Transcript NGAO Astrometry Presentation at Keck Strategic Planning Meeting (9/20/07)

NGAO Astrometric Science and
Performance
Astrometric Performance Budget Team: Brian Cameron, Jessica Lu, Matthew
Britton, Andrea Ghez, Rich Dekany, Claire Max, Chris Neyman
Keck Strategic Planning Meeting
September 20, 2007
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
2/15
Astrometric Science with NGAO
• KBO orbits
• Planet searches
• Stellar Dynamics
– Galactic Center
– Globular Clusters
– Galactic compact objects
– Stellar orbits
• And others…
3/15
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.
4/15
(2002); Gezari et al. (2002); Hornstein et al. (2002,2007); Lu et
al. (2005,2008);
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?)
NGAO Goal
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).
5/15
Galactic Center science requires good astrometric
precision AND astrometric accuracy.
Two current limitations:
1) Confusion with fainter undetected
sources
2) PSF variation due to anisoplanatism.
Benefits of NGAO:
- Higher Strehl -> Higher contrast ->
Reduced confusion
- Improved knowledge of the PSF
Ghez et al. (in prep)
NGAO Requirements:
• 0.1 mas relative astrometric precision
• 170-180 nm of WFE
• Measurements of the turbulence profile
6/15
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
NIRC2
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 Kband (limited by line-blending).
3” x 2” OSIRIS
• To achieve 10 km/s: R~15,000 and/or
7/15
unblended H-band lines.
How do we achieve this astrometric
science?
• Ultimate limit is measurement noise
 meas
  10 m  100 
 140 as



2.1 m  D SNR 
Lindegren 1978
• Understand other contributing factors:
 – Instrumental (Geometric Distortion)
– Atmospheric (Tilt Jitter, Differential Refraction)
– Astrophysical (Galactic Rotation)
8/15
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/wellcharacterized distortion mapping
9/15
http://www.astro.caltech.edu/~pbc/AO/
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)
10/15
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
   D 7 / 6
 tilt ~ 10 mas 

20" 10 m 

11/15
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
12/15
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)
13/15
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
14/15
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
15/15
Backup Slides
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
17/15
Grid Astrometry
- Construct a linear
combination of (ri) random
variables the describes
astrometry:
r
i
s
2
/ ri
i
1/ ri
2
r3
 Ar
i

- The change in the position
of the object   s1  s2
gives its proper motion. We
wish to understand the
properties of this statistic.
r2
r4
s
r5
r1

18/15
Probability of the Measurements
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.

P(r)  exp 0.5(r  r )T  r  r )
ij  ri  ri
rj 
rj

  A A

s
T

19/15
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
20/15
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
Parameter
Uncertainty
Noise
(uas)
Ground Temp.
3K
50
Pressure
8 mb
50
Zenith Angle
36”
10
Seperation
30 mas
10
Relative
Humidity
10%
Relative Stellar
Temp.
100-1700 K
Noise from correction:
–
–
Model Uncertainties
Uncertainties in 7 parameters.
10
21/15