A NEW ASTEROSEISMIC PROBE OF STELLAR STRUCTUR E
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Transcript of A NEW ASTEROSEISMIC PROBE OF STELLAR STRUCTUR E
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A NEW ASTEROSEISMIC PROBE
OF STELLAR STRUCTURE Jadwiga Daszyska-Daszkiewicz Instytut Astronomiczny, Uniwersytet Wrocawski, POLAND
Collaborators: Wojtek Dziembowski , Alosha Pamyatnykh29 June 2006, Ondejov
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PULSATING STARS CAN BE FOUND
ACCROS THE WHOLE HR DIAGRAM
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J. Christensen-Dalsgaard
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INSTABILITY DOMAINS IN THE MAIN SEQUENCEA. Pamyatnykh
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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.
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HOW CAN WE STUDY STELLAR INTERIOS ?
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OSCILLATION FREQUENCIES
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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 !
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MODE IDENTIFICATIONFor a given frequency, nm , we have to determine three quantum numbers: n, , m
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n the radial order, n=0,1,2,...
- the spherical harmonic degree, =0,1,2,
m the azimuthal order, |m|
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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
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Radial pulsation with n=2
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C. Schrijvers
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= 1, m=0 = 1, m=1 Tim Bedding
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= 2, m=1 = 2, m=2 Tim Bedding
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= 3, m=0 = 3, m=1 = 3, m=2 = 3, m=3 Tim Bedding
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= 5, m=0 = 5, m=2 = 5, m=3 Tim Bedding
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= 8, m=1 = 8, m=2 = 8, m=3 Tim Bedding
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In the case of Sun we get mode identifications from asymptotic relations: large and small separations.
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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
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and measure the average density and core composition, respectively.
Thus the mass and age of a star.
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In Sct, SPB and Cep stars we do not observe such
structures and more sophisticated methods are needed.
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Cep
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Sct
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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
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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.
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Eridani the most multimodal Cep star the best seismic informationEXAMPLE:
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OSCILLATION SPECTRUM OF ERIPamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS 350, 1022
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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 (?)
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SEISMIC MODEL OF ERIPamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS 350, 1022
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Pamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS 350, 1022
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Eri, evolutionary tracks, OPALPamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS 350, 1022
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NEW ASTEROSEISMIC TOOL
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linear nonadiabatic theory of stellar pulsationf parameter - the ratio of the relative luminosity variation to the relative radial displacement of the surface
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f values are very sensitive to:
mean stellar parameters
stellar convection
opacity data
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nm interior
f subphotospheric layer
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THE METHOD OF SIMULTANEOUS
EXTRACTING AND f FROM OBSERVATIONS
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MULTICOLOUR PHOTOMETRY AND RADIAL VELOCITY DATA
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AMPLITUDE OF MONOCHROMATIC FLUX VARIATIONS
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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)
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THE METHOD 2 minimization assuming trial values of
A set of observational equations for a number of passbands (1)
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RADIAL VELOCITY (the first moment of the spectral line variations)(2)
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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 .
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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
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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
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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, .
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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 .
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The effect of on the locations of modes for stellar model with logTeff=3.867.
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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
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FG Vir - the most multimodal Scuti pulsatorPhotometric campaigns in 2002, 2003 and 2004Spectroscopic campaign in 2002
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Oscillation spectrum of FG Vir67 independent frequencies !from Breger et al. 2005, A&A
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12 frequencies were detected both in photometry and Vrad
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CONSTRAINTS ON STELLAR CONVECTION
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Empirical and theoretical values of f .Model: MLT, convective flux freezing approximation
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Empirical and theoretical values of f .Model: non-local, time-dependent formulation of MLT
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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).
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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
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Eridani the most multimodal Cep star
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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 (?)
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Identification of degree for 1 photometryphotometry + spectroscopy
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Identification of degrees for 2 3 4
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f values for 1 ,2 ,3 ,4 should be nearly the same !
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new seismic models of Erithe f values are given for = 0, p1
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Influence of opacities data on the f values (=0)
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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
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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
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THANK YOU !