Source detection and characterization were done independently in each 2MASS band. J, H and Ks detections were then merged into a single source record using the positions and positional uncertainties in each band.
The band-merging process begins by selecting a seed detection in one band, searching other bands for matching detections, and storing pointers to any acceptable matches found. All detections in each band are used in turn as a seeds, and in this way a set of seed-candidate pairs are generated. First the J sources are taken as seeds; then the J-H pairwise matching is done, and this is followed by the J-Ks pairwise matching. The H sources are then taken as seeds, and H-J and H-Ks processing is done, after which the Ks sources are taken as seeds, and Ks-J and Ks-H processing is done.
Whether two detections in different bands are acceptable matches is decided exclusively on the basis of position. No brightness information is used to avoid biasing towards or against any class of astrophysical source. Matching is done in the U-scan (c.f. IV.6) coordinate system which is based on the pixel coordinates of extractions, so is independent of mapping into the astrometric reference frame. The match-decision algorithm assumes as a null hypothesis that the two sightings originated from a single point source, and their observed position differences are caused by random errors in the position reconstruction process, where these errors are described statistically by the position uncertainties in each band. The match decision is based on whether the error fluctuation level is below a specified density-dependent threshold. The fluctuation level is measured in terms of cumulative probability and thresholded accordingly.
The position error model is based on Gaussian random variables, where the errors on the in-scan and cross-scan axes are treated as generally unequal and correlated. The decision algorithm reduces to a simple 2 test with two degrees of freedom: if the position 2 is smaller than the threshold, the match is acceptable. The 2 for a seed-candidate-pair (sc) with separations X and Y and independent RSS'ed position uncertainties on each axis of scx and scy reduces to:
The 2 threshold is taken from a look-up table value indexed by source density, where the density used is the empirically measured density of extractions in the relevant bands. For extraction densities up to 95,000 deg-2, the 2 threshold is 36.0. The threshold drops with increasing densities, reaching 10.0 for 350,000 deg-2. In practice, though, densities above 95,000 deg-2 are rarely encountered.
In the absence of confusion, the seed matching process results in a set of symmetric seed-candidate pointers that can be linked consistently for the detections in the three bands. Confusion in the merging process is discussed below. Gaussian parameter refinement is used to compute new positions with reduced uncertainties for each merged source. Only detections in a band that are not confused and are not extremely faint are used to update positions.
i. Confusion in Band Merging
In regions of high source density, or in instances where multiple or extended sources are split inconsistently between bands, the seed-candidate pairing process can result in a confused scenario. If confusion is encountered during the band-merging process, the source is flagged with cc_flg="b" in the affected bands.
The simplest class of confusion occurs when there is more than one acceptable match per seed. In this case, the pairing is made between the detections with the lowest 2 value.
A more complex confusion state occurs when a seed points to a first-choice candidate, but the candidate points to a different first-choice candidate; i.e. the seed-pair matchings is not symmetric. Long chains of inconsistent pairings can theoretically occur. This confusion is resolved through a chain processing procedure that works down the set of possible seed-candidate links until a reciprocal relationship is found. Then the chain is broken at the previous link. Consider the triplet chain in which J-band detection S1 has a best candidate match in H-band detection S2. But S2 points to J detection S3 as a best match. If S3 points to S2 as a best match, then the S2-S3 pairing is reciprocal and the S1-S2 pairing is broken. If the relationship between S2 and S3 is not reciprocal, then one of two things must be in effect: either S3 does not have an acceptable pairing in H-band (which cannot happen because of the symmetry of the 2 matching), or S3 points to a different H detection than S2. In the latter case, the detection triplet is moved down the chain and reexamined. Detection S2 is moved into S1, S3 into S2, and the erstwhile S3's first-choice match candidate is moved into S3. This process is repeated until the reciprocal pairing is found.
Fortunately, the relative positional accuracy of detections in the three 2MASS bands is excellent and very stable because of the 3-channel camera designs. Therefore, confusion in bandmerging is a rare occurrence and is usually associated with inconsistent splitting of sources between bands. There are a total of 35,354 sources in the full PSC (0.008% of all sources) that have cc_flg="b" in one or more bands.
When a merged source does not have a detection in one or two bands, a band-fill is made by measuring the flux and noise in a 4´´ radius aperture on the Atlas Images in the undetected band(s), at the position of the source in the detected band(s). A sky reference annulus with inner and outer radii of 14" and 20", respectively, is used for the band-fill measurement. A 95% confidence (2 ) brightness upper limit is formed from the measurement and uncertainty measured in the aperture, and is reported in the default magnitude field ([jhk]_m) in the PSC. The reported upper limit is two times the noise level if no flux is detected in the aperture measurement, or the measured flux plus two times the noise level if positive flux is measured.
Multiple sources with separations near the resolution limit of 2MASS may not be split or deblended consistently in all detected bands. In these cases, the default magnitude field will contain the deblended magnitudes for each component in the resolved band(s). A band-fill upper limit will be listed in the default magnitude field(s) for the unresolved band(s). In these cases, the 95% confidence upper limits are measured from the Atlas Images in the same way that they are measured for non-detected bands. However, since the measurements are made on locations where there are detections, the limits provide useful constraints on source brightness. Inconsistent deblend upper limits (rd_flg="6") should not be confused with non-detection upper limits (rd_flg="0").
[Last Update: 2003 March 10, by R. Cutri and J. Fowler]