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Extrasolar Planets and Stellar Oscillations in K Giant Stars

Extrasolar Planets and Stellar Oscillations in K Giant Stars. Notes can be downloaded from www.tls-tautenburg.de→Teaching. Spectral Class. O. B. A. F. G. K. M. -10. Supergiants. -5. 1.000.000. 10.000. Main Sequence. 0. Giants. Absolute Magnitude. Luminosity (Solar Lum.).

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Extrasolar Planets and Stellar Oscillations in K Giant Stars

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

  2. Spectral Class O B A F G K M -10 Supergiants -5 1.000.000 10.000 Main Sequence 0 Giants Absolute Magnitude Luminosity (Solar Lum.) 100 +5 1 +10 0.01 White Dwarfs +15 0.0001 +20 20000 14000 10000 7000 5000 3500 2500 Effective Temparature

  3. Progenitors are higher mass stars K giants occupy a „messy“ region of the H-R diagram Why the interest in K giants for exoplanets and asteroseismology? 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. 1 1 2 2 2 [ ] S 2 Xj cos w(tj–t) [ ] S Xj sin w(tj–t) j S j Xj cos2w(tj–t) S Xj sin2w(tj–t) j Footnote: Period Analysis Lomb-Scargle Periodogram: Px(w) = + (Scos 2wtj) tan(2wt) = (Ssin 2wtj)/ j j Power is a measure of the statistical significance of that frequency (period): False alarm probability ≈ 1 – (1–e–P)N = probability that noise can create the signal N = number of indepedent frequencies ≈ number of data points

  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. p 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: • Pulsations (radial or non-radial) • Spots (rotational modulation) • Sub-stellar companions

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

  14. R r is the mean density Approximate: ≈ G r R t2 Footnote: The fundamental radial mode is related to the dynamical timescale: GM d2R = dt2 R2 The dynamical timescale is the time it takes a star to collapse if you turn off gravity t = (Gr)–0.5 For the sun t = 54 minutes

  15. What about radial pulsations? K Giant: M ~ 2 Mסּ , R ~ 20 Rסּ 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 = Vo sin (2pt/P), VoP p/2 DR =2 Vo sin (2pt/P) = ∫ p 0 b Gem: P = 590 days, Vo = 40 m/s, R = 9 Rסּ Brightness ~ R2 DR ≈ 0.9 Rסּ Dm = 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: r 1 dr dP ) ( – N2 = g G1 P dr dr r dP ( ) G1 = First adiabatic exponent P dr ad g is local acceleration of gravity r is density P is pressure Where does this come from?

  19. dr ) ( r = r0 + Dr dr Brunt Väisälä Frequency r DT Dr Change in density of surroundings: r* Change in density due to adiabatic expansion of blob: Dr dr dP ) ( r* = r0 + Dr dP dr r0 r0 r 1 dP ) ( r* = r0 + Dr G1 dr P

  20. Brunt Väisälä Frequency r Difference in density between blob and surroundings : DT Dr r* Dr = r– r* r 1 dP dr ) ( – = Dr Dr G1 dr P dr 1 1 dP ( ) dr = –r – Dr r dr dr G1 P r0 r0 Buoyancy force fb = – gDrdr Recall → w2 = k/m F = –kx This is just a harmonic oscillator with w2 = N2

  21. Brunt Väisälä Frequency However if r* < r, the blob is less dense than its surroundings, buoyancy force will cause it to continue to rise Criterion for onset of convection: r 1 dP dr ) ( < G1 dr dr P 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 Rסּ Rotation of K giant ≈ 1-2 km/s Prot ≈ 2pR/vrot 250–500 days Prot ≈ Its possible!

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

  24. Case Study: b Gem CFHT McDonald 2.1m McDonald 2.7m TLS

  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. The Planet around b Gem The Star M = 1.7 Msun [Fe/H] = –0.07

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

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

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

  34. a Tau

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

  36. The Planet around a Tau The Star M = 2.5 Msun [Fe/H] = –0.34

  37. g Dra

  38. The Planet around g Dra? The Star M = 2.9 Msun [Fe/H] = –0.14

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

  40. B1I V F0 V G2 V

  41. Planets around massive K giant stars g Dra 2.9 13 2.4 712 0.27 –0.14 a Tau 2.5 10.6 2.0 654 0.02 –0.34

  42. Period

  43. Characteristics: • Supermassive planets: 3-11 MJupiter 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.

  44. And now for the stellar oscillations…

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

  46. n • 0 F • 1H • 2H

  47. a Ari Alias n≈3 overtone radial mode

  48. g Dra

  49. g Dra : June 1992

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