Stellar Oscillations in Giant Stars K giants Mira RV Tau stars

1. Stellar Oscillations in Giant Stars • K giants • Mira • RV Tau stars

2. Progenitors are higher mass stars than the sun K giants occupy a „messy“ region of the H-R diagram Giant stars are A-K starts that have evolved off the main sequence and on to the giant branch

4. A 2 Mסּ star on the main sequence A 2 Mסּ star on the giant branch Giant stars are of particular interest to planet hunters. Why? Because they have masses in the range of 1-3 Mסּ Stars of higher mass than the Sun are ill-suited for RV searches. However the problem with this is getting a good estimate for the mass of the star

5. The story of variability in K giant stars began in 1989: Smith et al. 1989 found a 1.89 d period variation in the radial velocity of Arcturus:

6. 1989 Walker et al. Found that RV variations are common among K giant stars These are all IAU radial velocity standard stars !!! Inspired by the Walker et al. Paper, Hatzes & Cochran began a radial velocity survey of a small sample of K giant stars.

7. The Long Period Variability: Planets?

8. 1990-1993 Hatzes & Cochran surveyed 12 K giants with precise radial velocity measurements and found significant period

9. The „3 Muskateers“ Many showed RV variations with periods of 200-600 days

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

11. 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

12. 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

13. 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

14. 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

15. 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

16. The Planet around Pollux (b Gem) McDonald 2.1m CFHT TLS McDonald 2.7m The RV variations of b Gem taken with 4 telescopes over a time span of 26 years. The solid line represents an orbital solution with Period = 590 days, m sin i = 2.3 MJup.

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

18. Ca II emission variations for b Gem If there are no Ca II variations with the RV period, it probably is not activity

19. Hipparcos Photometry If there are no photometric variations with the RV period, spots on the surface are not causing the variations.

20. Test 2: Bisector velocity Spectral Line Bisectors From Gray (homepage) For most phenomena like spots, surface structure, or stellar pulsations, the radial velocity variations are all accompained by changes in the shape of the spectral lines. Planets on the other hand cause an overall Doppler shift of the line without an accompanying change in the lines. Spectral line bisectors are a common way to measure line shapes

21. The Spectral line shape variations of b Gem.

22. The Planet around b Gem The Star M = 1.9 Msun [Fe/H] = –0.07 Planets have been found around ~ 30 Giant stars

23. The Planet around i Dra Frink et al. 2002 P = 1.5 yrs M = 9 MJ

24. From Michaela Döllinger‘s thesis P = 517 d m = 10.6 MJ e = 0.09 M* = 1.84 Mסּ P = 272 d m = 6.6 MJ e = 0.53 M* = 1.2 Mסּ P = 657 d m = 10.6 MJ e = 0.60 M* = 1.2 Mסּ P = 159 d m = 3 MJ e = 0.03 M* = 1.15 Mסּ RV (m/s) P = 1011 d m = 9 MJ e = 0.08 M* = 1.3 Mסּ P = 477 d m = 3.8 MJ e = 0.37 M* = 1.0 Mסּ JD - 2400000 M sin i = 3.5 – 10 MJupiter

25. a Tau

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

27. g Dra

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

29. The evidence supports that the long period RV variations in many K giants are due to planets…so what? Setiawan et al. 2005 K giants can tell us about planet formation around stars more massive than the sun. The problem is the getting the mass. This is where stellar oscillations can help.

30. And now for the stellar oscillations…

31. Hatzes & Cochran 1994 Short period variations in Arcturus consistent with radial pulsations n = 1 (1H) n = 0 (F)

32. a Ari velocity variations: Alias n≈3 overtone radial mode

33. Photometry of a UMa with WIRE guide camera (Buzasi et al. 2000) Equally spaced modes in frequency → p-modes. Observed Dn = 2.94 mHz

34. M1/2 135 mHz Dn0≈ R3/2 Buzasi et al get a mean spacing of 2.94 mHz and a lowest frequency mode of 1.82 mHz (P = 6.35 d). a UMa has an interferometric radius of 28 Rסּ The Fundamental radial mode is given by: Q = P0 √r/rסּ Where the pulsation constant Q = 0.038 – 0.116, so P = 2.8, to 8.6 days, if M ≈ 4 Mסּ , close to the first frequency. But… Based on the known radius and observed spacing, this gives M ≈ 10 Mסּ. So actual spacing may be one-half as a large and one is not seeing all modes (odd or even radial order, n)

35. g Dra

36. g Dra : June 1992

37. g Dra : June 2005

38. g Dra The short period variations of g Dra can also be explained by radial pulsations, but only n order modes?

39. i Dra: A planet hosting K giant P1 = 7 hrs A1= 5 m/s n1 = 39.7 mHz Mean Dn = 4.05 mHz P2 = 6.4 hrs A2=6.35 m/s n2 = 43.4 mHz n2 = 47.8 mHz P3 = 5.9hrs d A3=4 m/s

40. M1/2 135 mHz Dn0≈ R3/2 nn,l= Dn0 (n + l/2 + d) Recall our Scaling Relations M/Mסּ 3.05 mHz nmax = (R/Rסּ)2√Teff/5777K Frequency spacing: Thes can be solved for the radius of the star: R ≈ ( n(mHz)max/3.05 )(135/Dn(mHz))2

41. We have 2 equations and 2 unknowns, these can be solved for M, R nmax ≈ 40 mHz (max peak at P = 7 hrs) = 0.04 mHz Mean Dn = 4.05 mHz • We have two cases: • These are nonradial modes and the observed spacing is one-half the large spacing • These are radial modes and the observed spacing is the large spacing Case 1: R = 3.6 Rסּ M = 0.17 Mסּ Case 2: R = 14.5 Rסּ M = 2.9 Mסּ Case 1 is in disagreement with evolutionary tracks (they cannot be that wrong!) and Hipparcos distance. Conclusion: this is a giant star and we are detecting radial modes.

42. Stellar Oscillations in b Gem Nine nights of RV measurements of b Gem. The solid line represents a 17 sine component fit. The false alarm probability of these modes is < 1% and most have FAP < 10–5. The rms scatter about the final fit is 1.9 m s–1

43. DFT Velocities Amplitude (m/s) Window

44. Observed RV Frequencies in b Gem Amplitude in m/s

45. DFT Fit

46. The Oscillation Spectrum of Pollux The p-mode oscillation spectrum of b Gem based on the 17 frequencies found via Fourier analysis. The vertical dashed lines represent a grid of evenly-spaced frequencies on an interval of 7.12 mHz

47. 7.12 mHz Dn0≈ M1/2 135 mHz Dn0≈ R3/2 Frequency Spacing Inteferometric Radius of b Gem = 8.8 Rסּ For radial modes → M = 1.89 ± 0.09 Mסּ For nonradial modes→ M = 7.5 Mסּ Evolutionary tracks give M = 1.94 Mסּ

48. MOST Photometry for b Gem 2K/Dm = 65 km/s/mag For n = 87 mHz

49. Observed Photometric Frequencies in b Gem