1. High Precision Astrometry and Parallax from Spatial Scanning Part 2 Adam Riess and Stefano Casertano

2. Distortion at the milli-pixel level Spatial Scanning Provides measurement 1D * precision of < 1 millipix which demands comparable control of distortions across frames millipixels *measurement direction always ΔX

3. Scale change and rotation of scan orientation Rotation apparent even in back-to-back scans using same guide stars Rotation of scan orient by a few arcsec, solved for in frame-to-frame registration Scale change mostly time-dependent velocity aberration, we interpolate va(t)  x,y Each accounts for up to ~20 mpix (800  as) in measured trail separation Sequential scans— correlation star pairs ΔY vs ΔX due to global scan axis rotations Combining Frames: Scale and Rotation

4. Combining Frames: Low Order Distortions Residual geometric distortion Amplitude up to 5 mpix (200  as) Typically well-fitted by registration with low (2 nd / 3rd order) polynomial in ΔX (x,y) After correction, residuals match to < 1 mpix (40  as) for long, high S/N trails Polynomial corrections show correlation w/ model focus/breathing Call this time-dependent or breathing dependent distortion, expected

5. Combining Frames: Fine Structure Also see static, fine structure residuals along scan (Y) relative to X residuals of about 5 mpix scale correlated on 10^2 pixel scale orbit phase, breathing independent as seen scans separated by min, hrs, up to 10 days Only apparent between scans with large shifts or local to a scan line, i.e. Y vs. X- Averages down for long lines but important loss of precision for short lines

6. Residuals That Persist for Years Comparing these static residuals in ΔX in X,Y spatial bins (100x100 pixels) across a year for M35 and Cepheid field stars shows strong correlation. Such residuals expected from PSF map (see Murphy’s Law) In Cycle 22 we will map these residuals on 50 pix scale using 20 dithers of scans in M67,M48 to make a look-up table. Also useful for staring mode.

7. Deep scan (F606W) Cepheid saturated ~40 usable trails Shallow scan (F673W) Cepheid not saturated ~8 usable trails A challenge for (bright) Cepheids: Dynamic range Pair shallow and deep scans asline separation filter independent, anchor Cepheid to all reference stars

8. Current Progress: 40 epochs for 19 Cepheids… full residuals Reduction to absolute from reference star distances using 12 bands+spectroscopy, e.g., σ D =0.3 mag for red giant at 8 kpc => 18  as, typical field ~ 10-12  as

9. 2.3 kpc (Riess et al 2014 ApJ, arXiv1401.0484R) Proper Motion subtracted, Parallax measurements field stars & Cepheid 8 kpc (  125 μas 15% error) 250 pc (  4 mas 1.8% error) Cepheid First Results from Pilot Program…Sample of 19 underway

10. Simulated results for 20 Cepheids After 5 epochs, Cycle 20-22, twice number, precision of FGS set + HST photometry + log P > 1 Expect to reach    when done, double current Given field, catalog, MW model, can fully simulate multi-epoch scans, final uncertainty Cepheid Parallax Measurements

11. The End

12. Reduction to absolute parallax Each field contains 30-100 reference stars Will obtain multiband photometry (UVIS broad + medium filters, WFC3 IR, 2MASS) + spectra + stellar models to estimate individual distances Typical uncertainty < 0.3 mag (15% in distance) One red giant at 8 kpc => 18  as All stars contribute; distant stars give best constraints Estimated final uncertainty ~ 10-12  as / field Incorrect reduction to absolute produces systematic bias in the estimated distance modulus Incorrect luminosity scale produces systematic bias in parallaxes of nearby objects