The astrometry in HSCv4 relies principally on Gaia DR3.  This page describes the algorithms and discusses the accuracy of the relative and absolute astrometry. A brief summary of the major points:

1. The astrometric solution is designed to minimize the scatter among positions of objects in HST images.  This is not the same as minimizing the error relative to the Gaia reference frame (streaming motions with fields are removed).
2. 88% of the images have alignment based on Gaia DR3.  8% of the images are aligned using the Pan-STARRS catalog.  2% have only relative alignments by cross-matching to overlapping HST images, and the remaining 2% have no alignment adjustments at all.  (Most of those are HST images in the parts of the extragalactic sky that were visited only once by Hubble.)
3. The absolute astrometric accuracy is about 10-15 milliarcseconds.
4. The relative astrometric accuracy (from repeated HST observations of the same source) is about 3 to 8 milliarcseconds, depending on the instrument.

Overview

The Hubble Source Catalog (HSC) combines more than 64,000 visit-based source lists derived from images from the Hubble Advanced Products (HAP) Single-Visit Mosaics and the Hubble Legacy Archive (HLA) into a single master catalog. The astrometric accuracy of the input source lists is highly variable.  The HAP products are often calibrated using Gaia DR3, which leads to good accuracy in the positions.  The older HLA source lists used for WFPC2 preceded the Gaia mission and so have lower accuracy positions.  The positions of the instrument apertures in the focal plane change with time, and the accuracy with which those positions are calibrated also changes.  The cameras have significant geometric distortions that also change over time.  The Guide Star positions have uncertainties that affect the pointing accuracy; those errors have been as large as an arcsecond in the past, but the current HST guide star catalog is based on Gaia and has much smaller errors.  Even with perfect guide star positions, occasionally the HST fine guidance system locks onto the wrong guide star, which can lead to very large errors in the coordinates (up to 90 arcsec, which is a large fraction of the field of view for the cameras).

Taken together, these effects lead to a wide range of astrometric accuracy for the input source lists used for the HSC.  The HSC data processing adapts to these astrometric errors and produces corrected astrometry for the input catalogs as well as accurate astrometry for the combined catalog.

Processing Steps

The calibration of astrometry in the HSC has two steps.  The description of the approach from the Whitmore et al. (2016) paper on the HSC is still generally correct, although the availability of Gaia as a reference catalog has led to changes in some details.

Note that this processing is designed to optimize the alignment of HST images.  It starts (when possible) from absolute calibrations based on the Gaia DR3 catalog, but those positions are adjusted in the relative alignment process to better align images for cross-matching between observations.

Step 1: Pre-offsets

The first step is to match source lists from individual HST observations to external reference catalogs.  The preferred catalog is naturally Gaia, which has both accurate positions and accurate proper motions for a large number of stars.  The small fields of view of the HST cameras mean that some fields (typically in the extragalactic part of the sky) have too few Gaia stars to determine a confident match to the HST catalogs.  In most cases that is because the Gaia catalog is sparse in the required sky region, but there are also cases where Gaia stars are too bright and heavily saturated in the deep HST images for an accurate position measurement.

When there are too few useful Gaia stars, other catalogs are used instead.  Most commonly we use the Pan-STARRS (PS1) DR2 catalog, which has accurate Gaia-calibrated positions and is several magnitudes deeper than Gaia.  That means that it has more available objects in sparse sky regions and also has fainter objects if saturation is an issue.  The principal disadvantage of PS1 is that it has no data for the southern sky (south of -30 deg declination).  Eventually other catalogs will fill in that hole, but for now we fall back on either 2MASS or SDSS.  Both of those are rarely used.

For the Gaia matches,  proper motions (PMs) in Gaia DR3 are used when available.  We know the epoch of each HST observation, and the Gaia proper motions (and parallaxes) are used to shift the Gaia stars to the epoch of the HST image.  The cross-match to HST sources then puts the HST catalog coordinates onto the Gaia reference frame.  That significantly improves the accuracy of the calibration compared with HSCv3, which relied on Gaia DR1 (which had no PMs).

