NGAO Astrometric Science and NGAO Astrometric Science and PerformancePerformance

Astrometric Performance Budget Team: Brian Cameron, Jessica Lu, Matthew Astrometric Performance Budget Team: Brian Cameron, Jessica Lu, Matthew Britton, Andrea Ghez, Rich Dekany, Claire Max, Chris NeymanBritton, Andrea Ghez, Rich Dekany, Claire Max, Chris Neyman

Keck Strategic Planning MeetingKeck Strategic Planning Meeting

September 20, 2007September 20, 2007

2/15

Outline

• Astrometric Science with AO– Astrometric science cases

– Case study: Science at the Galactic Center

• How do we achieve this science?Contributing factors:– Instrumental (Geometric Distortion)

– Atmospheric (Tilt Jitter, Differential Refraction)

– Astrophysical (Galactic Rotation)

• State of the Art

3/15

Astrometric Science with NGAO

• KBO orbits

• Planet searches

• Stellar Dynamics– Galactic Center

– Globular Clusters

– Galactic compact objects

– Stellar orbits

• And others…

4/15

The Galactic center is a unique laboratory for studying the impact of a supermassive black hole on its environment.

Keck GC studies over the past 12 years:• ~1 mas astrometry at r < 0.5” (speckle)

• LGSAO improved to ~0.2 mas in 2005

• definitive case for black hole at GC from stellar orbits

• detection of variable SgrA*-IR

• detection of young stars at r~100 AU

Reasons to study GC stellar dynamics:• black hole mass/distance• extended mass distribution• general relativistic effects• origin of young stars• accretion onto black hole

Ghez et al. (1998,2000,2003,2004,2005a,2005b); Tanner et al. (2002); Gezari et al. (2002); Hornstein et al. (2002,2007); Lu et al. (2005,2008);

5/15

Stellar orbits give information on the black hole properties, extended mass distribution and GR effects.

Black hole properties• mass• distance (Galactic structure)• motion (black hole binary?)

Extended mass distribution• stellar cusp• stellar mass black holes• dark matter• all cause orbital precession

GR effects• test in the strong gravity regime• orbital precession

Weinberg, Milosavljević & Ghez (2005).

NGAO Goal

6/15

Galactic Center science requires good astrometric precision AND astrometric accuracy.

Two current limitations:

1) Confusion with fainter undetected sources2) PSF variation due to anisoplanatism.

Benefits of NGAO:

- Higher Strehl -> Higher contrast -> Reduced confusion- Improved knowledge of the PSF

NGAO Requirements:• 0.1 mas relative astrometric precision• 170-180 nm of WFE• Measurements of the turbulence profile

Ghez et al. (in prep)

7/15

Instruments needed are a near-IR imager and IFU spectrograph (capable of 10 km/s precision).

High Quality Near-IR imager:• FOV ~> 10” to define reference frame.

• K-band and H-band optimal for GC

• small/well-characterized optical distortion

Near-IR IFU spectrograph:• IFU needed due to crowding and complex backgrounds.

• R~4,000 (OSIRIS) currently gives 20 km/s radial velocity measurements at K-band (limited by line-blending).

• To achieve 10 km/s: R~15,000 and/or unblended H-band lines.3” x 2” OSIRIS

NIRC2

8/15

How do we achieve this astrometric science?

• Ultimate limit is measurement noise

• Understand other contributing factors:– Instrumental (Geometric Distortion)

– Atmospheric (Tilt Jitter, Differential Refraction)

– Astrophysical (Galactic Rotation)

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9/15

Geometrical Distortion

Current System:

• NIRC2 (and all optical systems) suffers from distortion.

• Characterize with pin hole slit mask

– Polynomial fit

– Residuals ~0.1 pixels

• Stable within the errors over the last year.

• Contribution from AO+telescope?

• HST understood at the < 0.3 mas

NGAO:

• Requires small/well-characterized distortion mapping

http://www.astro.caltech.edu/~pbc/AO/

10/15

Differential Atmospheric Refraction

• Stars with different surface temperatures and zenith angles are refracted by different amounts.

• Simple models can be used to correct these effects

– RMS ~ 0.01 mas (Gubler & Tytler 1998)

11/15

Differential Atmospheric Tilt

• Image motion is corrected by the tip-tilt mirror along the guide star axis.

• Measured star separations change due to tilt anisoplanatism

– Error grows with – Offsets are correlated over the field

• Magnitude is approximately

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σ tilt ~ 10 masθ

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12/15

Current State of the Art and Implications for NGAO

State of the Art:

• Bright Globular Clusters at Palomar

• Galactic Center at Keck

Implications for NGAO

13/15

Globular Clusters at Palomar• Controlled Palomar experiment,

astrometry of a guide star in M5.

• Astrometric precision improves as 1/sqrt(t) and faster than 1/sqrt(ref. stars)

• 50 as accuracy

• Stable over consecutive nights

• Proper motions of the guide star ~300 as (implies 60 km/s @ 8 kpc, inconsistent with cluster dispersion).

• Achieved using a multivariate statistical analysis technique (Cameron, Britton & Kulkarni, in prep)

14/15

Galactic Center• Single night astrometric precision

– RMS of astrometry in 30 minute integrations

– R < 4”

Result: 150 as astrometric precision

• Consistent performance over many nights

15/15

Implications for Astrometry with NGAO• Why should the Keck community care about astrometry?

– Has motivated many future space missions: SIM, GAIA

– New science opened by large apertures: very favorable scalings with D• Direct measurements of distances and velocities

• NGAO– High Strehl

– Knowledge of the PSF

– Stability

• AO system and instruments with astrometry designed in from the start– Low, well characterized distortion

– Dispersion correction

Backup Slides

17/15

Bright Star Limit (NGS)

• Globular cluster M5 (d~8kpc) at Palomar

– 600 frames with 1.4 s integration

– 4 epochs over 2 months

– One, consistent dither position (control distortion)

– Narrow-band filter (control DCR)

– Same zenith angle (control DAR)

• Differential offsets are elongated parallel to the displacement

18/15

Grid Astrometry

r3

r4

r2

r1

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rs =

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r r

- Construct a linear combination of (ri) random variables the describes astrometry:

- The change in the position of the object gives its proper motion. We wish to understand the properties of this statistic.

r5

s

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δ =s1 − s2

19/15

Probability of the Measurements

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P(r)∝ exp −0.5(r − r )T Σ−1 (r − r ){ }

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Σij =r r i −

r r i( )

r r j −

r r j( )

AATs Σ=Σ r

Construct the covariance matrix for tilt jitter

1) From data

- Fast, easy, requires many images

2) From theory

- Important for control theory or limited data

The two agree well.

20/15

Single-epoch Precision

• Compute Allan deviation of astrometric timeseries

•Performing tilt tomography improves astrometric precision faster than 1/sqrt(N), roughly N-0.7

• Improves as the usual 1/sqrt(t)

• Achieved ~ 100 as in 2 minutes

• Estimated precision of ~50 as in ~15 minutes

21/15

Differential Atmospheric Refraction

• Stars with different surface temperatures and zenith angles are refracted by different amounts.

• 12 mas @ zenith angle of 45 degrees, separation of 30” and

T ~ 5000 K

• Noise from correction:– Model Uncertainties

– Uncertainties in 7 parameters.

Parameter Uncertainty Noise(uas)

Ground Temp. 3 K 50

Pressure 8 mb 50

Zenith Angle 36” 10

Seperation 30 mas 10

Relative Humidity

10%

Relative Stellar Temp.

100-1700 K 10