Chapter 3- Astrometry PHY6795O – Chapitres Choisis en Astrophysique Naines Brunes et Exoplanètes

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 measurements from space 3.9 Future Observations from space 3. AstrometryPHY6795O – Naines brunes et Exoplanètes2

The astronomical pyramid 3 Credit: A. Sozetti 3. Astrometry

3.1 Introduction (1) 3. 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

3.1 Introduction (2) 3. 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 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).

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. 3. AstrometryPHY6795O – Naines brunes et Exoplanètes6 (3.2)

3.1 Introduction (4) 3. AstromeryPHY6795O – Naines brunes et Exoplanètes7

3.1 Introduction (5) 3. AstromeryPHY6795O – Naines brunes et Exoplanètes8

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 AU. 3. AstrometryPHY6795O – Naines brunes et Exoplanètes9

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 measurements from space 3.9 Future observations from space 3. AstrometryPHY6795O – Naines brunes et Exoplanètes10

3.2 Astrometric accuracy from ground (1) 3. 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)

3.2 Astrometric accuracy from ground (2) 3. 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.

3.2 Astrometric accuracy from ground (3) 3. 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

3.2 Astrometric accuracy from ground (4) 3. 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)

3.2 Astrometric accuracy from ground (5) 3. 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 μ as precision. (3.8)

3.2 Astrometric accuracy from ground (6) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes16 Basic of Interferometric Astrometry Star-Baseline Geometry Credit: M. Shao

3.2 Astrometric accuracy from ground (7) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes17 Basic of Interferometric Astrometry Determining the external delay Credit: M. Shao

3.2 Astrometric accuracy from ground (8) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes18 Basic of Interferometric Astrometry Fringe position as a measure of pathlenght equality Credit: M. Shao

3.2 Astrometric accuracy from ground (9) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes19 Basic of Interferometric Astrometry Internal metrology Credit: M. Shao

3.2 Astrometric accuracy from ground (10) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes20 Basic of Interferometric Astrometry About fringes Credit: M. Shao

3.2 Astrometric accuracy from ground (11) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes21 Basic of Interferometric Astrometry Differential astrometry (with two stars) Credit: M. Shao

3.2 Astrometric accuracy from ground (12) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes22 Basic of Interferometric Astrometry  Expected performance on the ground (Mauna Kea)  Similar to equation 3.5 with telescope diameter D replaced by B, the interferometer baseline.  With (3.10)

3.2 Astrometric accuracy from ground (13) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes23 First claim of astrometric detections  Holmberg (1938)  A few Jupiter mass companion to Proxima Centauri  Reuyl & Holmberg (1943)  10 M J around 70 Oph  Strand (1943)  16 M J around 61 Cyg  Heinz (1978)  Presence of planets around 16 Cyg and 70 Oph excluded.  1963 – now  Dispute regarding the presence of two planets around Barnard’s star (0.5 and 0.7 M J ; P =12 and 20 yrs)  Simular dispute for Lalande (Gatewood 1996)

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 measurements from space 3.9 Future observations from space 3. AstrometryPHY6795O – Naines brunes et Exoplanètes24

3.3 Microarcsec astrometry (1) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes25 Light deflection due to General Relativity is a variable in the parametrized post-Newtonian (ppN) formalism. Measure of a departure of reality from General Relativity.  For a star at the ecliptic pole ( ψ =90°), r 0 = 1 AU,  In practice, effect from all planets must be taken into account True position Apparent position Observer (3.11)

3.3 Microarcsec astrometry (2) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes26 Light deflection in the Solar System

3.3 Microarcsec astrometry (3) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes27 Aberration  Displacement of an object’s observed position resulting from the observer’s motion with respect to the solar system barycenter.  First order (classical) aberration ( v ~30 km/s): 28 arcsec  Second order: 3.6 mas, third order: ~1 μ as. Requires knowledge of the observer’s velocity (barycentric coordinate) to within ~ 1 mm/s ! (3.12)

3.3 Microarcsec astrometry (4) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes28 Source motion  Perspective acceleration : A star’s velocity through space leads to a secular change in its observed proper motion. The radial component of its motion leads to a secular change in its trigonometric parallax. μ is the proper motion in arcsec/yr, v r the radial velocity in km/s, ω the parallax in arcsec and A is the astronomical unit (9.778x10 5 arcsec km yr s -1 ) (3.13) (3.14)