The accuracy of the resulting calibration still depends on the epoch of the observation.  It is best near the Gaia reference epoch 2016.0.  Far from that epoch, the errors and covariances in the Gaia parameters lead to increasing large errors in the computed positions of the Gaia stars.

For the other reference catalogs, we do not use proper motions.  That means that the accuracy is significantly poorer away from the epoch of the catalog (2012 to 2015 for PS1, depending on the sky location).  Nonetheless, the accuracy of these other catalogs allows us to discover and correct the worst astrometric errors in the input data, giving positions that are typically good to about 0.1 arcsec or better for most fields.

Step 2: Cross-matching

The second step is to cross-match catalogs from overlapping HST observations.  The cross-match algorithm was developed by Budavari & Lubow (2012) and allows for astrometric offsets for each image.  It also can handle stacks of many images (e.g., in the Hubble Deep Field there are thousands of overlapping observations).  

The cross-matching determines which measurements appear to be the same object in different images and so should be grouped together in matches.  It also determines a refined world coordinate system for every overlapping image and defines a single coordinate system for the combined catalog.

One side effect of the cross-matching is that it removes systematic streaming motions from the absolute astrometry.  The resulting astrometry in some fields may have subtle structures.  For example, in fields containing the globular cluster M4, most stars are members of the cluster and have significant common proper motions (approximately 23 mas/yr).  Those cluster members effectively define the coordinate system in the field.  But background stars (which in the Gaia frame have smaller PMs) have an implied PM relative to the cluster and so have increased (apparent) proper motions after cross-matching.

For HSCv3.1 we did additional work on the catalog to correct these effects in one field (the SWEEPS field).  That has not been done yet for HSCv4, and whether it will be done or not is to be determined.  Users who are interested in the fine details of astrometry should realize that the HSCv4 is designed to optimize relative astrometry and can have some variations in its absolute astrometry depending on the field.

Astrometric Reference Catalogs Used for HSCv4 Calibration

The astrometric calibration is now based on the Gaia DR3 catalog. Gaia has allowed the confident identification of large errors in the HST pointing, with shifts up to 100 arcsec correctly identified (all of the several hundred catalogs with shifts larger than 8 arcsec were checked by eye to confirm the accuracy of the shifts). An example of an image with a large shift is shown below.  Before the shift, most Gaia sources do not align with the image (orange circles); after the very large 97.4 arcsec shift (green circles), the Gaia stars match very well.  This shift is so large that only one of the the matching Gaia stars overlaps the original image position.

In HSCv4, 96% of the fields have matches to external astrometric reference catalogs.  88% have Gaia DR3 calibration and 8% have calibrations based on the PS1.  Note that the PS1 astrometry has also been recalibrated using Gaia DR3 (see Lubow et al. 2021 and White et al. 2022), so 96% of the fields have Gaia primary or secondary astrometry.

The fraction of fields with Gaia astrometry varies depending on the instrument.  More than 98% of the ACS/WFC catalogs have Gaia calibrations, while 80% of WFPC2 catalogs have Gaia matches.  The table below summarizes the astrometric calibration results for both HSCv4 and HSCv3.

The percentages give the fraction of visits having the specified calibration.  (All filters in a visit share the same astrometric correction.) The External column gives the percentage of fields that have a calibration based on some external catalog (nearly all in HSCv4 use either Gaia DR3 or PS1).  The Relative column gives the percentage that do not have an external reference calibration but do have relative calibrations from cross-matches with other HSC visits.  The None column gives the percentage of fields that have no astrometric calibration at all (often because they do not overlap any other HST observations).

The figure below shows the sky regions where different reference catalogs were used. About 7/8 of the images were calibrated using Gaia, with most of the remaining images using Pan-STARRS (at high Galactic latitudes in the northern sky). 4% of the images, mainly south of declination -30 degrees, have no external astrometric reference calibration (although half of those do have relative calibrations via cross-matches to other HSC fields).

