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 1 AU projects to 1 arcsecond at a distance of 1 pc = 3.26 light years

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

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 Hipparchus 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

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

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 = arcseconds) or milliarcseconds (0.001 arcseconds)

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 Focal „plane“ Detector Example

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?

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) reference stars to define plate solution 4. Reference lines are stable 4. Reference stars move! AstrometryRadial Velocity

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

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 13 years these have not been confirmed.

Real Astrometric Detections with the Hubble Telescope Fine Guidance Sensors

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

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

Interferometry with Koesters Prisms CONSTRUCTIVE INTERFERENCE 0

HST generates a so-called S-curve

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

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

One of our planets is missing: sometimes you need the true mass! HD b P = 2173 d Msini = 10.2 M Jup B i = 4 deg → m = 142 M Jup = M sun

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 ± 0.34 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

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!!

The Planet around  Eridani

What the eye does not see a periodogram finds: Radial Velocities Activity indicator FAP ≈ 10 –9

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

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

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  as V-mag 20: 200  as Launch Space Interferometry mission 60 solar-type stars precision of 4  as

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

Programs: 1. Detecting Earth-like Planets 2. Young Planets and Star Formation 3. Multiple Planet Systems SIMLiteZero?

Its 5 year mission is to boldly go where no planet hunter has gone before: Demonstrated precision of 1  as and noise floor of 0.3  as amplitude. Multiple measurements of nearest 60 F-, G-, and K- stars. Directly test rocky planet formation „This paucity of low mass planets is almost certainly an artfact of sensitivity, as the Doppler technique struggles to detect lower-mass planets. Thus, we have reached a roadblock in planetary science and astrobiology.“ Detecting Earth-like Planets

Jupiter only 1 milliarc-seconds for a Star at 10 parsecs

Multiple Planet Systems Goal is to get three-dimensional orbit information Relationship between terrestrial and giant planets Mean motion resonances Long term eccentricty evolution (co-planarity)

Multiple Planet Systems Detectabilty of Earth-mass planets investigated through blind tests Team A: generated 150 planetary systems with the best guess of mass and period distributions Team B: rotated systems, set up realistic observing schedules, created synthetic RV and astrometric signals and added noise. Team C: detection groups (4)

Multiple Planet Systems Reliability = ratio of true detections to all detections (true + false) Results: 1 group: 100% reliability 2 groups: over 80% 1 group over 40% Based on 1% false alarm probability

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

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

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 For a star like the sun, sunspots can cause an astrometric displacement of ~1  as

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

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 sucessful 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