V.E.4 Cluster Analysis Processing

IRAS Explanatory Supplement
V. Data Reduction
E. Overview of Small Extended Source Data Processing
E.4 Cluster Analysis Processing

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Before weeks-confirmation was attempted, it proved necessary to verify that the candidates were well-defined and relatively isolated.

When the focal plane passed over an object more extended than 10', structures within the object often gave rise to many detections whose properties depended on the scan direction. The simple detection algorithm grossly misrepresented such large sources, since only the flux at the spatial frequencies of the square-wave filters was detected. This value could be far less than the true total flux. Large extended objects were characterized by strings and clusters of sources. This behavior was found particularly pronounced at 100 µm.

A somewhat similar situation arose in regions with a high density of sources, or equavlently, because of complex backgrounds, such as the Galactic plane. The results from such regions were particularly sensitive to scan direction. Fluxes quoted in regions of complex structure should NEVER be taken at face value.

Before weeks-confirmation was attempted the sources were first analyzed by the cluster analysis processor, which looked for clusters of detections at the same wavelength and from the same hours-confirming coverage. If the cluster was below a certain critical size then its constituent detections were merged into a single source which was then ready for weeks-confirmation. If, however, the cluster was larger than the threshold size, then it was deemed part of a large extended object. In this case the detections contributing to the cluster were rejected from any future processing. All detections which were not found to be members of large clusters were kept for subsequent processing.

Clusters were identified by finding sources observed within 36 hours and which could be linked together spatially. A detection was considered to be linked to a cluster if it was a close neighbor to at least one other source in the cluster. Two detections were considered to be close neighbors if their link parameter, L, was less than a certain threshold. The link parameter, L, is given by,

L = D/(r1 + r2)

(V.E.4)

where D is the distance between the centroids of the two sources and r1 and r2 are the radii of their equivalent-area circles, i.e. if a and b are the semi-major and semi-minor axes of the source, then the equivalent-area circle has a radius given by

r =(a × b)

(V.E.5)

The value of the threshold on the link parameter was taken to be 3.5 for reasons discussed in Section V.E.7.a.

When the detections in a cluster were merged, the flux of the merged object was taken to be the sum of the fluxes of the constituent sources. The position was the flux-weighted centroid from all the constituent detections in the cluster. The extent of the source was obtained by combining the covariance matrices about the new centroid; the new matrix was then diagonalized to yield new estimates of the semi-major and semi-minor axes and twist angle. Relatively bright sources were not greatly altered when merged with fainter detections.

The maximum semi-major axis that a merged cluster could have before being rejected was set at 5', since extended source processing was not intended for larger sources and could not accurately estimate fluxes on size scales greater than about 8'.

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