(This section is the same as Section VI.1k.)
As with magnitudes, there are three basic ways to provide internal and external checks on the completeness of the Extended Source Catalog as a function of observational parameters for 2MASS. The first and simplest is to just look at the source counting statistics. The second is to compare the 2MASS Catalog against existing galaxy (etc.) catalogs and look for missing objects. The third is to compare the 2MASS Catalog with deeper 2MASS scans, such as those taken in calibration fields and those taken expressly for this purpose, or for other scientific programs.
i. Source Counts and V/Vm
The first set of methods for assessing the completeness of the Extended Source Catalog is to look at the source counts in the catalog. This can be done via the traditional log N vs. log S plot, where the completness limit is usually defined as the magnitude (or flux) at which the counts deviate from the Euclidean slope of four per magnitude. The necessary assumption is that the 2MASS sources are approximately Euclidean distributed. Given the approximate depth of the galaxy sample (redshift z ~ 0.1), this is reasonable, since the sample will not be dominated by small scale or local clustering, and the depth is not such that cosmological effects begin to be important.
Figure 1 shows this plot for the extended sources in the Catalog for the fiducial Ks magnitude (isophotal elliptical at 20 magnitudes arcsec-2) that are above 30° galactic latitude. The dotted line represents the slope=0.6 expected in an Euclidean space and is normalized to the observed counts at Ks=13.5 mag. The rolloff around magnitude 14 is indicative that incompleteness is setting in near that magnitude, comfortably below the survey requirement of 0.99 at Ks=13.5 mag.
Figure 2 shows the V/Vm analysis for the same dataset (sources above |b|= 30°, Ks fiducial magnitudes), and again indicates that the Catalog is complete to around Ks=14 mag. A Euclidean distrbution would have a mean V/Vm = 0.500. If anything, both plots show an excess of fainter sources. The errors on V/Vm are less than 0.3% over the full range plotted and are less than 1% on log N below (fainter than) Ks=11.5 mag. That V/Vm is less than 0.5 for the brighter magnitudes may be indicative of either incompleteness in middle magnitude range, an excess of spurious objects at bright magnitudes, or most likely real large scale structure. The presence of the Local Supercluster and the Great Wall is known to bias V/Vm low for optical galaxy samples.
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| Figure 1 | Figure 2 |
ii. Missing Objects in the Second Incremental Data Release
A second check on the Extended Source Catalog is to check for known galaxies that are missing from the 2MASS catalog. The best wide-area catalog extant is still, unfortunately, the Zwicky Catalog (Catalogue of Galaxies and of Clusters of Galaxies, Pasadena: Caltech). This catalog has been analyzed extensively in the process of performing the CfA redshift surveys, and has well-known characteristics. For Zwicky galaxies with magnitudes brighter than 15.5 mag, this optical catalog less deep by about 2 mag than 2MASS to its required goal of Ks = 13.5 mag.
The results of this search for the Second Incremental Data Release are as follows. There are 20,916 galaxies from Zwicky with m_Zw brighter than 15.5 mag in the blue, of which 10,262 are in the scan areas for the Release. A 0.5´ search centered on those 10,262 galaxies resulted in 475 galaxies with no matches in the Release. The galaxies that were not processed by GALWORKS are NOT included in that 475. A number of the 475 are low-surface brightness, but many of them are bright galaxies.
| Table 1: The 2MASS - Zwicky Comparison | |||||||||
| |b|<= | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
|---|---|---|---|---|---|---|---|---|---|
| # In Release | 618731 | 550045 | 456668 | 365775 | 263287 | 174398 | 108355 | 52618 | 14472 |
| # In Zwicky | 10262 | 10196 | 9237 | 7801 | 6078 | 4193 | 2580 | 1393 | 297 |
| # Found 0.5' | 9787 | 9727 | 8814 | 7442 | 5801 | 4002 | 2461 | 1327 | 286 |
| Release % | 95.37 | 95.40 | 95.42 | 95.40 | 95.44 | 95.44 | 95.39 | 95.26 | 96.30 |
A list of the bright (m_Zw brighter than or equal to 15.5 mag) missing galaxies in the Release can be found in this table. These objects generally tend to be low surface brightness galaxies, galaxies in confused regions, and, in some cases, galaxies with poor coordinates in the Zwicky Catalog (UZC, Falco et al. 1999, PASP 111, 438.). We intend to track down and verify each one.
iii. Deeper Scans
An analysis of deeper scans is in progress.
[Last updated 2000 February 11 by J. Huchra and J. Mader. Modified 2000 Sep 12 by S. Van Dyk.]