1. Extrasolar Planets and Stellar Oscillations in K Giant Stars Notes can be downloaded from www.tls-tautenburg.de→Teaching

2. 2000014000100007000500035002500 1.000.000 10.000 100 1 0.01 0.0001 OBAFG KM +20 +15 +10 +5 0 -5 -10 Absolute Magnitude Luminosity (Solar Lum.) Effective Temparature Spectral Class White Dwarfs Main Sequence Giants Supergiants

3. Why the interest in K giants for exoplanets and asteroseismology? K giants occupy a „messy“ region of the H-R diagram Progenitors are higher mass stars Evolved A-F stars

4. The story begins: Smith et al. 1989 found a 1.89 d period in Arcturus

5. 1989 Walker et al. Found that RV variations are common among K giant stars These are all IAU radial velocity standard stars !!!

6. First, planets around K giants stars…

7. 1990-1993 Hatzes & Cochran surveyed 12 K giants with precise radial velocity measurements

8. Footnote: Period Analysis Lomb-Scargle Periodogram: Power is a measure of the statistical significance of that frequency (period): 1 2 P x (  ) = [  X j sin  t j –  ] 2 j  X j sin 2  t j –  [  X j cos  t j –  ] 2 j  X j cos 2  t j –  j + 1 2 False alarm probability ≈ 1 – (1–e –P ) N = probability that noise can create the signal N = number of indepedent frequencies ≈ number of data points tan(2  ) =  sin 2  t j )/  cos 2  t j ) j j

9. If a signal is present, for less noise (or more data) the power of the Scargle periodogram increases. This is not true with Fourier transform -> power is the related to the amplitude of the signal.

10. Many showed RV variations with periods of 200-600 days

11.  Her has a 613 day period in the RV variations But what are the variations due to?

12. The nature of the long period variations in K giants Three possible hypothesis: 1.Pulsations (radial or non-radial) 2. Spots (rotational modulation) 3. Sub-stellar companions

13. What about radial pulsations? Pulsation Constant for radial pulsations: Q = P M MסּMסּ () 0.5 R RסּRסּ () –1.5 For the sun: Period of Fundamental (F) = 63 minutes = 0.033 days (using extrapolated formula for Cepheids) Q = 0.033 P  סּסּ () 0.5 =

14. Footnote: The fundamental radial mode is related to the dynamical timescale: d2Rd2R The dynamical timescale is the time it takes a star to collapse if you turn off gravity dt 2 = GM R2R2 Approximate: R  ≈ G  R  is the mean density For the sun  = 54 minutes  = (G  ) –0.5

15. What about radial pulsations? K Giant: M ~ 2 M סּ, R ~ 20 R סּ Period of Fundamental (F) = 2.5 days Q = 0.039 Period of first harmonic (1H) = 1.8 day → Observed periods too long

16. What about radial pulsations? Alternatively, let‘s calculate the change in radius V = V o sin (2  t/P),  R =2 V o sin (2  t/P) = ∫ 0  /2 VoPVoP   Gem: P = 590 days, V o = 40 m/s, R = 9 R סּ  R ≈ 0.9 R סּ Brightness ~ R 2  m = 0.2 mag, not supported by Hipparcos photometry

17. What about non-radial pulsations? p-mode oscillations, Period < Fundamental mode Periods should be a few days → not p-modes g-mode oscillations, Period > Fundamental mode So why can‘ t these be g-modes? Hint: Giant stars have a very large, and deep convection zone

18. Recall gravity modes and the Brunt–Väisälä Frequency The buoyancy frequency of an oscillating blob: N 2 = g ( 1   P dPdP drdr – dd drdr ) g is local acceleration of gravity  is density P is pressure Where does this come from?     P dPdP dd () ad First adiabatic exponent

19. Brunt Väisälä Frequency ** 00 00  T  rr  Change in density of surroundings:  =  0 + ( dd drdr ) rr  * =  0 + ( dd dPdP ) rr Change in density due to adiabatic expansion of blob: dPdP drdr  * =  0 + ( 1 11 ) rr dPdP drdr  P

20. Brunt Väisälä Frequency ** 00 00  T  rr  Difference in density between blob and surroundings :  =  –  * = rr ( 1 11 ) dPdP drdr  P dd drdr – Buoyancy force f b = – g   r = –  ( 1  ) dd drdr 1 11 dPdP drdr P – F = –kx →  2 = k/m Recall This is just a harmonic oscillator with  2 = N 2 rr

21. Brunt Väisälä Frequency Criterion for onset of convection: However if  * < , the blob is less dense than its surroundings, buoyancy force will cause it to continue to rise ( 1 11 )  dPdP drdr  P dd drdr In convection zone buoyancy is a destabilizing force, gravity is unable to act as a restoring force → long period RV variations in K giants cannot be g modes

22. What about rotation? Spots can cause RV variations Radius of K giant ≈ 10 R סּ Rotation of K giant ≈ 1-2 km/s P rot ≈ 2  R/v rot P rot ≈ 250–500 days Its possible!