3.3 Microarcsec astrometry (5) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes29 Source motion

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 measurements from space 3.9 Future observations from space 3. AstrometryPHY6795O – Naines brunes et Exoplanètes30

3.4 Astrophysical limits (1) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes31 Surface structure jitter  Spots, plages, granulation and non-radial oscillations produce fluctuations in the observed photocenter (Eriksson & Lindegren 2007).  σ m : RMS photometric jitter (mag) σ vr : RMS radial velocity jitter (km/s) σ pos : RMS photocenter jitter in ( μ as AU) Surface jitter is typically of the order 10 μ as/ d where d is the distance to the star. (3.15) (3.16)

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 measurements from space 3.9 Future Observations from space 3. AstrometryPHY6795O – Naines brunes et Exoplanètes32

3.5 Multiple planets and mandalas 1 3. AstrometryPHY6795O – Naines brunes et Exoplanètes33 1 Mandalas is ‘’circle’’ in sanskrit

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 measurements from space 3.9 Future observations from space 3. AstrometryPHY6795O – Naines brunes et Exoplanètes34

3.6 Modelling planetary systems(1) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes35 Proper motion and parallax  In the absence of orbiting companion, there are five observables which describes a star’s angular position on the sky:  Equatarial coordinate, α 0, δ 0, given at a specified epoch (e.g. J2000, and within a specified reference system (ICRS; International Celestial Reference System)  Proper motion: μ α cos δ, μ δ  Parallax:

3.6 Modelling planetary systems(2) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes36 Keplerian elements  As for the radial velocity method, we have the following 7 Keplerian parameters:  Semi-major axis a is measured in angular unit ( ) converted to linear measure using the star distance.  Orbit fitting of n p planets requires 5+ n p x7 parameters  Complex (non-linear) procedure using various minimization techniques (Levenberg-Marquardt or Markov Chain Monte Carlo analysis) Unlike radial velocity, astrometry yieds a and i seperately. With M ★ known from spectral type or evolutionary models, then M p is determined directly.

3.6 Modelling planetary systems(3) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes37 Combining astrometry and radial velocity  Four orbital elements are common:  Procedure:  Determine ‘’plate constants’’ (image scale, rotation, offsets, radial terms, parallax scale factors) from astrometric measurements.  Determine orbital elements K, e, P and ω from radial velocity.  Constrain orbit by minimize residuals (3.24)

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 measurements from space 3.9 Future observations from space 3. AstrometryPHY6795O – Naines brunes et Exoplanètes38

3.7 Astrometric measurements from ground (1) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes39  Palomar: STEPS (STEllar Planet Survey)  Astrometric survey of giants and brown dwarfs around 30 nearby M-dwarfs (Pravdo & Shaklan 2009a).  Several BDs detected over a 10-yr program.  Claimed detection of a ~6 M J around VB8 (M8V) ( α ~ 5 mas) but disproved through 10 m/s IR RV data with CRIRES on VLT (Bean et al. 2010b)  Palomar PTI: PHASES (Palomar Testbed Interferometer; Palomar High-precision Astrometric Search for Exoplanet Systems)  100m baseline with dual-feed interferometer  100 μ as accuracy for ~30 arcsec binaries  μ as accuracy for sub-arcsec binaries  Observations have excluded tertiary companions of a few M J with a < 2 AU in several binary systems (Muterspaugh et al 2006)

3.7 Astrometric measurements from ground (2) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes40  VKT-PRIMA: ESPRI  Four 8.2m + four (moveable) 1.8m telescopes + six long- stroke delay lines.  Baseline of 200m, wavelength coverage: 1-13 μ m.  Dual-feed capability  Goal of μ as.  Search of low-mass planets around nearby stars Ni major results so far  Keck: ASTRA (ASTrometric and phase-Referenced Astronomy)  Two 10m combined together as an interferometre  Baseline: 85m  Dual-feed capability  100 μ as accuracy for ~20-30 arcsec binaries

3.7 Astrometric measurements from ground (3) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes41  Las Campanas: CAPS (Carnegie Astrometric Planet Search)  2.5m du Pont telescope with specialized IR cameras  Optimized to follow 100 very nearby (<10 pc) low-mass (M,L, T) stars  10-yr project started in 2007 (Boss et al. 2009)  Astrometric accuracy of 300 μ as/hr  Could detect a 1 M J companion orbiting 1 AU from a late M at 10 pc.  No major results so far.

