1. Radial Velocity Detection of Planets: II. Results 1. Period Analysis 2. Global Parameters 3. Classes of Planets http://instruct1.cit.cornell.edu/courses/astro101/java/binary/binary.htm#instructions Binary star simulator:

2. The Nebraska Astronomy Applet Project (NAAP) This is the coolest astronomical website for learning basic astronomy that you will find. In it you can find: 1. Solar System Models 2. Basic Coordinates and Seasons 3. The Rotating Sky 4. Motions of the Sun 5. Planetary Orbit Simulator 6. Lunar Phase Simulator 7. Blackbody Curves & UBV Filters 8. Hydrogen Energy Levels 9. Hertzsprung-Russel Diagram 10. Eclipsing Binary Stars 11. Atmospheric Retention 12. Extrasolar Planets 13.Variable Star Photometry http://astro.unl.edu/naap/

3. The Nebraska Astronomy Applet Project (NAAP) On the Exoplanet page you can find: 1. Descriptions of the Doppler effect 2. Center of mass 3. Detection And two nice simulators where you can interactively change parameters: 1.Radial Velocity simulator (can even add data with noise) 2. 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 1. Least squares sine fitting: Fit a sine wave of the form: V(t) = A·sin(  t +  ) + Constant Where  = 2  /P,  = phase shift Best fit minimizes the  2 :  2 =  d i –g i ) 2 /N d i = data, g i = 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. Period Analysis 2. Discrete Fourier Transform: Any function can be fit as a sum of sine and cosines FT(  ) =  X j (T) e –i  t N0N0 j=1 A DFT gives you as a function of frequency the amplitude (power = amplitude 2 ) of each sine wave that is in the data Power: P x (  ) = | FT X (  )| 2 1 N0N0 P x (  ) = 1 N0N0 N 0 = number of points [(  X j cos  t j +  X j sin  t j ) ( ) ] 2 2 Recall e i  t = cos  t + i sin  t X(t) is the time series

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

10. 1. Period Analysis 2. 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

11. The first Tautenburg Planet: HD 13189

12. Least squares sine fitting: The best fit period (frequency) has the lowest  2 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 Lomb-Scargle Periodogram: Gives the power of each frequency that is present in the data. Power is a measure of statistical signficance Amplitude (m/s)

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

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

17. To summarize the period search techniques: 1. Sine fitting gives you the  2 as a function of period.  2 is minimized for the correct period. 2. Fourier transform gives you the amplitude (m/s in our case) for a periodic signal in the data. 3. Lomb-Scargle gives an amplitude related to the statistical signal of the data. 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/

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

19. Campbell & Walker: The Pioneers of RV Planet Searches 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. 1988:

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

21.  Eri was a „probable variable“

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

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 M Jupiter 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  Cep can be due to a 1.5 MJupiter companion. They think it is due to stellar rotation. 1995: Mayor & Queloz announce discovery of planet around 51 Peg Today: over 300 known extrasolar planets 1993: Hatzes & Cochran report long period RV variations in 3 K giant stars. Suggest planets may be one explanation

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

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

26. P(i <  ) = 1-cos  Probability an orbit has an inclination less than  e.g. for m sin i = 0.5 M Jup 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 Argument against stars #1 Argument against stars #2 Some planetary systems have multiple planets, for example msini = 5 M Jup, and msini = 0.03 M Jup. To make the first planet a star requires sini =0.01. Other planet would still be m true =3 M Jup

27. N(20 M Jupiter ) ≈ 0.002 N(1 M Jupiter ) There mass distribution falls off exponentially. 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 M Jup ) 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 Semi-major Axis (AU) Number 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=0.4e=0.6e=0.8  =0  =90  =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. 2 ´´  Eri Comparison of some eccentric orbit planets to our solar system At opposition with Earth would be 1/5 diameter of full moon, 12x brighter than Venus

34. Eccentricities Mass versus Orbital Distance

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. ~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) 3. Classes of planets: 51 Peg Planets

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 M Earth 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 M J mass tidal torques open a gap in the disk Disk torques on the planet cause it to migrate inwards Trilling et al 1998 Timescales ~ 500.000 years

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

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

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

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

46. 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? Why search for planets in binary stars? 3. Classes: Planets in Binary Systems

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 a binary system: Ca II is a measure of stellar activity (spots)

49. 2,13 AUa 0,2e 26,2 m/sK 1,76 M Jupiter Msini 2,47 YearsPeriode Planet 18.5 AUa 0,42 ± 0,04e 1,98 ± 0,08 km/sK ~ 0,4 ± 0,1 M Sun Msini 56.8 ± 5 YearsPeriode Binary  Cephei

51. Primärstern Sekundärstern Planet

52. The planet around  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  Cep this disk is truncated just at the ice line. No ice line, no solid core, no giant planet to migrate inward.  Cep can just be formed, a giant planet in a shorter period orbit would be problems for planet formation theory.

