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The orbital elements

The orbital elements. The precession of the periastron. attributed to the following causes: The correction by 42.98" is 3/2 multiple of classical prediction with  PPN parameters [6]. attributed to the following causes:

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The orbital elements

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  1. The orbital elements Tsevi Mazeh: Leuven-Spectrospic binaries

  2. The precession of the periastron Tsevi Mazeh: Leuven-Spectrospic binaries

  3. attributed to the following causes: The correction by 42.98" is 3/2 multiple of classical prediction with PPN parameters[6]. attributed to the following causes: The correction by 42.98" is 3/2 multiple of classical prediction with PPN parameters[6]. Precession of the perihelion Tsevi Mazeh: Leuven-Spectrospic binaries

  4. to observer i Spectroscopic Binaries Tsevi Mazeh: Leuven-Spectrospic binaries

  5. The shape determines e and Tsevi Mazeh: Leuven-Spectrospic binaries

  6. Spectroscopic elements: P The orbital period K The RV amplitude The argument of periastron e The eccentricity The periastron passage The RV of the system Constants of the motion a,e, , , , The gravitatonal field Tsevi Mazeh: Leuven-Spectrospic binaries

  7. Single-lined spectroscopic binary (SB1) Tsevi Mazeh: Leuven-Spectrospic binaries

  8. Single-lined spectroscopic binary (SB1) Tsevi Mazeh: Leuven-Spectrospic binaries

  9. Tsevi Mazeh: Leuven-Spectrospic binaries

  10. Tsevi Mazeh: Leuven-Spectrospic binaries

  11. Double-lined spectroscopic binary (SB2) Tsevi Mazeh: Leuven-Spectrospic binaries

  12. The relativistic Doppler effect (Margon et al. 1979) Tsevi Mazeh: Leuven-Spectrospic binaries

  13. Systematic surveys V t Tsevi Mazeh: Leuven-Spectrospic binaries

  14. V t Tsevi Mazeh: Leuven-Spectrospic binaries

  15. Latham, Mazeh et al. 1992 Tsevi Mazeh: Leuven-Spectrospic binaries

  16. Latham, Mazeh et al. 1992 Tsevi Mazeh: Leuven-Spectrospic binaries

  17. Short-period binaries • Circularization of short-period binaries • Mass-ratio distribution • Extra-solar planets Tsevi Mazeh: Leuven-Spectrospic binaries

  18. Spin and orbital angular momentum exchange in binary star systems. Keppens, R. 1997 Tsevi Mazeh: Leuven-Spectrospic binaries

  19. Circularization • Synchronization • Alignment Observational evidence Tsevi Mazeh: Leuven-Spectrospic binaries

  20. Circularization • Synchronization • Alignment Observational evidence 938 binaries found in LMC by the OGLE project, analyzed by EBAS (Mazeh, Tamuz & North 2006) Tsevi Mazeh: Leuven-Spectrospic binaries

  21. PMS Melo, C. H. F.; Covino, E.; Alcalá, J. M.; Torres, G. 2001, A&A, 378, 898 Tsevi Mazeh: Leuven-Spectrospic binaries

  22. Latham et al. 2002 Tsevi Mazeh: Leuven-Spectrospic binaries

  23. Tsevi Mazeh: Leuven-Spectrospic binaries

  24. Tsevi Mazeh: Leuven-Spectrospic binaries

  25. Tsevi Mazeh: Leuven-Spectrospic binaries

  26. Tsevi Mazeh: Leuven-Spectrospic binaries

  27. Tsevi Mazeh: Leuven-Spectrospic binaries

  28. Short-period binaries • Circularization of short-period binaries • Mass-ratio distribution • Extra-solar planets Tsevi Mazeh: Leuven-Spectrospic binaries

  29. Mazeh et al. 2003 Tsevi Mazeh: Leuven-Spectrospic binaries

  30. TODCOR (and TRICOR):How to derive radial velocities from composite spectra[TwO-Dimensional CORrelation] Shay Zucker & Tsevi Mazeh Tsevi Mazeh: Leuven-Spectrospic binaries

  31. Observed spectrum Template spectrum Cross- Correlation Radial Velocity The Cross-Correlation Function Tsevi Mazeh: Leuven-Spectrospic binaries

  32. The Cross-Correlation Function Observed spectrum Template Tsevi Mazeh: Leuven-Spectrospic binaries

  33. Observed spectrum Single-line Spectroscopic Binary SB1 Double-line Spectroscopic Binary SB2 Tsevi Mazeh: Leuven-Spectrospic binaries

  34. The Cross-Correlation Function The two peaks are blended Two nicely separated peaks Tsevi Mazeh: Leuven-Spectrospic binaries

  35. The Cross-Correlation Function • Blended peaks • Faint secondary spectrum • Spectral mismatch between secondary and template Tsevi Mazeh: Leuven-Spectrospic binaries

  36. Two-Dimensional CORrelation - Introduction Zucker & Mazeh 1994 Observed spectrum Primary template Secondary template Relative weight Tsevi Mazeh: Leuven-Spectrospic binaries

  37. Two-Dimensinal CORrelation - Introduction Tsevi Mazeh: Leuven-Spectrospic binaries

  38. Two-Dimensinal CORrelation - Introduction Tsevi Mazeh: Leuven-Spectrospic binaries

  39. Estimated pair of velocities Two-Dimensinal CORrelation - Introduction Function of two variables Two main ridges “Cuts” along the ridges (“freeze” one Velocity) Tsevi Mazeh: Leuven-Spectrospic binaries

  40. Two-Dimensinal CORrelation - Introduction Freeze the secondary velocity Freeze the primary velocity Tsevi Mazeh: Leuven-Spectrospic binaries

  41. Tsevi Mazeh: Leuven-Spectrospic binaries

  42. Tsevi Mazeh: Leuven-Spectrospic binaries

  43. SB1 SB2 Measuring mass ratios of SBs: Tsevi Mazeh: Leuven-Spectrospic binaries

  44. Mazeh et al. 2003 q=0.29+/-0.04 Tsevi Mazeh: Leuven-Spectrospic binaries

  45. G62-61 G26-38 The Mass-Ratio Distribution 2-3 measurements are enough ! Already have primary solution Just need to constrain the secondary solution Tsevi Mazeh: Leuven-Spectrospic binaries

  46. Mazeh et al. 2003 Tsevi Mazeh: Leuven-Spectrospic binaries

  47. Short-period binaries • Circularization of short-period binaries • Mass-ratio distribution • Extra-solar planets Tsevi Mazeh: Leuven-Spectrospic binaries

  48. P K to observer i Radial Velocity Time Test particle (planet) around a star with mass M Reflex motion of star Tsevi Mazeh: Leuven-Spectrospic binaries

  49. HD 114762 Tsevi Mazeh: Leuven-Spectrospic binaries

  50. Tsevi Mazeh: Leuven-Spectrospic binaries

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