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

What are solar-like oscillations? Linearly damped Stochastically excited Found in very non-solar-like stars

Where it all started Grec et al., Nature 288, 541; 1980

Basic properties of oscillations Behave like spherical harmonics: P l m (cos  ) cos(m  -  t) k h = 2  / h = [l(l+1)] 1/2 /r

Asymptotics of frequencies Acoustic-wave dispersion relation Hence Lower turning point r t where k r = 0:

Rays

More rays

Inversion with rays

The probe of the solar interior SOHO

Observing a Doppler image

VIRGO on SOHO (whole-disk): Data on solar oscillations Observations: MDI on SOHO

Observed frequencies m-averaged frequencies from MDI instrument on SOHO 1000  error bars

KNOWN `GLOBAL' PROPERTIES OF THE SUN Total mass M ¯ (assume no mass loss) Present surface radius R ¯ Present surface luminosity L ¯ (assuming isotropic radiation) Present age (depending slightly on models of solar-system formation) Present surface heavy-element composition, relative to hydrogen, (somewhat uncertain). Composition not known for helium

CALIBRATION OF SOLAR MODELS Adjust initial helium abundance Y 0 to obtain the observed present luminosity Adjust initial heavy-element abundance Z 0 to obtain observed present ratio Z s /X s Adjust parameter of convection treatment (e.g. mixing-length parameter  c ) to obtain observed present radius.

A reference solar model Model 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 dependence on solar structure Frequencies depend on dynamical quantities: However, from hydrostatic equilibrium and Poisson’s equation p and g can be determined from  Hence adiabatic oscillations are fully characterized by or, equivalently

Frequency differences, Sun - model

No settling The solar internal sound speed No settling Including settling Sun - model

The solar internal sound speed Sun - 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 effects Including relativistic effects Relativistic electrons in the Sun Elliot & Kosovichev (1998; ApJ 500, L199)

 MHD Testing solar thermodynamics  OPAL Basu, Dappen & Nayfonov (1999; ApJ 518, 985)

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 Tachocline Near 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 flows Rotation 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

Solar internal dynamics Rachel Howe

Local helioseismology Time-distance helioseismology Ring-diagram analysis Helioseismic holography Tomography of three-dimensional, time-dependent properties of solar interior

Rays for local helioseismology Recent Results and Theoretical Advances in Local Helioseismology", T.L. Duvall Jr., in proceedings of the SOHO6/GONG meeting in Boston, June 1998.

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

Supergranular flows Kosovichev (1996; ApJ 461, L55)

Supergranular flows Kosovichev (1996; ApJ 461, L55)

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

[Local inferred soundspeed]

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:

Small frequency separations α Cen B α Cen A : A : B

Also, small separation affected by details of outer parts of the star. Roxburgh & Vorontsov suggested considering ratios such as Note that  nl and  nl share the frequency scaling: Scaling of small separation Solar core, different outer layers

Echelle diagram

Asteroseismic HR diagram

Scaled asteroseismic HR diagram

Near-surface frequency effects Stellar structure and oscillation modelling deal inadequately with Treatment of convection in modelling (thermal structure, turbulent pressure) Mode damping excitation Dynamical effects of convection on oscillations Atmospheric structure These effects are concentrated very near the surface

Near-surface effects (II) General frequency differences between star and model can be represented as Note: Near-surface effects are contained in H 2 Solar data, l = Solar data, l =

Near-surface effects (III) From solar observations over a range of degrees, H 2 (¯) ( ) is known. Can that be used for other stars, somehow? Use as ansatz On physical grounds we expect

Mode damping Likely conclusion (Gough; Balmforth; Houdek et al.): observed modes are linearly damped. Hence externally driven. Growth rate: Note: Convection enters in  p t and F = F r + F c

Stochastic excitation Goldreich & Keeley (1977):

Issues of lifetime Strong variation appears inconsistent with modelling (e.g. Houdek et al. 1999) Sun3 d α Cen B3 d α Cen A1.5 d 2.7 d Procyon1.3 d~2.5 d β Hydri0.6 d~2 d Observations, analysis: Kjeldsen et al. (2003, 2004); Bedding et al. (2004). Based on frequency scatter, in observations and corresponding simulations. Hence there must be contributions to damping, so far ignored. Observation Model

Some solar-like pulsators

The present situation Bedding & Kjeldsen (2003)

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/ )

α Centauri A Bedding et al., ApJ, in press ( astro-ph/ ) Observed echelle diagram

Finding peaks

α Centauri B CORALIE, La Silla (Carrier & Bourban 2003; A&A 406, L23)

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 system Observable 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.) M A : M ¯ M B : M ¯ X 0 : Z 0 : Age: Gyr

α Centauri system OPAL EOS, OPAL96 opacity, He, Z settling (Teixeira et al.) M A : M ¯ M B : M ¯ X 0 : Z 0 : Age: 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

η Bootis

Observed power spectrum Kjeldsen et al. (1995)

Evolutionary state 1.66 M ¯ 1.6 M ¯ Pre-Hipparcos Post- Hipparcos

Characteristic frequencies Buoyancy frequency: Acoustic frequency

Mode trapping N, Sun S1S1 N,  Boo S2S2

Mode trapping Typical observed frequency

Mixed modes

Echelle diagram Di Mauro et al. (2003) ◦ : 0 ∆ : 1 □ : 2 ◊ : 3

ξ Hydrae

Stello et al.

Evolutionary state Teixeira et al. Ticks for every 5 Myr Core He burning

Typical observed frequency Mode trapping

ξ Hydrae

A / E -1/2 l = 0 l = 2 l = 1

Semiregular variables

MirasSemiregular variables AAVSO observations. Mattei et al. (1997)

Statistics of stochastically excited oscillators Energy is exponentially distributed. Hence amplitude distribution is

The future (I) ESO Very Large Telescope UVES spectrograph ESO 3.6 m + HARPS + HARPS clone?

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

The future? Rømer: a Danish micro-satellite project

The future????? Eddington: the obvious next step in asteroseismology