Measuring Stellar Properties with Asteroseismology and Interferometry

Tim White Georg-August-Universität Göttingen

Solar-Seminar – Max Planck Instutut für Sonnensystemforschung – 29 April 2014

Kepler-186f

NASA Ames/SETI Institute/JPL-Caltech

• Show cover of Science article, transit.

• This planet is interesting because it is in the habitable zone and Earth-sized.

• How do we know it’s Earth-sized?

Science, April 18 2014, Vol 344, Page 277

R*=0.472±0.052 R

Rplanet=1.11±0.14 R

Planet Validation

Seager & Mallen-Ornélas 2003

Galaxy Formation

E. L. Wright (UCLA), The COBE Project, DIRBE, NASA

Source: Ivan Baldry Samland & Gerhard, 2003

Asteroseismology

Arentoft et al. 2008

figure by Daniel Huber

figure by Daniel Huber

figure by Daniel Huber

figure by Daniel Huber

Huber et al. 2011, ApJ, 743, 143

16 Cyg A

The Sun

Δν

νmax

From oscillations to stellar parameters

1) Scaling relations 2) Grid method 3) Detailed modelling

M, R, age

Δν, νmax [Fe/H] log(g)

Teff

ν1,…, νn [Fe/H] log(g) Teff, ...

M, R, age

Difficulty Precision

M, R

Δν νmax Teff

21

3

/

R

Mν

eff2ac

TR

Mνν max

Ideal gas Adiabatic Oscillations Isothermal Atmosphere

Tassoul (1980) Brown et al. (1991)

1) Scaling relations

Why care about scaling relations?

21

3

/

R

Mν

eff2ac

TR

Mνν max

• They tell you

– Density

– Surface gravity

– Radius

– Mass

Without the need for detailed modelling!

Why care about scaling relations?

From oscillations to stellar parameters

1) Scaling relations 2) Grid method 3) Detailed modelling

M, R, age

Δν, νmax [Fe/H] log(g)

Teff

ν1,…, νn [Fe/H] log(g) Teff, ...

M, R, age

Difficulty Precision

M, R

Δν νmax Teff

Huber et al. 2011, ApJ, 743, 143

A lot

From oscillations to stellar parameters

1) Scaling relations 2) Grid method 3) Detailed modelling

M, R, age

Δν, νmax [Fe/H] log(g)

Teff

ν1,…, νn [Fe/H] log(g) Teff, ...

M, R, age

Difficulty Precision

M, R

Δν νmax Teff

Kepler-21 Howell et al. 2012

Δν = 60.86 ± 0.55 μHz νmax = 1153 ± 32 μHz

Kepler-36 Carter et al. 2012

Δν = 67.9 ± 1.2 μHz νmax = 1250 ± 44 μHz

KIC 11772920 From the ensemble in Chaplin et al. 2011

Δν = 158.6± 3.6 μHz νmax = 3800 ±100 μHz

Frequency (μHz)

PSD

(p

pm

2 μ

Hz-1

)

8/LC artifact

Verifying Transiting Planets

• Can infer stellar density through shape of the transit light curve (Seager & Mallen-Ornélas 2003)

• Asterodensity profiling (e.g. Kipping 2014)

• Does asteroseismic density = transit density?

Asteroseismic density Inferred transit density

(Sliski & Kipping 2014)

Population Studies: CoRoT Giants

Mass

Frac

tio

n

Miglio et al. 2013

Simulations

Scaling relations Scaling relations

Population Studies:

Chaplin et al. 2011

Scaling relations Population synthesis modelling

Kepler Dwarfs

But can we trust the scaling relations?

Population Studies:

Chaplin et al. 2011

Scaling relations Population synthesis modelling

Kepler Dwarfs

But can we trust the scaling relations?

Two ways to check:

1.Stellar models

2.Independent observations

Density

Surface gravity

Mass

Radius

Models

• Make a grid of stellar models and determine their oscillation frequencies.

• For each model we know M and R.

• For each model we can measure Δν

• Is ?

21

3

/

R

Mν

White et al. 2011

White et al. 2011

Mass 0.7 M

2.0 M

• Observed frequencies are not high enough

• Departures from homology

Why not?

So Δνobs is not equal to

Mass 0.7 M

2.0 M

[Fe/H] -0.9 +0.5

[Fe/H] -0.9 +0.5

[Fe/H] -0.9 +0.5

Scatter in metallicity

[Fe/H] -0.9 +0.5

Scatter in mass

But can we trust the scaling relations?

