Astrometry with Schmidt Plates Difficulty in attaining highly accurate positions -Bending of plates as they are placed in plate holder -Characteristics of Schmidt plate optics –Characteristics of image formation and algorithm which describes the properties of the image. -Others … Such deficiencies were noted in GSC1.0 (Russel, Lasker, McLean, Sturch and Jenkner 1990, AJ 99, 2059) and rigorously quantified (Taff et al. 1990, ApJ 353, L45)

Plates 0019 and 04JJ From Morrison,Roeser, McLean, Bucciarelli and Lasker 2001, AJ 121,1752 (GSC1.2)

Successful Reduction Techniques Sub–plate method (Taff 1989, AJ 98, 1912; Taff Lattanzi and Bucciarelli, 1990, ApJ 358,359 ) Collocation method (Fresneau 1978, AJ 83, 406; Lattanzi and Bucciarelli 1991, A&A 250, 565; Bucciarelli Lattanzi and Taff 1993, ApJS 84, 91) Mask method (Taff Lattanzi and Bucciarelli, 1990, ApJ 358,359 ) Local filters (Morrison, Smart and Taff 1998, MNRAS 296, 66; Roeser, Bastian and Kuzmin 1995, IAU Coll. 148, ASP Conf. Ser. Vol 84)

Characterization of Systematic Errors –Comparisons to external catalogs –Compare residuals from overlapping plates –Residuals (from 1 & 2) vs. magnitude Position-only dependent errors Magnitude and Position dependent errors. Global: common to a set of plates. Local: vary from plate to plate. Methods to Detect them:

I.ACT AC TYCHO All sky catalog 958,758 objects II.TYCHO million objects Position accuracy 10 – 100 mas Proper motion accuracy 1 – 3mas Limiting in magnitude ~ 11.5 External Reference Catalogs

I.NPM 300,000 stars - 23 to 90 ( 72% of northern sky) 8 < B < 18 II.SPM 25 to –40 but not in the galactic plane. 321,608 stars 5 < V < 18.5 III.2MASS Strip scans (currently 40% of sky) 8200 stars/square degree Complete to roughly V= 18 IV.UCAC1 Current catalog sky coverage south of –15 deg. Limiting in magnitude R = stars/square degree 20 mas for 10 to 14, 70 mas for 15 to limits External Faint Reference Catalogs

Input parameters: measured X,Y values and  and  of plate center, observation conditions. Output variables:  and  of every object on the plate 1.Plate_solution Pre-correct for differential refraction Equidistant projection Quadratic plate model Note: Resulting positions have the well known position and magnitude dependent errors: 0.8 to 1.4 arc seconds near the plate edges. 2.Astrometric Mask Using all available plates for a survey determines corrections common to a set of plates. GSCII Astrometric Pipeline

Z r – Z 0 = A tan(Z 0 ) + + B tan 3 (Z 0 ) + ….. A ~ 60”.3 B ~ 0.”067 Equidistant ProjectionDifferential Refraction Modelled Third Order Effects

3105 star pairs (every 5 th star plotted) Mean  residual: 0.37  Mean  residual: 0.53  Residuals from Overlapping Plates

Astrometric Mask Mask is created: Create a grid of closely spaced points.(40x40). Spacing of grid points needs to be smaller than scale of systematics. Around each grid point find all the reference stars contained in the filter and determine the ,  corrections. Mask is stored Mask is applied: Find the closest grid point and near by N grid points. Correction determined by weighting based on distance of object from grid points.

 Plates /N~500 Plate residuals stacked onto the Schmidt plate frame Consequence of : a. Physical deformation of the Schmidt plate. b. Characteristics of Schmidt plate optics. c. Characteristics of centroider and image formation. d. a,b and c result in effects which are not understood from a engineering/physics standpoint to be adequately represented in the plate model. Swirl Pattern of systematic errors varying across the plate (worse at the edges  1" ) Average number of stars/bin = 109 Vector Mask of Averaged Residuals

XJ MaskXP Mask

XS MaskER Mask

S Mask

XV Mask GR Mask

XI Mask: Palomar IRIS Mask: UK Schmidt IR

Overlapping Schmidt Plates comparing the positions of the same star imaged on 2 plates stars pairs (every 5 star plotted). Before mask applied After mask applied Mean xi residual: 0.37 arc seconds Mean eta residual: 0.53 arc seconds Mean xi residual: 0.20 arc seconds Mean eta residual: 0.37 arc seconds Residuals from Overlapping Plates

Central Image Matched Reference Star Filter Method: Transforms the plate-based system to a system defined by a dense and homogenous reference catalog. Corrections to each image on the plate are found by: Draw a circle around every image. Find all the reference stars in circle. For each match determine , . Corrections to the central object: weighted average of all , . Reducing Systematics on Individual Plates

Plate Solution MaskFilter stars 1/10 th of stars plotted Plate Solution:  residual: 0.40   0.58  residual: 0.12   0.43 Mask:  residual: 0.40   0.26  residual: 0.11   0.25 Filter:  residual: 0.26   0.22  residual: 0.10   0.20 Residuals from Overlapping Plates

Experience with GSC I  Global magnitude equation (coma- like) (Morrison, Roeser, Lasker, Smart and Taff 1996, AJ 111, 1405). Plate-to-Plate positional magnitude- dependent errors (guiding) (Lu, Platais, Girard, Kozhurina-Platais, van Altena 1998, IAU Symp. 179, p.384) Magnitude Dependent Systematics Magnitude Equation

Overlapping plates a. Same bandpass b. Different bandpasses (full plate overlaps) c. A set of co-added pairs (for the same geometric overlap pattern). Faint reference catalog for comparison Limited relevance to GSC2.2 because of the method of selecting position – chose the one closest to plate center  reduced magnitude dependence Magnitude Dependent Systematics Detect and quantify

Preliminary testing on GSCII database -Using 55 GSC II plates (OOP files) compared GSC II positions with those in the SPM. Residuals showed a magnitude dependence in the positions. Increase in the amplitude of the residuals starting at 11.5 and steadily increasing with magnitude.

Test study: 55 plates SPM - GSC II database magnitude test

Summary of GSCII Astrometric Calibrations Plate Solution: equidistant projection, differential refraction, least-squares fit Astrometric mask: reduces global position-only systematic errors Magnitude correction: reduces magnitude-dependent systematic errors (currently in testing). Filter method : reduces local small-scale systematic errors remaining across individual plates (currently in testing).

Plate Solution + Astrometric Mask: –Averaged over all plates: accuracy ~ 0.25” positional –Plate-to-Plate variations exist up to arcseconds per coordinate GSC2.2 Positional Accuracy

”” GSC2 – SPM (STARS) mFmF  (  *cos  ) = (_____)  (  ) = (……..)

GSC2 – SPM (STARS) __  ” ________ (  *cos  ) = (_____) ____ (  ) = (……..) mFmF

”” GSC2 – NPM (STARS)  (  *cos  ) = (_____)  (  ) = (……..) mFmF

GSC2 – NPM (STARS) ________ (  *cos  ) = (_____) ____ (  ) = (……..) __  ” mFmF

CATALOGS USED FOR COMPARISON WITH GSC2 CATALOGS TOTAL OBJECTS % OF OUTLIERS >10” NPM STARS SPM STARS SUB-CATALOGS GOOD OBJS. (*) RETAINED OBJS. IN 3  % OBJECTS GSC2S - NPMS GSC2S - SPMS (*) Are the objs. with |  *cos  | and |  |<10” and 0 < mF < 24