Astrometric Detection of Exoplanets. The Astrometric Detection of Planets

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1 Astrometric Detection of Exoplanets

2 Detection and Properties of Planetary Systems Schedule of Lectures 05. Apr: Introduction and Background 12. Apr: The Radial Velocity Method: Method and Tools 19. Apr: The Radial Velocity Method: Results 26. Apr: Astrometric Detections 03. May: Direct Imaging 10. May: The Transit Method 17. May: Transiting Exopanets : Results 24. May: Atmospheres and Interiors 31. May: Gravitational Microlensing 07. Jun: The Timing Method (Dr. Eike Guenther) 14. Jun: Host Stars (Dr. Eike Guenther) 21. Jun: TBD 28. Jun: In Search of Habitable Planets 06. Jul: No Class

3 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

4 Brief History 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. Galileo was the first to try measure distance to stars using a 2.5 cm telescope. He of course failed. Hooke, Flamsteed, Picard, Cassini, Horrebrow, Halley also tried and failed

5 1838 first stellar parallax (distance) was measured independently by Bessel (heliometer), Struve (filar micrometer), and Henderson (meridian circle). Modern astrometry was founded by Friedrich Bessel with his Fundamenta astronomiae, which gave the mean position of 3222 stars Pritchard used photography for astrometric measurements

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

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

9 Astrometry: Parallax So why did Galileo fail? θ= 1 arcsecond d = 1/θ, d in parsecs, θ in arcseconds d = 1 parsec 1 parsec = cm = 3.26 light years F D f = F/D

10 Astrometry: Parallax So why did Galileo fail? D = 2.5cm, f ~ 20 (a guess) Plate scale = 360 o = 2 π F arcsecs F F = 500 mm Scale = 412 arcsecs / mm Displacement of α Cen = mm Astrometry benefits from high magnification, long focal length telescopes

11 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

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

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

14 Astrometry: Orbital Motion The astrometric signal is given by: θ = m M a D This is in radians. More useful units are arcseconds (1 radian = arcseconds) or milliarcseconds (0.001 arcseconds) = mas m = mass of planet M = mass of star a = orbital radius D = distance of star θ = m P 2/3 M 2/3 D 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

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

16 Orbital elements solved with astrometry and RV: P - period T - epoch of periastron ω - longitude of periastron passage e -eccentricity Solve for these with astrometry α - semiaxis major i - orbital inclination Ω - position angle of ascending node µ - proper motion π - parallax Solve for these with radial velocity γ - offset K - semi-amplitude

17 All parameters are simultaneously solved using non-linear least squares fitting and the Pourbaix & Jorrisen (2000) constraint α A s i n i ω a b s = P K 1 ( 1 - e 2 ) 2 π α = semi major axis ω = parallax K 1 = Radial Velocity amplitude P = period e = eccentricity

18 So we find our astrometric orbit But the parallax can disguise it And the proper motion can slinky it Julian Date x x10 6 Julian Date Julian Date x10 6

19 The Space motion of Sirius A and B

20 Astrometric Detections of Exoplanets The Challenge: for a star at a distance of 10 parsecs (=32.6 light years): Source Displacment (µas) Jupiter at 1 AU 100 Jupiter at 5 AU 500 Jupiter at 0.05 AU 5 Neptune at 1 AU 6 Earth at 1 AU 0.33 Parallax Proper motion (/yr) µas = 10-6 arcsec

21 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

22 * * * * * Astrometry, a simple example 5 "plates" different scales different orientations * * * * * * * * * * * * * Observations are taken at different times, different instrument setups and sometimes different telescopes * * * * 4 * * * * * * * * 5 Result of Overlap Solution to Plate #1 Precision = standard deviation of the distribution of residuals ( ) from the model-derived positions (*) * * * * * * Frames have to rotated, stretched, aligned and stacked I0.002 arcsec

23 The Importance of Reference stars Example Focal plane Detector Perfect instrument Perfect 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 Typical plate scale on a 4m telescope (Focal ratio = 13) = 3.82 arcsecs/mm = 0.05 arcsec/pixel (15 µm) = 57 mas/pixel. The displacement of a star at 10 parsecs with a Jupiter-like planet would make a displacement of 1/100 of a pixel ( mm)

24 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)

25 Where are your reference stars?

26 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

27 A saturated bright star:

28 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

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

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

34 Lalande 21185

35 Lalande Gatewood 1973 Gatewood 1996: At a meeting of the American Astronomical Society Gatewood claimed Lalande did have a 2 M jupiter planet in an 8 yr period plus a second one with M < 1M jupiter at 3 AU. After 21 years these have not been confirmed.