53. M 1 = 1.06 s.m. M 2 = 0.96 s.m. P = 25.7 yrs a = 12.3 AU e = 0.5 m sin i = 1.14 M J P = 3.35 days a = 0.05 AU e = 0.0 Konacki (2005) Disk truncated at 1.3 – 1.5 AU! Binary Orbit Planet Orbit HD 188753

54. Eggenberger et al. 2007

55. Eggenberger et al. 2007 could not confirm presence of planet

56. 3. Planetary Systems

57. 33 Extrasolar Planetary Systems (18 shown) Star P (d) M J sini 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 1.10.25 919 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) M J sini 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

58. The 5-planet System around 55 CnC 5.77 M J Red: solar system planets 0.11 M J 0.17M J 0.03M J 0.82M J

59. The Planetary System around GJ 581 7.2 M E 5.5 M E 16 M E Inner planet 1.9 M E

60. Resonant Systems Systems Star P (d) M J sini 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 1.10.25 919 3.21 1.76 0.17 2:1 → Inner planet makes two orbits for every one of the outer planet → → 2:1 →3:1 →4:1 →2:1

61. Eccentricities Period (days) Red points: Systems Blue points: single planets

62. Eccentricities Mass versus Orbital Distance Red points: Systems Blue points: single planets

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

64. A0 A5 F0 F5 RV Error (m/s) G0G5 K0 K5 M0 Spectral Type Main Sequence Stars Ideal for 3m class tel. Too faint (8m class tel.). Poor precision ~10000 K~3500 K 2 M sun 0.2 M sun

65. 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.):~200 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

68. GL 876 System 1.9 M J 0.6 M J Inner planet 0.02 M J

69. Exoplanets around massive stars Difficult with the Doppler method because more massive stars have higher effective temperatures and thus few spectral lines. Plus they have high rotation rates. Result: few planets around early-type, more massive stars, and these around F-type stars (~ 1.4 solar masses)

70. Galland et al. 2005 HD 33564 M * = 1.25 msini = 9.1 M Jupiter P = 388 days e = 0.34 F6 V star

71. HD 8673

72. Frequency (c/d) Scargle Power P = 328 days Msini = 8.5 M jupiter e = 0.24 An F4 V star from the Tautenburg Program M * = 1.2 M סּ

73. Parameter30 Ari BHD 8673 Period (days)3381628 e0.210.711 K (m/s)278290 a (AU)1.062.91 M sin i (M Jup )10.112.7 Sp. TF4 VF7 V Stellar Mass (M סּ )1.41.2 The Tautenburg F-star Planets

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

75. A 1.9 M סּ main sequence star A 1.9 M סּ K giant star

76. „…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.“ Hatzes & Cochran 1993

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

78. CFHT McDonald 2.1m McDonald 2.7m TLS The Planet around Pollux The RV variations of  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 M Jup. Mass of star = 1.9 x that of sun

79. HD 13189 P = 471 d Msini = 14 M J M * = 3.5 M sun

80. Period471 ± 6 d RV Amplitude173 ± 10 m/s e0.27 ± 0.06 a1.5 – 2.2 AU m sin i14 M Jupiter Sp. Type K2 II – III Mass3.5 M sun V sin i2.4 km/s HD 13189 HD 13189 b

81. HD 13189 is also a pulsating star This explains the large scatter in the RV measurements

82. From Michaela Döllinger‘s Ph.D thesis M sin i = 3.5 – 10 M Jupiter P = 272 d Msini = 6.6 M J e = 0.53 M * = 1.2 M סּ P = 159 d Msini = 3 M J e = 0.03 M * = 1.15 M סּ P = 477 d Msini = 3.8 M J e = 0.37 M * = 1.0 M סּ P = 517 d Msini = 10.6 M J e = 0.09 M * = 1.84 M סּ P = 657 d Msini = 10.6 M J e = 0.60 M * = 1.2 M סּ P = 1011 d Msini = 9 M J e = 0.08 M * = 1.3 M סּ

83. M (M סּ ) N Stellar Mass Distribution: Döllinger Sample Mean = 1.4 M סּ Median = 1.3 M סּ ~10% of the intermediate mass stars have giant planets

84. Eccentricity versus Period Blue points are results from Giant stars

85. M sin i (M jupiter ) N Planet Mass Distribution for Solar-type Dwarfs P> 100 d Planet Mass Distribution for Giant and Main Sequence stars with M > 1.1 M סּ More massive stars tend to have a more massive planets and at a higher frequency

86. Preliminary results from Surveys of Intermediate Mass Stars More massive stars have a higher frequency of planets compared to solar type stars (~factor of two) More massive stars tend to have more massive planets

87. Jovian Analogs: Giant Planets at ≈ 5 AU Definition: A Jupiter mass planet in a 11 year orbit (5.2 AU) In other words we have yet to find one. Long term surveys (+15 years) have excluded Jupiter mass companions at 5AU in ~45 stars Period = 14.5 yrs Mass = 4.3 M Jupiter e = 0.16

88. Long period planet Very young star Has a dusty ring Nearby (3.2 pcs) Astrometry (1-2 mas) Imaging (  m =20-22 mag) Other planets?  Eri Clumps in Ring can be modeled with a planet here (Liou & Zook 2000)

89. Radial Velocity Measurements of  Eri Large scatter is because this is an active star Hatzes et al. 2000

90. Scargle Periodogram of  Eri Radial velocity measurements False alarm probability ~ 10 –8 Scargle Periodogram of Ca II measurements

92. Expectations based on one example are often wrong! Expectations 1. Planets should be common 2. Giant planets at 5 AU 3. Planets are in circular orbits 4. One Jovian-mass planet Reality 1. 5-10% of solar type stars have Giantplanetary companions 2. Giant planets have a wide range ofa down toa= 0.02 3. Many planets with very eccentric orbits. 4. ESP systems can have several Jovian-mass planets