GSC-ACT files and information

Last updated 16 December 1999

Overview of the project: The purpose of the GSC-ACT project is to recalibrate the Hubble Guide Star Catalog (GSC), version 1.1, using the ACT (Astrographic Catalog/Tycho) data from the US Naval Observatory.

The reasons for doing this will be apparent to long-time GSC 1.1 users. GSC 1.1 was calibrated using the AGK3 for plates with centers near or north of +2 declination, and the SAO for plate centers down to declination -60. The CPC was used south of this limit. The fit was done to include terms up to third (cubic) order.

We now have considerably better catalogs than were available back in 1989. ACT offers better positions and more stars. The latter means that the astrometric fit can include more terms... and this is a very good thing, because the plates include distortions that the simple third-order GSC 1.1 fit cannot accommodate. (In GSC-ACT, terms up to order 5 are included.)

The Space Telescope Science Institute did address some of these issues, through a recalibration resulting in the GSC 1.2 catalog. The biggest problem with GSC 1.2 is access; data is available in small chunks through this GSC 1.2 request form at STScI ; or through this GSC 1.2 request form through VizieR, at the Centre de Données Astronomiques de Strasbourg in France.

Accessing GSC-ACT data via Internet: There is now a link for querying the the GSC-ACT at the Université de Strasbourg, which allows you to get parts of the catalog without the need for CD-ROMs or the software on this site. Click here to access GSC-ACT via this method.

The above method is very convenient if you want to grab all the GSC-ACT data for a given chunk of the sky. But certain programs, such as Astrometrica, use the GSC in its "original", pseudo-FITS format. (In this format, the sky is divided into 9537 "regions", and a FITS file with extension .GSC is provided for each region.) These .GSC files may be made available by ftp, but it will probably not be possible until late October 1999.

Methods used: The recalibration consists of the following steps. First, a version of the Tycho catalog was made that consisted of the original data in the tyc_main file provided by the European Space Agency, combined with the proper motions from the ACT.

Second, each record was matched with corresponding record(s) in GSC 1.1. (Many stars were recorded on multiple plates, resulting in multiple records in the GSC.) The result was stored on a per-plate basis, so that for a given plate, there would be a file containing data for each ACT star on that plate. The data would consist of (full) Tycho data, the ACT proper motion (if any), and (full) GSC 1.1 data.

Up to this point, no real math has been performed; the records have simply been cross-indexed and arranged in a "by-plate" basis, rather than in a "sorted by GSC number" basis. But this form is very convenient; it allows one to easily fetch all data for a given plate, in order to recalibrate it.

The third step is really the key. The data for each plate was loaded, and the ACT positions were corrected for proper motion. Then the GSC 1.1 and ACT positions were converted to (xi, eta) space, and residuals (delta_xi, delta_eta) were computed. This was then used as input to a least-squares fitting routine. Cases where the distance between the GSC 1.1 and ACT positions were greater than 1" were thrown out as doubtful. (As will be seen, this was not as drastic a limit as one might first think. On most plates, well over 90% of the stars fell within this limit, even before adjustment began.)

The least-squares fit was repeated six times for each plate. Convergence generally took two or three iterations, but some plates took an extra step, and the process runs quickly enough (about two hours on a 200 MHz Pentium) that one cannot begrudge the extra iterations.

The result of this step was a set of 42 coefficients (21 for xi, 21 for eta) that define, for the plate in question, the transformation from (xi, eta) GSC 1.1 to (xi, eta) GSC-ACT. The number of stars falling outside the 1" limit before the fitting began; the number falling outside the limit after fitting was completed; and the RMS errors in each case, were tabulated, and the coefficients stored.

It is this table of coefficients, and the software for using it, that constitute the "results" of this project.

You'll notice that, in this entire process, the original plate coefficients remain unused. There was really no particular need to consider them for this sort of "differential" calibration.

How much of an improvement is GSC-ACT over GSC 1.x? This issue has been the source of some quite understandable confusion. The short version is this: for any one star, the improvement is usually not all that wonderful. If you're examining the positions of a set of stars in a region (to perform an astrometric reduction, for example), the improvement can be a truly wonderful thing.

