Chapitre 3- Astrometry

PHY6795O – Chapitres Choisis en Astrophysique

Naines Brunes et Exoplanètes

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Contents

3.1 Introduction 3.2 Astrometric accuracy from ground3.3 Microarcsec astrometry3.4 Astrophysical limits3.5 Multiple planets and mandalas3.6 Modelling planetary systems3.7 Astrometric measurements from ground3.8 Astrometric from space3.9 Future Observations from space

3. AstrometryPHY6795O – Naines brunes et Exoplanètes

2. Radial Velocities 3

The astronomical pyramid

Credit: A. Sozetti

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3.1 Introduction (1)

2. AstrometryPHY6795O – Naines brunes et Exoplanètes

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)

2. AstrometryPHY6795O – Naines brunes et Exoplanètes

‘’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 quasi-

intertial 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

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.

2. AstrometryPHY6795O – Naines brunes et Exoplanètes

(3.2)

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3.1 Introduction (4)

2. AstromeryPHY6795O – Naines brunes et Exoplanètes

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3.1 Introduction (5)

2. AstromeryPHY6795O – Naines brunes et Exoplanètes

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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.

2. AstrometryPHY6795O – Naines brunes et Exoplanètes

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Contents

3.1 Introduction 3.2 Astrometric accuracy from ground3.3 Microarcsec astrometry3.4 Astrophysical limits3.5 Multiple planets and mandalas3.6 Modelling planetary systems3.7 Astrometric measurements from ground3.8 Astrometric from space3.9 Future Observations from space

3. AstrometryPHY6795O – Naines brunes et Exoplanètes

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3.2 Astrometric accuracy from ground (1)

2. AstrometryPHY6795O – Naines brunes et Exoplanètes

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)

2. AstrometryPHY6795O – Naines brunes et Exoplanètes

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)

2. AstrometryPHY6795O – Naines brunes et Exoplanètes

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)

2. AstrometryPHY6795O – Naines brunes et Exoplanètes

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

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.

(3.5)

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3.2 Astrometric accuracy from ground (5)

2. AstrometryPHY6795O – Naines brunes et Exoplanètes

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)

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.

(3.8)