Comparison of 2MASS Catalog Positions/Uncertainties with Tycho-2

Figure 1 plots normalized histograms of 2MASS:Tycho-2 differences, with cross-scan in the left panel and in-scan in the right panel. Tycho-2(1) data are plotted using heavy black lines and Tycho-2(2) using light red lines. 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 Tycho-2 position. When "dy" is positive 2MASS position is north of the Tycho-2 position. Note that the Tycho-2(1) cross-scan and in-scan difference sigmas are close (81 and 86 mas respectively) and the biases are small (-1 and +5 mas respectively). For Tycho-2(2) the sigmas are increased to 144 and 133 mas and the biases become +1 and +10 mas.

Figure 2 plots normalized histograms of 2MASS:Tycho-2 radial differences. As before, the Tycho-2(1) data are plotted using heavy black lines and Tycho-2(2) using light red lines. The mean radial difference for Tycho-2(1) is 100 mas and for Tycho-2(2) is 161 mas.

In Figure 3 normalized histograms comparing the quoted uncertainties for 2MASS and Tycho-2 are presented. Comparison plots are divided into 4 panels with the Tycho-2(1) data presented in the left panels and Tycho-2(2) data in the right panels. Cross-scan sigmas are presented in the upper panels and in-scan in the lower. In each case only the 2MASS sigmas for sources matched to the specified Tycho-2 subset are presented. 2MASS histograms are in solid black and Tycho-2 in light red. Note that the quoted 2MASS sigmas overlap the high end of the Tycho-2(1) sigmas and the low end of the Tycho-2(2) sigmas.

Combining the measured differences (dx, dy) with quoted 2MASS (sigx2m, sigy2m) and Tycho-2 (sigxt2, sigyt2) 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 +sigxt2*sigxt2)

chi2y = (dy*dy)/(sigy2m*sigy2m +sigyt2*sigyt2)

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 Tycho-2) is off. Figure 4 plots histograms of chi-square values for both Tycho-2(1) and Tycho-2(2) matches. Cross-scan is in the left panel and in-scan in the right. The mean chi-square values from the Tycho-2(1) differences are 1.12 and 1.17, for cross-scan and in-scan respectively. The corresponding values for Tycho-2(2) differences are 1.51 and 1.14. Assuming the Tycho-2 sigmas are properly stated, this indicates the quoted 2MASS sigmas tend to be a little too low. The cross-scan chi-square values for Tycho-2(2) differences stand out.

II. Variation with Sky Position:

Figure 5 plots mean cross-scan (upper panels) and in-scan (lower panels) position differences with respect to both Tycho-2(1) and Tycho-2(2) as a function of RA (left panels) and Dec (right panels). Although small deviations are present, there do not appear to be any large systematic errors as a function of sky position.

Mean radial differences for both Tycho-2(1) and Tycho-2(2) matches are plotted as a function of RA (left panel) and Dec (right panel) in Figure 6. Note from the Tycho-2(1) numbers that there is a gradual increase approaching the South pole from values less than 100 to more than 120 mas. The increase can also be seen approaching the North pole but it's only about half as large. Interestingly, these effects are not obvious in the Tycho-2(2) data.

The RMS of the 2MASS:Tycho-2 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. In addition to being much larger the 2MASS:Tycho-2(2) RMS values show systematic changes with sky position not seen with 2MASS:Tycho-2(1).

Figure 7 plots mean chi-square values as a function of RA (left panels) and Dec (right panels). Cross-scan chi-squares are plotted in the upper panels and in-scan in the lower panels. In each case Tycho-2(1) and Tycho-2(2) values are plotted separately. Note that the mean cross-scan chi-square values associated with Tycho-2(2) differences are not only larger but also show greater systematic changes with both RA and Dec. There are peaks near RA values of 95 and 175 degrees. As for Dec, values are highest near the equator, dropping almost to one near the poles. The mean cross-scan chi-square values associated with Tycho-2(1), on the other hand, remain near one over most of the Dec range, rising to higher values only near the poles. These differences are difficult explain in terms of 2MASS uncertainty errors.

