Asteroseismology of solartype stars Jrgen ChristensenDalsgaard Institut for

Asteroseismology of solar-type stars Jørgen Christensen-Dalsgaard Institut for Fysik og Astronomi, Aarhus Universitet Dansk Astero. Seismologisk Center

Solarlike pulsators

Mode damping Damping rate: amplitude / exp( t), with Perturbation in convective flux and effect of turbulent pressure perturbation d pt appear to yield negative , i. e. , damped modes

Characteristics of solar-like oscillations • Intrinsically damped by the effects of convection • Stochastically excited by the effects of convection • Typically very small amplitudes (20 cm/sec or 5 ppm for main-sequence stars) Found in stars that are not very solar-like

Asymptotics of low-degree p modes Large frequency separation:

Small frequency separations

Echelle diagram Present Sun

25 years ago: the start of global helioseismology

Now: the start of solar-like asteroseismology a Cen A (Bedding et al. 2004; Ap. J 614, 380)

The observational breakthrough Very stable spectrographs, motivated by search for exo-planets ESO Very Large Telescope UVES spectrograph ESO 3. 6 m + HARPS clone?

The slightly out -of-date situation Bedding & Kjeldsen (2003; Publ. Astron. Soc. Australia 20, 203)

α Centauri A

α Centauri A Observations with UVES on VLT (Butler et al, 2004; Ap. J 600, L 75)

α Centauri A VLT(UVES) and AAT(UCLES) optimally combined Bedding et al. (2004; Ap. J 614, 380)

α Centauri B UVES (VLT) and UCLES (AAT) Kjeldsen et al. (2005; submitted to Ap. J)

Classical observables (a) Pourbaix et al. (2002; Astron. Astrophys. 386, 280) (b) Pijpers (2003; Astron. Astrophys. 400, 241) (c) Kervella et al. (2003; Astron. Astrophys. 404 1087)

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 MA: 1. 11111 M¯ MB: 0. 92828 M¯ X 0: 0. 71045 Z 0: 0. 02870 Age: 6. 9848 Gyr OPAL EOS, OPAL 96 opacity, He, Z settling (Teixeira et al. )

A borderline case Best-fit model Model with convective core

α Centauri A Model problems?

α Centauri B

η Bootis

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

Evolutionary state Pre-Hipparcos Post. Hipparcos 1. 66 M¯ 1. 6 M¯ Christensen-Dalsgaard et al. (1995; Ap. J 443, L 29)

Mode trapping N, Boo S 2 N, Sun S 1

Mixed modes

Echelle diagram ◦ : 0 ∆: 1 □: 2 ◊: 3 Di Mauro et al. (2003; Astron. Astrophys. 404, 341)

Semiregular variables

Semiregular variables Miras AAVSO observations. Mattei et al. (1997; ESA SP-402, 269)

Statistics of stochastically excited oscillators Energy is exponentially distributed. Hence amplitude distribution is Christensen-Dalsgaard et al. (2001; Ap. J 562, L 141)

Large-scale surveys OGLE-II observations of LMC AGB RGB Kiss & Bedding (2003; MNRAS 343, L 79) (Colour indicates J - K)