23. Rotation (and pulsations) should be accompanied by other forms of variability 1.Have long lived and coherent RV variations 2. No chromospheric activity variations with RV period 4. No spectral line shape variations with the RV period 3. No photometric variations with the RV period Planets on the other hand:

24.  Case Study  Gem CFHTMcDonald 2.1m McDonald 2.7mTLS

25. Ca II H & K core emission is a measure of magnetic activity: Active star Inactive star

26. Ca II emission variations

27. Hipparcos Photometry

28. Test 2: Bisector velocity From Gray (homepage)

29. Spectral line shape variations

30. Period590.5 ± 0.9 d RV Amplitude40.1 ± 1.8 m/s e0.01 ± 0.064 a1.9 AU Msin i2.9 M Jupiter The Planet around  Gem M = 1.7 M sun [Fe/H] = –0.07 The Star

31. Frink et al. 2002 P = 1.5 yrs M = 9 M J

32. P = 711 d Msini = 8 M J Setiawan et al. 2005

33. Setiawan et al. 2002: P = 345 d e = 0.68 M sini = 3.7 M J

34.  Tau

36.  Tau has line profile variations, but with the wrong period Hatzes & Cochran 1998

37. Period653.8 ± 1.1 d RV Amplitude133 ± 11 m/s e0.02 ± 0.08 a2.0 Msin i10.6 M Jupiter The Planet around  Tau M = 2.5 M sun [Fe/H] = –0.34 The Star

38.  Dra

39. Period712 ± 2.3 d RV Amplitude134 ± 9.9 m/s e0.27 ± 0.05 a2.4 Msin i13 M Jupiter The Planet around  Dra? M = 2.9 M sun [Fe/H] = –0.14 The Star

40. Setiawan et al. 2005 The evidence supports that the long period RV variations in many K giants are due to planets…so what?

41. B1I V F0 V G2 V

42. Planets around massive K giant stars  Dra 2.9 13 2.4 712 0.27 –0.14  Tau 2.5 10.6 2.0 654 0.02 –0.34

43. Period

44. Characteristics: 1. Supermassive planets: 3-11 M Jupiter Theory: More massive stars have more massive disks 2. Many are metal poor Theory: Massive disks can form planets in spite of low metallicity 3. Orbital radii ≈ 2 AU Theory: Planets in metal poor disks do not migrate because they take so long to form.

45. And now for the stellar oscillations…

46. Hatzes & Cochran 1994 Short period variations in Arcturus n = 1 (1H) n = 0 (F)

47. n 0 F 1 1H 2 2H

48.  Ari Alias n≈3 overtone radial mode

49.  Dra

50.  Dra : June 1992

51.  Dra : June 2005

53.  Dra

54. Photometry of a UMa with WIRE guide camera (Buzasi et al. 2000) 0 1 2 3 Radial modes n =

55. Conclusion: most (all?) K giant stars pulsate in the radial and low-overtone modes. So what?

56. HD 13189 P = 471 d Msini = 14 M J M * = 3.5 s.m.

57. P = 4.8 days P = 2.4 days HD 13189 short period variations For M = 3.5 M סּ R = 38 R F = 4.8 d 2H = 2.7 d → oscillations can be used to get the stellar mass

58. Current work on K giants 1. TLS survey of 62 K giants (Döllinger Ph.D.) 2. Multi-site campaigns planned (GLONET) 3. MOST campaign on  Oph and  Gem 4. CoRoT additional science program (150 days of photometry) 5. Lots of theoretical work to model pulsations needs to be done

59. Döllinger Ph.D. work: 62 K giants surveyed from TLS ≈ 10% show long period variations that may be due to planetary companions

63. Time (days) Intensity 5.7 days Aldebaran with MOST

64. Summary K giant (IAU radial velocity standards) are RV variable stars! Multi-periodic on two time scales: 200-600 days and 0.25 – 8 days Long period variations are most likely due to giant planets around stars with M star > 1 M סּ Short period variations are due to radial pulsations in the fundamental and overtone modes Pulsations can be used to get funamental parameters of star