Figure 8 plots 2MASS RMS values derived by substracting in quadrature the quoted Tycho-2 sigmas from the 2MASS:Tycho-2 difference RMS values displayed earlier. If the quoted Tycho-2 sigmas were perfectly characterized these would be the true 2MASS RMS values, but if the quoted Tycho-2 sigmas are too low the derived 2MASS RMS values will be too high and vice-versa. The derived 2MASS RMS values are plotted 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. Values derived from Tycho-2(1) matches are plotted in solid black lines and Tycho-2(2) in light red. For comparison quoted 2MASS sigmas are plotted with dotted lines using the same color code. They are slightly different because 2MASS sources matched to Tycho-2(2) tend to be fainter than those matched to Tycho-2(1). A marked increase in 2MASS RMS near the poles stands out from the Tycho-2(1) data as well as a lessor increase near the equator.. The quoted 2MASS sigmas tract the Tycho-2(1) derived 2MASS RMS values rather well. The 2MASS RMS values derived from Tycho-2(2) data show much different characteristics and the quoted 2MASS sigmas do not track them.

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 (upper panel) and in-scan (lower panel) differences as function of segment number. Note that there is virtually no change in Tycho-2(1) or Tycho-2(2) differences with segment number. Mean radial differences are plotted as a function of segment number in Figure 10. The large differences between the Tycho-2(1) and Tycho-2(2) lines are the due to the fact that random errors in Tycho-2(2) are much larger. The very slight upturn in the end segments indicate a small increase in 2MASS reconstruction errors near scan ends.

Figure 11 which plots mean chi-square values as a function of segment number indicates that the quality of the quoted 2MASS uncertainties is unaffected by in-scan position. This is borne out by the derived 2MASS RMS plots of Figure 12. Note that the Tycho-2(1) derived 2MASS RMS curves are simply displaced a bit upward from the quoted 2MASS sigma curves, with no change in shape. The Tycho-2(2) derived 2MASS RMS curves also have this shape but with a much larger upward displacement, especially in cross-scan.

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). The "X_us" parameter increases to the west. Northern observatory results are found in the left panels and southern in the right. Tycho-2(1) differences are plotted in black and Tycho-2(2) differences in red. Read1 differences are plotted with light lines and Read2-Read1 differences with heavy lines. 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 there is little difference between Tycho-2(1) and Tycho-2(2) results. In each case 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.

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. The Tycho-2(1) differences for the northern hemisphere are relatively constant across most of the scan width, but rise steeply near the east edge. The southern hemisphere plot is almost a mirror image with a sharp rise near the west edge. The amplitude of the southern edge rise is only about half the northern rise. For both hemispheres the edge rise is very much reduced with the Tycho-2(2) differences.

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. Northern mean cross-scan chi-square values derived from Tycho-2(1) matches become significantly greater that 1.0 only hear the east edge, whereas for southern data the increase is only near the west edge. Cross-scan chi-square values Tycho-2(2) matches are elevated over the entire scan width.

Figure 16 plots derived 2MASS RMS values as a function of cross-scan position. As before, the dotted lines plot mean quoted 2MASS sigmas. This simply drives home the message from the previous figure. Cross-scan 2MASS RMS values derived from Tycho-2(1) differences shoot up only near the east edge for northern data and the west edge for southern. Cross-scan values derived from Tycho-2(2) differences are elevated over the entire scan width.

V. Variation with Magnitude:

Before proceeding into a discussion of variations with magnitude it's important to note that the magnitude range of Tycho-2(2) matches is shifted fainter than that of the Tycho-2(1) matches, as can be seen in Figure 17. This shift is reflected in the figures to follow. Figure 18 plots mean cross-scan (upper panels) and in-scan (lower panels) position differences as a function of Ks magnitude. As before, northern data are presented in the left panels and southern in the right. Tycho-2(1) differences are plotted in solid black and cover the Ks magnitude range from 2.0 to 11.5. Tycho-2(2) differences are plotted in light red and cover the Ks magnitude range from 4.5 to 12.5. The primary message from these plots is that there are systematic errors for sources brighter than a Ks magnitude of 4, growing in amplitude to as large as 50 mas by magnitude 2.0. This is true in both hemispheres and scan directions, although in-scan error growth is somewhat less.