36 Real Astrometric Detections with the Hubble Telescope Fine Guidance Sensors

37 HST uses Narrow Angle Interferometry!

38 The first space interferometer for astrometric measurements: The Fine Guidance Sensors of the Hubble Space Telescope Uses a Koersters Prism

39 Fossil Astronomy at its Finest - 1.5% Masses -0.1 W 1062 AB 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 Declination (arcsec) HST astrometry on a Binary star (N) 90 (E) RA (arcsec)

40 Image size at best sites from ground HST is achieving astrometric precision of mas

41 One of our planets is missing: sometimes you need the true mass! HD b B P = 2173 d, Msini = 10.2 M Jup Bean et al. 2007AJ B i = 4 deg m = 142 M Jup = M sun

42 M- dwarf host star Period = 60.8 days GL 876

43 The Radial Velocity Curve of Gl 876

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45 The astrometric perturbation of GL 876

46 The mass of Gl876 b 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

47 55 Cnc d Perturbation due to component d, P = 4517 days α = 1.9 ± 0.4 mas i = 53 ± 7 M d sin i = 3.9 ± 0.5 M J Combining HST astrometry and ground-based RV M d = 4.9 ± 1.1 M J McArthur et al ApJL, 614, L81

48 The 55 Cnc (= ρ 1 Cnc) planetary system, from outerto inner-most ID r(au) M (M Jup ) d ± 1.1 c ± 0.07 b ±0.19 e ± 0.02 = (17.8 ± 5.6 M earth ) a Neptune!! Where we have invoked coplanarity for c, b, and e

49 The Planet around ε Eridani Distance = 3.22 pcs = 10 light years Period = 6.9 yrs

50 HST Astrometry of the extrasolar planet of ε Eridani

51 The x- y- displacement of ε Eri ε Eri π = arcsec (parallax) a = 2.2 mas (semi-major axis) i = 30 (inclination) X-displacement (arc-seconds) Y-displacement (arc-seconds) Mass (true) = 1.53 ± 0.29 M Jupiter

52 Orbital inclination of 30 degrees is consistent with inclination of dust ring

53 Astrometric Masses of Exoplanets

54 Astrometric measurements of HD 38529

55 α A s i n i ω a b s = P K 1 ( 1 - e 2 ) 2 π Brown Dwarf

56 The x- y- perturbation of HD 38529

57 The Astrometric Orbit of HD 38529b

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59 The Planetary System of υ And

60 The Orbital Inclinations of υ And c,d Note: the planets do not have the same inclination!

61 TheAstrometric Perturbation of υ And

62 The Astrometric Perturbation of υ And

63 The Astrometric Orbits of υ And c,d

64 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.

65 The x- y- perturbation of Vb 10 Vb 10 Control star

66 The control stars are constant Control star Control star

67 The Periodograms show a significant signal at 0.74 years

68 The astrometric perturbation of Vb 10

69 The astrometric orbit of Vb 10 Mass = 6.4 M Jup

70 But there are no Radial Velocity Variations! A possible problem: The RV measurements show no variability, but these are at low precision It is unlikely that it is a more massive companion in an eccentric orbit Red lines: A high amplitude radial velocity model showing that the measurements would have missed the periastron passage

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

73 The IR measurements shows no radial velocity variations no planet!

74 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.

75 Is there something different about the first point? 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 Taken with a different slit width!

76 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 Radial Velocity 1. Measure a displacement of a spectral line on a detector 2. Thousands of spectral lines (decrease error by N lines ) 3. Hundreds of reference lines (Th- Ar or Iodine) to define plate solution (wavelength solution) Astrometry 1. Measure a displacement of a stellar image on a detector 2. One stellar image reference stars to define plate solution 4. Reference lines are stable 4. Reference stars move!

77 Space: The Final Frontier 1. Hipparcos 3.5 year mission ending in 1993 ~ Stars to an accuracy of 7 mas 2. Gaia stars V-mag 15: 24 µas V-mag 20: 200 µas Launch December 2013

78 GAIA from the Thüringer Landessternwarte Tautenburg

79 Gaia Sky Coverage Sky coverage due to motion about sun Sky coverage due to spacecraft tilt with respect to sun direction Sky coverage due to spin of spacecraft

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

81 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

82 Sources of Noise Secular changes in proper motion: Small proper motion Large proper motion Perspective effect

83 dµ dt = 2v r AU µπ dπ dt = v r AU π 2 In arcsecs/yr 2 and arcsecs/yr if radial velocity v r in km/s, π in arcsec, µ in arcsec/yr (proper motion and parallax)

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

86 Sources of Noise Relativistic correction to stellar aberration: No observer motion observer motion θ = angle between direction to target and direction of motion α aber v c sin θ 1 4 v 2 c 2 sin 2 θ v 3 c 3 sin 2 θ ( sin 2 θ) = arcsecs = 1-3 mas = ~ µas

87 Gravitational deflection of light: Sources of Noise α defl = 4 GM R o c 2 cot ψ 2 M = mass of perturbing body R o = distance between solar system body and source c, G = speed of light, gravitational constant ψ = angular distance between body and source

88 Source d min (1 µas) Sun o Mercury 83 9 Venus o.5 Earth o (@10 6 km) Moon 26 5 o (@10 6 km) Mars Jupiter o Saturn o Uranus Neptune Ganymede Titan Io Callisto Europa Triton Pluto d min is the angular distance for which the effect is still 1 µas α is for a limb-grazing light ray

89 Spots : y Brightness centroid x

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

91 Our solar system from 32 light years (10 pcs) 1 milliarcsecond 40 µas In spite of all these problems GAIA has the potential to find planetary systems

92 Summary 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. We have to await space based missions to have a real impact