100 µas Astrometry with Adapve Opcs on Moderate-Sized Telescopes

Drs. Richard Dekany and Nick Law Caltech Optical Observatories Workshop on Astronomy with Adaptive Optics on Moderate-Sized Telescopes

22 August 2011 Ground-Based Astrometric Surveys

u Pointed, faint targets, customizable cadence & sensitivity

u Limited by: u SNR (sensitivity, telescope size) u FWHM u Accuracy u Telescope time

u Accuracy can be handled by dedicated instruments and careful experimental design

u But how can we improve FWHM & sensitivity?

Ground-Based Astrometric Surveys Optimizing AO Astrometric precision

For a well-controlled infrared AO measurement, differential tilt jitter is the dominant astrometric noise source. u AO corrects the guide star. u Astrometric reference stars are seen through slightly different bits of the atmosphere. u Produces random (but correlated) motion in reference stars

Cameron et al. 2009 AJ 137 83 Differential Atmospheric Tilt

S Stars separated by some angle sample same turbulence at low altitudes

S In principle correction is exact only for guide star

S Thus error will grow with θ

S Removing correlated differential tilts results in a fundamental limit for single guide star AO astrometry

σDT = RMS tilt anisoplanatism between points separated by θ 7/6 -1/2 ~ 20 mas (θ/20”)(5m/D) (N wind-crossings) but astrometric precision can be considerably better as we’ll show 5/25

(More rigorous) Atmospheric Differential Tilt

D = telescope diameter [m] θ = off-axis angular distance [rad] th µm = the m height moments of the turbulence distribution

6/25

Galactic Center data shows strongly anisoplanatic astrometric error

• In each frame, measure the position relative to the reference star, which is close to the laser spot.

• Take the RMS from all frames.

• The RMS positional error can be decomposed into radial and tangential components relative to the laser position (or reference source).

Slides from UCLA Galactic Center Group (Ghez, Lu) Optimizing AO Astrometric Precision

u Cameron et al. method (simplified), proven with Palomar 5m telescope AO:

1. Make a vector from the target star to each reference star

2. Apply weights to each vector to sum to the target star position

3. Optimize the weights such that the uncertainty in the target star position is minimized Cameron et al. 2009 AJ 137 83 Optimizing AO Astrometric precision

10 X-axis Y-axis

1 Precision / milliarcsecs

0.1 1 10 100 IntegrationN timeframes / seconds Bright Star Limit (NGS) (Thesis work of B. Cameron)

S Cluster M5 at Palomar S 1.4s exposures S 600 images

S Differential offsets are elongated parallel to the displacement S Offsets are correlated over the field

11/25 Achieved precision on 5m

• Resolving the differential tilt allows determination of the target star position to improve faster than 1/sqrt(N)

• The tilt jitter also averages away as 1/sqrt(t) – Estimated precision of 50 µas in ~15 minutes of integration time – Achieved 100 µas in ~2 min

• Apparently stable for 2-min data for timescales of weeks

12/25 Magnetars

S Sources heavily extincted

S AV ~ 3-30 mag

S 4/6 magnetars visible to Keck have published faint NIR/optical counterparts. S Kp ~ 19.5-22.5 mag

S Two possible new counterparts based on astrometry and variability. S ΔKp~1 mag

1E 1841-045 13/25 Thesis work of P. Brian Cameron; slide courtesy S. Kulkarni Magnetar Proper Motions

9/2005 S Proper motion limits show magnetars have relatively low 10,12/2006 velocities S ~200-300 km/s

S Implies the population is older 8/2006 than previously thought 4U 0141+61

1E 2259+586 S Draws into question popular 2005 theories of magnetar formation.

2006

14/25 S. Kulkarni Proper Motions of Halo Objects (WFPC2, STIS)

Fornax

Proper Motion: 48±5, -36±5 mas/century 15/25 Piatek et al. 2007 M-dwarf astrometry

u MAAPS – M-dwarf Astrometric AO Planet Survey u Ongoing Palomar 200” program u Targeting M-dwarfs in galactic plane u 100-300 microarcsec precision u Sensitive to Jupiter-mass planets in few-month orbits u 100 microarcsec astrometry is competitive with 5– 10 m/s RV around mid M-dwarfs MAAPS precision & accuracy

2 milliarcsec Factors for successful astrometry

ü AO correction is essential ü Improves SNR on position determination ü Resolves away confusion in crowded fields ü Typically provides 10x denser astrometric field references for systematic control

ü Lots of integration time ü Multi-target astrometric surveys require lots of AO telescope time to get many epochs on many stars ü Example: Few % target frequency of gas giant planets around M-dwarfs (MAAPS) ü The highest-precision programs require careful calibration sequences to mitigate many real effects. Robo-AO has these factors

u AO provides smaller PSFs, higher SNR and more ref stars u 2 arcmin field of view also increases number of ref stars (within isokinetic patch) u Dedicated, stable instrument – so can contemplate long term astrometric programs u Infrared – can target M-dwarfs too optically faint for GAIA or SIM u Prediction: 100 uas precision in 10-30 minutes (depending on reference star configuration) on a 2m telescope

u Scaling relation verified using Palomar 200” & Keck Scaling up MAAPS

10-year M-dwarf survey with 5 Robo-AO equipped 2m-class telescopes

10 RV planets J

1 800 targets

200 targets

0.1 50 targets Mass sensitivity / M

0.01 1 10 Period / years Summary

u Law has demonstrated 100 uas astrometry in an M-dwarf exoplanet search u The next step, following hundreds of targets, requires a dedicated facility u Low-cost AO designed for small telescopes can provide: u ~100 uas astrometric precision and accuracy u and large amounts of telescope time u Robo-AO observations will confirm our precision shortly!