Tsevi Mazeh: Leuven-Spectrospic binaries 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].PPN parameters [6] Sources of the precession of perihelion for Mercury Amount (arcsec/Julian century)Cause Gravitational tugs of the other planets Oblateness of the Sun (quadrupole moment)quadrupole moment [4][5] [4][5] General relativity ±0.69Total ±0.65 [3] [3] Observed attributed to the following causes: The correction by 42.98" is 3/2 multiple of classical prediction with PPN parameters [6].PPN parameters [6] Precession of the perihelion

4Tsevi Mazeh: Leuven-Spectrospic binaries i to observer

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 a,e,,,, Constants of the motion 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

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 t V Systematic surveys

Tsevi Mazeh: Leuven-Spectrospic binaries 14 t V

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

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

19 Circularization Synchronization Alignment Observational evidence

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

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

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

23Tsevi Mazeh: Leuven-Spectrospic binaries

24Tsevi Mazeh: Leuven-Spectrospic binaries

25Tsevi Mazeh: Leuven-Spectrospic binaries

26Tsevi Mazeh: Leuven-Spectrospic binaries

27Tsevi Mazeh: Leuven-Spectrospic binaries

28 Short-period binaries Circularization of short-period binaries Mass-ratio distribution Extra-solar planets

29 Mazeh et al Tsevi Mazeh: Leuven-Spectrospic binaries

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

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

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

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

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

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

36 Two-Dimensional CORrelation - Introduction Observed spectrum Primary template Secondary template Relative weight Zucker & Mazeh 1994 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 Two-Dimensinal CORrelation - Introduction Function of two variables Two main ridges “Cuts” along the ridges (“freeze” one Velocity) Estimated pair of velocities Tsevi Mazeh: Leuven-Spectrospic binaries

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

41Tsevi Mazeh: Leuven-Spectrospic binaries

42Tsevi Mazeh: Leuven-Spectrospic binaries

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

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

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

46 Mazeh et al Tsevi Mazeh: Leuven-Spectrospic binaries

47 Short-period binaries Circularization of short-period binaries Mass-ratio distribution Extra-solar planets

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

Tsevi Mazeh: Leuven-Spectrospic binaries 49 HD

Tsevi Mazeh: Leuven-Spectrospic binaries 50

Tsevi Mazeh: Leuven-Spectrospic binaries 51 Grether & Lineweaver 2006 The Brown-Dwarf Desert

Extrasolar Planets Aug Earth Jupiter Neptune RV Going smaller ~20% of the nearby stars have super-earth planets with periods < 50 d

53 HD A visual pair – K1V/M2V Separation ~ 0.5 arc-sec V-magnitude difference 3.7 Parallax 23 milli-arc-sec Observed regularly in CORALIE Tsevi Mazeh: Leuven-Spectrospic binaries

54 HD A long-term trend of the residuals Santos et al A B Tsevi Mazeh: Leuven-Spectrospic binaries

55 HD HD41004B HD41004A A long-term trend Short-period modulation disappeared Zucker, Mazeh, Santos, Udry & Mayor 2003 TODMOR – Two Dimension Correlation A B Ba Tsevi Mazeh: Leuven-Spectrospic binaries

56 HD Follow-up revealed the orbit of a planet around HD41004A Zucker, Mazeh, Santos, Udry & Mayor 2004 Tsevi Mazeh: Leuven-Spectrospic binaries

57 HD B A Tsevi Mazeh: Leuven-Spectrospic binaries

58Tsevi Mazeh: Leuven-Spectrospic binaries

59 (Not to scale!) A Planet and a Brown Dwarf in the same system Tsevi Mazeh: Leuven-Spectrospic binaries

60 Kepler mission

Tsevi Mazeh: Leuven-Spectrospic binaries 61

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Tsevi Mazeh: Leuven-Spectrospic binaries 65 Kepler binaries

Tsevi Mazeh: Leuven-Spectrospic binaries 66

Tsevi Mazeh: Leuven-Spectrospic binaries 67

Tsevi Mazeh: Leuven-Spectrospic binaries 68

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Tsevi Mazeh: Leuven-Spectrospic binaries 71

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Tsevi Mazeh: Leuven-Spectrospic binaries 73 Kepler GO 0025

Tsevi Mazeh: Leuven-Spectrospic binaries 74 Kepler GO 0025

75Tsevi Mazeh: Leuven-Spectrospic binaries Test particle around a star with mass M

76 Spectroscopic Binaries Tsevi Mazeh: Leuven-Spectrospic binaries

77 Single-lined spectroscopic binary (SB1)

Tsevi Mazeh: Leuven-Spectrospic binaries 78 Double-lined spectroscopic binary (SB2)