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 3. Motion due to the presence of companion 4. „Fake“ motion due to physical phenomena (noise)

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.

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 first stellar parallax (distance) was measured independently by Bessel (heliometer), Struve (filar micrometer), and Henderson (meridian circle).

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.

Astrometry: Parallax Distant stars

Astrometry: Parallax So why did Galileo fail? d = 1 parsec  = 1 arcsec F f = F/D D d = 1/  d in parsecs,  in arcseconds

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

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

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

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

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

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

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

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

The Space motion of Sirius A and B

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

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

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

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)

Where are your reference stars?

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

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

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

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

Lalande 21185

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 10 years these have not been confirmed.

Real Astrometric Detections with the Hubble Telescope Fine Guidance Sensors

GL 876 M- dwarf host star Period = 60.8 days

Gl 876

The more massive companion to Gl 876 (Gl 876b) has a mass M b = 1.89 ± 0.34M Jup and an orbital inclination i = 84° ± 6°. Assuming coplanarity, the inner companion (Gl 876c) has a mass M c = 0.56M Jup The mass of Gl876B

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

The RV orbit of the quadruple planetary system 55 Cancri e

The 55 Cnc (=  1 Cnc) planetary system, from outer- to inner-most IDr(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!!

Distance = 3.22 pcs = 10 light years Period = 6.9 yrs

HST Astrometry of the extrasolar planet of  Eridani

Mass (true) = 1.53 ± 0.29 M Jupiter  Eri  = arcsec (HIP) M A ~ 0.8 M sun, M B ~ M sun  = 2.2 mas, i = 30°

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

The Future: Space Interferometry Mission 9 m baseline Expected astrometric precision : 4  as

The SIM Reference Grid Must be a large number of objects K giant stars V = 10–12 mag Distance ≈ several kilopcs Currently 4000 K giants are being observed with precise radial velocity measurements to assure that they are constant

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

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)

The Secular Acceleration of Barnard‘s Star (Kürster et al. 2003). Similar effect in radial velocity:

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

Sources of „Noise“ Gravitational deflection of light:  defl = 2 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

Source  (  as)d min (1  as) Sun1.75× o Mercury839´ Venus4934 o.5 Earth o 6 km) Moon265 o 6 km) Mars11625´ Jupiter o Saturn 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

Spots : y x Brightness centroid

…and pulsations:

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

Astrometric signal as a function of spot filling factor A ast (  as) = 7.1f 0.92 (10/D) D = distance in pc, f is filling factor in percent

1 milliarcsecond Our solar system from 32 light years (10 pcs) 40  as