1. Astrometric Detection of Exoplanets

2. Stellar Motion There are 4 types of stellar „motion“ that astrometry can measure: 1. Parallax (distance): the motion of stars caused by viewing them from different parts of the Earth‘s orbit 2. Proper motion: the true motion of stars through space 3. Motion due to the presence of companion 4. „Fake“ motion due to other physical phenomena

3. Astrometry - the branch of astronomy that deals with the measurement of the position and motion of celestial bodies It is one of the oldest subfields of the astronomy dating back at least to Hipparchus (130 B.C.), who combined the arithmetical astronomy of the Babylonians with the geometrical approach of the Greeks to develop a model for solar and lunar motions. He also invented the brightness scale used to this day. Brief History Hooke, Flamsteed, Picard, Cassini, Horrebrow, Halley also tried and failed Galileo was the first to try measure distance to stars using a 2.5 cm telescope. He of course failed.

4. 1887-1889 Pritchard used photography for astrometric measurements Modern astrometry was founded by Friedrich Bessel with his Fundamenta astronomiae, which gave the mean position of 3222 stars. 1838 first stellar parallax (distance) was measured independently by Bessel (heliometer), Struve (filar micrometer), and Henderson (meridian circle).

5. Astrometry is also fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy. Astrometric applications led to the development of spherical geometry. Mitchell at McCormick Observatory (66 cm) telescope started systematic parallax work using photography Astrometry is also fundamental for cosmology. The cosmological distance scale is based on the measurements of nearby stars.

6. Astrometry: Parallax Distant stars 1 AU projects to 1 arcsecond at a distance of 1 pc = 3.26 light years

7. Astrometry: Parallax So why did Galileo fail? d = 1 parsec  = 1 arcsecond F f = F/D D d = 1/  d in parsecs,  in arcseconds 1 parsec = 3.08 ×10 18 cm

8. Astrometry: Parallax So why did Galileo fail? D = 2.5cm, f ~ 20 (a guess) Plate scale = 360 o · 60´ ·60´´ 2  F = 206369 arcsecs F F = 500 mmScale = 412 arcsecs / mm Displacement of  Cen = 0.002 mm Astrometry benefits from high magnification, long focal length telescopes

9. Astrometry: Proper motion Discovered by Halley who noticed that Sirius, Arcturus, and Aldebaran were over ½ degree away from the positions Hipparchus measured 1850 years earlier

10. Astrometry: Proper motion Barnard is the star with the highest proper motion (~10 arcseconds per year) Barnard‘s star in 1950Barnard‘s star in 1997

11. Astrometry: Orbital Motion × a1a1 a2a2 a 1 m 1 = a 2 m 2 a 1 = a 2 m 2 /m 1 D To convert to an angular displacement you have to divide by the distance, D

12. m M a D  = The astrometric signal is given by: m = mass of planet M = mass of star a = orbital radius D = distance of star  = m M 2/3 P 2/3 D Astrometry: Orbital Motion Note: astrometry is sensitive to companions of nearby stars with large orbital distances Radial velocity measurements are distance independent, but sensitive to companions with small orbital distances This is in radians. More useful units are arcseconds (1 radian = 206369 arcseconds) or milliarcseconds (0.001 arcseconds) = mas

13. Astrometry: Orbital Motion With radial velocity measurements and astrometry one can solve for all orbital elements

14. Orbital elements solved with astrometry and RV: P - period T - epoch of periastron  - longitude of periastron passage e -eccentricity Solve for these with astrometry  - true semi-major axis i - orbital inclination  - position angle of ascending node  - proper motion  - parallax Solve for these with radial velocity  - offset K - semi-amplitude

15. All parameters are simultaneously solved using non-linear least squares fitting and the Pourbaix & Jorrisen (2000) constraint  = semi major axis  = parallax K 1 = Radial Velocity amplitude P = period e = eccentricity  A sin i  abs = PK 1 √ (1 - e 2 ) 2  × 4.705

16. So we find our astrometric orbit But the parallax can disguise it And the proper motion can slinky it

17. The Space motion of Sirius A and B

18. Astrometric Detections of Exoplanets The Challenge: for a star at a distance of 10 parsecs (=32.6 light years): Source Displacment (  as) Jupiter at 1 AU100 Jupiter at 5 AU500 Jupiter at 0.05 AU5 Neptune at 1 AU6 Earth at 1 AU0.33 Parallax100000 Proper motion (/yr)500000

