A NEW ASTEROSEISMIC PROBE

OF STELLAR STRUCTURE Jadwiga Daszyska-Daszkiewicz Instytut Astronomiczny, Uniwersytet Wrocawski, POLAND

Collaborators: Wojtek Dziembowski , Alosha Pamyatnykh29 June 2006, Ondejov

PULSATING STARS CAN BE FOUND

ACCROS THE WHOLE HR DIAGRAM

J. Christensen-Dalsgaard

INSTABILITY DOMAINS IN THE MAIN SEQUENCEA. Pamyatnykh

Sir Arthur Eddington (1882 1944)

At first sight it would seem that the deep interior of the sunand stars is less accessibleto scientific investigation thanany other region of the universe.

HOW CAN WE STUDY STELLAR INTERIOS ?

OSCILLATION FREQUENCIES

ASTEROSEISMOLOGY

A way of constraining stellar parameters.Verification of stellar evolution theory.

We can compare observed frequencies, j,obs ,and their properties with theoretical values, j,cal .

Time is the most accurately measured physical parameter !

MODE IDENTIFICATIONFor a given frequency, nm , we have to determine three quantum numbers: n, , m

n the radial order, n=0,1,2,...

- the spherical harmonic degree, =0,1,2,

m the azimuthal order, |m|

n the number of nodes in the radial direction

- the total number of nodal lines on the surface

m - the number of nodal lines perpendicular to the equator

-|m| - the number of nodal lines parallel to the equator

Radial pulsation with n=2

C. Schrijvers

= 1, m=0 = 1, m=1 Tim Bedding

= 2, m=1 = 2, m=2 Tim Bedding

= 3, m=0 = 3, m=1 = 3, m=2 = 3, m=3 Tim Bedding

= 5, m=0 = 5, m=2 = 5, m=3 Tim Bedding

= 8, m=1 = 8, m=2 = 8, m=3 Tim Bedding

In the case of Sun we get mode identifications from asymptotic relations: large and small separations.

Small section of the solar amplitude spectrum with (n, l) values for each mode. The large and small separations are indicated.Bedding& Kjeldsen, PASA, 2003, 20, 203

and measure the average density and core composition, respectively.

Thus the mass and age of a star.

In Sct, SPB and Cep stars we do not observe such

structures and more sophisticated methods are needed.

Cep

Sct

PS -- parameters of the model: the initial values of M0, X0, Z0, the angular momentum (or Vrot,0 ), age (or logTeff ) SEISMIC MODEL OF THE STAR

j,obs=j,cal(nj , j , mj , PS ,PT)PT -- free parameters of the theory:convection (e.g. MLT parameter ), overshooting distance,parameters describing mass loss angular momentum evolutionmagnetic field

The fit quality is measured by

2 = 1/J (obs -cal )2/ 2obs

where J is the number of modes in the data set.

For seismic models of the Sun we have 2 ~1

We are far from such good fits in asteroseismology.

Eridani the most multimodal Cep star the best seismic informationEXAMPLE:

OSCILLATION SPECTRUM OF ERIPamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS 350, 1022

MODE IDENTIFICATION

1=5.7632 c/d =0, p1 2=5.6539, 3=5.6200, 4=5.6372 =1, g1

5=7.8986 =1, p2

6=6.2448, 7=6.2623, 9=6.2230 =1, p1

8=7.2006 =2 (?)

SEISMIC MODEL OF ERIPamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS 350, 1022

Pamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS 350, 1022

Eri, evolutionary tracks, OPALPamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS 350, 1022

NEW ASTEROSEISMIC TOOL

linear nonadiabatic theory of stellar pulsationf parameter - the ratio of the relative luminosity variation to the relative radial displacement of the surface

f values are very sensitive to:

mean stellar parameters

stellar convection

opacity data

nm interior

f subphotospheric layer

THE METHOD OF SIMULTANEOUS

EXTRACTING AND f FROM OBSERVATIONS

MULTICOLOUR PHOTOMETRY AND RADIAL VELOCITY DATA

AMPLITUDE OF MONOCHROMATIC FLUX VARIATIONS

Derivatives of the monochromatic flux, F(Teff ,g), are calculatedfrom static atmosphere models (Kurucz, NEMO2003).

h(Teff ,g) - limb-darkening coefficient from nonlinear law (Claret, Barban)

THE METHOD 2 minimization assuming trial values of

A set of observational equations for a number of passbands (1)

RADIAL VELOCITY (the first moment of the spectral line variations)(2)

quantities to be determinedEach passband, , yields r.h.s. of equations (1).