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 measurements from space 3.9 Future observations from space 3. AstrometryPHY6795O – Naines brunes et Exoplanètes42

3.8 Astrometric measurements from space (1) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes43 Hipparcos  Led by Europe (ESA), in operation from  Astrometric accuracy: 1 mas  100 measurements of stars  Huge scientific legacy in stellar astrophysics  Parallax and proper motions  Results  Upper limits on M p for 47 Uma (< 7 M J ), 70 Vir (< 38 M J ), and 51 Peg (< 500 M J )  Mass constraints on triple planet system ν And: Outer companion: (from RV; M J sin i =4 M J ) Mass estimates for other two planets:  Good upper mass limits of several RV-detected planets Stellar companion excluded

3.8 Astrometric measurements from space (2) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes44 HST- Fine Guidance Sensor  Inteferometric guiding system with accuracy at the level of 1-2 mas but 0.25 mas possible with multiple mesurements Results  55 Cnc. Upper mass limit for 55 Cnc b (<30 M J )  55 Cnc e:  GJ876  Combined HST-FGS +RV:  Constraint on relative inclination of b and c:  A few planets demoted to BD and M-dwarfs  e.g. HD33636 (Bean et al. 2007) and HD (Martioli etal. 2010)

3.8 Astrometric measurements from space (3) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes45 HST- Fine Guidance Sensor – GJ 876

3.8 Astrometric measurements from space (4) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes46 HST- Fine Guidance Sensor – ε Eri

3.8 Astrometric measurements from space (5) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes47 HST- Fine Guidance Sensor – ν And

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 measurements from space 3.9 Future observations from space 3. AstrometryPHY6795O – Naines brunes et Exoplanètes48

3.8 Astrometric measurements from space (2) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes49 GAIA  Led by ESA:  Will survey 1 billion stars to V~20  80 distinct measurements  Accuracy of ~ 8 μ as on bright stars  Should discover several 1000s giants with a=3-4 AU out to 200 pc  Will characterize 100s multiple-planet system  Meaningful tests of coplanarity with inclination uncertainties less than 10 degrees.  Strong synergy with RV surveys  Will revolutionarize stellar astrophysics  BD and young stars

3.8 Astrometric measurements from space (3) 3. AstrometryPHY6795O – Naines brunes et Exoplanètes50

3.8 Astrometric measurements from space (4) 2. AstrometryPHY6795O – Naines brunes et Exoplanètes51

2. Radial Velocities52

2. Radial Velocities53

3.9 Summary (1)  Importance. Provides determination of all Keplerian orbital parameters as well as the distance to the object.  Astrometric signal equation  Jupiter analog at 10 pc: α =0.5 mas  Median RV planet has α ~15 μ as  Instrumentation  Cameras and interferometers  Astrometric accuracy from the ground:  Photon-noise limit on 10m telescopes in 1 hr: μ as  Limitation from atmospheric turbulence: 1-3 mas  Best performance (short term): μ as  Astrometric accuracy from space:  Hipparcos: 1 mas  HST-FGS: 1-2 mas (0.25 mas with multiple measurements) 3. Astrometry54PHY6795O – Naines brunes et Exoplanètes

3.9 Summary (2)  Astrophysical limitations  Light deflection due to General Relativity  Stellar aberration  Surface ‘’jitter’’  Science highlights  No detection of new planets through astrometry  Several astrometric detection of known RV planets (all with HST- FGS) Constraints on mass and inclination, in particular relative inclination for multiple systems  GAIA  On-going space mission  Parallax and proper motion for 1 billion stars.  Astromeric accuracy: ~10 μ as  Should find 1000s of giants with a=3-4 AU within 200 pc. 55PHY6795O – Naines brunes et Exoplanètes3. Astrometry