Comparison of 2MASS Catalog Positions/Uncertainties with UCACr10

Figure 1 plots normalized histograms of 2MASS:UCACr10 differences, with cross-scan in the left panel and in-scan in the right panel. The "dx" cross-scan difference parameter is roughly equivalent (except near the poles) to a true-angle RA difference, but opposite in sign. Thus, when "dx" is positive the 2MASS position is west of the UCACr10 position. When "dy" is positive 2MASS position is north of the UCACr10 position. Note that the cross-scan and in-scan difference sigmas are close (80 and 82 mas respectively) and the cross-scan bias is small (+3 mas) with a somewhat larger (+13 mas) in-scan bias. Figure 2 plots a normalized histogram of 2MASS:UCACr10 radial differences. Note that the global mean of the radial differences, which includes the effects of both the systematic and random errors of both the 2MASS and UCACr10 catalogs, is 95 mas.

In Figure 3 normalized histograms comparing the quoted uncertainties for 2MASS and UCACr10 are presented. Comparison plots are divided into 2 panels with the cross-scan data presented in the left panel and in-scan data in the right. 2MASS histograms are in solid black and UCACr10 in light red. Note that the quoted 2MASS sigmas overlap the high end of the UCACr10 sigmas.

Combining the measured differences (dx, dy) with quoted 2MASS (sigx2m, sigy2m) and UCACr10 (sigxuc, sigyuc) sigmas one can obtain a measure of how well those sigmas reflect the actual errors. The chi-square parameters (chi2x, chi2y) are computed as follows:

chi2x = (dx*dx)/(sigx2m*sigx2m +sigxuc*sigxuc)

chi2y = (dy*dy)/(sigy2m*sigy2m +sigyuc*sigyuc)

The mean of chi-square (given a large number of measurements) has an expected value of 1.0, if the quoted sigmas are exactly right. A value larger than 1.0 indicates the quoted sigmas are too low and less than 1.0 that they are too high. Of course there's no way to tell for sure which of the sigmas (2MASS or UCACr10) is off. Figure 4 plots histograms of chi-square values for cross-scan in the left panel and in-scan in the right. The mean chi-square values from the UCACr10 differences are 1.16 and 1.19, for cross-scan and in-scan respectively. Assuming the UCACr10 sigmas are properly stated, this indicates that overall the quoted 2MASS sigmas tend to be a little too low.

II. Variation with Sky Position:

Figure 5 plots mean cross-scan and in-scan position differences as a function of RA (left panel) and Dec (right panel). The magnitude of the systematic differences with sky position are somewhat larger than anticipated, particularly in declination. Previous comparison to Tycho-2 did not show this effect. This could be a magnitude effect since 2MASS sources matched to UCACr10 average over 2 magnitudes fainter. The other possibility is that it's due to systematic differences between the Tycho-2 and UCACr10 catalogs.

Mean radial differences are plotted as a function of RA (left panel) and Dec (right panel) in Figure 6. The variation with declination is consistent with the Tycho-2(1) results but the variation with RA is not. The RMS of the 2MASS:UCACr10 differences are plotted as a function of RA (left panels) and Dec (right panels), with cross-scan in the upper panels and in-scan in the lower panels. Note that the increased variation with RA shows up equally in both cross-scan and in-scan.

Figure 7 plots mean chi-square values as a function of RA (left panel) and Dec (right panel). Cross-scan chi-squares are plotted in black and in-scan in red. Accepting the UCACr10 uncertainties as quoted, this says that the 2MASS uncertainties are underestimated particularly near the pole and in the RA range from -60 to +90. Tycho-2(1) comparisons agree regarding the pole but not the RA range.

Figure 8 plots 2MASS RMS values derived by substracting in quadrature the quoted UCACr10 sigmas from the 2MASS:UCACr10 difference RMS values displayed earlier. If the quoted UCACr10 sigmas are perfectly characterized these will be the true 2MASS RMS values, but if the quoted UCACr10 sigmas are too low the derived 2MASS RMS values will be too high and vice-versa. The derived 2MASS RMS values are plotted in black as a function of RA in the left panels and Dec in the right panels. Cross-scan is plotted in the upper panels and in-scan in the lower panels. For comparison quoted 2MASS sigmas are plotted in red.

