2MASS Galaxy Redshift Catalog (XSCz)

"Finger of God" Radial Velocity Artifacts

Spectroscopic velocities are biased to cluster galaxies with infall space motions that are primarily along the line of sight. The end result for a cluster is a set of redshifts that are enhanced along the radial direction and suppressed (or more accurately, neutral) along the perpendicular direction. The cluster thus appears "cigar" shaped, seemingly stretched along the radial direction (for a better explanation of the 'caustic' shape, see Liz Praton's Infall Artifact article). The higher the velocity dispersion, the more stretched the cluster appears. As legend has it, Brent Tully referred to these artifacts as "fingers of god", a colorful description of how the stretched cluster seemed to point back to the Earth, as if they were a big god-like finger. Perhaps the most famous finger is seen in the CfA Great Wall pie-diagram produced by Huchra & Gellar, showing the radial stretching of the Coma Cluster that points back to the observer, perpendicular to a coherent string of clusters that is collectively known as the Great Wall.

For the purpose of improving the 4-D visualization, the radial velocity artifacts are 'statistically corrected' for a set of well-defined galaxy clusters. The method does not attempt to derive the actual Z-location for a given cluster galaxy, but instead derive a statistically accurate representation for the cluster. Knowing the cluster kinematics, physical size, and radial density distribution, it is possible to modify the Z locations so that the XYZ locations of cluster galaxies collectively portray the cluster parameters of dispersion, size and distribution. We make the assumption that the cluster radial size is between 1 and 2 Mpc, depending on the number of cluster galaxies (i.e., total mass) and that the galaxies are radially gaussian distributed (although the density distribution may be more accurately described with a R^1/4 or even isothermal King profile, a gaussian is adequate for our means). The spatial location and velocity dispersion comes from cluster catalog extracted from NED, ZCAT and the Abell catalog. Clusters that do not have catalogued dispersions are assumed to have a value of 1000 km/s. XSCz cluster candidates are identified by their equatorial coordinates and redshifts such that they fall within the expected dispersion of the catalogued galaxy cluster. Candidates that are located behind the cluster center (i.e., redshifted relative to cluster center) are relocated to Z-locations behind the cluster center that are determined using a monte-carlo gaussian distribution appropriate to the cluster. Likewise, galaxies in front of the cluster ("blue-shifted") are gaussian distributed in front of the cluster. For galaxies with zero redshift relative to the center (i.e., their peculiar motion is perpendicular to the radial direction), they are gaussian distributed along the perpendicular direction. Galaxies with kinematics between line-of-sight and across-sight are correspondingly treated to fill the cluster gaussian sphere. In this way, the cigar-shaped cluster is reshaped into a spherical-shaped cluster with a gaussian distribution. For isolated clusters, this is a relatively straight-forward process (see the Coma Cluster example below). Complications arise for clusters that are in close proximity, potentially mixing populations as some galaxies may be 'pulled' into the wrong cluster (e.g., see the Hercules Cluster example below).

The table below illustrates the performance of the finger-of-god correction process for a few prominent clusters (both isolated and complex).

Coma Cluster: redshift versus equatorial position "pie diagram" showing the distribution of galaxies in the vicinity of the Coma Cluster. On the left side is the diagram with pure radial velocities. Note the long "finger of god" from this fully relaxed cluster, pointing toward the origin. Coma Cluster members are identified and redistributed in a shape that is more consistent with the true morphology of the cluster. The right side shows the resulting distribution.
Virgo Cluster: This cluster is not an isolated, relaxed cluster like that of Coma (see above), but is more of an agglomeration. The reconstructed distribution shown here is too simplistic, but it nevertheless greatly reduces the radial velocity bias that spreads Virgo galaxies all over the Local Supercluster. Note that the "before" image seems to show a horizonal line of galaxies -- this is just Virgo galaxies with the same assigned distance (e.g., from Cepheids or T-F), which is also not an accurate description of the cluster size morphology.
Hercules Cluster: A concentration of cluster comprise the Hercules Supercluster. Here the main cluster has been reconstructed. Even after removing the main finger-of-god, it is clear that another finger exists, undoubtedly due to a nearby cluster.
Abell 3558 of the Shapley Concentration: The densest and most complex region that the XSCz covers. As the pie diagram shows, there are several clusters within this "concentration", with the largest being A3558. The reconstructed cluster is not perfect, but is nevertheless an improvement over the strung-out radial distribution. This is a good example of what happens when the target cluster is part of a group or concentration of clusters.
Abell 3627 "Norma Cluster": The Great Attractor region is complex with connecting structures from Pavo (to the south), and Hydra-Cen to the North. Moreover, the Milky Way is a major obscuration problem, cutting off some of the Norma Cluster. Nevertheless, the finger-of-god appears to be adequately corrected for this cluster.
Ophiuchus Cluster: Located just above the Galactic Center, this cluster is one of the most challenging to decipher due to extreme source confusion. As the diagram seems to indicate, the region may have more than one cluster.

Last updated by T. Jarrett on Dec 9, 2006