Appendix 5. Working Database Source Reliability Estimation

2. Extended Source Reliability Estimation

Each extraction in the Survey Extended Source Reject Table, and the 6x and calibration scan extended source Working Databases (XSWDBs) is assigned a reliability score, rel, that is related to the probability that the extraction is a detection of a real astrophysical source at the time of the 2MASS observation and that the source is truly extended with respect to the instantaneous point spread function. The reliability score is a single character with values A-F that maps into a probability range according to Table 1.

The algorithm for assigning the reliability score to extended source extractions is based on a large, empirically-developed "truth table" of WDB extractions whose images have been visually examined to assess whether or not they are valid source detections and truly extended rather than single or multiple stars. The empirical relationships that describe how the fractional reliability of the ensemble changes with source parameters are converted into a matrix of scoring rules that are used to assign reliability scores to each extended source extraction.

Table 1 - Estimated Range of Probabilities for Each Value of the Extended Source Reliability Score, rel
relProbability Range
A P>90%
B 80<P<90%
C 70<P<80%
D 50<P<70%
E 20<P<50%
F P<20%

a. Extended Source Truth Table

An internal (to 2MASS) "truth table" for developing the extended source reliability scoring algorithm was built by visually examining and classifying over 700,000 extended source extractions from the Survey, 6x and Calibration WDBs that span diverse range of source parameters. The examination and classification process is described in IV.5.a.iv

Visual examination consisted of viewing a J+H+Ks three-color composite image of the extraction, tabular data that summarizes source size, shape and photometry, and when available an optical of the object from the Digitized Sky Survey. Based on the images and tabular data, each entry was classified as fitting into one of several categories that include galaxies, Galactic nebulae, single or multiple point sources, artifacts or not unambiguously classifiable. The results of the visual classification are included in the vc column in the Survey XSRT, 6x XSWDB/XSC and Calibration XSWDB.

b. Reliability Matrices

A set of reliability matrices were generated by compiling the empirically determined net reliability of the truth table extractions as a function of galaxy brightness and e_score/g_score extended source "pseudo-probabilities" in several foreground source density ranges. Separate matrix sets were generated for the Survey and 6x truth tables. The Survey reliability matrices were used to assign reliability scores to the Calibration XSWDB entries.

Tables 2-13 and 14-22, linked below, contain the reliability matrices for the Survey and 6x XSWDB samples, respectively. These tables give the number of objects in each classification category in 0.5 mag brightness bins, and the for three ranges of e_score/g_score. Within each e_score/g_score range, tables are presented for four (Survey) or three (6x) ranges of foreground stellar density environments. Reliability was computed as a function of J-band magnitude in the fiducial Ks=20 mag arcsec-2 elliptical isophote (j_m_k20fe) for the Survey extractions, and as a function of Ks-band fiducial elliptical isophotal magnitude (k_m_k20fe) for 6x extractions. The stellar foreground density ranges in the Survey reliability matrices are: low - den < 3.0, low-to-moderate - den < 3.6, moderate-to-high, and high - den > 4.0, where den is the stellar number density metric equal to the logarithm of the number of point source extractions with Ks<14.0 mag in the field. For the 6x matrices, the stellar density ranges are: low - den < 3.0, moderate - 3.0 < den < 3.6, and high - den > 3.6.

The last two columns in each reliability matrix summarize the reliability in each magnitude bin:

Reliability (R) = 1.0 - (N_false / N_false + N_true)
where N_false is the total number of "false" extended sources (e.g.stars, artifacts, double/triples) per mag bin interval, and N_true is the total number of "catalog" extended sources per mag bin interval.

Adjusted Reliability (Radj) = 1.0 - (N_false_expected / N_true_expected)
This is the reliability after factoring in knowledge of "false" sources based on the visual examination; where N_false_expected is total number of "expected" false sources minus the total number of known false sources, and N_true_expected is the total number of "expected" true extended sources. The rate of true extended sources is the total number of known true extended sources divided by the total number of sources (both true and false). Note that for mag intervals in which the visual inspection is fully complete, one can in principle construct a catalog that is nearly 100% reliable.

Tables 2-13 - Survey Extended Source Reliability Matrices

Tables 14-22 - 6x Extended Source Reliability Matrices

c. Reliability Scoring Algorithm

The reliability score for each extraction in the Survey XSRT, 6x XSWDB/XSC and Calibration XSWDB is determined as follows:

  1. The reliability matrix appropriate for the data set, e_score/g_score and foreground stellar density for the extraction is selected. The Survey Extended Source Reliability Matrices were used for extractions in the Calibration XSWDB.
  2. The reliability probability is computed by interpolating based on on the source magnitude. For Survey and Calibration XSWD extractions, the J-band magnitude in the fiducial Ks=20 mag arcsec-2 elliptical isophote is used (j_m_k20fe). The Ks-band fiducial elliptical isophotal magnitude (k_m_k20fe) is used for 6x XSWDB extractions. The probability is then mapped into the appropriate rel score based on Table 1.
  3. If an extraction has been identified as a spurious detection of an image artifact according to the contamination and confusion flag (cc_flg="A") or as a result of the visual examination process, it is assigned a reliability of rel="F", regardless of magnitude, e_score/g_score or foreground stellar density.
  4. A special case of unreliable extended source extractions is "galaxy chaff" - objects that are fragments of large galaxies, knots or bright HII regions in galaxies, globular clusters around the galaxies (in the case of M31), or stars superimposed on galaxy disks. These are identified in the extended source tables by a contamination/confusion quality flag value of cc_flag= "z". While these objects are technically real and sometimes truly extended, they are assigned a reliability score of rel="F" because they do not accurately indicate the location and characteristics of the large galaxy. In most cases, their photometry is of poor quality due to the background gradient from the surrounding large extended source.

Figure 1 - Examples of rel="F" "galaxy chaff" associated with M31 and M32 in the Survey Extended Source Reject Table. Extractions of knots and fragments of these two large galaxies are shown by the green circles. The red circles denote the entries for the two galaxies in the All-Sky XSC.

[Last Update: 2006 October 2, by T. Jarrett and R. Cutri]

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