III. Variation with In-Scan Position:

To help evaluate changes with in-scan position each of the 6 degree long survey scans is divided into 12 segments, numbered from south to north. Figure 9 plots mean cross-scan (black) and in-scan (red) differences as function of segment number. Note that there is very little change in mean cross-scan difference with segment number. There is however a small downward slope to the mean in-scan difference with increasing segment number. This is puzzling since it doesn't show up in the Tycho-2 comparisons and is the wrong sign to be a result of the overall change in mean 2MASS-UCACr10 difference with Dec. Mean radial differences are plotted as a function of segment number in Figure 10. The very slight upturn in the end segments indicate a small increase in 2MASS reconstruction errors near scan ends. This is to be expected due to the increased errors resulting from extrapolation as opposed to interpolation.

Figure 11 which plots mean chi-square values as a function of segment number indicates that the quality of the quoted 2MASS uncertainties changes little with in-scan position. This is borne out by the derived 2MASS RMS plots of Figure 12. Note that the derived 2MASS RMS curves are simply displaced a bit upward from the quoted sigma curves, with no change in shape.

IV. Variation with Cross-Scan Position:

Since differences with cross-scan position include telescope/camera specific affects (such as residual distortion), data taken from the northern and southern telescopes need to be considered separately. Read1 and Read2-Read1 sources are also considered separately, given their dual paths through a portion of the pipeline with separate distortion removal. Figure 13 plots mean cross-scan (upper panels) and in-scan (lower panels) position differences as a function of cross-scan position (X_us). Mean Read1 differences are plotted in black and Read2-Read1 differences in red. The "X_us" parameter increases to the west. Northern observatory results are found in the left panels and southern in the right. Since the read flags were not available in the files from which these plots were generated and adding them would have taken a great deal of time, the read type was estimated from the Ks magnitude. All sources with a Ks magnitude less than 8 were tagged "Read1" and all sources with Ks magnitudes greater than 9 tagged "Read2-Read1". Sources with Ks magnitudes between 8 and 9 are typically a mix and were not used.

Note that the distortion is well corrected for Read2-Read1 sources but not for Read1 sources. It was only recently discovered that due to a coding error the Read1 positions were pulled out of PFPrep before the distortion correction was applied. This error remained undiscovered during the QA monitoring because Read1 and Read2-Read1 sources were lumped together and Read1 sources make up a small percentage of the total. As it turns out, Read1 sources have larger errors anyway, so the distortion is a relatively small contributor. This problem had not been identified at the time of the previous Tycho-2 comparison. Read1 and Read2-Read1 sources were not separated out. It's interesting, however, that since Tycho-2(1) sources were more often matched to Read1's and Tycho-2(2) sources to Read2-Read1's the effect can be seen. The results are consistent.

Figure 14 plots mean radial difference as a function of cross-scan position for the northern hemisphere observations in the left panel and southern in the right panel. Read1 values are plotted in black and Read2-Read1 values in red. The Read2-Read1 mean radial differences are essentially constant with cross-scan position except near the edges. Overall the southern hemisphere results are better but have a more pronounced edge effect. Mean radial errors average 18-19 mas higher for Read1's. Like the Read2-Read1's, they go up at the edges, but they are not as flat across most of the scan.

Figure 15 plots mean chi-square values as a function of cross-scan position. Northern hemisphere data are presented in the left panels and southern data in the right panels, with cross-scan chi-squares on top and in-scan on the bottom. Read1 values are plotted in black and Read2-Read1 values in red. Although the Read2-Read1 mean chi-square values are a little greater than 1.0 over the cross-scan range, Read1 values are twice that high and more. Read1 values rise to 3 near the east edge for the northern hemisphere and the west edge for the southern hemisphere. These Read1 edge effects are likely due to the unremoved distortion which is not reflected in the uncertainties.

