VI. Analysis of the 2MASS Second Incremental Release Catalogs

1. Comparison of Achieved Performance of Second Incremental Release Catalogs with Level 1 Science Specification

j. Extended Source Reliability

2MASS uses a strict definition of reliability: only galaxies count as reliable sources.

For |b| > 20°, the differential reliability of "G" sources in the XSC near the sensitivity limit of the Catalog is probably ~97-99%, somewhat below the Level 1 Specification of 99%. The unreliable sources are nearly all sources with small measured sizes. Sources that are larger than point sources by 10 times the point source dispersion have reliabilities above 99%.

For 20° > |b| > 10°, the differential reliability of "G" sources in the XSC near the sensitivity limit of the Catalog is probably ~95-98%, much better than the Level 1 Specification of 80%.

There is no Level 1 Specification for other portions of the XSC, but the reliability ranges from 50% for "E"-only sources at high galactic latitude to as low as ~20% for either "E" or "G" sources in the regions of highest source density.

The Reliability Level 1 Reliability Specification for the Extended Source Catalog is quite different from the usual reliability specification for an Extended Source Catalog in that only galaxies count as reliable sources. That is, other extended sources outside the Galactic Plane, such as double and triple stars just under the ability of 2MASS to resolve them into separate sources, count as unreliable sources despite being "extended" in that they are not well-fit by a single PSF. The usual reliability specification accepts such groups of multiple stars as reliable extended sources, and counts as unreliable only sources that do not exist in the sky, or that in fact are fit well by a single PSF.

It was still required that an Extended Source Catalog be produced, and not just a Galaxy Catalog, to pick up truly extended sources in the Galactic Plane. This inherent conflict between detecting extended sources and distinguishing galaxies from them led to the concept of a catalog within a catalog.

The XSC consists of two separate catalogs: "E" (Extended) sources selected only by measures of spatial extent, and "G" (Galaxy) sources additionally selected by color. The color selection is needed in order to help discriminate galaxies from extended sources made of groups of multiple stars. The reliability requirement applies only to the "G" sources, with no requirement on the "E" sources. About 90% of the sources in the XSC are both "E" and "G" sources, with only 10% of the sources being "E"-only sources.

The reliability requirement for the "G" sources in the XSC is that for stellar densities < 3.4, roughly corresponding to |b| > 20°, 99% of the unconfused sources in the last half-magnitude bin above the completeness limit must be galaxies and not groups of multiple stars or spurious detections. The reliability is relaxed to 80% for stellar densities of 3.4 - 4.0, roughly corresponding to 20° > |b| > 10°. Density is defined as the log of the number of point sources with Ks < 14.0 mag.

The requirement of 99% is an ambitious goal, given the variety of ways that non-galaxies can be picked up by the processor as extended sources:

Given this reliability specification, the only way to measure the reliability is for a human to examine a set of sources and determine one by one whether each source is truly a galaxy. This is not as easy as it may appear to be. Some of problems are:

For high galactic latitudes, the second problem dominates the results of human classification. Sources that could not be clearly identified as stars or galaxies have been classified as unknown. Consequently, our measures of reliability given below necessarily have some uncertainty attached to them depending on the treatment of these unknown sources.

A statistical analysis of the unknowns reveals that most of the unknowns, perhaps 85% of them, are in fact galaxies. In the analysis below, however, we will present three numbers for the reliability:

Ultimately, the only way to be sure a given source is a galaxy is to measure its redshift, a task that will require years of followup work.

Our measured reliability, using detailed human examination of over 10,000 unconfused sources that fall in the magnitude ranges and area of the sky for which the reliability specification is defined, is the following:

|b| > 20° (density < 3.4) (99% requirement)
bandMag rangeNo. of truth sourcesReliability (%)
MinimumBest EstimateMaximum
J14.5 - 15.0 5802 91 97 98
H13.8 - 14.3 5349 92 97 98
K13.0 - 13.5 4484 97 99 99

20° > |b| > 10° (3.4 < density < 4.0) (80% requirement)
bandMag rangeNo. of truth sourcesReliability (%)
MinimumBest EstimateMaximum
J 14.5 - 15.0 1700 91 95 96
H 13.8 - 14.3 1611 93 97 98
K 13.0 - 13.5 1579 96 98 98

As can be seen, the current 2MASS release falls somewhat short of the requirement for |b| > 20°, except possibly at Ks, but vastly exceeds the requirement for 20° > |b| > 10° in all bands. However, because the unreliable sources are nearly all sources with small measured sizes, it is possible to achieve 99% reliability for |b| > 20° for a subsample of the catalog by reducing the completeness of the subsample. For example, sources that are larger than point sources by 10 times the point source dispersion have reliabilities above 99%, and the vast majority of galaxies are above that threshold as well. The original 2MASS proposal recognized that such a size restriction might be needed to meet the 99% reliability goal.

Aside from the unknowns, it is instructive to look at the known sources of unreliability for |b| > 20°:

Unreliability Percentage Due To Groups Of Stars (%)
Band No. stars
H 1.0 0.6 0.0
K 0.3 0.2 0.0

We have spent considerable effort in exploring a variety of algorithms to reject double and triple stars, and it is likely that the numbers for them in the table above are as good as can be done. Thus although the reliability specification may be achievable at Ks, it is likely that we cannot ever achieve a 99% reliability specification at J given that there are other sources of unreliability in addition to double and triple stars.

The number of single stars is higher than expected, and needs more investigation. It is possible that this is due to the inevitable inclusion of small pieces of scans that have untracked seeing that cannot be reliably identified in the 2MASS data due to a sparsity of sources that can be used to track the seeing. If that is the case, we will have to relax the reliability specification for |b| > 20°, since the existence of this problem was unforeseen when we originally set the requirement.

The raw data for the above numbers, and much more discussion about the caveats involved in their determination, is found in Section VI.4c.

The numbers for reliability in the tables have been slightly decreased from the raw numbers in order to account for some of the biases mentioned in the caveats section. In particular, there are probably an additional ~0.2% of sources that are unreliable due to meteor trails and other artifacts that were automatically excluded from the analysis for database reasons.

At lower galactic latitudes, because there is no requirement on reliability we emphasized completeness in order to maximize the number of galaxies detected in this region of interest. The reliability is as low as ~20% for "G" sources in the regions of highest source density.

Although there is no requirement on the reliability of "E"-only sources, the measured reliabilities are as follows. Outside of the galactic plane, the reliability of "E"-only sources is about 35% at J and H, and about 60% at Ks, and include blue galaxies discriminated against in the "G" classification by the color test.

In high source density regions, the reliability of "E"-only sources, now counting true extended galactic sources, such as HII regions, as reliable sources, drops to ~10% at J and H and ~30% at Ks, with the vast majority of all the "E"-only sources being groups of multiple stars. Most true extended sources, such as planetary nebulae, are also "G" sources, restricting the number of true extended sources that are "E"-only sources.

[Last updated 2000 February 10 by T. Chester. Modified 2000 Sep 11 by S. Van Dyk.]

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