Absolute Astrometric Accuracy

We have measured the absolute astrometric accuracy of HSCv4 by matching to external astrometric reference catalogs.  To eliminate astrophysical variations from proper motions (since HSCv4 does not currently include proper motions), we have chosen reference catalogs that do not have significant PMs.

Match to ICRF2

The International Celestial Reference Frame version 2 catalog (ICRF2; Ma et al. 2009) contains 3,414 sources with accurate radio positions.  These sources are extragalactic objects (often at great cosmic distances) and so have negligibly small proper motions for our purposes.  This catalog helped define the reference frame for Gaia.

We have matched HSCv4 to ICRF2.  (See the Whitmore et al. 2016 paper for a similar cross-match to HSCv1.)   The cross-match used a relatively large matching radius of 8 arcsec to determine which fields are affected by crowding.  Note that the optical counterparts to ICRF2 sources are not necessarily point sources such as quasars; many of them are in highly crowded parts of the HSC sky.  For example, one source is the nucleus of the galaxy M87 (Virgo A), which has many sources in HSCv4 that are associated with the M87 jet, star clusters in the galaxy, and other structures in the extended object.

To produce a clean comparison sample, we excluded sources where the closest (primary) HSCv4 match was offset by more than 0.4 arcsec from the ICRF2 position, or where the second closest match was less than 5 times the distance to the primary match (a "confused" field).  Those cuts leave 240 HSCv4-ICRF2 matches (with 34 additional ICRF2 sources that have associated HSCv4 matches but that were excluded).  For comparison, we also matched the HSCv3 catalog using the same selection criteria; that yielded 202 HSCv3-ICRF2 matches (with 29 omitted due to the selection cuts).  

The plot below compares the results for HSCv4 (left) and HSCv3 (right).  The distribution is clearly tighter for HSCv4.  We prefer the median absolute deviation estimate of the noise because there is real astrophysical noise for individual sources that can lead to offsets between radio positions and the optical positions (e.g., a radio active nucleus may be obscured by dust in the optical or UV observations)  The MAD value for HSCv3 was 59 milliarcseconds (mas), while the MAD value for HSCv4 is 17 mas, smaller by a factor of 4. 

The improvement between HSCv3 and HSCv4 is due to a combination of factors. HSCv3 used Gaia DR1, which had no proper motions.  HSCv4 also benefits from improved geometrical distortion models for the cameras; that improves the accuracy of source positions near image edges and also improves the overall accuracy of the Gaia match even for objects near the center of the camera. 

Note that these noise levels are instrument-dependent.  This table summaries the MAD values by instrument for HSCv4 and HSCv3.

These results complicate the interpretation of the improvement in HSCv4. The instrument for each match is determined by counting the number of images from each detector that are included in the match.  Many objects have contributions from multiple instruments, and in some cases there are ties for which instrument is dominant.  (That is why the sum of the counts for the instruments add up to more than the total.) Clearly WFPC2 has the poorest quality positions (unsurprising since it has large pixels with undersampled images). The additional of new observations for the active instruments has shifted the balance of the observations to rely less on WFPC2 in HSCv4 than in HSCv3.  That makes HSCv3 look a bit worse than it actually is in the overall comparison, since we are sometimes comparing WFPC2 "apples" to ACS or WFC3 "oranges". 

Regardless of the complications, it is clear that HSCv4 has significantly more accurate absolute astrometry for these ICRF2 sources.  This is a powerful test because it tests the final astrometric accuracy of our catalog, including all effects that influence the astrometry (such as removal of streaming motions and the need to rely on non-Gaia reference catalogs for some fields).