Figure 16 plots derived 2MASS RMS values as a function of cross-scan position with solid lines. As before, Read1 values are plotted in black and Read2-Read1 values in red. The dotted lines plot mean quoted 2MASS sigmas. This figure simply drives home the message from the previous figure. Note that even for the worst case (Read1 edge) the derived 2MASS RMS does not exceed 130 mas.

V. Variation with Magnitude:

Before proceeding into a discussion of variations with magnitude it should be noted that the 2MASS Ks magnitude range (Figure 17) for matches to UCACr10 sources is shifted 2 to 3 magnitudes fainter than matches to Tycho-2 from the previous analysis. This shift is reflected in the figures to follow. Figure 18 plots mean cross-scan (black) and in-scan (red) position differences as a function of Ks magnitude. As before, northern data are presented in the left panel and southern in the right. In all cases (both hemispheres and both scan directions) there is an abrupt change of amplitude ~10 mas between a Ks magnitude of 8 and 9. This corresponds to the transition from Read1 to Read2-Read1 sources. It's not surprising that such a difference would exist because of the previously mentioned dual path through a portion of the pipeline for Read1 and Read2-Read1 sources. The previous Tycho-2 difference analysis showed such a ramp for the southern hemisphere but not the northern.

Figure 19 plots mean radial 2MASS:UCACr10 differences as a function of Ks magnitude for northern (black) and southern (red) observations. The two hemispheres show very similar results, but with the southern hemisphere consistently better over the entire magnitude range. The southern hemisphere advantage diminishes at the faint end. Mean radial differences for both hemispheres start on a high plateau at the bright end corresponding to unsaturated Read1 sources. The differences drop to a minimum around a Ks magnitude of 9 where the Read2-Read1 region begins in earnest. They increase gradually then until about a Ks magnitude of about 13 where they begin to rise more rapidly with increasing magnitude. The RMS of the 2MASS:UCACr10 differences are plotted as a function of Ks magnitude with northern data in the left panels and southern the right. Cross-scan results are in the upper panels and in-scan results the lower.

Figure 20 plots mean chi-square values as a function of Ks magnitude with in-scan in red and cross-scan in black. The panels are laid out as before, with the northern data on the left and the southern on the right. In both hemispheres mean chi-square values are greatest for Ks magnitudes between 5 and 8 and rise again at the faint end.

Figure 21 presents these results in terms of derived 2MASS RMS values plotted as a function of Ks magnitude in black. Mean sigmas as quoted in the 2MASS catalog are plotted in red. This is telling us that in the northern hemisphere the quoted 2MASS sigmas are too low by about 10-12 mas over most of the magnitude range, slightly more at the faint end and considerably more for the bright unsaturated Read1 sources. The southern hemisphere 2MASS uncertainties are better characterized but are still underestimated at the bright and (to a lessor extent) the faint end.

VI. Effects of Scan Direction:

VII. Conclusions:

Based on UCACr10 comparisons, the overall 2MASS reconstruction accuracy (RMS) appears to be around 84 mas cross-scan and 86 mas in-scan for northern hemisphere observations and 74 mas cross-scan and 77 mas in-scan for the southern hemisphere. These numbers reflect both systematic and random errors. Thus part of the uncertainty increase in the north is due to relatively large systematic differences (-23.6 mas cross-scan & +23.7 mas in-scan) between 2MASS and UCACr10. In order to be conservative these differences were treated as 2MASS errors. The reconstruction accuracy numbers given above indicate that the quoted 2MASS uncertainties are on average about 20% too low for the northern observations and 14% low for the southern.

In general the 2MASS errors are both lower and better characterized away from scan edges, and when neither too bright (Ks mag < 8.5) nor too faint (Ks mag > 13.5). UCACr10 comparison results are in general consistent with the earlier comparison to Tycho-2. The most notable exceptions to this are some of the variations with sky position which are seen in the UCACr10 comparison but not the Tycho-2 comparison. Both agree, however, that 2MASS errors increase approaching a pole.