2.  Introduction to Stellar Pulsations  RR Lyrae Stars and the Blazhko Effect  Part I of the Thesis Work:  Temporal Behaviour of the RR Lyrae Data  Part II of the Thesis Work:  Trying to Unravel the Blazhko Effect  Conclusions and Future Prospects

3.  Stars: General Properties  Stellar Spectra... and what they learn us  Variable Stars } Pulsating Stars  Asteroseismology

4. Apparent magnitude m ~luminosity Brightness Colour ~surface temperature Absolute magnitude M

8. 1 Photometry and Spectroscopy

10. The Spectroscopic Principle

11. Absorption Lines

12. Plotting a Spectrum Spectral Line Shapes µ "Line Profiles"

14. µ velocity of the vehicle

15. REDSHIFTED BLUESHIFTED

16. µ radial velocity

18. Naked eye: 3% variable stars We studied intrinsic variables, more precisely...

19. 1 Pulsation Cycle 1 Pulsation Phase î: 0µ1

20. Accurately 1 "Pulsation Modes"... the Study of Stellar Pulsations

22. n = radial order number of node surfaces between center and surface l = degree m = azimuthal number -l < m < l

23. l = degree m = azimuthal number number of node lines on the stellar surface

24. l = degree m = azimuthal number number of node lines on the stellar surface |m|= number of meridian lines

25. l = degree m = azimuthal number number of node lines on the stellar surface |m|= number of meridian lines

26. (l,m) = (3,2) tesseral (l,m) = (3,3) sectoral Blue } Moving towards Observer Red } Moving away from Observer (l,m) = (3,0) axisymmetri c [ m=0] [0@|m|@ l] [|m|= l]

27. 1. Period or Frequency Analysis which pulsation frequencies are present?... the Study of Stellar Pulsations

28. Periodogram or Frequency Spectrum highest peaks ~ most prominent frequencies in the signal  

29. 1. Period or Frequency Analysis which pulsation frequencies are present?... the Study of Stellar Pulsations 2. Mode Identification which pulsation modes (l,m) are related to those frequencies?

30. Pulsation 1 Periodically Moving Spectral Lines "Line Profile Variations" 1 Information on Pulsation Modes (l,m)... the Study of Stellar Pulsations

31. What's the use??? Stellar Pulsations 1 Inner Structure of the Star 1 Stellar Models 1 Stellar & Galactic Evolution 1 Understanding the Universe...... the Study of Stellar Pulsations

32.  General Properties  The Blazhko Effect  Explanations for the Blazhko Effect  Objectives of our Research

33. " Cluster Type Variables " short periods (< 1 day) variations of ~ 1 mag Also in the Galactic Field   RR Lyrae Standard Candles Witnesses of the Universe at Young Age "Pure Radial Pulsators"

35.   : Blazhko Amplitude Modulation 20-30% RR ab 2 % RR c

37.  Resonance between Radial Modes?  Resonance between the Radial Mode and a Nonradial Mode of low degree l

38. [ l=2 ]

41. 1958: Babcock 1994: Romanov et al. controversial... Magnetic Field of ~1 kGauss required...

42. " Up to now: Photometric Data " Better diagnostic: High-Resolution Spectra

43. Detect and Identify Nonradial Components in the Line Profile Variations of RR Lyrae  Part I: Temporal Behaviour ~ Period Analysis  Part II: Mode Identification 1 Crucial Test for the Models 1 l < 3 ?

45. Brightest RR Lyrae and Blazhko star m v = 7.06 - 8.12 P 0 = 13 h 36 mn ~ f 0 =1.7642 c/d P B = 40.8 d ~ f B =0.0245 c/d

46. High-Resolution Spectrograph Attached to 1.93m telescope at the Observatoire de Haute-Provence (France)

47. Collaboration with Dr. M. Chadid and Dr. D. Gillet (France) 669 spectra - 16 nights 1996 &1997 Time Resolution 5 %

48. Coverage of the Pulsation Cycle (13h36mn) (km/s)

49. Coverage of the Blazhko Cycle (40.8 days) (km/s)

50. Data Reduction by Dr. M. Chadid First Line Profile Study of a Blazhko Star!

51. Main Frequency...

52. Nonlinearity of the Radial Mode...... up to 8 th order

53. Multiplet Structure...

54. Nonradial Modes!

55. Nonlinearity & Multiplet

57. RR Lyrae: multiperiodic... for the special case of RR Lyrae Radial Mode (0,0) : well known! Very prominent Nonlinear behaviour Nonradial Mode(s) (l,m) : to be identified Much less prominent

