NGAO Astrometric Science and Performance Astrometric Performance Budget

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

Astrometric Science with NGAO • KBO orbits • Planet searches • Stellar Dynamics – Galactic Center – Globular Clusters – Galactic compact objects – Stellar orbits • And others… 3

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 Sgr. A*-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, 2005 a, 2005 b); Tanner et al. 4 (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

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

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 H-band optimal for GC • small/well-characterized optical distortion NIRC 2 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 unblended H-band lines.

How do we achieve this astrometric science? • Ultimate limit is measurement noise Lindegren 1978 • Understand other contributing factors: – Instrumental (Geometric Distortion) – Atmospheric (Tilt Jitter, Differential Refraction) – Astrophysical (Galactic Rotation) 8

Geometrical Distortion Current System: • NIRC 2 (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 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

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 11

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

Globular Clusters at Palomar • Controlled Palomar experiment, astrometry of a guide star in M 5. • 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

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

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

Backup Slides

Bright Star Limit (NGS) • Globular cluster M 5 (d~8 kpc) 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

Grid Astrometry - Construct a linear combination of (ri) random variables the describes astrometry: r 3 r 2 r 4 - The change in the position of the object gives its proper motion. We wish to understand the properties of this statistic. r 5 s r 1 18

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. 19

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

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. 3 K 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 in 7 parameters. 10 21