I. 2MASS Final Data Release Explanatory Supplement: Comparison With The Level 1 Requirements

1. XSC

b. Completeness

The Level 1 Specifications call for 90% completeness at galactic latitudes more than 30° from the Galactic plane. The specification indicates that completeness and reliability be calculated "per magnitude in the faintest magnitude bin." The 2MASS project has used the Level 1 sensitivity specification (15.0, 14.3, 13.5 mag for 10-sigma at J, H, and Ks respectively) to define the faint end of the lowest bin in each waveband.

Two different analyses show that the XSC significantly exceeds the completeness specification, with a completeness of ~95-99%, significantly above the requirement of 90%.

Two analyses have measured the completeness of the XSC:

1. A comparison of the log N / log S curve for the XSC with previous infrared counts; and

2. A comparison of optical galaxy catalogs, the Updated Zwicky Catalog, the Sloan Preliminary Data Release, and the APM/2dF Survey, to the XSC.

i. Comparison to previous infrared counts

T. Jarrett has carefully plotted the log N / log S curve for the XSC at galactic latitudes more than 25° from the Galactic plane, taking into account unsurveyed areas due to the several sources of coverage holes. Figure 1 presents the curves for each band, along with previous K-band data from Glazebrook et al (1994) and Gardner et al (1997).

The 2MASS isophote used was the fiducial elliptical isophotal (20 mag arcsec^-2 in the Ks band) integrated fluxes. Glazebrook et al used fixed apertures of 8 arcsec. In the magnitude range compared here, these apertures are roughly comparable, so that any shifts in the curves due to photometric differences between the two datasets are small. Furthermore, the photometric system correction between the UKIRT system and the 2MASS system is only ~0.007 mag for typical galaxies with J-K ~ 1 mag, and so can be ignored.

The 2MASS log N / log S for K-band is in virtually complete agreement with the previous infrared data of Glazebrook et al at K mags of 12.5 to 13.5, the faintest magnitude bin at K used for the Level 1 spec comparison. (The brightest Glazebrook data point was at Ks = 13.5 mag, with a model fit to brighter magnitudes.) The total number of galaxies per square degree in this magnitude bin predicted by the Glazebrook numbers is 10.0 ± ~ 1.0. The total number of galaxies per square degree in the XSC in this magnitude bin is 11.0617 ± 0.0005. From these numbers, the nominal completeness of the XSC is 100%, with a 95% confidence lower limit of 92%. (See Notes.)

No comparison was made to the Gardner data, since it is very uncertain at bright magnitudes, as can be seen in the above plot.

For more information, see 2MASS XSC Source Counts.

ii. A comparison of optical galaxy catalogs, the Updated Zwicky Catalog, the Sloan Preliminary Data Release, and the APM/2dF Survey, to the XSC.

John Huchra et al have done an extensive comparison of optical catalogs to the XSC globally. While this analysis cannot give direct estimates of the infrared completeness, due to the variable infrared / optical colors for individual galaxies, it is an excellent check for problems in completeness that might escape the previous comparisons. In particular, it checks for problems over a broad range of infrared brightness.

The comparison overall looks quite good. The match rate between these catalogs is uniformly high at nearly all optical magnitudes at which ones expects the source to appear in the XSC. The match rate is 90-94% for the Updated Zwicky Catalog, 95-97% for the Sloan Survey, and 99-100% for the APM/2dF Survey. Almost all of the missing objects from the Updated Zwicky Catalog are of low surface brightness that were expected to be missing from the XSC.

For example, the following figure shows the match rate with Sloan vs Sloan's blue mag j, not the 2MASS J band:

For typical galaxy colors, j = 13 mag for Sloan in the above plot corresponds with J = 15 mag for 2MASS.

The other feature of the comparisons was that very bright galaxies have a somewhat lower match rate, as expected due to problems with the size of these galaxies compared to the 2MASS arrays. The Large Galaxy Atlas is slowly fixing the brighter galaxies.

For more information, see 2MASS Checks VS External Galaxy Catalogs.

Notes on the Glazebrook comparison:

1. Glazebrook et al gave no uncertainty for the model fit, which we used to derive their total number of 10 galaxies per square degree. Judging from the uncertainties in their four data points used to fit the model, which range from 14% to 50%, we estimated that the uncertainty in the model fit normalization is about 10%.

2. There is an additional uncertainty in the computed 95% lower limit to the completeness due to the known variation in galaxy density across the sky. We have not included this uncertainty, as its calculation is complex and because three other lines of analysis support a high completeness for the XSC.

3. One major benefit of the 2MASS XSC is immediately apparent from the extremely low uncertainty of the mean galaxy density. The mean density of galaxies at Ks in this magnitude range has been improved a factor of 2000.

4. The overdensity of 10% for XSC compared to Glazebrook is only 0.04 in the log, about one quarter of the typical "stair-step rise" in the 2MASS log N / log S curve. Hence it is virtually impossible to see in the plot.

[Last Updated: 2003 Jan 31; by T. Jarrett and T. Chester]