Kein Folientitel

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Astrometric Detection of Exoplanets
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Angles Coordinates

• 1 full circle 360 degrees
• 1 degree 60 arcminutes
• 1 arcminute 60 arcseconds 1 inch _at_ 100
  yards (2.908 cm at 100 meters)
• 1 milliarcsec (mas) 0.001 arcsec
• 1 microarcsec (µas) 0.000001 arcsec
• Astronomical coordinates on sky
• E-W Right Ascension (RA) in hms (0-24h)
• N-S Declination (DEC) in degarcmarcs (-90 -
  90)

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

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• 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

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• 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.

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Astrometry Parallax
Distant stars
1 AU projects to 1 arcsecond at a distance of 1
pc 3.26 light years
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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
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Astrometry Proper motion
Barnard is the star with the highest proper
motion (10 arcseconds per year)
Barnards star in 1950
Barnards star in 1997
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Astrometry Orbital Motion
a1m1 a2m2
a1 a2m2 /m1
a2

a1
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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) mas
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
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Astrometry Orbital Motion
With radial velocity measurements and astrometry
one can solve for all orbital elements
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Astrometric Detections of Exoplanets
The Challenge for a star at a distance of 10
parsecs (32.6 light years)
Source Displacment (mas)
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 100000
Proper motion (/yr) 500000
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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

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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

Typical plate scale on a 4m telescope (Focal
ratio 13) 3.82 arcsecs/mm 0.05 arcsec/pixel
(15 mm) 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)
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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)
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Astrometric detections attempts and failures
To date no extrasolar planet has been discovered
with the astrometric method, although there have
been several false detections
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Hershey 1973
Van de Kamp detection was most likely an
instrumental effect
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Real Astrometric Detections with the Hubble
Telescope Fine Guidance Sensors
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HST uses Narrow Angle Interferometry!
G. Fritz Benedict (McD Obs.)
HST is achieving astrometric precision of 0.11
mas !
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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 142 MJup 0.142 Msun
Bean et al. 2007AJ....134..749B
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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

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55 Cnc d

• Perturbation due to component d,
• P 4517 days
• 1.9 0.4 mas
• i 53 7
• Mdsin i 3.9 0.5 MJ
• Md 4.9 1.1 MJ

Combining HST astrometry and ground-based RV
McArthur et al. 2004 ApJL, 614, L81
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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!!
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The Planet around e Eridani
Distance 3.22 pcs 10 light years Period 6.9
yrs
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HST Astrometry of the extrasolar planet of e
Eridani
e Eri
p 0.3107 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 MJupiter
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Orbital inclination of 30 degrees is consistent
with inclination of dust ring
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One worrisome point The latest radial velocities
do not fit the orbit
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The Planetary System of u And
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Note the planets do not have the same
inclination!
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Planets c and d are inclined by 30 degrees to
each other!
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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.
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The astrometric perturbation of Vb 10
Mass 6.4 MJup
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The RV data does not support the astrometry. The
only way is to have eccentric orbits which is
ruled out by the astrometric measurements.
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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
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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