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Astrometric Detection of Planets

Astrometric Detection of Planets. 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

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Astrometric Detection of Planets

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  1. Astrometric Detection of Planets

  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 physical phenomena (noise)

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

  4. 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). • 1887-1889 Pritchard used photography for astrometric measurements

  5. 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.

  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? q= 1 arcsec 1 parsec = 3.08 ×1018 cm d = 1 parsec d = 1/q, d in parsecs, q in arcseconds f = F/D F D

  8. 360o · 60´ ·60´´ 206369 arcsecs 2 p F F Astrometry: Parallax So why did Galileo fail? D = 2.5cm, f ~ 20 (a guess) Plate scale = = F = 500 mm Scale = 412 arcsecs / mm Displacement of a 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 1950 Barnard‘s star in 1997

  11. D To convert to an angular displacement you have to divide by the distance, D Astrometry: Orbital Motion a1m1 = a2m2 a1 = a2m2 /m1 a2 × a1

  12. q = P2/3 m D M2/3 Astrometry: Orbital Motion The astrometric signal is given by: This is in radians. More useful units are arcseconds (1 radian = 206369 arcseconds) or milliarcseconds (0.001 arcseconds) m a q = M D m = mass of planet M = mass of star a = orbital radius D = distance of star 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. • Orbital elements solved with astrometry and RV: P - period T - epoch of periastron w - longitude of periastron passage e -eccentricity • • Solve for these with astrometry • - semiaxis major i - orbital inclination • W - position angle of ascending node • m - proper motion p- parallax • • Solve for these with radial velocity • g - offset • K - semi-amplitude

  15. All parameters are simultaneously solved using non-linear least squares fitting and the Pourbaix & Jorrisen (2000) constraint - a √ ( 1 e ) 2 s i n i P K 1 = A w p × 4.705 2 a b s • a = semi major axis • = parallax K1 = Radial Velocity amplitude P = period e = eccentricity

  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):

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

  20. The Importance of Reference stars Example Focal „plane“ Detector Perfect instrument Perfect instrument at a later time • Reference stars: • Define the plate scale • Monitor changes in the plate scale (instrumental effects) • Give additional measures of your target

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

  22. Where are your reference stars?

  23. Radial Velocity Astrometry 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 √Nlines) 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! 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

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

  26. Scargle Periodogram of Van de Kamp data False alarm probability = 0.0015! A signal is present, but what is it due to?

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

  28. Lalande 21185

  29. Gatewood 1996: At a meeting of the American Astronomical Society Gatewood claimed Lalande 21185 did have a 2 Mjupiter planet in an 8 yr period plus a second one with M < 1Mjupiter at 3 AU. After 13 years these have not been confirmed. Lalande 21185 Gatewood 1973

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

  31. HST uses Interferometry! The first space interferometer for astrometric measurements: The Fine Guidance Sensors of the Hubble Space Telescope

  32. Interferometry with Koesters Prisms Transmitted beam has phase shift of l/4 Reflected beam has no phase shift

  33. Interferometry with Koesters Prisms 0 CONSTRUCTIVE INTERFERENCE

  34. HST generates a so-called S-curve

  35. Fossil Astronomy at its Finest - 1.5% Masses MTot =0.568 ± 0.008MO MA =0.381 ± 0.006MO MB =0.187 ± 0.003MO πabs = 98.1 ± 0.4 mas HST astrometry on a Binary star

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

  37. One of our planets is missing: sometimes you need the true mass! B HD 33636 b P = 2173 d Msini = 10.2 MJup i = 4 deg → m = 142MJup = 0.142 Msun

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

  39. Gl 876

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

  41. 55Cnc d • Perturbation due to component d, • P = 4517 days • = 1.9 ± 0.4 mas i = 53° ± 7° Mdsin i = 3.9 ± 0.5MJ Md= 4.9 ± 1.1MJ Combining HST astrometry and ground-based RV • McArthur et al. 2004 ApJL, 614, L81

  42. The RV orbit of the quadruple planetary system 55 Cancri e

  43. The 55 Cnc (= r1 Cnc) planetary system, from outer- to inner-most ID r(AU) M (MJup) d 5.26 4.9 ± 1.1 c 0.24 0.27 ± 0.07 b 0.12 0.98 ±0.19 e 0.04 0.06 ± 0.02 Where we have invoked coplanarity for c, b, and e = (17.8 ± 5.6 Mearth) a Neptune!!

  44. The Planet around e Eridani

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