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

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Chapter 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 measurements from space
3.9 Future Observations from space
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The astronomical pyramid
Credit: A. Sozetti
3. Astrometry
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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 measurements 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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3.2 Astrometric accuracy from ground (6)
Basic of Interferometric Astrometry
Star-Baseline Geometry
Credit: M. Shao
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3.2 Astrometric accuracy from ground (7)
Basic of Interferometric Astrometry
Determining the external delay
Credit: M. Shao
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3.2 Astrometric accuracy from ground (8)
Basic of Interferometric Astrometry
Fringe position as a measure of pathlenght equality
Credit: M. Shao
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3.2 Astrometric accuracy from ground (9)
Basic of Interferometric Astrometry
Internal metrology
Credit: M. Shao
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3.2 Astrometric accuracy from ground (10)
Basic of Interferometric Astrometry
About fringes
Credit: M. Shao
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3.2 Astrometric accuracy from ground (11)
Basic of Interferometric Astrometry
Differential astrometry (with two stars)
Credit: M. Shao
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3.2 Astrometric accuracy from ground (12)
Basic of Interferometric Astrometry
 Expected performance on the ground (Mauna Kea)
(3.10)
 Similar to equation 3.5 with telescope diameter D replaced by
B, the interferometer baseline.
 With
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3.2 Astrometric accuracy from ground (13)
First claim of astrometric detections
 Holmberg (1938)
 A few Jupiter mass companion to Proxima Centauri
 Reuyl & Holmberg (1943)
 10 MJ around 70 Oph
 Strand (1943)
 16 MJ 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 MJ; P=12 and 20 yrs)
 Simular dispute for Lalande 21185 (Gatewood 1996)
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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 measurements from space
3.9 Future observations from space
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3.3 Microarcsec astrometry (1)
Light deflection due to General Relativity
(3.11)
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°), r0= 1 AU,
 In practice, effect from all planets must be taken into account
Apparent position
True position
Observer
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3.3 Microarcsec astrometry (2)
Light deflection in the Solar System
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3.3 Microarcsec astrometry (3)
Aberration
 Displacement of an object’s observed position resulting from the
observer’s motion with respect to the solar system barycenter.
(3.12)
 First order (classical) aberration (v~30 km/s): 28 arcsec
 Second order: 3.6 mas, third order: ~1 μas.
Requires knowledge of the observer’s velocity
(barycentric coordinate) to within ~ 1 mm/s !
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3.3 Microarcsec astrometry (4)
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 .
(3.13)
(3.14)
μ is the proper motion in arcsec/yr, vr the radial
velocity in km/s, ω the parallax in arcsec and A is the
astronomical unit (9.778x105 arcsec km yr s-1)
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3.3 Microarcsec astrometry (5)
Source motion
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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 measurements from space
3.9 Future observations from space
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3.4 Astrophysical limits (1)
Surface structure jitter
 Spots, plages, granulation and non-radial oscillations produce
fluctuations in the observed photocenter (Eriksson & Lindegren
2007).
(3.15)
(3.16)
 σm: RMS photometric jitter (mag)
σvr: RMS radial velocity jitter (km/s)
σpos: RMS photocenter jitter in (μas AU)
Surface jitter is typically of the order 10 μas/d
where d is the distance to the star.
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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 measurements from space
3.9 Future Observations from space
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3.5 Multiple planets and mandalas1
1
Mandalas is ‘’circle’’ in sanskrit
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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 measurements from space
3.9 Future observations from space
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3.6 Modelling planetary systems(1)
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, α0, δ0, given at a specified epoch (e.g.
J2000, and within a specified reference system (ICRS;
International Celestial Reference System)
 Proper motion: μα cos δ, μδ
 Parallax:
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3.6 Modelling planetary systems(2)
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 np planets requires 5+npx7 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 Mp is
determined directly.
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3.6 Modelling planetary systems(3)
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)
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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 measurements from space
3.9 Future observations from space
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3.7 Astrometric measurements from ground (1)
 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 MJ 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 μas accuracy for ~30 arcsec binaries
20-50 μas accuracy for sub-arcsec binaries
Observations have excluded tertiary companions of a few MJ
with a < 2 AU in several binary systems (Muterspaugh et al
2006)
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3.7 Astrometric measurements from ground (2)
 VKT-PRIMA: ESPRI
 Four 8.2m + four (moveable) 1.8m telescopes + six longstroke delay lines.
 Baseline of 200m, wavelength coverage: 1-13 μm.
 Dual-feed capability
 Goal of 10-50 μas.
 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 μas accuracy for ~20-30 arcsec binaries
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3.7 Astrometric measurements from ground (3)
 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 μas/hr
 Could detect a 1 MJ companion orbiting 1 AU from a late M at
10 pc.
 No major results so far.
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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 measurements from space
3.9 Future observations from space
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3.8 Astrometric measurements from space (1)
Hipparcos




Led by Europe (ESA), in operation from 1989-93
Astrometric accuracy: 1 mas
100 measurements of 118 000 stars
Huge scientific legacy in stellar astrophysics
 Parallax and proper motions
 Results
 Upper limits on Mp for 47 Uma (< 7 MJ), 70 Vir (< 38 MJ), and 51
Peg (< 500 MJ)
 Mass constraints on triple planet system ν And:
• Outer companion:
(from RV; MJsin i =4 MJ)
• Mass estimates for other two planets:
 Good upper mass limits of several RV-detected planets
• Stellar companion excluded
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3.8 Astrometric measurements from space (2)
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 MJ)
 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 HD136118 (Martioli etal.
2010)
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3.8 Astrometric measurements from space (3)
HST- Fine Guidance Sensor – GJ 876
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3.8 Astrometric measurements from space (4)
HST- Fine Guidance Sensor – ε Eri
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3.8 Astrometric measurements from space (5)
HST- Fine Guidance Sensor – ν And
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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 measurements from space
3.9 Future observations from space
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3.8 Astrometric measurements from space (2)
GAIA
 Led by ESA: 2013-2018
 Will survey 1 billion stars to V~20
 80 distinct measurements
 Accuracy of ~ 8 μas 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
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3.8 Astrometric measurements from space (3)
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3.8 Astrometric measurements from space (4)
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2. Radial Velocities
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2. Radial Velocities
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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 μas
 Instrumentation
 Cameras and interferometers
 Astrometric accuracy from the ground:
 Photon-noise limit on 10m telescopes in 1 hr: 20-30 μas
 Limitation from atmospheric turbulence: 1-3 mas
 Best performance (short term): 100-300 μas
 Astrometric accuracy from space:
 Hipparcos: 1 mas
 HST-FGS: 1-2 mas (0.25 mas with multiple measurements)
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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 HSTFGS)
• 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 μas
Should find 1000s of giants with a=3-4 AU within 200 pc.
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