VI. Analysis of the 2MASS Second Incremental Release Catalogs

5.Position Reconstruction Performance

The position reconstruction accuracy achieved for the vast majority of sources in the 2MASS Second Incremental Release is better than the 0.5´´ 1- Level 1 Science Requirement by a considerable margin. This is demonstrated below by comparisons with the ACT catalog used in the reconstruction, as well as from the repeatability of positions of multiply observed sources in Tile overlap regions and by comparisons to two new astrometric catalogs (Tycho-2 and UCAC), released just before and after this 2MASS Release, respectively. A relatively few Tiles in this Release have position reconstruction errors well above the average, due to a local sparsity of ACT reference stars. These errors can in extreme cases reach as high as 2´´. Particular care has been taken to assure that the position uncertainties associated with the sources from these problem Tiles are adequate. In fact, the quoted position uncertainties for the entire Release, based on the same comparisons listed above, are believed to be conservative.

a. Comparison to ACT Reference Catalog Positions

Figure 1 presents a histogram of right ascension (RA) differences (true angle) of 2MASS positions with respect to (w.r.t.) the corresponding ACT positions for all 25493 survey Tiles. Figure 2 shows a histogram of the declination (Dec) differences w.r.t. the ACT. Note that the are approximately 0.1´´ in both directions (slightly more in Dec and less in RA) with mean differences that are essentially zero.

Figure 1	Figure 2

These histograms include data from 421 Tiles for which the number and/or distribution of ACT stars was insufficient to use them as reference stars during data processing. For these Tiles the USNOA catalog was used, resulting in reduced reconstruction accuracy. One measure of that reduction can be seen in residual histograms w.r.t. the few (but unused) ACT stars in the 421 Tiles. The RA differences are presented for these Tiles alone in Figure 3 and the Dec differences in Figure 4. Although the ACT differences shown here do not exceed 0.5´´, the reconstruction errors can be systematically larger.

Figure 3	Figure 4

b. Comparison of Tile Overlap Positions and Uncertainties

Since the ACT is used in 2MASS position reconstruction, comparison of the reconstructed ACT star 2MASS positions does not provide a measure of the astrometric accuracy for random 2MASS sources. For example, 2MASS positional errors are expected to be small in the vicinity of ACT reference stars, but errors would grow between ACT stars because of accumulating random-walk errors in the measured 2MASS relative frame-to-frame position offsets. Differences in the reconstructed positions of multiply-observed stars in Tile overlap regions reveal how consistent the reconstructions are because the astrometric solutions are evaluated independently for each Tile using different ACT stars.

Figure 5 shows a histogram of cross-scan (RA) position differences for 11 million overlap match source pairs covering the entire Second Incremental Data Release, and Figure 6 shows a histogram of the corresponding in-scan (Dec) differences. Note that the standard deviation () of the cross-scan overlap differences is 152 milliarcseconds (mas) and of the in-scan overlap differences is 167 mas. Since these statistics are based on differences of two essentially independent position determinations from overlapping Tiles, a measure of the 2MASS position reconstruction errors can be obtained by dividing the difference by the square-root of two. This yields = 107 mas and 118 mas for cross-scan and in-scan, respectively. Only unconfused sources, clear of artifacts, with a J magnitude brighter than 15.8, an H magnitude brighter than 15.1, or a K_s magnitude brighter than 14.3 were eligible to form the overlap match pairs upon which these statistics are based.

Figure 5	Figure 6

To verify that the quoted uncertainties for this preliminary release are a conservative representation of the true astrometric errors, the ² values for the overlap differences were also examined. The ² parameter is formed by dividing the square of the position difference by the sum of the quoted variances of the two positions being differenced. Provided the quoted uncertainties faithfully represent the actual errors, the expected mean value of ² over a large sample is unity. Figure 7 shows a histogram of the cross-scan overlap ² for the entire Release, and Figure 8 presents the in-scan ². It can be seen that the mean ² values are well below unity (~0.5) in both directions. This would indicate that the quoted position uncertainties are quite conservative. They are, in fact, more conservative than first intended, as will be explained later during the discussion of Tycho-2 comparisons.