58.  Mode Identification from Nonadiabatic Observables  A Nonlinear Model for the Radial Mode

59. Idea: 1 Program for Theoretical Line Profiles Velocity Profile Intrinsic Profile Nonlinear Velocity Expression Temperature Variations due to Pulsation

60. Influence of a Nonradial Mode upon the Line Profile Variations:

61. Idea: 1 Program for Theoretical Line Profiles Nonlinear Velocity Expression Temperature Variations due to Pulsation Compare with Observational Profiles 1 Nonradial Modes Velocity Profile Intrinsic Profile

62. Ingredients: Velocity Profile Intrinsic Profile Values derived from Literature 1 Intrinsic profiles from Static Atmosphere Models

63. Ingredients: Velocity Profile Intrinsic Profile  First Step: 3 rd Order Velocity Expression  Nonlinear Pulsation Theory (Van Hoolst 1996)  ARGUMENTS:  Period Analysis: f 0 ±f B appears right after f 0, 2 f 0 and 3 f 0  Nonlinear Theory only exists up to 3 rd Order

64. ....... Observations Theory

65.  Second Step: 8 th Order Velocity Expression  Pragmatic "ad hoc" Approach of the Radial Mode  REMARKS:  Based on the Observations  Contains no Physics... Ingredients: Velocity Profile Intrinsic Profile

66. Line Doubling ~ Shock Wave ~ Hydrodynamical Models....... Observations Theory

67. ....... Observations Theory (km/s) (km/s) 2 First Moment Second Moment

68. ....... Observations Theory (km/s) (km/s) 2 First Moment Second Moment

69. ARGUMENT:  Contains the Physics ! QUESTION:  Can these Models yield good correspondance in the Profiles? Ingredients: Velocity Profile Intrinsic Profile (Fokin & Gillet 1997) Collaboration with Dr. A. Fokin (Russia)

70. ....... Observations Theory

71. Results  Eighth Order Model: good agreement, but not physical  Hydrodynamical Models: further development is the best way to proceed! For Now:  Turn to the Moment Variations

72.  Mode Identification from Nonadiabatic Observables  A Nonlinear Model for the Radial Mode  An Adapted Version of the Moment Method

73. Idea: (Aerts 1993) Observed Moments & Theoretical Moments Which (l,|m|) gives the best agreement? Based on Linear Pulsation Theory Succesful in Identifying Linear Nonradial Modes in Main Sequence Stars

74. ... to the special case of RR Lyrae Amplitudes of "Blazhko Terms" from First and Second Moment Coupling with Radial Mode Nonradial Modes have Small Amplitudes 1 Linear Treatment Applicable to each Nonradial Mode separately Ingredients:

75. On Artificial data Radial Mode: Eighth Order Model Nonradial Mode ~ Conclusions: Accurate Determination of l and |m| Some (l,|m|) Configurations are hard to distinguish

76. (1,1) (2,1) (2,2) Conclusion: l < 3 and m @ 0 (l,|m|) =...

77. (1,1) (2,1) (2,2) :i = 0 deg :i = 40 deg :i = 90 deg Inclination angle

78. (km/s) 2 Time (days)

84. Discriminant works well!

85.  Evidence for a Triplet Structure in our Frequency Spectra  Evidence for Nonradial Modes (l,m)  Adapted Version of the Moment Method: l < 3 and m@0  Evaluation through Line Profile Calculations: Dipole Modes (1,1) are most probable First Line Profile Study of a Blazhko Star  Nonradial Modes which Effects vary through the Blazhko Cycle

86.  More Spectroscopic Observations better spread over the Blazhko Cycle  Include all Nonradial Components in the Identification  Exclude Quintuplet Structure?  Further Development of the Hydrodynamical Models  Refinement of the Identification Techniques

87. ...