Asteroseismology of solar-type stars

Jørgen Christensen-Dalsgaard

Institut for Fysik og Astronomi, Aarhus Universitet

Dansk AsteroSeismologisk Center

Solarlike pulsators

Mode damping

Damping rate: amplitude / exp( t), with

Perturbation in convective flux and effect of turbulent pressure perturbation 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 diagramPresent Sun

25 years ago:the start of global helioseismology

Now: the start of solar-like asteroseismology

Cen A (Bedding et al. 2004; ApJ 614, 380)

The observational breakthrough

ESO Very Large Telescope

UVES spectrograph

ESO 3.6 m + HARPS+ HARPS clone?

Very stable spectrographs, motivated by search for exo-planets

The slightly out-of-date situation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; ApJ 600, L75)

α Centauri A

VLT(UVES) and AAT(UCLES)

optimally combined

Bedding et al. (2004; ApJ 614, 380)

α Centauri B

UVES (VLT) and UCLES (AAT)

Kjeldsen et al. (2005; submitted to ApJ)

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 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

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

1.66 M¯

1.6 M¯

Pre-Hipparcos

Post-Hipparcos

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

Mode trapping

N, Sun

S1

N, Boo

S2

Mixed modes

Echelle diagram

Di Mauro et al. (2003; Astron. Astrophys. 404, 341)

◦ : 0∆ : 1

□ : 2

◊ : 3

Semiregular variables

Semiregular variables

MirasSemiregular variables

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; ApJ 562, L141)

Large-scale surveys

Kiss & Bedding (2003; MNRAS 343, L79)

OGLE-II observations of LMC

(Colour indicates J - K)

AGB

RGB