Seismology of the Sun and solar-like stars

Jørgen Christensen-Dalsgaard

Institut for Fysik og Astronomi, Aarhus Universitet

Collaborators

• M. J. Thompson• R. Howe• J. Schou• S. Basu• R. M. Larsen• J. M. Jensen

• Hans Kjeldsen• Teresa Teixeira• Tim Bedding • Maria Pia Di Mauro• Andrea Miglio

Where it all started

Grec et al., Nature 288, 541; 1980

Basic properties of oscillations

•Behave like spherical harmonics: Plm(cos ) cos(m - t)

•kh = 2 / h = [l(l+1)]1/2/r

Asymptotics of frequenciesAcoustic-wave dispersion relation

Hence

Lower turning point rt where kr = 0:

Rays

Inversion with rays

Observing a Doppler image

VIRGO on SOHO (whole-disk):

Data on solar oscillationsObservations:

MDI on SOHO

Observed frequencies

m-averaged frequencies from MDI instrument on SOHO

1000 error bars

A reference solar modelModel S:

•OPAL96 equation of state

•OPAL 92 opacities

•Nuclear parameters from Bahcall & Pinsonneault (1994)

•Diffusion and settling of helium and heavy elements from Michaud & Proffitt (1993)

•Mixing-length theory of convection

Frequency differences, Sun - model

No settling

The solar internal sound speed

No settling

Including settling

Sun - model

The solar internal sound speedSun - model

Changes in composition

The evolution of stars is controlled by the changes in their interior composition:

• Nuclear reactions

• Convective mixing

• Molecular diffusion and settling

• Circulation and other mixing processes outside convection zones

Nuclear burning

Settling

No relativistic effectsIncluding relativistic effects

Relativistic electrons in the Sun

Elliot & Kosovichev (1998; ApJ 500, L199)

Improvements:

•Non-LTE analysis

•3D atmosphere models

Consistent abundance determinations for a variety of indicators

Revision of solar surface abundances

Asplund et al. (2004; A&A 417, 751):Pijpers, Houdek et al.

Model S

Z = 0.015

How do we correct the models?

Basu & Antia (2004; ApJ 606 L85): an opacity increase to compensate for lower Z is required

Seaton & Badnell (submitted): recent Opacity Project results do indicate such an increase over the OPAL values.

Rotational splitting

Kernels for rotational splitting

Inferred solar internal rotation

Base of convection

zone

TachoclineNear solid-

body rotation of

interior

Rotation of the solar interior

BiSON and LOWL data; Chaplin et al. (1999; MNRAS 308, 405)

Tachocline oscillations

See Howe et al. (2000; Science 287, 2456)

● GONG-RLS

▲MDI-RLS

∆ MDI-OLA

Zonal flowsRotation rate - average value at solar minimum

Vorontsov et al. (2002; Science 296, 101)

Radial development of zonal flows

Howe et al., in preparation

Observed and modelled dynamics

6 1/2 year MDI inversion, enforcing 11-yr periodicity

Vorontsov et al.

Non-linear mean-field solar dynamo models

Covas, Tavakol and Moss

Local helioseismology

• Time-distance helioseismology

• Ring-diagram analysis

• Helioseismic holography

Tomography of three-dimensional,

time-dependent properties of solar interior

Rays for local helioseismology

Kosovichev et al. (2000; Solar Phys. 192, 159)

Near-surface flows

Time-distance analysis; Beck et al. (2002; ApJ 575, L47)

Meridional component

Zonal component

16:00 11 Jan 98

00:00 12 Jan 98

08:00 12 Jan 98

Emerging active region

Kosovichev et al. (2000; Solar Phys. 192, 159

Far-side imaging

Lindsey & Braun (2000; Science 287, 1799)

Far-side monitoring

MDI on SOHO

From the Sun to the stars

What we expect:the solar case

Grec et al., Nature 288, 541; 1980

Asymptotics of p modes

Large frequency separation:

Small frequency separations

Frequency separations:

Asteroseismic HR diagram

The present situation

Bedding & Kjeldsen (2003)

α Centauri A

α Centauri A

Observations with UVES on VLT

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

α Centauri A

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

α Centauri A

VLT(UVES) and AAT(UCLES)

optimally combined

Bedding et al., ApJ, in press (astro-ph/0406471 )

α Centauri B

UVES (VLT) and UCLES (AAT)

Kjeldsen et al. (in preparation)

Classical variables

(a) Pourbaix et al. (2002)

(b) Pijpers (2003)

(c) Kervella et al. (2003)

Fitting the α Cen systemObservable quantities for the system

Model parameters:

Fit using Marquardt method, with centred differences, using an 8-processor Linux cluster, implemented by T. C. Teixeira

Choice of oscillation variables, from Bedding et al. fits to Butler et al. observations:

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 system

: A: B

α Centauri A

Observations: use Bedding et al. fits

Models: surf = 0.75

α Centauri B

Observations: use Bedding et al. fits

Models: surf = 0.75

α Centauri A

Observations: use Bedding et al. fits

Models: surf = 0.75

α Centauri B

Observations: use Bedding et al. fits

Models: surf = 0.75

Procyon

Radial-velocity observations

Brown et al. (1991; ApJ 368, 599)

Martić et al. (2004; A&A 418, 295)

MOST results

Matthews et al. (2004; Nature 430, 51 – July 1)

An interpretation of the MOST results

Kjeldsen simulations:

• 1.5 times solar granulation

•Stochastic excitation

•1.9 days lifetime of modes

• Amplitude scaled from velocity observations

No noise

MOST signal level

ξ Hydrae

ξ Hydrae

Stello et al.

Evolutionary state

Teixeira et al.

Ticks for every 5 Myr

Core He burning

The future

COROT (France, ESA, ...); launch 2006

The future?????

Eddington: the obvious next step in asteroseismology