I. Introduction

2. The 2MASS Sky

a. Redshifts Derived from Galaxy Color

The color of a "normal" galaxy is strongly dependent on the redshift of the object. As such, in order to derive the zero-redshift color of a galaxy, you need to apply a color correction to compensate for the "reddening" of the galaxy, due to wavelength redshift (the so-called "K correction"; also, galaxy evolution plays an increasing role in the color modification at high redshifts). Conversely, one may deduce the redshift of a galaxy by its colors and K-correction model. '

Question: how well can 2MASS estimate redshifts based upon measured colors?

2MASS will detect galaxies well out to z=0.1, with decreasing completeness thereafter. For z=0 to 0.1, this translates to about 0.3 mag change in H-K_s color (J-H is much less sensitive to redshift for this z range). In order to differentiate redshift at the 0.01 to 0.02 level, this translates to better than 3% to 6% error measurement in H-K_s color. This is clearly only possible for the brightest (and therefore, nearest) sources -- it should apply for Coma, Abell 262, and possibly, Hercules. A more realistic measurement error for the color is between 10% and 15%, which translates to 0.03 to 0.05 in redshift resolution, which is adequate for the more distant (z > 0.05) clusters.

Several thousands galaxies were available for an initial pilot study, including galaxies from Coma, Hercules, and the nights of 1997 Nov 10, 1997 Dec 5, and 1998 Jan 25 (all in the north). All galaxies are found in relatively low stellar source density fields (to minimize effects due to confusion and reddening). Only a fraction of this sample has known redshifts (about 900 galaxies in total). It is the latter subsample that defines the "truth set." We assume that the redshifts found in NED are correct and for the most part have small measurement uncertainties (this is undoubtedly true, but there are always a few outliers in the sample, although they should "wash out" in the statistical noise).

i. Procedure

We matched 2MASS galaxies with the NED catalog(s) and separated out galaxies with known (measured) redshifts. We then culled out galaxies with poor J, H or K_s measurements (due to source confusion, bad pixels, edge effects, etc). Finally, we culled out galaxies with color measurement errors greater than some specified limit (e.g., 10%).

Given the J-H and H-K_s colors for a galaxy, we then deduced the redshift by comparing the colors with a K-correction model. The K-corrections correspond to SAB type galaxies with no evolution (from models Bruzual & Charlot 1993, ApJ, 405, 538, and McLeod & Rieke 1995, ApJ, 454, 611; tables provided by R. Cutri) and K-corrections corresponding to ellipticals with passive evolution (using models of Bruzual & Charlot; tables courtesy of P. Eisenhardt & A. Stanford). We do this comparison in two different ways:

(1) We find the point on the "spiral" K-correction track that is closest to the J-H and H-K_s color of the galaxy. This is referred to as the "spiral - project solution." This point is orthogonal to the K-correction track.
(2) We find the point on the track that corresponds to the "intercept" of the track and a line defined by the galaxy color and the slope of the "giant" stellar track. In the near-IR, we are most sensitive to an old-population of stars, corresponding to roughly the giant track and, to a lesser extent, the red dwarf track (because they are intrinsically faint). Therefore, we expect a spread in color (at zero redshift) that follows this track. As the results show, this method is indeed better than method (1). This method is referred to as the "spiral - intercept solution."

The following figures show the results for data combined ("all") and for the individual clusters of Coma and Hercules. The combined data span several nights, so systematics, due, e.g., to calibration, will average down better than the data from Coma or Hercules (because they were acquired on single nights only). We have also combined all known "spirals", "S0" and "elliptical" morphological types of galaxies.

The figures show the known redshift vs. the redshift difference between what is known and what is deduced from the colors and K-correction track.

Colors are derived from apertures magnitudes corresponding to fixed 7´´-radius circular apertures -- unless when otherwise noted.

All Galaxy Fields
Figure 1	Figure 2	Figure 3
Galaxies in JHKscolor-color plane: color 0.05	Redshift Results for color 0.05	Redshift Results for color 0.05 fid Ks ellip aper

Figure 4	Figure 5	Figure 6
Galaxies in JHKscolor-color plane: color 0.10	Redshift Results for color 0.10	Redshift Results for color 0.10 fid Ks ellip aper

Figure 7	Figure 8	Figure 9
Galaxies in JHKscolor-color plane: color 0.15	Redshift Results for color 0.15	Redshift Results for color 0.15 fid Ks ellip aper

Figure 10	Figure 11	Figure 12
Galaxies in JHKscolor-color plane: color 0.20	Redshift Results for color 0.20	Redshift Results for color 0.20 fid Ks ellip aper

10 Duplicate Fields of Coma Core
Figure 13	Figure 14
Galaxies in JHKs color-color plane: color 0.10	Redshift Results for color 0.10
Figure 15	Figure 16
Galaxies in JHKs color-color plane: color 0.15	Redshift Results for color 0.15

5 Duplicate Fields of the Hercules Cluster
Figure 17	Figure 18
Galaxies in JHKs color-color plane: color 0.10	Redshift Results for color 0.10
Figure 19	Figure 20
Galaxies in JHKs color-color plane: color 0.15	Redshift Results for color 0.15

ii. Comments

We are systematically finding redshifts that are too high for galaxies that are nearby (z < 0.02). We seem to do rather well, on average, for 0.2 < z < 0.1. The errors range from a few % to 30%.

The nearby sample (z < 0.02) is clearly not behaving as we expect. The colors are too red (thus giving redshifts that are too large). This may be due to the fact that nearby galaxies are large (on the sky), and so we are really measuring only their inner cores (bulge component), which is known to be redder than the outer parts of galaxies. Our small circular aperture, r=7´´, is simply too small to provide a realistic color for nearby large galaxies (conversely, a large aperture may work better, except that 2MASS is not optimized to measure the fluxes of large galaxies; but, see results for elliptical aperture colors). There are undoubtedly other systematics are work here (e.g., our nearby sample might be dominated by a singe morphological type, e.g., ellipticals, due to small sample statistical fluctuations ). This requires additional work in the future.

All Galaxy fields: Low Redshift (z < 0.01)
Figure 21	Figure 22	Figure 23
Galaxies (z < 0.01) in JHKs color-color Plane: color 0.10	Redshift Results (z < 0.01) for color 0.10 Circ. Aper, r=7´´	Redshift Results (z < 0.01) for color 0.10 Ellip Ks-fid Aper

[Last Updated: 1998 Apr 30; by T. Jarrett]