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A NEW ASTEROSEISMIC PROBE OF STELLAR STRUCTUR E

This study explores the use of asteroseismology, the study of stellar oscillations, to investigate the structure and properties of stars. It demonstrates how oscillation frequencies can be used to constrain stellar parameters and verify stellar evolution theory. The method of mode identification is explained, and a seismic model of a star is discussed. The method of simultaneous extraction of the degree of oscillation and a parameter related to stellar convection is also presented. The study concludes by discussing the application of this new tool in identifying modes in the oscillation spectrum of a specific star.

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A NEW ASTEROSEISMIC PROBE OF STELLAR STRUCTUR E

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  1. A NEW ASTEROSEISMIC PROBE OF STELLAR STRUCTURE Jadwiga Daszyńska-Daszkiewicz Instytut Astronomiczny, Uniwersytet Wrocławski, POLAND Collaborators: Wojtek Dziembowski , Alosha Pamyatnykh 29 June 2006, Ondřejov

  2. PULSATING STARS CAN BE FOUND ACCROS THE WHOLE HR DIAGRAM

  3. J. Christensen-Dalsgaard

  4. INSTABILITY DOMAINS IN THE MAIN SEQUENCE A. Pamyatnykh

  5. Sir Arthur Eddington (1882 – 1944) „At first sight it would seem that the deep interiorof the sun and starsis less accessible to scientific investigationthan any other region of the universe.”

  6. HOW CAN WE STUDY STELLAR INTERIOS ?

  7. OSCILLATION FREQUENCIES

  8. Time is the most accurately measured physical parameter ! We can compare observed frequencies, j,obs , and their properties with theoretical values, j,cal . A way of constraining stellar parameters. Verification of stellar evolution theory. ASTEROSEISMOLOGY

  9. MODE IDENTIFICATION For a given frequency, nm , we have to determinethree quantum numbers: n, , m

  10. n – the radial order, n=0,1,2,... - the spherical harmonic degree, =0,1,2, … m – the azimuthal order, |m| 

  11. 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

  12. Radial pulsation with n=2

  13. C. Schrijvers

  14.  = 1, m=0  = 1, m=1 Tim Bedding

  15.  = 2, m=1  = 2, m=2 Tim Bedding

  16.  = 3, m=0  = 3, m=1  = 3, m=2  = 3, m=3 Tim Bedding

  17.  = 5, m=0  = 5, m=2  = 5, m=3 Tim Bedding

  18.  = 8, m=1  = 8, m=2  = 8, m=3 Tim Bedding

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

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

  21.  and  measure the average density and core composition, respectively. Thus the mass and age of a star.

  22. In  Sct,SPB and  Cep stars we do not observe such structures and more sophisticated methods are needed.

  23.  Cep

  24.  Sct

  25. SEISMIC MODEL OF THE STAR j,obs=j,cal(nj , j , mj , PS ,PT) PS -- parameters of the model: the initial values of M0, X0, Z0, the angular momentum (or Vrot,0), age (or logTeff) PT -- free parameters of the theory: convection (e.g. MLT parameter ), overshooting distance, parameters describing mass loss angular momentum evolution magnetic field

  26. 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.

  27. EXAMPLE:  Eridani– the most multimodal  Cep star the best seismic information

  28. OSCILLATION SPECTRUM OF  ERI Pamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS 350, 1022

  29. 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 (?)

  30. SEISMIC MODEL OF  ERI Pamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS 350, 1022

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

  32.  Eri, evolutionary tracks,  OPAL Pamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS 350, 1022

  33. NEW ASTEROSEISMIC TOOL

  34. linear nonadiabatic theoryof stellar pulsation fparameter - the ratio of the relative luminosity variation to the relative radial displacement of the surface

  35. f values are very sensitive to:  mean stellar parameters stellar convection opacity data

  36. nm interior fsubphotospheric layer

  37. THE METHOD OF SIMULTANEOUS EXTRACTING  AND fFROM OBSERVATIONS

  38. MULTICOLOUR PHOTOMETRY AND RADIAL VELOCITY DATA

  39. AMPLITUDE OF MONOCHROMATIC FLUX VARIATIONS

  40. Derivatives of the monochromatic flux, F(Teff ,g), are calculated from static atmosphere models (Kurucz, NEMO2003). h(Teff ,g) - limb-darkening coefficient from nonlinear law (Claret, Barban)

  41. THE METHOD 2 minimization assuming trial values of  A set of observational equations for a number of passbands  (1)

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

  43. Each 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 . quantities to be determined

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

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

  46. 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,  .

  47. 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 .

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

  49. 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 stellarconvection

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