To see why, suppose we are in a part of the sky where the GSC 1.1 data has random position errors of about .4 arcseconds, and systematic position errors of about .3 arcseconds. In other words, if you examined a statistically significant sample of stars in this region, you would find that they averaged, say, .3 arcseconds east of their "correct" locations, with a scatter of about .4 arcseconds around that erroneous point. (This is a fair example of the level of error involved.)

In the same region of sky, GSC-ACT would have random position errors of about .4 arcseconds, since the recalibration did nothing to clean up such errors. But the systematic errors were pretty thoroughly squashed down to zero.

If you examined one particular star in this region, its total error in GSC 1.1 would be about .5 arcseconds. (That number comes from error propagation:)

total_error ^ 2 = systematic_error ^ 2 + random_error ^ 2

(.5) ^ 2 = (.3) ^ 2 + (.4) ^ 2

For that same star in GSC-ACT, where the systematic error is basically zero, total error is just about equal to random error, or .4 arcseconds. This amounts to a 20% improvement, and scarcely seems worthwhile.

However, suppose we're using a sample of sixteen stars, perhaps for use in astrometric reduction. (Even a small CCD camera usually produces images covering sixteen GSC stars.) Systematic error isn't helped at all by the extra stars. Measure with a bad ruler a zillion times, and you'll still be measuring with a bad ruler. But the random errors will drop by the square root of the number of stars used. For both GSCs, the random error will therefore drop to .4 / 4 = .1 arcsecond.

This results in a modest improvement for GSC 1.1: the total error is now the square root of (.3) ^ 2 + (.1) ^ 2, or the square root of .1, or about .316 arcseconds. The systematic error is causing trouble here; we could measure a zillion stars, but still hit that .3 arcsecond systematic error.

But use of GSC-ACT suddenly looks pretty good: its total error is still equal to the random error, which is now a mere .1 arcsecond. Instead of having 80% of the error of GSC 1.1, it has less than 33% of the error of GSC 1.1!

Similar comments apply in the case of GSC-ACT vs. GSC 1.2, but in this case, the improvement is not nearly so dramatic. GSC 1.2 already did a good job of quashing systematic error, so it already gathered much of the benefit of recalibrating the data.

It should be noted, by the way, that your astrometry software is not going to see so great an improvement. From its point of view, the main impact of GSC-ACT use is simply that the image appears "shifted" by about .3 arcseconds compared to the result of a GSC 1.1 calibration. But if you got a lot of observations, following an extended arc in the sky, the elimination of systematic errors would mean that the orbit would have greatly reduced residual errors.

I expect the main use of GSC-ACT will be in asteroid astrometry. And for this purpose, the answer to the question of "How much of an improvement is GSC-ACT over GSC 1.x?" is: "It cuts down errors a lot."

What about photometry?: There have been numberless complaints voiced over the years about the photometric inadequacies of the GSC. In late 1999, I started work on an attempt to recalibrate the photometry. So far, the results are moderately encouraging. Click here to read about the current status of the photometric recalibration of GSC. First, there is a lack of suitable data. The Tycho dataset provides excellent photometry for stars down to about magnitude 11, and it is true that this could be used to recalibrate bright stars. But it would not necessarily help much at fainter magnitudes (i.e., for about 90% of GSC.) (But this objection may vanish. It does appear that Brian Skiff's LONEOS.PHOT photometric database could extend the range of "decent" photometry quite nicely.)

Second, it's not clear that the photometry could be improved very much. The raw magnitude data coming in from GSC 1.1 is sufficiently "random" that recalibration might not result in much of a benefit.

And thirdly, Dave Monet has recalibrated the A1.0 dataset (both photometrically and astrometrically), using ACT. This resulted in a much better photometric dataset than GSC-ACT could hope to be. (Click here for information about A2.0.) And it's likely, too, that A2.0 be further improved, using LONEOS.PHOT.

