T. Jarrett, IPAC
(980618)
The venerable Abell catalog of galaxy clusters is now
over two decades old (with some supplemental
updates along the way). The new generation of all sky surveys
will more than double the current Abell catalog with deeper
and more complete data sets. For example, the APM galaxy
survey (cf. MNRAS, 289, 263) will contain a few million galaxies
comprising several thousand clusters. Other major projects,
like DPOSS (using POSS II) and Sloan DSS will construct massive digitized
catalogs in due course. Roy Gal (Caltech) has described a
method that DPOSS will employ to identify and catalog
clusters from their 3-band photographic plates (POSS II);
see
NoSOCS: The Northern Sky Optical Cluster Survey
for more information on the DPOSS cluster survey. 2MASS is also capable of
detecting and generating catalogs of galaxy clusters, but with distinct
advantages over the previously noted surveys in that it has
a uniform all sky data set (northern and southern hemispheres) and
the near-IR can penetrate the "zone of avoidance" (the Milky Way).
This document describes a method to identify clusters and estimate
their redshift. Some test cases are given to demonstrate the
effectiveness of the technique.
Galaxies that comprise a "cluster" have two basic (1st order) properities that help reveal their location: first, they are spatially correlated and second, they have roughly the same color. Clusters by definition have a relative scatter in their Vh velocity of less than about 1000 km/s (in contrast to "groups" which have a much tighter distribution, around 200 km/s). Thus, cluster galaxies have a relative redshift that is about the same. Cluster galaxies are located in roughly the same direction of the sky (i.e., their relative sky projected position is typically within 1 degree of arc). Finally, owing to their redshift, cluster galaxies have a systematic reddening of their colors that distinguishes them from non-cluster galaxies at different redshifts. 2MASS can exploit the latter two points: accurate astrometry (which is not particularly essential) and accurate JHK photometry (essential), to identify new clusters (not seen by Abell) and to estimate the redshift. The latter is important to help target candidate clusters for spectral observations to nail down the redshift more accurately. With the location and redshift of clusters one can then study the large-scale structure of the local universe and build angular correlation functions.
The 2MASS method to identify galaxy clusters was previously introduced in the document Redshifts Derived from Galaxy Color and the method was demonstrated using a strip of data passing through the core of the Hercules cluster of galaxies (presented at the 1998 AAS, San Diego). See 2MASS Galaxy Colors : Hercules Cluster . The algorithm is now more finely tuned and can be used to find clusters with the newly reduced 2MASS data. The following case studies show the cluster finding results for known clusters, including Coma, Hercules, Abell 3558 and a random field.
Algorithm Notes
In order to separate the real clusters from chance spatial alignments of field (and separate/background cluster) galaxies, we need to use the J-H and H-K colors. Here we require very accurate colors (something like 10% or better) in order to identify true cluster members (the scatter in the colors needs to be comparable to the intrinsic scatter in the colors due to different morphological types comprising the cluster). We use the colors a bit more cleverly than this, however. Since clusters tend to have large bright galaxies near their centers (Virgo and Coma come to mind), we weight the bright galaxies higher than their more numerous fainter cousins. This weighting scheme tightens the histogram of inferred "z" redshifts for the candidate cluster distribution (see next paragraph).
The centers of the density enhancements act as initial (first-guess) position targets for more detailed "color-color" analysis. A circular area (radius = 20 arcmin) is centered on each density enhancement. Galaxies located within the area (and with high SNR photometry) are used to build a distribution of "z" (inferred redshift based upon their J-H and H-K colors and the K-correction curve). The galaxies that comprise the "z" histogram are heavily weighted according to their brightness (to be more accurate, according to the estimated uncertainty in their H-K color). This bolsters the importance of brighter galaxies which presumably demark the centers or close to the centers of clusters.
Galaxy colors are de-reddened for Galactic extinction based upon the source galactic coordinates and an extinction model given in Jarrett (1992, thesis; 1994, ApJ).
We evalute the histogram by computing the mode, mean , z at mode, z at mean, # galaxies in mode bin and % of all galaxies in bin mode. Here we use bin sizes of 0.02 in "z" (the bin size reflects our ability to resolve the "z" curve with scatter in the photometry and the "z" curve itself as the primary culprets limiting the resolution). Real clusters will have a large fraction of galaxies located in the mode of the histogram. We look for histograms with at least ~50% of all the candidate galaxies located in the mode bin. Secondly we want the total number of galaxies in the mode to be as large as possible (given our spatial window size of 40' in size (see more on size below) and a precision limit of 10:1, this means that real clusters will have greatern than 5 to 10 galaxies in the mode bin).
The above step is iterated 3 times with adjustment in the target position given by the mean in the RA/DEC position of the candidate cluster members. In this way, the target can move around several arcminutes at each iteration, with the last iteration settling upon the best position of the cluster (we maximize the % of all galaxies within the mode bin of the z histogram).
The final results are cross-indentified with the Abell cluster and with a catalog generated from NED (containing some 8000 clusters of all kinds and stripes).
A quick note on known cluster sizes. After generating a catalog of nearly 8000 clusters using NED (with Abell comprising a large fraction thereof), I was able to glean the size distribution of known clusters. Caveat: most clusters do not have a size (why? I don't know, but NED does not carry it). The bottom line is that cluster sizes are usually smaller than 40' or so, with large clusters being much rarer than small clusters (i.e., the tail of the distribution is weighted toward the small size end).
