Transcript Chap3-Astrometry-cx - Groupe d`Astronomie et Astrophysique

PHY6795O – Chapitres Choisis en Astrophysique
Naines Brunes et Exoplanètes
Chapitre 3- Astrometry
Contents
3.1 Introduction
3.2 Astrometric accuracy from ground
3.3 Microarcsec astrometry
3.4 Astrophysical limits
3.5 Multiple planets and mandalas
3.6 Modelling planetary systems
3.7 Astrometric measurements from ground
3.8 Astrometric from space
3.9 Future Observations from space
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The astronomical pyramid
Credit: A. Sozetti
2. Radial Velocities
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3.1 Introduction (1)
Fundamental (Absolute Astrometry)
 Measure positions over the entire sky (including Sun)
 Determination of Fundamental (Inertial) Reference
frame
 Determination of Astronomical Constants
 Timekeeping
 Traditionally done with Meridian Circle
 Very few sites now doing this
 Space-borne instruments have taken over
Credit: A. Sozetti
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3.1 Introduction (2)
‘’Differential’’ Astrometry
 Positions are measured relative to reference ‘’stars’’ in the same
field whose positions are known.
 Actual stars not ideal reference that stars are all moving!
 Use of distant (non-moving) extragalactic sources (Quasars)
is used in practice.
 The International Celestial Reference Frame (ICRF) is q quasiintertial reference frame centered at the barycentr of the Solar
system, defined by measured positions of 212 extragalactic
sources (quasars).
 ICRF1 adopted by IAU in 1998. Noise floor: 250 uas.
 ICRF2 (2009) updated with 3414 compact radio sources.
Noise floor: 40 uas.
 Applications: parallax, proper motion, astrometric binaries
(including exoplanets), positions of solar system objects (comets,
minor planets, trans-neptunian objects)
 Effects of precession, nutation, stellar aberration, nearly constant
across field and can (usually) be ignored).
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3.1 Introduction (3)
 Principle: the motion of a single planet in orbit around a star causes
the star to undergo a reflex motion around the barycenter (center of
mass) defined as
As seen from a distance d, the angular displacement α of the reflex
motion of the star induced by to the planet is a★/d, or
(3.2)
 Astrometry is sensitive to relatively massive, long-period (P > 1 yr)
planets.
 Reflex motion is on top of two other classical astrometric effects:
 Linear path of the system’s barycenter, i.e. the proper motion.
 Reflex motion of the Earth (parallax) resulting from the Earth’s orbital motion
around the sun.
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3.1 Introduction (4)
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3.1 Introduction (5)
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3.1 Introduction (6)
Size of the effect
 Jupiter at 10 pc around a solar-type
star: α=0.5 mas
 For the >400 planets detected as in
late 2010: α=16 μas (median value) or
10-3 AU.
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Contents
3.1 Introduction
3.2 Astrometric accuracy from ground
3.3 Microarcsec astrometry
3.4 Astrophysical limits
3.5 Multiple planets and mandalas
3.6 Modelling planetary systems
3.7 Astrometric measurements from ground
3.8 Astrometric from space
3.9 Future Observations from space
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3.2 Astrometric accuracy from ground (1)
Photon-noise limit
 Single aperture
 Theoretical photon-noise limit of a diffraction-limited
telescope of diameter D colecting N photons is given by
(3.4)
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3.2 Astrometric accuracy from ground (2)
Photon-noise limit
 For V=15 mag, λ=600 nm, D=10m, system throughput
τ=0.4, integration time of 1 hr yield
.
 With photgraphic plates (<.80’):
.
 Advent of CCDs in mid-80’s has improved accuracy by
an order of magnitude, to be limited by atmospheric
turbulence.
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3.2 Astrometric accuracy from ground (3)
Differential Chromatic Refraction (DCR)
 Atmospheric refraction itself is not a problem, as long as it is the
same for all stars. It is not!
 DCR depends on the colour of the star
 Correction requires knowledge of temperature, pressure, humidity
and star color.
 Easier to correct for smaller bandpass
 Use narrow-band filters if possible
 DCR is wavelength dependent, smaller in red than in the
blue)
 Deoending on particulars of the observing program, DCR is
often the limiting factor for ground-based astrometry
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3.2 Astrometric accuracy from ground (4)
Atmospheric turbulence
 Atmospheric turbulence affects the
stellar centroid randomly with a
magnitude that varies within the
field of view.
 For small separations < 1 arcmin,
the time-averaged precision with
which the angle between two stars
near the zenith can be measured is
(3.5)
where D is the telescope diameter
in m, θ the angular separations of
the two stars in radians and t the
exposure time in seconds.
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3.2 Astrometric accuracy from ground (5)
Atmospheric turbulence
 For θ=1 arcmin, D=1 m and t= 1 hr
 With several reference stars and novel approach (pupil
apodization, assigning weights to reference stars) yield further
improvement (Lazorenko & Lazorenko 2004)
(3.8)
Here,
is determined by the number of
refrences objects N,
is a term dependent on k and the
magnitude and distribution of reference stars.
 This yields to performance of ~100 μas for 10m class telescopes
with very good seeing and t~600 s
 Narrow-field imagers on Palomar and VLT, including adaptive
optics have demonstrated short-term 100-300 μas precision.
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