Figure 19 plots mean radial differences as a function of Ks magnitude with northern data in the upper panel and southern in the lower. The two hemispheres show very similar results. Although the boundaries are fuzzy one can interpret these curves in terms of the read type and saturation state. Note that there is a plateau between Ks magnitudes 5 and 8, which roughly corresponds to the unsaturated Read1 regime. Mean radial differences rise as one moves from the unsaturated Read1 plateau toward brighter sources. It peaks just to the bright side of Ks magnitude 4, which roughly corresponds to Read1 saturation. Moving from the unsaturated Read1 plateau toward fainter sources the mean radial difference values drop to a minimum around Ks magnitude 9, where we're fully into the Read2 regime. From this point there's a more gradual increase in mean radial difference with increasing magnitude. Tycho-2(2) differences show a faster rise than Tycho-2(1). The RMS of the 2MASS:Tycho-2 differences for Tycho-2(1) [black] and Tycho-2(2) [red] 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. The panels are laid out as before, with northern data in left panels and southern in the right, cross-scan in the upper panels and in-scan in the lower. Both Tycho-2(1) and Tycho-2(2) chi-squares are significantly greater than one (approaching 2) in the unsaturated Read1 magnitude range. In the saturated Read1 regime the mean chi-square values drop to approximately 0.2. In the Read2 range mean Tycho-2(1) chi-square values are a little less than 1.0, but for Tycho-2(2) mean chi-square values start above one and increase with magnitude.

Figure 21 presents these results in terms of derived 2MASS RMS values. The Tycho-2(1) data tell us the quoted 2MASS sigmas are too low by approximately 20 mas in the unsaturated Read1 region, slightly too high in the Read2 region and considerably too high for sources brighter than Ks magnitude 4. Tycho-2(2) says they're too low throughout the Read2 region and get progressively worse increasing magnitude.

VI. Conclusions:

Based on Tycho-2(1) comparisons, the overall 2MASS reconstruction accuracy appears to be in the range of 70-80 mas both in cross-scan and in-scan. One should bear in mind, however, that 2MASS sources matched to Tycho-2 are relatively bright. Positional accuracy for fainter sources may be reduced. Also, the fact that Tycho-2 was used as the reference catalog means one must be very careful using it as a measure of success. In theory, one could nail the Tycho-2 stars and still leave everything in-between much worse off. That's why it will be very important to analyze the scan overlaps as well.

Comparisons with Tycho-2(1) cross-scan and in-scan as well as Tycho-2(2) in-scan show the quoted 2MASS sigmas to be overall about 7% too low. This appears to be a result of the following three problem areas:

1) Increased errors near the eastern scan edge in the northern data and western scan edge in the southern data that are not reflected in the quoted uncertainties.

2) Increased errors near the poles that are not adequately tracked (especially in the north) by the quoted uncertainties.

3) Increased errors in the unsaturated Read1 magnitude range that are not reflected in the quoted uncertainties.

Comparison with Tycho-2(2) indicates the the quoted 2MASS sigma in cross-scan is about 23% too low, as opposed to the 7% from Tycho-2(1). There are reasons to suspect this could possibly be due to problems with the Tycho-2(2) uncertainties in RA. The discrepancy needs to be resolved. Analysis of 2MASS:UCAC differences and scan-overlap differences should help.

NOTE ADDED December 04, 2002:

Global comparisons with UCACr10 as well as 2MASS overlap analysis confirm the Tycho-2(1), not the Tycho-2(2), results. The 2MASS:UCACr10 comparison is available via URL and a third URL combining 2MASS:Tycho-2, 2MASS:UCACr10 and 2MASS overlap results is in the works.