Astrometric Detection of Exoplanets

Angles & Coordinates:• 1 full circle = 360 degrees• 1 degree = 60 arcminutes• 1 arcminute = 60 arcseconds ~ 1 inch @ 100 yards

(2.908 cm at 100 meters)

1 milliarcsec (mas) = 0.001 arcsec1 microarcsec (µas) = 0.000001 arcsec

Astronomical coordinates on sky:E-W: Right Ascension (RA) in h:m:s (0-24h)N-S: Declination (DEC) in deg:arcm:arcs (-90 - +90)

Stellar Motion

There are 4 types of stellar „motion“ that astrometry canmeasure:

1. Parallax (distance): the motion of stars caused byviewing them from different parts of the Earth‘sorbit

2. Proper motion: the true motion of stars throughspace

3. Motion due to the presence of companion

4. „Fake“ motion due to other physical phenomena

1 milliarcsecond

Our solar system from 32 light years (10 pcs)

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 triedand failed

• Modern astrometry was founded by Friedrich Bessel with his Fundamentaastronomiae, 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 astrometricmeasurements

• 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. Astrometricapplications 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.

Astrometry: Parallax

Distant stars

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

Astrometry: Proper motion

Discovered by Halley who noticed that Sirius, Arcturus, and Aldebaran were over ½ degree away from the positionsHipparchus measured 1850 years earlier

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

Astrometry: Orbital Motion

a1m1 = a2m2

a1 = a2m2 /m1

×a1

a2

D

To convert to an angular displacementyou have to divide by the distance, D

Astrometry: Orbital Motion

The astrometric signal is given by:This is in radians. More useful units arearcseconds (1 radian = 206369 arcseconds) ormilliarcseconds (0.001 arcseconds) = mas

m aθ =M D

m = mass of planetM = mass of stara = orbital radiusD = distance of star

θ = mM2/3

P2/3

D

Note: astrometry is sensitive to companions of nearby stars with large orbital distances

Radial velocity measurements are distance independent, butsensitive to companions with small orbital distances

Astrometry: Orbital Motion

With radial velocity measurements and astrometry one cansolve for all orbital elements

-9.45

-9.40

-9.35

-9.30

-9.25

53.5053.4553.4053.3553.30

53.50

53.45

53.40

53.35

53.30

2.4500x106

2.44902.4480Julian Date

So we find our astrometric orbit

-9.45

-9.40

-9.35

-9.30

-9.25

53.5053.4553.4053.3553.30

53.50

53.45

53.40

53.35

53.30

2.4500x106

2.44902.4480Julian Date

But the parallax can disguise it

-9.5

-9.4

-9.3

-9.2

-9.1

-9.0

-8.9

-8.8

53.853.653.4

53.8

53.6

53.4

2.4500x106

2.44902.4480Julian Date

And the proper motion can slinky it

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 100Jupiter at 5 AU 500Jupiter at 0.05 AU 5Neptune at 1 AU 6Earth at 1 AU 0.33Parallax 100000Proper 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 theposition of the stars

The Importance of Reference stars

Focal „plane“Example

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 (0.00015 mm)

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)

Astrometric detections: attempts and failures

To date no extrasolar planet has been discovered with theastrometric method, although there have been several falsedetections

Barnard´s star

New cell in lensinstalled Lens re-aligned Hershey 1973

Van de Kamp detection was most likely an instrumental effect

Real Astrometric Detections with the Hubble Telescope Fine Guidance Sensors

HST uses „Narrow Angle Interferometry“!

G. Fritz Benedict(McD Obs.)

HST is achieving astrometric precision of 0.1–1 mas !

One of our planets is missing: sometimes you need the true mass!HD 33636 b

P = 2173 dMsini = 10.2 MJup

B

i = 4 deg → m = 142 MJup

= 0.142 Msun

Bean et al. 2007AJ....134..749B

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

55 Cnc d

Perturbation due to component d, P = 4517 daysα = 1.9 ± 0.4 masi = 53° ± 7°Mdsin i = 3.9 ± 0.5 MJMd = 4.9 ± 1.1 MJCombining HST astrometry and

ground-based RV

McArthur et al. 2004 ApJL, 614, L81

The 55 Cnc (= ρ1 Cnc) planetary system, from outer-to inner-mostID r(AU) M (MJup)d 5.26 4.9 ± 1.1c 0.24 0.27 ± 0.07b 0.12 0.98 ±0.19e 0.04 0.06 ± 0.02

Where we have invoked coplanarity for c, b, and e

= (17.8 ± 5.6 Mearth) a Neptune!!

The Planet around ε Eridani

Distance = 3.22 pcs = 10 light years

Period = 6.9 yrs

Mass (true) = 1.53 ± 0.29 MJupiter

ε Eriπ = 0.3107 arcsec (parallax)a = 2.2 mas (semi-major axis)i = 30° (inclination)

X-d

ispl

acem

ent(

arc-

seco

nds)

Y-d

ispl

acem

ent(

arc-

seco

nds)

HST Astrometry of the extrasolar planet of ε Eridani

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

One worrisome point: The latest radial velocities do notfit the orbit:

The Planetary System of υ And

Note: the planets do not have the sameinclination!

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

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 cameramounted on the Palomar 5m. 9 years of data were obtained.

The astrometric perturbation of Vb 10

Mass = 6.4 MJup

The RV data does not support theastrometry. The only way is to haveeccentric orbits which is ruled out by

the astrometric measurements.

Comparison between Radial Velocity Measurementsand Astrometry.

Astrometry and radial velocity measurements are fundamentallythe 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 √Nlines)

2. One stellar image

3. Hundreds of reference lines (Th-Ar or Iodine) to define „platesolution“ (wavelength solution)

3. 1-10 reference stars to defineplate solution

4. Reference lines are stable 4. Reference stars move!

AstrometryRadial Velocity

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 becausethe precision is about a factor of 1000 too large.

• Will have to await space based missions to have a real impact