1. Chapitre 3- Astrometry PHY6795O – Chapitres Choisis en Astrophysique Naines Brunes et Exoplanètes

2. 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 3. AstrometryPHY6795O – Naines brunes et Exoplanètes2

3. The astronomical pyramid 2. Radial Velocities3 Credit: A. Sozetti

4. 3.1 Introduction (1) 2. AstrometryPHY6795O – Naines brunes et Exoplanètes4 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

5. 3.1 Introduction (2) 2. AstrometryPHY6795O – Naines brunes et Exoplanètes5 ‘’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).

6. 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 Exoplanètes6 (3.2)

7. 3.1 Introduction (4) 2. AstromeryPHY6795O – Naines brunes et Exoplanètes7

8. 3.1 Introduction (5) 2. AstromeryPHY6795O – Naines brunes et Exoplanètes8

9. 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 μ as (median value) or 10 -3 AU. 2. AstrometryPHY6795O – Naines brunes et Exoplanètes9

10. 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 3. AstrometryPHY6795O – Naines brunes et Exoplanètes10

11. 3.2 Astrometric accuracy from ground (1) 2. AstrometryPHY6795O – Naines brunes et Exoplanètes11 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)

12. 3.2 Astrometric accuracy from ground (2) 2. AstrometryPHY6795O – Naines brunes et Exoplanètes12 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.

13. 3.2 Astrometric accuracy from ground (3) 2. AstrometryPHY6795O – Naines brunes et Exoplanètes13 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

14. 3.2 Astrometric accuracy from ground (4) 2. AstrometryPHY6795O – Naines brunes et Exoplanètes14 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)

15. 3.2 Astrometric accuracy from ground (5) 2. AstrometryPHY6795O – Naines brunes et Exoplanètes15 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 μ as 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 μ as precision. (3.8)