a distributed Product-of-Experts GP to

model the correlated noise in Hubble Space

Telescope observations of exoplanets’ day sides.

By using ACI to split the calculations over 15

physical CPUs with 20 threads each, we

complete a 2 week-long analysis in slightly over 1

hour. Published in Beatty et al.

(2017)

Period-Radius Distribution of Kepler’s Planets

(including strong planet candidates)

Kepler/Burke+ 2015/Jontof-Hutter

Planet Masses Measured

with Doppler Follow-up Observations

Kepler/Burke+ 2015/Jontof-Hutter

Detection Biases Complicate

Interpretation of Exoplanet Populations

Especially for objects near threshold of detectability

M. Shabram 2015

Bayesian Modeling of Exoplanet Populations

Population

Parameters

True Planet

Parameters

(radii, masses)

Observationsphotometry, RVs...

Wolfgang, Rogers & Ford 2016

Hierarchical Bayesian Modeling to Infer the

Planetary Mass-Radius Relation

Wolfgang, Rogers & Ford 2016

Hierarchical Modeling of

Exoplanet Populations

Foreman-Mackey et al. 2014

Shabram et al. 2014

Wolfgang et al. 2015

Wolfgang et al. 2016Morehead Ph.D. 2015

Period-Radius DistributionMultiplicity, Inclination &

Duration Distribution

Mass-Eccentricity Distribution

Mass-Radius Distribution (empirical)

Mass-Radius-Flux Distribution (w/ models)

Modeling Exoplanet Populations

Foreman-Mackey et al. 2014

Shabram et al. 2014

Wolfgang et al. 2015

Wolfgang et al. 2016Morehead Ph.D. 2015

Period-Radius DistributionMultiplicity, Inclination &

Duration Distribution

Mass-Eccentricity Distribution

Mass-Radius Distribution (empirical)

Mass-Radius-Flux Distribution (w/ models)

Approximate Bayesian Computing

• ABC is a “Likelihood-free” method

• Replaces specifying likelihood with:

– A forward model

– Defining a distance function between two

sets of observations

– Choosing a tolerance (i.e., maximum

distance that is “close enough”)

ABC in Cartoons

R. Moorehead+ in prep.

Observations

HyperpriorSimulated

data sets

“posterior”


ABC for a Normal Target Distribution

Iterationx

pdf(

x)

pdf(

x)


ABC for a Normal Target Distribution

Iterationx

pdf(

x)

pdf(

x) Iterationmean std dev

Characterizing Distribution of Orbital

Shapes & Inclinations with ABC

• The multiple planet

systems identified

by Kepler are

typically very nearly

coplanar.


Questions?

CyberScience and Hunting for Planets Beyond our Solar System · “Super-Earth” Jupiter Analog...

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