Asteroseismology from solar-like oscillations · Asteroseismology for exoplanet hosts • Determine mass, radius (with some dependence on stellar models) • Constrain age • Constrain

Asteroseismology from solar-like

oscillations

The playing

field

Fitting surface term:

Legacy Kepler data for 16 Cyg A

l = 0

l = 1

l = 3

l = 2

Original: Model S

Modified: replace convection zone

by polytrope with 1 = 5/3

Separation

ratios

Roxburgh & Vorontsov (2003;

A&A 411, 215) Otí Floranes et al. (2005;

MNRAS 356, 671)

Kernels for separations

d02

r02

Otí Floranes et al. (2005; MNRAS 356, 671)

α Centaruri

α Centauri

α Centauri A

(Butler et al, 2004; ApJ 600, L75)

α Centauri B

UVES (VLT) and UCLES (AAT)

Kjeldsen et al. (2005; ApJ 635, 1281)

An initial analysis

Classical variables

(a) Pourbaix et al. (2002)

(b) Pijpers (2003)

(c) Kervella et al. (2003)

α Centauri system

OPAL EOS, OPAL96 opacity, He, Z settling

(Teixeira et al.)

MA: 1.11111 M¯

MB: 0.92828 M¯

X0: 0.71045

Z0: 0.02870

Age: 6.9848 Gyr

α Centauri A

Model

problems?

α Centauri B

A borderline case

Best-fit model

Model with

convective core

16 Cyg

16 Cyg A, full set of Kepler data

l = 0

l = 1

l = 3

l = 2


l = 0

l = 1

l = 3

l = 2


16 Cyg B, full set of Kepler data



Average quantities

16 Cyg A 16 Cyg B

𝑀/𝑀⨀ 1.059 ± 0.016 1.004 ± 0.014

𝑅/𝑅⨀ 1.220 ± 0.006 1.102 ± 0.005

Age (Gyr) 6.67 ± 0.39 7.02 ± 0.34

𝑋0 0.693 ± 0.008 0.696 ± 0.008

𝑍0 0.026 ± 0.001 0.023 ± 0.001

Bootis

The first observations of solar-

like oscillations in a distant star

Kjeldsen et al. (1995; AJ 109, 1313)

Fit to first data

Christensen-Dalsgaard et al. (1995; ApJ 443, L29)

Location in HR diagram

1.6 M¯

1.66 M¯

C-D & Houdek (2010; ApSS 328, 51)

Characteristic

frequencies

N2 'g2½

p(rad ¡ r+r¹) ;

l = 1

l = 2

l = 1

C-D & Houdek (2010;

ApSS 328, 51)

l = 1

l = 0

l = 2

C-D & Houdek (2010;

ApSS 328, 51)

l = 2

l = 0

Surface term for mixed modes

Fit to more

recent data

No surface term

With surface term

Di Mauro & C-D

SONG

μ Hercules

200 nights of SONG observations

μ Hercules

Asteroseismology for exoplanet

hosts • Determine mass, radius (with some

dependence on stellar models)

• Constrain age

• Constrain rotation period and possibly

orientation of rotation axis

Rotational

splitting

Gizon & Solanki (2003; ApJ 589, 1009)

Analysis of Kepler-65

Chaplin et al. (2013; ApJ 766, 101)

Rotationally split peaks, l = 1

Probability distributions

Rotational

splitting

Inclination

Rotation axis in the plane

of the sky

Red giants

Red-giant evolution

Central

hydrogen

burning

Shell hydrogen

burning

Shell hydrogen

burning, and

core helium

burning

Evolution, 2.5 𝑀⊙

Teixeira et al.

The first detection of solar-like

oscillations in a red giant

Frandsen et al. (2002; A&A 394, L5)

Nonradial

oscillations in

red giants

De Ridder et al. (2009; Nature 459, 398)

CoRoT observations

Ophiuchi

MOST

photometry

Barban et al. (2007;

A&A 468, 1033)

2.35 M¯ evolution sequence

+: 5 Myr steps

2.35 M¯ evolution sequence

N2 'g2½

p(rad ¡ r+r¹) ;

Characteristic

frequencies

Mode inertia

+ l = 0

* l = 1

l = 2

l = 3

Eigenfunctions

The CoRoT and Kepler era

A HR diagram in

terms of max

Huber (2012)

Red

clump

Kepler

CoRoT

Beck et al.

Science (2011; 332, 205)

Kepler observations of solar twin

Frequency(mHz)

Pow

er

1 1 1

1 1

0

0

0 0

2 2

2

2

Kepler observations of red giant

Beck et al. (2011; Science 332, 205)

Pe

rio

d s

pa

cin

gs

(se

c)

Obs.

Model

Two types of modes in one star

An sdB star in the core of a red giant

sdB star in

the core of

the red giant

N/2𝜋

𝑆𝑙/2𝜋

l = 2

1

p region g region

Characteristic frequencies, red

giant (1.3 𝑀⨀, 6.2 𝑅⨀)

g-mode period spacings

Mode inertia, red giant

(1.3 𝑀⨀, 6.2 𝑅⨀)

Integrands of inertia, l = 1 (1.3 𝑀⨀, 6.2 𝑅⨀)

g-dominated mode

p-dominated mode

ν = 79.1 μHz

ν = 84.3 μHz

Bedding et al. (Nature, 2011, 471, 608)

Kepler observations

Hydrogen burning

Helium burning


Buoyancy frequencies

Red giant Early He burning

He burning

convective

core

2.5 M¯ , ~70 L¯

End of He burning

Ensemble asteroseismology

Hydrogen shell burning

Helium flash

No helium flash


Red-giant and clump stars

Mosser et al. (2014; A&A 572, L5)

Core rotation in red giants Fine structure

core structure

Hyperfine

structure

Core rotation

Beck et al.

(2012; Nature, 481, 55)

Frequency

Pow

er

l = 1 l = 1 l = 1 l = 0 l = 2

Rotational weight functions

Beck et al.(2012; Nature, 481, 55)

Rotational

splitting

weight

l = 2

l = 2

l = 1

l = 1


Fast rotation of the stellar core

• More g-dominated dipolar modes show

larger splitting

• More g-dominated dipolar modes have

smaller βnl

• For more g-dominated dipolar modes the

weight is dominated by the stellar core

[The data are] compatible with a core

rotating ten times faster than the surface


Ensemble rotation

Mosser et al. (2013; A&A 548, A10)

Rotation evolution

With no angular momentum transport,

angular momentum J is locally conserved

1.1 𝑀⊙

m/M = 1 .5

.3

.2

.1

.15

𝑟𝑠ℎ𝑒𝑙𝑙

Modelling core rotation

No additional transport

Eggenberger et al. (2012; A&A 544, L4)

1.5 M¯

Evolved to 12.6 L¯

Bottom of

convective envelope He core

Observed value: ~ 0.5 μHz

Angular-momentum transport

• Turbulence

• Circulation (driven by rotation)

• Magnetic fields (primordial or dynamo-

generated)

• Gravity waves

Not enough!

Rotation evolution

Cantiello et al. (2014; ApJ 788, 93)

Observations

Core rotation period

TS: Tayler-Spruit dynamo

Rotation evolution

Cantiello et al. (2014; ApJ 788, 93)

Observations

Core rotation period

TS: Tayler-Spruit dynamo

Documents

Asteroseismology from solar-like oscillations · Asteroseismology for exoplanet hosts • Determine mass, radius (with some dependence on stellar models) • Constrain age • Constrain