5.4 Field-Level Position Mode Errors

Position Mode astrometry involves observations of several objects in a given visit followed by subsequent visits to the same field over the lifetime of the observing program, which can span years. The scientific goal is typically to measure systematic temporal changes in the angular separations between one or more objects and the reference field. Just as the individual observations in each visit must be mapped onto a common fixed coordinate system to define the visit's virtual plate, the visits themselves must also be mapped to a common reference frame to produce a plate overlay. The errors associated with several of the pipeline corrections will not manifest themselves until data from individual visits are compared via the plate overlay process.

A plate overlay is performed by translating and rotating the individual plates from each visit and adjusting their relative scales to form a single master plate common to all visits. The locations of the individual reference stars on each plate determine how to map the data from that visit onto the common master plate. Because the reference star positions for each visit are themselves slightly uncertain, the master plate will not be error free but rather an optimal compromise. The quality of the fit for a given visit can be assessed by comparing the positions of the reference stars in that visit with their positions on the master plate. The rms residuals of the fit, referred to as the plate overlay residuals, can be as small as 1 mas or as large as 6 mas.

Two commonly used plate solutions are the four-parameter and the six-parameter plate solutions. The four-parameter solution adjusts for translation, rotation, and relative scale, while the six-parameter solution adjusts the relative scale independently along the x and y axes. The six-parameter solution can be used only when enough reference stars are available to provide the necessary degrees of freedom. Typically five or six reference stars will suffice; otherwise, the four parameter technique must be used.

Often an observer realizes that the reference stars, initially assumed to be fixed on the sky, in fact do have measurable parallaxes and proper motions. If these apparent motions are not accounted for, they will contaminate the master plate, resulting in needlessly large residuals that compromise the scientific investigation. For the sake of overall error assessment, let us assume that all the stars in every visit are fixed on the sky, so that any residuals in the master plate can be traced to errors in the individual measurements made during the individual observations.

The most dominant source of error in Position Mode data reduction is the OFAD correction, followed by the uncertainty of the corrections to the star selector RhoA and KA values used in the pipeline for a given epoch. The third most important source of error is the drift correction. The size of this error depends most importantly upon the check star scenario used and to a much lesser extent the amplitude and temporal signature of the drift experienced during the visits.

Target magnitude is not an important contributor to the overall error until V > 16, after which it can quickly dominate. Before the DIFF/SUM correction was added to the pipeline, stars with V > 15 were found to have large residuals in the plate overlays (> 4 mas). With the DIFF/SUM correction, such residuals have decreased to about 2.5 mas.

The cross filter effect (F5ND to F583W) contributes only about 1 mas to the residual of targets requiring this correction, provided the observations are made at a place in the FGS where this effect has been calibrated. The lateral color effect, not corrected for in the pipeline, shows up either as noise or is absorbed in a correction for presumed apparent parallax of a reference star.

Table 5.3 summarizes the contributions from a variety of sources to the overall Position Mode error budget. Also indicated are the typical size of the corrections that are made during the calibration process. If these errors were “root sum squared,” the resulting uncertainty would be about 2.7 mas (for bright stars). Note that these estimates are based on a number of assumptions about the observation strategy and star distribution across the pickel: it is assumed that all of the stars are brighter than about V = 14.4, that they are widely distributed across the pickle, and that an adequate check star scenario was used in the observing sequence.

Overall, the plate residuals for a field of numerous bright stars confined to near the pickle's center can be as small as 1 mas per axis. More often the observer finds that the reference field is sparse or faint, the stars are not confined to the central region of the FGS, or that an optimal check star strategy was not used. In less optimal cases with these deficiencies, the residuals might still be as good as 3 mas but can be as large as 7 mas.

Table 5.3: POSITION Mode Corrections and Errors