1. Radial Velocity Detection of Planets:II. Observations • Period Analysis • Global Parameters • Classes of Planets • Dependence on Stellar Parameters • Sources of Noise Lecture notes: www.tls-tautenburg.de Click on Teaching -> lectures -> Extrasolar Planets Binary star simulator: http://instruct1.cit.cornell.edu/courses/astro101/java/binary/binary.htm#instructions Also: www.exoplanet.eu

2. 1. Period Analysis How do you know if you have a periodic signal in your data? What is the period?

3. Try 16.3 minutes:

4. Lomb-Scargle Periodogram of the data:

5. 1. Period Analysis • Least squares sine fitting: • Fit a sine wave of the form: • V(t) = A·sin(wt + f) + Constant • Where w = 2p/P, f = phase shift • Best fit minimizes the c2: • c2 = S (di –gi)2/N • di = data, gi = fit Note: Orbits are not always sine waves, a better approach would be to use Keplerian Orbits, but these have too many parameters

6. 1 N0 1. Period Analysis • 2. Discrete Fourier Transform: • Any function can be fit as a sum of sine and cosines N0 FT(w) =  Xj (T) e–iwt Recall eiwt = cos wt + i sinwt j=1 X(t) is the time series Power: Px(w) = | FTX(w)|2 N0 = number of points 2 1 2 ( [( ] ) ) S S Px(w) = Xj cos wtj + Xj sin wtj N0 A DFT gives you as a function of frequency the amplitude (power) of each sine wave that is in the data

7. P Ao Ao t FT 1/P w A pure sine wave is a delta function in Fourier space

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 1. Period Analysis 2. 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

10. Least squares sine fitting: The best fit period (frequency) has the lowest c2 Discrete Fourier Transform: Gives the power of each frequency that is present in the data. Power is in (m/s)2 or (m/s) for amplitude Amplitude (m/s) Lomb-Scargle Periodogram: Gives the power of each frequency that is present in the data. Power is a measure of statistical signficance

11. False alarm probability ≈ 10–14 Alias Peaks Noise level

12. Alias periods: Undersampled periods appearing as another period

13. Lomb-Scargle Periodogram of previous 6 data points: Lots of alias periods and false alarm probability (chance that it is due to noise) is 40%! For small number of data points sine fitting is best.

14. Raw data False alarm probability ≈ 0.24 After removal of dominant period

15. Campbell & Walker: The Pioneers of RV Planet Searches 1988: 1980-1992 searched for planets around 26 solar-type stars. Even though they found evidence for planets, they were not 100% convinced. If they had looked at 100 stars they certainly would have found convincing evidence for exoplanets.

16.  e–0.3 Planet: M < 13 MJup→ no nuclear burning Brown Dwarf: 13 MJup < M < ~70 MJup→ deuterium burning Star: M > ~70 MJup→ Hydrogen burning Global Properties of Exoplanets 2. Mass Distribution The Brown Dwarf Desert

17. There mass distribution falls off exponentially. N(20 MJupiter) ≈ 0.002 N(1 MJupiter) There should be a large population of low mass planets. Brown Dwarf Desert: Although there are ~100-200 Brown dwarfs as isolated objects, and several in long period orbits, there is a paucity of brown dwarfs (M= 13–50 MJup) in short (P < few years) as companion to stars

18. Semi-Major Axis Distribution Number Number Semi-major Axis (AU) Semi-major Axis (AU) The lack of long period planets is a selection effect since these take a long time to detect

19. 2. Eccentricity distribution

20. e=0.4 e=0.6 e=0.8 w=0 w=90 w=180

21. e Eri 2 ´´

22. Mass versus Orbital Distance Eccentricities

23. 3. Classes of planets: 51 Peg Planets Discovered by Mayor & Queloz 1995 How are we sure this is really a planet?

24. Curvature Span Bisectors can measure the line shapes and tell you about the nature of the RV variations: • What can change bisectors: • Spots • Pulsations • Convection pattern on star

26. The David Gray Controversy Gray & Hatzes 1997 If the bisector variations were real then 51 Peg has no planet

27. Hatzes et al. : No bisector variations

28. The final proof that these are really planets: The first transiting planet HD 209458

29. 3. Classes of planets: 51 Peg Planets • ~25% of known extrasolar planets are 51 Peg planets (selection effect) • 0.5–1% of solar type stars have giant planets in short period orbits • 5–10% of solar type stars have a giant planet (longer periods)

30. 3. Classes of planets: Hot Neptunes McArthur et al. 2004 Santos et al. 2004 Butler et al. 2004 Msini = 14-20 MEarth

31. 3. Classes: The Massive Eccentrics • Masses between 7–20 MJupiter • Eccentricities, e>0.3 • Prototype: HD 114762 m sini = 11 MJup

32. There are no massive planets in circular orbits 3. Classes: The Massive Eccentrics

33. 3. Classes: Planets in Binary Systems Why search for planets in binary stars? • Most stars are found in binary systems • Does binary star formation prevent planet formation? • Do planets in binaries have different characteristics? • For what range of binary periods are planets found? • What conditions make it conducive to form planets?(Nurture versus Nature?) • Are there circumbinary planets?