Summary of results: In most cases, the rms error (GSC - ACT) dropped by about a factor of two, and the number of stars with residuals of over an arcsecond dropped by a similar factor. There is some variation in this. Some plates in the extreme southern hemisphere improved by a much greater factor. A complete table showing the effects of the transformation on a per-plate basis is available.

In reality, the drop in RMS error was probably even greater than indicated in this table. When comparing GSC 1.1 to ACT, it was common for a large percentage of the stars to be outside the one-arcsecond limit; dropping them leads to an underestimation of the RMS error. (The same effect applies in comparing GSC-ACT to ACT, but to a lesser extent; the percentage of rejected stars was much lower in this case.)

Note also that some plates remain uncalibrated; only the 1518 plates listed in the original GSC 1.1 calibration data were considered, and of these, one (plate 06EL) still failed to converge (the remaining 1517 plates presented no difficulties).

How to use this data: For a long time, GSC 1.1 was available on two CD-ROMs, produced by the Space Telescope Science Institute and sold by the Astronomical Society of the Pacific. However, I understand they've ceased doing this. I'm now making available GSC-ACT on two CD-ROMs for the cost of replication. These disks have the same format as the "original" GSC 1.1, which is a Good Thing. There are dozens of programs already out there that have been set up to work with the two-CD GSC 1.1 distribution; as far as I know, all of them will be perfectly happy to read the two-CD GSC-ACT distribution instead.

There's an alternative to getting the new CDs. There are plenty of copies of GSC 1.1 out in the world already; it really should not be essential that new CDs be made available to users of these disks. An algorithmic method allows one to switch from GSC 1.1 to GSC-ACT with great ease; you don't need to keep both datasets floating around. Also, if the algorithm or coefficients are improved, you can just download new data and be up and running right away. (I don't expect this to happen at all soon, but the new Tycho 2 dataset might, hypothetically, tempt me to re-process the calibration to generate new coefficients. I say "hypothetically" because it looks unlikely that such a recalibration would really help.)

The following files will enable one to convert GSC 1.1 data to GSC-ACT data algorithmically.

You must first download the ZIPped data (about 560 KBytes). This consists mostly of the compressed plate coefficients; the C/C++ source code is quite small in comparison, is fairly well-commented, and should be easily understood. The extension '.cpp' is used, although the files could be renamed to '.c'; no C++ features are used.

The core of the algorithm is in GSC_ACT.CPP and GSC_ACT.H. These contain the definition of the plate data structure, functions to convert between RA/dec and xi/eta (plate coordinates), functions to access plate data in a cached manner, and a function which, given a GSC 1.1 position and the plate it came from, will turn it into a GSC-ACT position.

Also included is GSC11ACT.CPP. This is an example program that will read in a .GSC file from the GSC 1.1 CD-ROMs distributed by the Space Telescope Science Institute/Astronomical Society of the Pacific, and will produce a file with the same format, with positions in the ACT frame. There are several reasons for providing such a program. First, quite a few programs make use of these CDs already; this example program lets you produce files they are already built to understand. Second, it makes a good example of how the process works: for each star in the original file, the plate data is loaded; if the plate data is successfully found, the position is adjusted from GSC 1.1 to GSC-ACT; then the result is written to the output file. One does not really need a detailed understanding of how the astrometric reduction was done or of the math behind it.

A final benefit of the program is that it provides yet another check on the workings of the transformation. When the same star is found on separate plates, the difference between the measurements is computed, both in the original GSC 1.1 and in the new GSC-ACT. The RMS average of these differences generally drops by a factor of two. The real importance of this is that it indicates an improvement in astrometric precision for faint stars, even though the recalibration only involved ACT stars.

The code should port easily to other platforms, with one small exception. The data is stored in its raw binary form. This will cause problems on "wrong-endian" machines. Evading this restriction would be simple in the case of integer data, but getting the 8-byte "double" values loaded would be a greater problem. An ASCII version could easily be made available for this reason, though the data size would bloat by about a factor of two. If such a file would be useful to you, please e-mail me, and I'll set up the file for you.