Abell 3558
The galaxy cluster Abell 3558 is a southern cluster (dec = -32 deg) located at z = 0.048 -- which is relatively nearby, but much further then Virgo or Coma. A nice JHK pic of the central 30' can be found here Abell 3558 Galaxy Cluster.
Our dataset consists of 20 scans, giving about 16.6 square degrees of coverage. The area contains about 900 galaxies (very abundant region!). We have eliminated the duplicate observations (between 5 and 10% of the sources are dupes).
What do we find?
white crosses: galaxies used to find density enhancements
orange dots: galaxies used in the color-color vs. "z" analysis
red circles: area comprising candidate cluster (20' radius)
green triangle & number : cluster center and ID
large yellow crosses: position of known cluster (from NED catalog)
blue diamond: Abell cluster position
(note: sorry about using a gif, but generating an html table is far too tedious for this step)
table legend:
rac,decc : final J2000 position of cluster
mode: "z" redshift value corresponding to mode of "z" histogram
bmean: mean "z" of galaxies located in histogram mode bin
nc: number of galaxies in mode bin
Pc: % of all galaxies in z distribution located in mode bin
mode2: "z" redshift value corresponding to second mode of "z" histogram
nc2: number of galaxies in second mode bin
Pc2: % of all galaxies in z distribution located in 2nd mode bin
ra0,dec0 : J2000 position of spatial (initial position) cluster
n0: total number of galaxies located in spatial cluster window
glong, glat: galactic longitude and latitude
Av,Ak,Ah,Aj : assumed galactic extinction at V, K, H and J
deltaR : position offset from known cluster (NED cat)
cluster name: name of known cluster
z : redshift of known cluster
size : diameter in arcmin of known cluster
The primary target, Abell 3558, was clearly identified by the cluster finder (see cluster #1 in table above, ahd histogram below). Furthermore, the deduced redshift (z = 0.051 or z = 0.050, depending on whether using the mode bin center or the mean within the mode bin) is quite close to the actual redshift of 0.048. (note that the histogram bin size is 0.02; see histo below). It stands out from the other cluster candidates in that it has many sources (27 in total) within the "z" mode bin. The clusters #2 and #4 have 8 members each in the mode bin, with #2 near a real cluster: SC 1327-312, and the inferred "z" and measured "z" in close agreement (0.047 vs. 0.049).
Hercules Cluster
Our dataset consists of 5 scans, all repeat scans of one strip passing through the core of Hercules (Abell 2151). One scan covers about 0.83 sq. deg containing nearly 200 galaxies. Results are given for one scan ("047" on 970521n) and the statistical averages are given for all 5 scans.
What do we find?
The Hercules cluster is easily detected, with most of the galaxies (78%) located in the 20' window clustering in the z=0.039 mode bin (the true cluster redshift is 0.036). The smaller cluster, Abell 2152, also part of the supercluster, is also clearly detected at z = 0.037 (matching the measured redshift of 0.037). Two other clusters are identified, but they are probably not real clusters or as least we do not have enough information to discern their true nature.One strip through the region is not sufficient to fully evaluate the performance of the cluster finder. Nevertheless, the duplicate scans do allow a check on the repeatibiity of the cluster finder. The following table gives the inferred "z" and % of galaxies in the mode bin for the Hercules Cluster (Abell 2151) and for Abell 2152 from the 5 repeat scans of the region.
The repeats demonstrate the effect of noise on the
inferred redshifts (via the J-H and H-K colors). For the Hercules
cluster, the "z" as determined from the histogram mode or mean
(within mode bin) repeats very well, 0.036 +- 0.004, which matches
the true redshift. But for Abell 2152, the smaller cluster, the
repeatibility is only 0.045 +- 0.013 (as compared to the true
redshift of 0.037). It is probably so that 6 to 8 stars in the
mode bin is not enough to accurately pin down the redshift (uncertainties
due to the colors and the intrinsic spread in the K-correction curve
need to be averaged down, this requires a lot of sources).
Coma Cluster
Our dataset consists of several scans, all repeat scans of one strip passing
through the core of Coma (Abell 1656).
One scan covers about 0.83 sq. deg containing nearly 130 galaxies.
Results are given for one scan ("014" on 970521n).
What do we find?
random field
A 32 sq. degree field centered at
ra = 24.4d and dec= 28d from one of the
2MASS RTB data sets is examined with the
cluster finder.
What do we find?
- || Herc Cluster || -- Abell 2152 --
scan mode bmean nc Pc mode bmean nc Pc
047 0.039 0.037 12 0.78 0.037 0.035 6 0.71
048 0.039 0.041 11 0.69 0.051 0.051 7 0.53
049 0.035 0.038 10 0.76 0.061 0.060 7 0.47
050 0.029 0.025 8 0.62 0.051 0.045 8 0.73
051 0.037 0.036 11 0.78 0.027 0.027 7 0.51
- - - - - - - - -
ave 0.036 0.035 - - 0.045 0.044 - -
- 0.004 0.006 - - 0.013 0.013 - -