Measurements of the radial velocity yield r.h.s. of equation (2). The equations are solved by LS method for specified .

SCUTI STARSJ. Daszyska-Daszkiewicz, W. A. Dziembowski, A. A. Pamyatnykh, 2003, A&A 407, 999J. Daszyska-Daszkiewicz, W.A. Dziembowski, A.A.Pamyatnykh, 2004, ASP Conf. Series 310, 255J. Daszynska-Daszkiewicz, W. A. Dziembowski, A. A. Pamyatnykh, M. Breger, W. Zima, 2004,IAUS 224, 853J. Daszynska-Daszkiewicz, W. A. Dziembowski, A. A. Pamyatnykh,M. Breger, W. Zima, G. Houdek, 2005, A&A 438, 653

photometric amplitudes and phases exhibit a strong dependence on subphotospheric convection convection enters through the complex parameter, f , giving the ratio of the local flux variation to the radial displacement at the photosphere

The real and imaginary part of the f parameter for radial oscillations of a 1.9 M star in the MS phase, for three values of the MLT parameter, .

The effect of on the locations of unstable modes with =0,1,2 in the photometric diagnostic diagram for Scuti models of 1.9 M .

The effect of on the locations of modes for stellar model with logTeff=3.867.

this strong sensitivity is NOT necessarily a bad news if we are able to determine simultaneously and f from observations

f may yield a valuable constraint on stellar convection

FG Vir - the most multimodal Scuti pulsatorPhotometric campaigns in 2002, 2003 and 2004Spectroscopic campaign in 2002

Oscillation spectrum of FG Vir67 independent frequencies !from Breger et al. 2005, A&A

12 frequencies were detected both in photometry and Vrad

CONSTRAINTS ON STELLAR CONVECTION

Empirical and theoretical values of f .Model: MLT, convective flux freezing approximation

Empirical and theoretical values of f .Model: non-local, time-dependent formulation of MLT

Identification of can be done without priori knowledge of f . It is possible to extract f values from observations. We proposed a way how to combine the photometry and spectroscopy The method yields constraints on stellar convection . Inferred values of f are crudely consistent with models calculated assuming inefficient convection (0.0).

CEPHEI STARSJ. Daszyska-Daszkiewicz, W. A. Dziembowski, A. A. Pamyatnykh, 2005, A&A 441, 641J. Daszyska-Daszkiewicz, W. A. Dziembowski, A. A. Pamyatnykh, 2006, MmSAI 77, 449

Eridani the most multimodal Cep star

IDENTIFIED FREQUENCIES

1=5.7632 c/d =0, p1 2=5.6539, 3=5.6200, 4=5.6372 =1, g1

5=7.8986 =1, p2

6=6.2448, 7=6.2623, 9=6.2230 =1, p1

8=7.2006 =2 (?)

Identification of degree for 1 photometryphotometry + spectroscopy

Identification of degrees for 2 3 4

f values for 1 ,2 ,3 ,4 should be nearly the same !

new seismic models of Erithe f values are given for = 0, p1

Influence of opacities data on the f values (=0)

unique identification of spherical harmonic degree, , requires both photometric and spectroscopic data theoretical f values are very sensitive to the opacity data f parameter is a laboratory for testing the atomic physics

How does the method work for another pulsators,

e.g. Dor, SX Phe,SPB, sdB.

And what kind of information can yield ?Application of the method to Slowly Pulsating B stars J. Daszyska-Daszkiewicz, W. A. Dziembowski, A. A. Pamyatnykh, in preparation

THANK YOU !