Status of solar and stellar modelling

Jørgen Christensen-Dalsgaard

Stellar Astrophysics Centre

Aarhus University

Excellent?

Excellent?

Probably poor!

What kind of models?

• Model of eclipsing-binary system

• Stellar atmospheric model

• Models of convection-zone dynamics

• Dynamo models of stellar activity

• Flare models

• Oscillation background model

• Models of stellar structure and evolution

• Models of stellar oscillations

SELECTED PROBLEMS

• Numerical accuracy of model computations

• Consistency between evolution codes

• Microphysics (equation of state, opacity, …)

SELECTED PROBLEMS • Numerical accuracy of model computations

• Consistency between evolution codes

• Microphysics (equation of state, opacity, …)

• Stellar hydrodynamics

– Near-surface convection

– Convective overshoot

– Rotational mixing

– Evolution of rotation

– Effects of rotation on oscillations

SELECTED PROBLEMS • Numerical accuracy of model computations

• Consistency between evolution codes

• Microphysics (equation of state, opacity, …)

• Stellar hydrodynamics

– Near-surface convection

– Convective overshoot

– Rotational mixing

– Evolution of rotation

– Effects of rotation on oscillations

• Stellar magneto-hydrodynamics!!

A part of the problem Transport processes

Mathis (2010; AN 331, 883)

Can helio- and asteroseismology

help?

Can helio- and asteroseismology

help?

Probably!

Kawaler: Harmonious stars can upset the false harmony

of our models

Relevant data • Eclipsing binaries

• ‘Classical’ stellar data (log g, Teff, composition, …)

– Note: very well known for the Sun, including age (although composition??)

• Surface rotation

• Surface magnetic field

• Stellar ‘noise’ background

• Oscillation data

– Frequencies

– Frequency combinations

– Excitation

– Amplitude ratios, phase differences

Kawaler

Kawaler

An old opacity correction

C-D & Petersen (~1992) Also talk by Salmon

Los Alamos

Livermore

Another opacity problem?

Dziembowski & Pamyatnykh (2008; MNRAS 385, 2061)

Approach to diffusive equilibrium in sdB stars

log HB age

(years)

Stable modes

Unstable modes

Nonadiabatic

asteroseismology

Fontaine et al. (2006;

Mem. S. A. It. 77, 49)

5.25

Unstable modes in sdB star

Stable modes

Unstable modes

Fontaine et al. (2006;

Mem. S. A. It. 77, 49)

log HB age(years)

No relativistic effects

Relativistic electrons in the Sun

Elliot & Kosovichev (1998; ApJ 500, L199)

No relativistic effects Including relativistic effects

Relativistic electrons in the Sun

Elliot & Kosovichev (1998; ApJ 500, L199)

Sun - model

Model S: C-D et al. (1996; Science 272, 1286)

New surface composition

Model S

AGS05

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

AGSS09

Can opacity corrections solve the problem?

AGS05

AGSS09

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

Inferred solar internal rotation

Base of

convection

zone

Tachocline

Near solid-

body

rotation of

interior

Chaplin et al. (2011; Science 332, 213)

Stars with solar-like oscillations, from Kepler

Solar near-twins: 16 Cygni

Metcalfe et al. (2012; ApJ 748, L10)

A

B

Required precision

Strassmeier: Signal amplitude Signal precision Asteroseismic equivalent: Effect on frequency Frequency error

Sharp features in stellar models

HeII ionization

No overshoot

With overshoot

Effect of acoustic glitches

Very crudely

¿g

He II

BCZ

He I

Houdek & Gough (2007;

MNRAS 375, 861)

Fit to acoustic glitches

Fit

Diffusion

No diffusion

2 M¯

Growing convective cores

X

Diagnostics of a small convective core

1.3 M¯

0.25 Gyr

5.25 Gyr

Cunha & Metcalfe (2007; ApJ 666, 413)

Diagnostics of a small convective core

1.3 M¯

Cunha & Metcalfe (2007; ApJ 666,413)

g-mode period spacings

Miglio et al. (2008; MNRAS 386, 1487)

Observed period variations

SPB star

» 7 M¯

Degroote et al. (2010; Nature 464, 259)

Beck et al.

(2012; Nature, 481, 55)

Frequency

Po

we

r

Into the heart of a giant Fine structure ¢P: core structure

l = 1 l = 2

l = 0

Two types of oscillations in one star

p-mode behaviour

g-mode behaviour

Red giants: adiabatic frequencies

Dziembowski et al. 2001; Christensen-Dalsgaard, 2004

Eggenberger et al. 2010; Dupret et al 2010; Mazumdar et al. 2010

Modes trapped in the envelope (low E)

acoustic dominant

character

Modes trapped in the center

(high E)

g dominant character

Montalbán

Evolution of a 1.5 Msun

Montalbán

Evolution of a 1.5 Msun

Montalbán

Evolution of a 1.5 Msun

Montalbán

RedG evolution of a 1.5 Msun

Montalbán

RedG evolution of a 1.5 Msun

DP ~ 20-60s

Montalbán

RedG evolution of a 1.5 Msun

DP ~ 180-240s

Montalbán

Echelle Diagram : RC vs RGB

M=1.5 Msun

RC

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

RGB

Montalbán

Period spacing in red giants

Core Helium

burning phase

H-shell burning

RGB

Bedding et al. 2011

Kepler

CoRoT Mosser et al. 2011

Montalbán

KIC7341231, an unevolved red giant

[Fe/H] = -1 M/M¯ = 0.836 R/R¯ = 2.62 Age = 12.2 Gyr

Deheuvels et al. (2012; ApJ 756, 19)

Rotational splitting

Deheuvels et al. (2012; ApJ 756, 19)

Fitted rotational splittings

Solid-body rotation /2¼= 328 nHz Two-zone model Convective envelope, radiative core c/2¼= 696 nHz e/2¼= 51 nHz

Deheuvels et al. (2012; ApJ 756, 19)

Into the heart of a giant Fine structure

core structure

Hyperfine

structure

Core rotation

Beck et al.

(2012; Nature, 481, 55):

Core rotates at least

at 10 times

the surface rate

Frequency

Pow

er

Fitting individual frequencies

• Characterize model by set of parameters

– P = {M, age, Z0, Y0, ®ML, ®OV, …}

• Compute frequencies

• Minimize

• If min(χ2) >> 1 something is wrong with

– Model: interesting

– Data errors: a little boring

Dealing with large χ2: inversion?

• No adequate model within the given set, specified by the parameters

• Determine corrections to best-fitting model

• Identify origin of discrepancies in physical terms

Challenges

• Improve stellar modelling

• Develop probes that are sensitive to potential problems with the stellar models

– Location of glitches

– Frequency region of unstable modes

• Test the significance of identified problems

• Provide additional observational data, further to constrain the models

Prospects

• Improved asteroseismic data: more accurate frequencies, modes at lower frequencies, broader range of stars – Further extend CoRoT and Kepler

– BRITE

– TESS?

– PlanetVision?

– PLATO?

– SONG

Prospects

• Improved asteroseismic data: more accurate frequencies, modes at lower frequencies, broader range of stars – Further extend CoRoT and Kepler

– BRITE

– TESS?

– PlanetVision?

– PLATO?

– SONG

2012

2013

Hail to the chief

Hail to the chief