Radial Velocity Detection of Planets: II. Results

1. Radial Velocity Detection of Planets:II. Results • Period Analysis • Global Parameters • Classes of Planets Binary star simulator: http://instruct1.cit.cornell.edu/courses/astro101/java/binary/binary.htm#instructions

2. The Nebraska Astronomy Applet Project (NAAP) http://astro.unl.edu/naap/ This is the coolest astronomical website for learning basic astronomy that you will find. In it you can find: • Solar System Models • Basic Coordinates and Seasons • The Rotating Sky • Motions of the Sun • Planetary Orbit Simulator • Lunar Phase Simulator • Blackbody Curves & UBV Filters • Hydrogen Energy Levels • Hertzsprung-Russel Diagram • Eclipsing Binary Stars • Atmospheric Retention • Extrasolar Planets • Variable Star Photometry

3. The Nebraska Astronomy Applet Project (NAAP) On the Exoplanet page you can find: • Descriptions of the Doppler effect • Center of mass • Detection And two nice simulators where you can interactively change parameters: • Radial Velocity simulator (can even add data with noise) • Transit simulator (even includes some real transiting planet data)

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

5. Try 16.3 minutes:

6. Lomb-Scargle Periodogram of the data:

7. 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

8. 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 = amplitude2) of each sine wave that is in the data

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

10. 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

11. The first Tautenburg Planet: HD 13189

12. 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

13. False alarm probability ≈ 10–14 Alias Peak Noise level

14. Alias periods: Undersampled periods appearing as another period

15. 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.

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

17. Most algorithms (fortran and c language) can be found in Numerical Recipes Period04: multi-sine fitting with Fourier analysis. Tutorials available plus versions in Mac OS, Windows, and Linux http://www.univie.ac.at/tops/Period04/ • To summarize the period search techniques: • Sine fitting gives you the c2 as a function of period. c2 is minimized for the correct period. • Fourier transform gives you the amplitude (m/s in our case) for a periodic signal in the data. • Lomb-Scargle gives an amplitude related to the statistical signal of the data.

18. Results from Doppler Surveys Butler et al. 2006, Astrophysical Journal, Vol 646, pg 505

19. 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.

20. Campbell, Walker, & Yang 1988 „Probable third body variation of 25 m s–1, 2.7 year period, superposed on a large velocity gradient“

21. e Eri was a „probable variable“

22. Probably the first extrasolar planet: HD 114762 with Msini = 11 MJ discovered by Latham et al. (1989) Filled circles are data taken at McDonald Observatory using the telluric lines at 6300 Ang.

23. A short time-line of Radial Velocity (RV) Planet Discoveries 1979: Campbell und Walker use HF cell to survey 26 solar-type stars. They find evidence for possible companions around e Eri and g Cep. 1989: Latham et al (1989) report 11 MJupiter companion round the star HD 114762. 1992: Wolszczan discovers planets around pulsars 1992: Walker et al. Publish the discovery of RV variations with 2,47 years in g Cep can be due to a 1.5 MJupiter companion. They think it is due to stellar rotation. 1993: Hatzes & Cochran report long period RV variations in 3 K giant stars. Suggest planets may be one explanation 1995: Mayor & Queloz announce discovery of planet around 51 Peg Today: over 300 known extrasolar planets

24.  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

25. One argument: Because of unknown vsini these are just low mass stars seen with i near 0 i decreasing probability decreasing

26. Argument against stars #2 Some planetary systems have multiple planets, for example msini = 5 MJup, and msini = 0.03 MJup. To make the first planet a star requires sini =0.01. Other planet would still be mtrue=3 MJup Argument against stars #1 Probability an orbit has an inclination less than q P(i < q) = 1-cos q e.g. for m sin i = 0.5 MJup for this to have a true mass of 0.5 Msun sin i would have to be 0.01. This implies q = 0.6 deg or P =0.00005

27. There mass distribution falls off exponentially. N(20 MJupiter) ≈ 0.002 N(1 MJupiter) There should be a large population of very 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

28. An Oasis in the Brown Dwarf Desert: HD 137510 = HR 5740

29. 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

30. 2. Eccentricity distribution Fall off at high eccentricity may be partially due to an observing bias…

31. e=0.4 e=0.6 e=0.8 w=0 w=90 w=180 …high eccentricity orbits are hard to detect!

32. For very eccentric orbits the value of the eccentricity is is often defined by one data point. If you miss the peak you can get the wrong mass!

33. At opposition with Earth would be 1/5 diameter of full moon, 12x brighter than Venus e Eri 2 ´´ Comparison of some eccentric orbit planets to our solar system

34. Mass versus Orbital Distance Eccentricities

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

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

37. 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)

39. So how do you form a Giant planet at 0.05 AU? • Prior to 1995 the standard model was: • Giant planets form beyond the „ice line“ at 3-5 AU • Enough ices to form a 10-13 MEarth core • Once core forms it can accrete gaseous envelope • Voila! A giant planet at > 5 AU

40. Solution: • Form planet in ``normal´´ manner • When planet has 1 MJ mass tidal torques open a gap in the disk • Disk torques on the planet cause it to migrate inwards Timescales ~ 500.000 years Trilling et al 1998

41. Problem for giant planet formation at 0.05 AU: • At a < 0.1 AU disk is too hot for grains to form • Too little solid material to form 10-15 Mearth core • Too little gas to build envelope

42. Migration Theory is not without problems: • What stops the migration? • Jupiter should not exist!! You will learn more from the planet formation part of the course

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

44. 3. Classes: The Massive Eccentrics • Masses between 7–20 MJupiter • Eccentricities, e > 0.3 • Prototype: HD 114762 discovered in 1989! m sini = 11 MJup

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

46. 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?

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

48. The first extra-solar Planet may have been found by Walker et al. in 1992 in abinary system: Ca II is a measure of stellar activity (spots)

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