VIII.D.4 Completeness and Reliability Outside of the Galactic Plane

IRAS Explanatory Supplement
VIII. Sky Coverage, Confusion, Completeness and Reliability
D. Point Source Catalog Reliability and Completeness

D.4 Completeness and Reliability Outside of the Galactic Plane

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  1. Estimates from Minisurvey Data
  2. Verification of the Completeness from Source Counts
  3. Reliability of Point Sources with Flux Densities of Moderate Quality

D.4.A Estimates from Minisurvey Data

A preliminary analysis of the 12 µm completeness and reliability is given here for a 70°2 area of the minisurvey covered by seven HCONs. It was bounded by ecliptic longitudes 60.5° and 64.0° and by ecliptic latitudes -40° and +10° and was thus out of the region of extremely high source densities near the Galactic plane. Table VIII.D.1 gives the number of sources in the seven HCON area, broken down by flux density range and number of observed HCONs, as well as the derived estimates of p, q, and u. The weeks-confirmation area A, was taken to be 30" × 90".

Completeness and Reliability in 7 HCON Area
Table VIII.D.1
Rand in 12 µm Flux Density (Jy) Numbers of HCONs in 70 sq. deg 7 HCON Area Parameters
N=1 2 3 4 5 6 7 p^ ¹ q^ ² û ³
0.25-0.32 26 5 1 0 0 0 0 0.911 0.018 0.699
0.32-0.40 31 4 4 1 4 0 0 0.555 0.060 0.208
0.40-0.50 22 0 3 2 2 5 7 0.201 0.045 0.270
0.50-0.63 9 0 0 1 2 5 13 0.082 0.018 0.300
0.63-0.79 6 0 0 0 0 3 8 0.039 0.012 0.157
0.79-1.58 10 0 0 0 0 2 18 0.014 0.020 0.286
>1.58 0 0 0 0 0 0 25 0.000 0.000 0.364
¹ p^ is the probability of failing to detect a genuine source in a single HCON.
² q^ is the probability, per sq. deg that a false source is created on a single HCON coverage of the sky.
³ û is the probability, per sq. deg of there being a true source in a given region of the sky.

The reliability of a two HCON source found in regions of the sky observed with two or three HCONs can be deduced from the values in the table and always exceeds 0.99997 in every range of flux density. The reliability of two HCON sources in regions with many more than two coverages, such as the minisurvey, is, however, considerably less than this value. A source seen only twice in a seven HCON area may have a reliability as low as 0.5. Sources with three or more HCONs are, however, almost completely reliable at any depth of HCON coverage, given the values of p^ and q^ deduced above.
Figure VIII.D.1 a) Completeness at 12 µm calculated for a two HCON survey (top); and b) for a three HCON survey (bottom).
larger largest

The completeness is plotted as a function of flux density in Fig. VIII.D.1a for a two HCON survey and in Fig. VIII.D.1b for a three HCON survey. Note that these figures give the differential completeness, not the cumulative completeness above a given flux density. The completeness is essentially unity above 1.5 Jy for a two HCON survey and above 0.6 Jy for a three HCON survey. It begins to fall sharply at 0.5 Jy for a two HCON survey and at 0.4 Jy for a three HCON survey. Some of the physical reasons for missing HCONs are discussed in Section VII.E.3.

The completeness and reliability values quoted here for 12 µm also apply to 25 and 60 µm sources with the sharp fall-off in the completeness occurring at 0.5 and 0.6 Jy at 25 and 60 µm for a three HCON survey. The reliability is decidedly worse for sources seen only at 25 µm. The 100 µm values cannot be obtained from the minisurvey due to extensive cirrus contamination.

D.4.b Verification of the Completeness from Source Counts

The completeness of the catalog can be verified by the differential source-counts shown in Fig. VIII.C.1 for the four wavelength bands for |b| > 50°. The counts fall away sharply at 0.4, 0.5, 0.6, 1.0 Jy at 12, 25, 60, 100 µm. The completeness at 100 µm is severely degraded by cirrus below these Galactic latitudes.

D.4.c Reliability of Point Sources with Flux densities of Moderate Quality

A moderate quality flux density is based on at least four detections (Section V.H.5), but the moderate status means that the source also failed to be detected on at least one occasion when it should have been seen. If there were no alibis from dead detectors, the source may have only been detected on four occasions out of a possible eight. If the source had a good quality flux density in another band, the reality of the source is established in that band. In this case there is a reasonable certainty that the source detection in the moderate quality band is real, but the quoted uncertainty in the quoted flux density is larger than that for good quality fluxes, typically by a factor of 1.41. Moderate quality flux densities should be used with caution. Sources with moderate quality flux densities in two adjacent bands are reliable.

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