Two ways to check:

1.Stellar models

2.Independent observations

Independent Measurements

• Interferometric radii

• Dynamical masses

• Transit densities

Interferometry Point source

Interferometry Point source

Interferometry Point source Resolved disc

Fringe visibility is a function of source size, baseline length, and wavelength

Visibility

0.2 mas

0.5 mas 1.5 mas

λ

B

PAVO at the CHARA Array

0.2 mas

0.5 mas 1.5 mas

λ

B

PAVO (visible)

MIRC (infrared)

θLD = 0.753±0.009 mas R = 1.48±0.02 R

White et al. 2013

Interferometry of Kepler and CoRoT stars

Huber et al. 2012

Asteroseismology of Kepler and CoRoT stars

Huber et al. 2012

Density

Surface gravity

Mass

Radius

Huber et al. 2012

Giants dominated by parallax uncertainties

Measured Radius

From scaling relations

16 Cyg

16 Cyg A

16 Cyg B

Metcalfe et al. 2012

θLD = 0.539±0.007 mas R = 1.22±0.02 R

White et al. 2013

θLD = 0.490±0.006 mas R = 1.12±0.02 R

White et al. 2013

Huber et al. 2012

Measured Radius

From scaling relations

White et al. 2013

PAVO (visible)

MIRC (infrared)

θLD = 0.753±0.009 mas R = 1.48±0.02 R

White et al. 2013

θ Cyg

Guzik et al. 2011

Let’s have another look at the Δν scaling relation

using the brightest stars with

independent measurements of mass and radius

α Cen A R=1.225±0.004 R

(interf. + parallax, Kervella et al. 2003, Söderhjelm 1999)

M=1.105±0.007 M (binary orbit, Pourbaix et al. 2002)

Δν = 105.7±0.3 μHz (Bedding et al. 2004)

α Cen B R=0.864±0.005 R

(interf. + parallax, Kervella et al. 2003, Söderhjelm 1999)

M=0.934±0.006 M (binary orbit, Pourbaix et al. 2002)

Δν = 161.7±0.2 μHz (Kjeldsen et al. 2005)

Procyon A R=2.059±0.015 R

(interf. + parallax, Kervella et al. 2004, van Leeuwen 2007)

M=1.461±0.025 M (binary orbit, Girard et al. 2000, Gatewood & Han 2006)

Δν = 55.9±0.3 μHz (Bedding et al. 2010)

TrES-2 (Kepler-1) ρ=1.105±0.011 ρ

(transit, Southworth, 2011)

Δν = 141.0±1.4 μHz (Huber et al. 2013)

HAT-P-7 (Kepler-2) ρ=0.2023±0.0024 ρ

(transit, Southworth, 2011)

Δν = 59.2±0.6 μHz (Huber et al. 2013)

HD 17156

Δν = 83.44±0.15 μHz (Gilliland et al. 2011) 2011) al. et Nutzman (transit, ρ3710 0150

0130.

..

ρ

16 Cyg A R=1.22±0.02 R

(interf. + parallax, White et al. 2013, van Leeuwen 2007)

M=1.06±0.03 M (H-R diagram, Casagrande et al. 2011)

Δν = 103.5±0.1 μHz (Metcalfe et al. 2012)

16 Cyg B R=1.12±0.02 R

(interf. + parallax, White et al. 2013, van Leeuwen 2007)

M=1.04±0.04 M (H-R diagram, Casagrande et al. 2011)

Δν = 117.0±0.1 μHz (Metcalfe et al. 2012)

θ Cyg R=1.49±0.02 R

(interf. + para., White et al. 2013, van Leeuwen 2007)

M=1.39±0.02 M (H-R diagram, Casagrande et al. 2011)

Δν = 84.0±0.4 μHz (Guzik et al. 2011)

Giants?

Huber et al. 2012

Giants dominated by parallax uncertainties

Measured Radius

From scaling relations

KIC 8410637

• Giant in an eclipsing binary (Hekker et al. 2010)

– Δν = 4.57 ± 0.03 μHz

• Mass and radius determined by Frandsen et al. 2013

– M = 1.557 ± 0.028 M

– R = 10.74 ± 0.11 R

KIC 8410637

What we need:

We need the brightest stars with the best measurements.

• Better parallaxes Gaia

• Asteroseismology of nearby, bright stars K2, SONG, TESS, PLATO

• Interferometry AO system at CHARA

• Dynamical masses