Measuring High-Precision Astrometry with the Infrared Array Camera on the Spitzer Space Telescope

The Infrared Array Camera (IRAC) on the Spitzer Space Telescope currently offers the greatest potential for high-precision astrometry of faint mid-IR sources across arcminute-scale fields, which would be especially valuable for measuring parallaxes of cold brown dwarfs in the solar neighborhood and proper motions of obscured members of nearby star-forming regions. To more fully realize IRAC's astrometric capabilities, we have sought to minimize the largest sources of uncertainty in astrometry with its 3.6 and 4.5 $\mu$m bands. By comparing different routines that estimate stellar positions, we have found that Point Response Function (PRF) fitting with the Spitzer Science Center's Astronomical Point Source Extractor produces both the smallest systematic errors from varying intra-pixel sensitivity and the greatest precision in measurements of positions. In addition, self-calibration has been used to derive new 7$^{\rm th}$ and 8$^{\rm th}$ order distortion corrections for the 3.6 and 4.5 $\mu$m arrays of IRAC, respectively. These corrections are suitable for data throughout the mission of Spitzer when a time-dependent scale factor is applied to the corrections. To illustrate the astrometric accuracy that can be achieved by combining PRF fitting with our new distortion corrections, we have applied them to archival data for a nearby star-forming region, arriving at total astrometric errors of $\sim$20 and 70 mas at signal to noise ratios of 100 and 10, respectively.