19. The Observable Model Must take into account: 1. Location and motion of target 2. Instrumental motion and changes 3. Orbital parameters 4.Physical effects that modify the position of the stars

21. The Importance of Reference stars Perfect instrumentPerfect instrument at a later time Reference stars: 1. Define the plate scale 2. Monitor changes in the plate scale (instrumental effects) 3. Give additional measures of your target Focal „plane“ Detector Example Typical plate scale on a 4m telescope (Focal ratio = 13) = 3.82 arcsecs/mm = 0.05 arcsec/pixel (15  m) = 57mas/pixel. The displacement of a star at 10 parsecs with a Jupiter-like planet would make a displacement of 1/100 of a pixel (0.00015 mm)

22. Good Reference stars can be difficult to find: 1. They can have their own (and different) parallax 2. They can have their own (and different) proper motion 3. They can have their own companions (stellar and planetary) 4. They can have starspots, pulsations, etc (as well as the target)

23. Where are your reference stars?

24. In search of a perfect reference. You want reference objects that move little with respect to your target stars and are evenly distributed in the sky. Possible references: K giant stars V-mag > 10. Quasars V-mag >13 Problem: the best reference objects are much fainter than your targets. To get enough signal on your target means low signal on your reference. Good signal on your reference means a saturated signal on your target → forced to use nearby stars

25. Astrometric detections: attempts and failures To date no extrasolar planet has been discovered with the astrometric method, although there have been several false detections Barnard´s star

29. Scargle Periodogram of Van de Kamp data False alarm probability = 0.0015! A signal is present, but what is it due to? Frequency (cycles/year)

30. New cell in lens installed Lens re-aligned Hershey 1973 Van de Kamp detection was most likely an instrumental effect

31. Lalande 21185

32. Gatewood 1973 Gatewood 1996: At a meeting of the American Astronomical Society Gatewood claimed Lalande 21185 did have a 2 M jupiter planet in an 8 yr period plus a second one with M < 1 M jupiter at 3 AU. After 16 years these have not been confirmed.

33. Real Astrometric Detections with the Hubble Telescope Fine Guidance Sensors

34. HST uses Narrow Angle Interferometry !

35. The first space interferometer for astrometric measurements: The Fine Guidance Sensors of the Hubble Space Telescope

36. Fossil Astronomy at its Finest - 1.5% Masses M Tot =0.568 ± 0.008M O M A =0.381 ± 0.006M O M B =0.187 ± 0.003M O π abs = 98.1 ± 0.4 mas HST astrometry on a Binary star

37. Image size at best sites from ground HST is achieving astrometric precision of 0.1–1 mas

38. One of our planets is missing: sometimes you need the true mass! HD 33636 b P = 2173 d msini = 10.2 M Jup B i = 4 deg → m = 142 M Jup = 0.142 M sun Bean et al. 2007AJ....134..749B

39. GL 876 M- dwarf host star Period = 60.8 days

40. Gl 876

42. The more massive companion to Gl 876 (Gl 876b) has a mass M b = 1.89 ± 0.34 M Jup and an orbital inclination i = 84° ± 6°. Assuming coplanarity, the inner companion (Gl 876c) has a mass M c = 0.56 M Jup The mass of Gl876b

43. Cambel and Walker  Eri was a „probable variable“ The Planet around  Eridani

45. What the eye does not see a periodogram finds: Radial Velocities Activity indicator FAP ≈ 10 –9 Period = 6.9 years

47. Mass (true) = 1.53 ± 0.29 M Jupiter  Eri  = 0.3107 arcsec (parallax) a = 2.2 mas (semi-major axis) i = 30° (inclination) X-displacement (arc-seconds) Y-displacement (arc-seconds)

48. Orbital inclination of 30 degrees is consistent with inclination of dust ring

49. One worrisome point: The latest radial velocities do not fit the orbit:

51. Astrometric measurements of HD 38529

52.  A sin i  abs = PK 1 √ (1 - e 2 ) 2  × 4.705 Brown Dwarf

56. The Planetary System of  And

57. Note: the planets do not have the same inclination!

63. The Purported Planet around Vb10 Up until now astrometric measurements have only detected known exoplanets. Vb10 was purported to be the first astrometric detection of a planet. Prada and Shalkan 2009 claimed to have found a planet using the STEPS: A CCD camera mounted on the Palomar 5m. 9 years of data were obtained.

