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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 arcsec
1 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 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 other physical phenomena
Our solar system from 32 light years (10 pcs)
1 milliarcsecond
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 tried
and failed
• 1838 first stellar parallax (distance) was measured
independently by Bessel (heliometer), Struve (filar micrometer),
and Henderson (meridian circle).
• Modern astrometry was founded by
Friedrich Bessel with his Fundamenta
astronomiae, which gave the mean position
of 3222 stars.
• 1887-1889 Pritchard used photography for astrometric
measurements
• 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.
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 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 1950
Barnard‘s star in 1997
Astrometry: Orbital Motion
a1m1 = a2m2
a1 = a2m2 /m1
a2
×
a1
D
To convert to an angular displacement
you have to divide by the distance, D
Astrometry: Orbital Motion
The astrometric signal is given by:
q= m
M
a
D
This is in radians. More useful units are
arcseconds (1 radian = 206369 arcseconds) or
milliarcseconds (0.001 arcseconds) = mas
m = mass of planet
M = mass of star
a = orbital radius
D = distance of star
m P2/3
q = 2/3
M D
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
So we find our astrometric orbit
But the parallax can disguise it
And the proper motion can slinky it
-9.25
-8.8
-9.25
-8.9
-9.30
-9.30
-9.35
-9.35
-9.0
-9.1
-9.2
-9.40
-9.3
-9.40
-9.4
-9.45
-9.5
-9.45
53.30
53.35
53.40
53.45
53.50
53.30
53.35
53.40
53.45
53.50
53.50
53.50
53.45
53.45
53.8
53.40
53.40
53.6
53.35
53.35
53.30
53.30
53.4
53.6
2.4480
2.4490
53.8
53.4
2.4480
2.4490
2.4500 x1 0
Julia n Date
6
2.4480
2.4490 2.4500x10
Julian Date
6
2.4500 x1 0
Julian Date
6
Astrometric Detections of Exoplanets
The Challenge:
for a star at a distance of 10 parsecs (=32.6 light years):
Source
Jupiter at 1 AU
Jupiter at 5 AU
Jupiter at 0.05 AU
Neptune at 1 AU
Earth at 1 AU
Parallax
Proper motion (/yr)
Displacment (mas)
100
500
5
6
0.33
100000
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
Example
Focal „plane“
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 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)
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 the
astrometric method, although there have been several false
detections
Barnard´s star
New cell in lens
installed
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 bB
Bean et al. 2007AJ....134..749B
P = 2173 d
Msini = 10.2 MJup
i = 4 deg → m = 142 MJup
= 0.142 Msun
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
Combining HST astrometry and
ground-based RV
McArthur et al. 2004
ApJL, 614, L81
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
The 55 Cnc (= r1 Cnc)
planetary system, from outerto 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
= (17.8 ± 5.6 Mearth) a Neptune!!
e
0.04 0.06 ± 0.02
Where we have invoked
coplanarity for c, b, and e
The Planet around e Eridani
Distance = 3.22 pcs = 10 light years
Period = 6.9 yrs
Y-displacement (arc-seconds)
e Eri
p = 0.3107 arcsec (parallax)
a = 2.2 mas (semi-major axis)
i = 30° (inclination)
X-displacement (arc-seconds)
HST Astrometry of the extrasolar planet of e Eridani
Mass (true) = 1.53 ± 0.29 MJupiter
Orbital inclination of 30 degrees is consistent with inclination of
dust ring
One worrisome point: The latest radial velocities do not
fit the orbit:
The Planetary System of u And
Note: the planets do
not have the same
inclination!
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 camera
mounted 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 the
astrometry. The only way is to have
eccentric orbits which is ruled out by
the astrometric measurements.
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
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 (ThAr 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!
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