V.E.5 Weeks-Confirmation

IRAS Explanatory Supplement
V. Data Reduction
E. Overview of Small Extended Source Data Processing
E.5 Weeks-Confirmation

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After cluster analysis processing, the remaining small extended sources were tested for repeatability on the weeks/months timescales of weeks to months. Only those detections found on at least two hours-confirming coverages were accepted as reliable sources. Two sources were regarded as being weeks-confirmed if,
  1. they were in the same wavelength band
  2. they had detection times which differed by at least 36 hours;
  3. they satisfied a position confirmation criterion detailed below;
    and
  4. the ratio of the flux of the brighter detection to that of the fainter was less than 3.

The link parameter for weeks-confirmation was taken to be the 2 statistic of the two-dimensional position-match confidence of the two detections; in computing 2, each detection was modeled as a two-dimensional Gaussian distribution characterized by the extent matrix. Two detections positionally confirmed if their link parameter was less than 1.4 (see Section V.E.7.b).

When a group of two or more weeks-confirming sources was identified, it was merged into a single weeks-confirmed source. The flux was taken to be the average of the fluxes of the two sources. The centroid and extent matrix of the weeks-confirmed source were calculated and the extent matrix was diagonalized to yield semi-major and semi-minor axes and the twist angle between the semi-major axis and the ecliptic meridian. The number of hours-confirmed sightings that make up the weeks-confirmed source is called NCOVR in Section X.C.

If all the hours-confirmed sources contributing to a weeks-confirmed source positionally confirmed each other, then the source was said to be mutually confirmed. If an hours-confirmed source (denoted by A) weeks-confirmed with two or more other sources (denoted by B1, B2, etc.) which did not mutually confirm, the following was done to extract the best weeks-confirmed source. First, a decision function, D, was evaluated for each of sources B1, B2, etc., where

D =(2) × (1 + 2) + (R - 1) × R

(V.E.6)

and 2 is the link parameter between sources A and B and R is the ratio of the brighter flux to that of the fainter.

The source for which D was the smallest was found and the ratio D/Dmin was found for each of the sources B1, B2, etc. All sources for which D/Dmin was above a threshold of 2 were discarded. If only one source remained then this was chosen as the weeks-confirming partner of source A. Otherwise, the source was considered confused and the candidates were rejected.

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