Match to Gaia DR3 subset

We have done a similar cross-match to a subset of stars selected from Gaia DR3.  The sample is restricted to:

• Gaia stars in regions covered by HSCv4 (or HSCv3)
• Relatively faint stars with Gaia phot_g_mean_mag > 19.0 (to reduce the impact of saturation in the HST data)
• Stars that have known but small proper motions, with PM < 0.7 mas/yr

The last restriction results in a sample of slowly moving objects. The oldest HSC measurements have epochs of 1994, so they have 22 years of proper motion from the Gaia DR3 epoch 2016.0.  Even with this tight restriction, the oldest measurements can have PM shifts of 15 mas (similar to the offsets that we measure).

With these restrictions there are 12,577 low PM, faint Gaia sources in the HSCv4 area.  For HSCv3 the counts are smaller by about 30% (consistent with the increase in sky area from 40.3 square degrees in HSCv3 to 56.2 square degrees in HSCv4).  After removal of matches in confused regions (as for the ICRF2 match), there are 11,706 HSCv4-Gaia matches and 8,328 HSCv3-Gaia matches.  The plot below shows the distributions.

There are some interesting differences compared with the ICRF2 cross-match:

• The MAD values are much more similar for HSCv3 and HSCv4.  That is probably due to the more uniform image properties of the Gaia objects (which are mainly point sources).  The poorer astrometry for WFC3/IR for HSCv4 also is a contributing factor (see below for more discussion of that).
• The asymmetry of the HSCv3 distribution is obviously different than HSCv4.  That is likely due to the absence of PMs in the Gaia DR1 catalog used for HSCv3; that leads to some complicated changes in the astrometry (although it apparently does not create large biases). 
• The small bump on the right side for HSCv4 is due to a population of WFPC2 sources with early mean epochs; taking out the PMs for those sources removes the bump.  We have chosen not to apply PMs to this measurement because they complicate the interpretation.

Another way to compare these results is to look at the histogram of offsets.  A moderate improvement can be seen for HSCv4 compared with HSCv3.

As for ICRF2, these distributions vary with instrument.  For the Gaia comparison, we have computed new mean positions for the HSC matches that separate the matches by detector.  That generates a much larger comparison sample for the instruments and avoids trying to test the instrument properties using match positions that average data from multiple instruments.  To produce a reliable comparison between HSCv4 and HSCv3, we restrict the results to a sample of Gaia stars that have measurements for the same instrument in both HSC versions.  That means that the plots below for HSCv3 and HSCv4 have exactly the same number of points (for the same collection of Gaia stars).

The plot below shows the distributions separated by instrument for HSCv4 (top row) and HSCv3 (bottom row).  The four columns show the distributions for ACS/WFC, WFC3/IR, WFC3/UVIS and WFPC2.  

The second plot shows histograms of the HSC-Gaia source separations for the different instruments.  

Comparison of the HSCv4 distributions to the HSCv3 distributions show that the HSCv4 histograms are tighter and have a higher peak, indicating smaller astrometric errors.  The median noise for these Gaia stars in HSCv4 is 10 milliarcsecond or less for ACS/WFC, WFC3/IR, and WFC3/UVIS.  The WFPC2 noise is larger (15 mas).

The table below summarizes the results from the Gaia tests.

Relative Astrometric Accuracy

The source detections (and non-detections) that correspond to the same physical object (as determined by the algorithms defined in Budavari & Lubow 2012) are given a unique MatchID number and an associated match position (MatchRA, MatchDec). Each member of the match, including non-detections, also has an assigned MemID value and a source position (SourceRA, SourceDec). As part of the matching process, astrometric corrections are made to overlapping images, with all sources in an image moved uniformly to create the smallest scatter about the match positions. Each source detection and non-detection has a separation distance, D (small d in the plots below), from the match position.

