Astrometric Detection of Exoplanets

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1 Astrometric Detection of Exoplanets

2 Angles & Coordinates: 1 full circle = 360 degrees 1 degree = 60 arcminutes 1 arcminute = 60 arcseconds ~ yards (2.908 cm at 100 meters) 1 milliarcsec (mas) = arcsec 1 microarcsec (µas) = arcsec Astronomical coordinates on sky: E-W: Right Ascension (RA) in h:m:s (0-24h) N-S: Declination (DEC) in deg:arcm:arcs ( )

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 Our solar system from 32 light years (10 pcs) 1 milliarcsecond

5 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

6 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

7 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.

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

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 1950 Barnard s star in 1997

11 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

12 Astrometry: Orbital Motion The astrometric signal is given by: θ = m a M 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 M 2/3 P 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

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

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

15 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)

16 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

17 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) = 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 ( mm)

18 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)

19 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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21

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

24 Real Astrometric Detections with the Hubble Telescope Fine Guidance Sensors

25 HST uses Narrow Angle Interferometry! G. Fritz Benedict (McD Obs.) HST is achieving astrometric precision of mas!

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

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28 The mass of Gl876b 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

29 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

30 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 Where we have invoked coplanarity for c, b, and e = (17.8 ± 5.6 M earth ) a Neptune!!

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

32 HST Astrometry of the extrasolar planet of ε Eridani 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

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

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

35

36 The Planetary System of υ And

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38 Note: the planets do not have the same inclination!

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40 Planets c and d are inclined by 30 degrees to each other!

41 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.

42 The astrometric perturbation of Vb 10 Mass = 6.4 M Jup

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

44 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!

45 Summary Astrometry is the oldest branch of Astronomy It is sensitive to planets at large orbital distances complimentary to radial velocity Gives you the true mass Very useful for system architecture (e.g. ups And) Least successful of all search techniques because the precision is about a factor of 1000 too large. Will have to await space based missions to have a real impact

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