SWEEPS Proper Motions in HSC v3.1

Cross matching detections and determining astrometric objects

In HSC version 3.0, source detections of the same star are grouped together into matches that are designated by a MatchID. Proper motions in SWEEPS caused detections of the same star to be split into different matches. To circumvent this problem in HSC version 3.1, we use a coarser criterion for detection membership in an object. We refer to that object as an astrometric object that has an ObjID instead of a MatchID. The membership criterion is based on a friends-of-friends algorithm for nearby detections within a 0.1 arcsec radius. HSC version 3.0 further split up these matches using the so-called chainbreaker code that looks for spatial clusters within matches (Budavari & Lubow 2012). This step is generally useful for fields without significant source shifts due to proper motions. Since the observations in SWEEPS are largely taken over two epochs that are widely separated in time, the chainbreaker often splits objects into different matches. For version 3.1 in the SWEEPS field, we omit this step. With this new scheme, SWEEPS sources are now grouped by astrometric object identifiers. Each ObjID corresponds to one or more HSC version 3.0 MatchIDs. But each MatchID corresponds to a single ObjID. The mapping between them is contained within table AstromSourcePositions. The general properties of the astrometric objects are listed in tables AstromSumMagAper2 and AstromPropSumMagAper2Cat.

Astrometry

HSC version 3.0 applied astrometric corrections in two steps. First each visit level white light source list was cross matched against standard catalogs (Gaia DR1, PanSTARRS, Pan-STARRS, SDSS, or 2MASS) to obtain a shift correction for the source list by means of a histogram method. Next, source lists for overlapping HLA detection images were cross matched. A shift and rotation was determined for each of these source lists to minimize their relative offsets (Budavari & Lubow 2012). This step eliminates any possible streaming motions. But streaming motions could not be accurately determined prior to Gaia DR2.

In HSC version 3.1 for the SWEEPS field astrometry, we apply only the first step using only Gaia DR2 with its proper motion and parallax information. For each HLA source list, we determine the faintest typically 200 Gaia DR2 sources that lie within the detection image. Their positions are shifted to the epoch of the HLA source list. Each Gaia source is then cross matched to HLA source list positions for HLA sources that are brighter than mag 22 in any HST filter used, roughly covering the Gaia magnitude range. The search radius about each Gaia source is typically 30 arcsec. A preliminary image shift is first determined by a histogram method, typically with 0.1 arcsec bins. The updated source list positions are then applied to the continuous (gridless) shift and rotation algorithm of Budavari & Lubow (2012) between the HLA source list and Gaia to obtain better astrometric corrections for the HLA source list. This step carries out similar preliminary cross matching steps as the histogram method, but involving a typical search radius around each selected Gaia source of 0.3 arcsec. The final shifts are then applied to the HLA source lists and the results are stored in table AstromSourcePositions. Notice that this approach does not minimize the relative shifts between HLA source lists of overlapping HLA images, as was done in HSC version 3.0. The new scheme provides streaming motions through the use of Gaia DR2.

Proper Motions

Using the updated HLA source list astrometry based on Gaia DR2, we determine the proper motions of each astrometric object. The proper motion of each astronomical object is determined by the medfit linear regression algorithm in Numerical Recipes (Press et al. 1993). For each astronomical object, we determine linear fits of position as a function of the time difference between the source detection and the mean time of all the detections of the object. These fits are done independently for proper motions of right ascension and declination and also for Galactic longitude and latitude. This algorithm is median-based and therefore insensitive to outliers. The first step in this algorithm is to obtain a least squares fit. This step can be run rapidly, since there is a closed form analytic expression for the fit (e.g., MathWorld), as well as standard error determinations for the intercept and slope (proper motion). Subsequent steps are carried out to minimize the mean absolute deviation of the fit from the data. This minimization is carried out iteratively, since no closed form solution exists. Table AstromProperMotions contains the resulting object positions at the mean time and the proper motions, as well as three error estimates: the standard error in the position at the mean time, the standard error in the proper motion, both obtained from the least squares fit in the first step, and the mean absolute deviation that is minimized in the final step. Table AstromSourcePositions contains positions of each detection of an object, including position shifts relative to the object position at the mean time. In some cases, the proper motion standard error is small, while the mean absolute deviation is not. This situation can occur because the standard error is reduced for objects that cover a long time duration, even though there is considerable scatter of individual points from the fit. The quality of the fit can also be explored graphically using the functions provided in the Python script.

Future Plans

This work on the SWEEPS field is a prototype for the next version of the Hubble Source Catalog. SWEEPS is one of the more challenging fields processed in the HSC due to its extreme crowding. It is also has time coverage spanning more than a decade. In the next version of the HSC we plan to extend these same algorithms to all fields in the catalog that have adequate time coverage for the measurement of proper motions. We also will explore the calculation of parallaxes along with the proper motions. (That is more challenging than it might appear because small errors in the instrument distortion model can mimic the motions from parallaxes due to the 6-month cadence in camera orientation for Hubble observations.)

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