The two plots show (in blue) the distribution of the relative astrometric errors in version 4 of the HSC corrected astrometry, as measured by the positional offsets of the sources contributing to multi-visit matches from their match positions. Plotted in orange are the corresponding distributions of astrometric errors based on the original HST image astrometry. The areas under the blue and orange curves in the left plot are the same, but the original distribution (orange curve) has a long tail that extends far beyond the limits of the plot.  Note that the HAP astrometry was already calibrated using Gaia DR3 and other external catalogs, but the HSCv4 astrometry is nonetheless significantly improved compared with the original positions.

The right plot shows the distribution using a larger distance scale (x-axis) than the left plot. Furthermore, the right plot has a logarithmic vertical scale.  Large astrometric errors up to 5 arcsec occur for both the HAP catalogs (orange) and the HSCv3 catalog (green). Such large errors are rare, but even larger errors occur in the worst cases. HSCv4 (blue) has completely eliminated the long tail of sources with large errors.

In HSCv4, the peak (mode) of the HSC corrected astrometric error distribution is 3.4 mas, while the median offset is 6.9 mas. For comparison, the values for HSCv3 were 3.0 mas (mode/peak) and 7.6 mas (median).  The increase in the mode for HSCv4 is due to degradation in the WFC3/IR astrometry. 

The accuracy of the relative astrometry is different for different cameras.  The plot compares the distributions for HSCv4.

The table summarizes the properties of the distributions for different instruments, comparing HSCv4 to HSCv3.  The mode (peak) of the distribution ranges from 2.5 to 8 mas, while the median (affected more by the long tail) ranges from 6 to 18 mas.

The comparison with HSCv3 here is complicated by the fact that the underlying source list properties have changed dramatically for HSCv4.  Some instruments have deeper catalogs (leading to more faint sources and higher noise) and some have shallower catalogs (more bright sources and lower noise).  The change in pixel size for WFC3/IR is definitely making the HSCv4 astrometry worse.

For a more direct comparison of source properties, we have cross-matched the HSCv4 catalog with HSCv3.  We include in this sample all sources that have separations less than 0.1 arcsec and where the second-closest source is at least 3 times farther away than the closest source.  That avoids possible mis-matches in crowded fields.  The resulting plot and table are shown below.

The changes from the numbers with all sources are modest.

The relative astrometric errors are slightly larger for most instruments for HSCv4 than for HSCv3.  Naturally the WFPC2 results are similar since they use the same source lists.  The calibration using Gaia DR3 proper motions may contribute to these changes since it introduces more scatter among the source positions before the cross-matching steps.

To summarize, the relative astrometric error distribution in the original HST images has a long tail that has been greatly reduced by the HSC corrections, and the tail for HSCv4 is much improved compared with HSCv3.  The HSCv4 relative astrometry is however slightly degraded compared with HSCv3, with the largest changes for WFC3/IR measurements where the larger HAP pixel size has reduced the data quality.

Summary

The results for the two absolute astrometry tests are similar: the absolute astrometry in HSCv4 has a typical noise level of about 12.5 mas.  The noise varies with instrument, ranging from approximately 10 mas (for ACS/WFC, WFC3/IR, and WFC3/UVIS) to 15–25 mas for WFPC2.  The noise in absolute astrometry is lower in HSCv4 compared with HSCv3 for all instruments, including both WFPC2 (which used the same input catalogs from HSCv3) and WFC3/IR (which is based on lower-resolution images in HSCv4).  

The relative astrometric scatter (between repeated measurements of the same source) is considerably smaller.  In HSCv4, the peak (mode) of the HSC corrected astrometric error distribution is 3.4 mas, while the median offset is 6.9 mas. For comparison, the values for HSCv3 were 3.0 mas (mode/peak) and 7.6 mas (median). 

The relative astrometry is generally better than the absolute astrometry because the HSC cross-matching is designed to reduce the scatter between source measurements in different images.  A future reanalysis of the HSCv4 data could improve the absolute astrometry (by better preserving astrometry in fields with streaming motions) while simultaneously computing proper motions for many HSC fields.  A similar pilot project for HSCv3 produced HSCv3.1, which has proper motions in the SWEEPS field.