# 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.

rel | Probability 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+K_{s}
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 K_{s}=20 mag arcsec^{-2}
elliptical isophote (*j_m_k20fe*)
for the Survey extractions, and as a function of
K_{s}-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 K_{s}<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:

- 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. - 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 K
_{s}=20 mag arcsec^{-2}elliptical isophote is used (*j_m_k20fe*). The K_{s}-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. - 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. - 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.

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

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