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

Chapter 3- Astrometry

PHY6795O – Chapitres Choisis en Astrophysique

Naines Brunes et Exoplanètes

2

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 measurements from space3.9 Future Observations from space

3. AstrometryPHY6795O – Naines brunes et Exoplanètes

3

The astronomical pyramid

Credit: A. Sozetti 3. Astrometry

4

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

5



‘’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.


(3.2)

7


3. AstromeryPHY6795O – Naines brunes et Exoplanètes

8


3. AstromeryPHY6795O – Naines brunes et Exoplanètes

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 μas (median value) or 10-3 AU.


10

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 measurements from space3.9 Future observations from space


11

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)

12



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



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



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



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)

16



Basic of Interferometric Astrometry Star-Baseline Geometry

Credit: M. Shao

17



Basic of Interferometric Astrometry Determining the external delay

Credit: M. Shao

18



Basic of Interferometric Astrometry Fringe position as a measure of pathlenght equality

Credit: M. Shao

19



Basic of Interferometric Astrometry Internal metrology

Credit: M. Shao

20



Basic of Interferometric Astrometry About fringes

Credit: M. Shao

21



Basic of Interferometric Astrometry Differential astrometry (with two stars)

Credit: M. Shao

22



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)

23



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)

24

Contents



25

3.3 Microarcsec astrometry (1)


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°), r0= 1 AU, In practice, effect from all planets must be taken into

account

True position

Apparent position

Observer

(3.11)

26



Light deflection in the Solar System

27



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 μas.

Requires knowledge of the observer’s velocity (barycentric coordinate) to within ~ 1 mm/s !

(3.12)

28



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, 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)

(3.13)

(3.14)

29



Source motion

30

Contents



31

3.4 Astrophysical limits (1)


Surface structure jitter Spots, plages, granulation and non-radial oscillations

produce fluctuations in the observed photocenter (Eriksson & Lindegren 2007).

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.

(3.15)

(3.16)

32

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 measurements from space3.9 Future Observations from space


33

3.5 Multiple planets and mandalas1


1 Mandalas is ‘’circle’’ in sanskrit

34

Contents



35

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:

36



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.

37



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)

38

Contents



39

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)

40



VKT-PRIMA: ESPRI Four 8.2m + four (moveable) 1.8m telescopes + six

long-stroke 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

41



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.

42

Contents



43

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

44



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)

45



HST- Fine Guidance Sensor – GJ 876

46



HST- Fine Guidance Sensor – ε Eri

47



HST- Fine Guidance Sensor – ν And

48

Contents



49



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

50



51



2. Radial Velocities 52

2. Radial Velocities 53

54

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)


55

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 μas Should find 1000s of giants with a=3-4 AU within 200 pc.

PHY6795O – Naines brunes et Exoplanètes 3. Astrometry

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

Documents

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