Figure 7	Figure 8

c. Comparison to Tycho-2(not in Tycho-1) Catalog Positions and Uncertainties

The Tycho-2 Catalog was released just prior to the 2MASS Second Incremental Data Release. This was too late to be factored into the position reconstruction, but does provide an additional measure of the effect of random walk between ACT stars. For this purpose Tycho-2 stars flagged as previously in Tycho-1 are ignored, since they are effectively the same set of stars as contained in the ACT. The comparison is limited to new Tycho-2 stars which are not double and for which proper motions are available. Only 2MASS sources detected in all three bands and brighter than magnitudes 15.8, 15.1 and 14.3 in J, H and K_s, respectively, are used. Figure 9 presents a histogram of RA differences (true angle) of 2MASS positions w.r.t. the corresponding new Tycho-2 positions and Figure 10 shows a histogram of the Dec differences. The difference are 194 mas cross-scan and 181 mas in-scan.

Figure 9	Figure 10

Limited pre-release access to Tycho-2 during the final stages of preparation for this 2MASS Release indicated that the mean 2MASS:Tycho-2(not in Tycho-1) ² would exceed unity. This indicated that either the 2MASS errors or the Tycho-2(not in Tycho-1) errors, or both, were under estimated. In order to be sure that the 2MASS uncertainties for this preliminary Release are conservative, they were adjusted for better consistency with the Tycho-2 data. Since most of the discrepancy was driven by sources with the lowest 2MASS uncertainties, the floor on quoted 2MASS position for the Release was raised from 0.10´´ to 0.13´´. Figure 11 shows a histogram of the resulting cross-scan 2MASS:Tycho-2(not in Tycho-1) ² for the entire Release, and Figure 12 presents the in-scan ². The mean ² values are 1.0 and 0.9 for cross-scan and in-scan, respectively.

Figure 11	Figure 12

d. Comparison to UCAC Positions and Uncertainties

The first release of the U.S. Naval Observatory CCD Astrograph Catalog (UCAC) covering most of the southern hemisphere became publicly available within a few weeks after this 2MASS Release. Even though it covers a little less than half the sky, the UCAC positions are more accurate and have higher density than the Tycho-2 (not in Tycho-1). Figure 13 presents a histogram of RA differences (true angle) for 6.6 million 2MASS:UCAC match pairs, and Figure 14 shows a histogram of the Dec differences. Note that the difference are 126 mas cross-scan and 127 mas in-scan, demonstrationing a much better agreement between 2MASS:UCAC than 2MASS:Tycho-2(not in Tycho-1). Only 2MASS sources detected in all three bands and brighter than magnitudes 15.8, 15.1 and 14.3 in J, H and K_s respectively, were eligible for matching to UCAC stars.

Figure 13	Figure 14

UCAC can also shed light on the previously noted ² discrepancy. Figure 15 shows a histogram of the cross-scan 2MASS:UCAC ², and Figure 16 presents the in-scan ². Note that the mean ² are ~0.5 in both directions, in excellent agreement with the 2MASS overlap data. The fact that the 2MASS:Tycho-2 (not in Tycho-1) ² differ is likely related to an inconsistency recently noted by Zacharias et al. during a comparison of UCAC with Tycho-2.

Figure 15	Figure 16

e. Variation of Quoted 2MASS Uncertainties

The uncertainties assigned to the 2MASS positions for the Second Incremental Data Release are presented in Figure 17, which shows a histogram of the cross-scan (RA) uncertainties and Figure 18, which shows a histogram of the in-scan (Dec) uncertainties. Note that the mean assigned in cross-scan is 141 mas and in-scan is 144 mas.

Figure 17	Figure 18

Figure 19 presents a galactic aitoff projection plot of the major axis of the mean quoted position uncertainty ellipse for sources with K_s magnitudes between 10 and 10.5, averaged into 10´ spatial bins. The full range of the display is 0.1´´-0.5´´,with blue showing the smallest uncertainties, red showing the largest, and green near the mid point of the range. The image is centered on the Galactic center. Note that increases in the uncertainties occur primarily near Tile ends and toward the Galactic pole. There are also a few Tiles with increased uncertainties in the heavily obscured region near the Galactic center. Tile ends have increased position reconstruction errors, because the reconstruction is carried out for one Tile at a time. It is, in a sense, extrapolating from the last ACT star near a Tile end, as opposed to interpolating between ACT stars elsewhere along the Tile. The other uncertainty increases are generally associated with a relative sparsity of ACT reference stars, which occurs near the Galactic poles, as well as very near the heavily obscured Galactic center.

Figure 19

[Last Updated: 2000 July 13, by H. McCallon and R. Cutri. Modified 2000 Aug 30 by S. Van Dyk.]