64. Vb 10Control star

66. The Periodograms show a significant signal at 0.74 years

67. The astrometric perturbation of Vb 10 Mass = 6.4 M Jup

69. Looks like a confirmation with radial velocity measurements, but it is only driven by one point

71. The RV data does not support the previous RV model. The only way is to have eccentric orbits which is ruled out by the astrometric measurements.

72. Is there something different about the first point? Taken with a different slit width! “Science is a way of trying not to fool yourself. The first principle is that you must not fool yourself, and you are the easiest person to fool.” – Richard Feynman

73. Comparison between Radial Velocity Measurements and Astrometry. Astrometry and radial velocity measurements are fundamentally the same: you are trying to measure a displacement on a detector 1. Measure a displacement of a spectral line on a detector 1. Measure a displacement of a stellar image on a detector 2. Thousands of spectral lines (decrease error by √N lines ) 2. One stellar image 3. Hundreds of reference lines (Th- Ar or Iodine) to define „plate solution“ (wavelength solution) 3. 1-10 reference stars to define plate solution 4. Reference lines are stable 4. Reference stars move! AstrometryRadial Velocity

74. Space: The Final Frontier 1. Hipparcos 3.5 year mission ending in 1993 ~100.000 Stars to an accuracy of 7 mas 2. Gaia 1.000.000.000 stars V-mag 15: 24  as V-mag 20: 200  as Launch 2011 2012 2013

77. detection Parameters determined GAIA Detection limits Red: G-stars Blue: M Dwarfs Casertano et al. 2008

78. Number of Expected Planets from GAIA 8000 Giant planet detections 4000 Giant planets with orbital parameters determined 1000 Multiple planet detections 500 Multiple planets with orbital parameters determined

79. 1 milliarcsecond Our solar system from 32 light years (10 pcs) 40  as In spite of all these „problems“GAIA has the potential to find planetary systems

80. 1. Astrometry is the oldest branch of Astronomy 2. It is sensitive to planets at large orbital distances → complimentary to radial velocity 3. Gives you the true mass 4.Least successful of all search techniques because the precision is about a factor of 1000 to large. 5.Will have to await space based missions to have a real impact Summary

81. Sources of „Noise“ Secular changes in proper motion: Small proper motion Large proper motion Perspective effect

82. dd dt = – 2v r AU  dd dt = – v r AU  In arcsecs/yr 2 and arcsecs/yr if radial velocity v r in km/s,  in arcsec,  in arcsec/yr (proper motion and parallax)

84. The Secular Acceleration of Barnard‘s Star (Kürster et al. 2003).

85. Sources of „Noise“ Relativistic correction to stellar aberration: No observer motionobserver motion  aber ≈ v c sin  – 1 4 v2v2 c2c2 sin 2  + 1 6 v3v3 c3c3 ( 1 + 2 sin 2  ) = 20-30 arcsecs = 1-3 mas  = angle between direction to target and direction of motion = ~  as

86. Sources of „Noise“ Gravitational deflection of light:  defl = 4 GM Ro c2Ro c2 cot  2 M = mass of perturbing body R o = distance between solar system body and source c, G = speed of light, gravitational constant  = angular distance between body and source

88. Source  (  as) @limbd min (1  as) Sun1.75×10 6 180 o Mercury839´ Venus4934 o.5 Earth574123 o (@10 6 km) Moon265 o (@10 6 km) Mars11625´ Jupiter1626090 o Saturn578017 o Uranus208071´ Neptune253351´ Ganymede3532´´ Titan3214´´ Io3119´´ Callisto2823´´ Europa1911´´ Triton100.7´´ Pluto70.4´´ d min is the angular distance for which the effect is still 1  as  is for a limb-grazing light ray

89. Spots : y x Brightness centroid

90. Astrometric signal of starspots 2 spots radius 5 o and 7 o, longitude separation = 180 o  T=1200 K, distance to star = 5 pc, solar radius for star Latitude = 10 o,60 o Latitude = 10 o,0 o Horizontal bar is nominal precision of SIM