34. Some Planets in known Binary Systems: Nurture vs. Nature?

35. The first extra-solar Planet may have been found by Walker et al. in 1992 in abinary system:

36. g Cephei Periode 2,47 Jahre Msini 1,76 MJupiter e 0,2 a 2,13 AE K 26,2 m/s Planet Periode 56.8 ± 5 Jahre Msini ~ 0,4 ± 0,1 MSun e 0,42 ± 0,04 a 18.5 AE K 1,98 ± 0,08 km/s Doppelstern

38. Primärstern g Cephei Sekundärstern Planet

39. The planet around g Cep is difficult to form and on the borderline of being impossible. Standard planet formation theory: Giant planets form beyond the snowline where the solid core can form. Once the core is formed the protoplanet accretes gas. It then migrates inwards. In binary systems the companion truncates the disk. In the case of g Cep this disk is truncated just at the ice line. No ice line, no solid core, no giant planet to migrate inward. g Cep can just be formed, a giant planet in a shorter period orbit would be problems for planet formation theory.

40. 3. Planetary Systems

41. 25 Extrasolar Planetary Systems (18 shown) Star P (d) MJsini a (AU) e HD 82943 221 0.9 0.7 0.54 444 1.6 1.2 0.41 GL 876 30 0.6 0.1 0.27 61 2.0 0.2 0.10 47 UMa 1095 2.4 2.1 0.06 2594 0.8 3.7 0.00 HD 37124 153 0.9 0.5 0.20 550 1.0 2.5 0.40 55 CnC 2.8 0.04 0.04 0.17 14.6 0.8 0.1 0.0 44.3 0.2 0.2 0.34 260 0.14 0.78 0.2 5300 4.3 6.0 0.16 Ups And 4.6 0.7 0.06 0.01 241.2 2.1 0.8 0.28 1266 4.6 2.5 0.27 HD 108874 395.4 1.36 1.05 0.07 1605.8 1.02 2.68 0.25 HD 128311 448.6 2.18 1.1 0.25 919 3.21 1.76 0.17 HD 217107 7.1 1.37 0.07 0.13 3150 2.1 4.3 0.55 Star P (d) MJsini a (AU) e HD 74156 51.6 1.5 0.3 0.65 2300 7.5 3.5 0.40 HD 169830 229 2.9 0.8 0.31 2102 4.0 3.6 0.33 HD 160691 9.5 0.04 0.09 0 637 1.7 1.5 0.31 2986 3.1 0.09 0.80 HD 12661 263 2.3 0.8 0.35 1444 1.6 2.6 0.20 HD 168443 58 7.6 0.3 0.53 1770 17.0 2.9 0.20 HD 38529 14.31 0.8 0.1 0.28 2207 12.8 3.7 0.33 HD 190360 17.1 0.06 0.13 0.01 2891 1.5 3.92 0.36 HD 202206 255.9 17.4 0.83 0.44 1383.4 2.4 2.55 0.27 HD 11964 37.8 0.11 0.23 0.15 1940 0.7 3.17 0.3 m Ara: 4 planets

42. Resonant Systems Systems Star P (d) MJsini a (AU) e HD 82943 221 0.9 0.7 0.54 444 1.6 1.2 0.41 GL 876 30 0.6 0.1 0.27 61 2.0 0.2 0.10 55 CnC 14.6 0.8 0.1 0.0 44.3 0.2 0.2 0.34 HD 108874 395.4 1.36 1.05 0.07 1605.8 1.02 2.68 0.25 HD 128311 448.6 2.18 1.1 0.25 919 3.21 1.76 0.17 → 2:1 → 2:1 → 3:1 → 4:1 → 2:1 2:1 → Inner planet makes two orbits for every one of the outer planet

43. Eccentricities • Period (days)

44. Mass versus Orbital Distance Eccentricities

45. 4. The Dependence of Planet Formation on Stellar Mass Setiawan et al. 2005

46. Too faint (8m class tel.). Poor precision Ideal for 3m class tel. Main Sequence Stars RV Error (m/s) M0 K5 F0 K0 A5 G0 G5 A0 F5 Spectral Type

47. Exoplanets around low mass stars • Ongoing programs: • ESO UVES program (Kürster et al.): 40 stars • HET Program (Endl & Cochran) : 100 stars • Keck Program (Marcy et al.): 200 stars • HARPS Program (Mayor et al.):~100 stars • Results: • Giant planets (2) around GJ 876. Giant planets around low mass M dwarfs seem rare • Hot neptunes around several. Hot Neptunes around M dwarfs seem common

48. Exoplanets around massive stars Difficult on the main sequence, easier (in principle) for evolved stars

49. Hatzes & Cochran 1993 „…it seems improbable that all three would have companions with similar masses and periods unless planet formation around the progenitors to K giants was an ubiquitous phenomenon.“

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