Using the red sequence to find clusters in the DLS
Rebecca Wilcox, University of Washington (glingglo29@yahoo.com) *My UW website (main)
Advisor: Dara Norman, CTIO
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Abstract: The detection and mapping of galaxy clusters is an important element of understanding the structure of the universe, its history and its future. Presented here is a demonstration of a newer method of cluster detection, called the cluster red sequence method (CRS), which uses the observed red sequence of elliptical galaxies as a sign of a cluster. The red sequence is an observed property of all rich clusters, which have cores composed of coeval elliptical galaxies. At a particular redshift, the ellipticals that make up the sequence are redder than all normal galaxies at a lower redshift. This fact allows us to eliminate contamination from foreground galaxies. Other advantages are the relative ease of obtaining approximate redshifts and the need for images in only two common filters. One limitation of the CRS method is that it assumes a particular definition of a cluster, i.e., a rich cluster with a core of ellipticals, and hence is may not be capable of finding younger clusters, groups, or other structures that do not fit this definition, such as dark clusters.
We analyze one subfield (F1p22) of the Deep Lens Survey (DLS) in order to test the usefulness and expediency of the red sequence method of cluster detection. With limited results, we find that the method can be a sucessful and expedient way of detecting galaxy clusters.
Introduction: The CRS method was first described in a paper by Gladders and Yee (2000), which we use as a guide for this project. The method relies upon the well-known evolution of elliptical galaxies in clusters (Stanford, Eisenhardt, & Dickinson 1998). It is observed that these galaxies fall along "red sequence" paths on a color-magnitude diagram. Based on models of cluster elliptical evolution, the position of a cluster's red sequence on the diagram indicates its redshift. The color-magnitude diagram below shows the expected slopes of the red sequence at different redshifts.
Because ellipticals that make up the sequence are redder than all normal galaxies at a lower redshift, it is easy to eliminate contamination from foreground galaxies using this method. This is a major advantage since projection effects can be a significant source of false-positive cluster detections, and have been with previous optical cluster-finding techniques.
The other major advantage to the method is that it requires data in only two filters, though they must sample the 4000 Å break. This means that data that could be used with this method is abundant and relatively easy to obtain from several optical surveys.
The CRS method detects clusters by searching for overdensities in color (galaxies lying along the same red sequence), position on the sky, and magnitude (as galaxies in the same cluster have roughly the same magnitude). We compute the probability that a galaxy is a cluster member using each of these criteria separately, then combine the results to find clusters.
Method:
The CRS method requires two-band optical/near IR images which sample the 4000 Å break. We use V and I filter data from the F1p22 DLS subfield, which was chosen because it is the only subfield with I data.
Beginning with a catalog of all objects in the subfield, we selected objects with I (Vega) magnitudes less than 24 that did not raise any error flags. We select the galaxies in the catalog by using the objects' ellipticities.
Finding clusters with the CRS method is based upon using three selection criteria: color, surface density, and magnitude. Probabilities of each galaxy being part of a cluster are computed separately for these criteria and then combined. Galaxies in a good cluster candidate would have a high probability for each of the three criteria.
Color selection is based upon the red sequence. Since the position of the red sequence gives the redshift of a cluster, and because elliptical galaxies in a particular cluster's red sequence are redder than normal galaxies at lower redshift, taking a color cut can eliminate contamination from foreground galaxies. It therefore makes sense to look at one slice of color at a time. The plot below is a magnitude-color diagram of our sample of galaxies with the slice boundries overlaid.
Rather than simply looking at where a galaxy falls on the mag-color diagram to determine which slice it is in (and therefore it's approximate redshift), it is more accurate to calculate the probability that a galaxy is in a certain slice based on the galaxy's color error. To include the color error into the calculation, each galaxy on the mag-color diagram is considered to be a gaussian into a third "probability" dimension where the FWHM of the gaussian is the galaxy's color error. The probability that a galaxy is in a slice is the fraction of the error-defined gaussian that lies inside the slice. We determined the probability of each galaxy being in each slice separately. This computation was done using an IDL program written by R. Wilcox. It is important to note that the color slice technique does not use any information about where each galaxy is on the sky. This is why the surface density and magnitude selections are necessary.
The surface density selection is done by looking for overdensities in a contour map of the subfield. Separate maps are made for each redshift slice based on the estimated size of a cluster at each redshift. An IDL program written by D. Norman accomplishes this. The program uses a bootstrapping method (where the same process is performed on fake data) to define significant overdensities. Below are examples of the surface density maps. Remember that these maps are of the exact same field.
z = .15 z = .45
By looking at the surface density maps, we can pick out cluster candidates as overdensities and we can also pick out low density regions from which we can determine the level of field galaxy contamination. Magnitude selection is done after these regions are selected. It is based on the assumption that all the ellipticals in a cluster will have about the same magnitude. So if a galaxy is surrounded by many galaxies of similar magnitude within a cluster-sized radius, then it is likely to be a cluster member. Of course this does not eliminate the possibility of field galaxy contamination, nor does it give a very good estimation of distance, which is why it is used together with the color slice technique.
Another IDL program by R. Wilcox finds the probability of each galaxy being in a cluster using the selected cluster candidates. The same estimated cluster size used for the surface density maps is used by the magnitude selection program. The program counts the number of galaxies within the estimated cluster radius at the particular redshift of the map being analyzed. It then bins the galaxies by their magnitudes and the number of galaxies in each bin is counted. So for each overdensity center, we determine Ncf (M), the total number of galaxies as a function of magnitude. The same is done with the low-density points except these are all averaged to find Nf(M), the average number of field galaxies over the whole map as a function of magnitude. An average is taken to improve the statistics because there may be very few field galaxies in each low-density region. For each galaxy, the probability that it is in a cluster is P(M) = [Ncf(M) - Nf(M)] / Ncf(M).
Results/Conclusions:
When both the color and magnitude probabilities have been computed, they can be plotted against each other to see how they compare. Below is the plot for z = .4 to .5
On the left side, there are several galaxies which had similar magnitudes to those around them, but did not fall within the color boundries of this slice. These are likely field galaxies which only happened to have the right magnitude to get a good magnitude probability. There is even a galaxy with negative magnitude probability, probably because the field galaxies happened to outnumber the galaxies of a similar magnitude near this one. This is the kind of statistical problem we would hope to overcome by taking more samples of low-density regions. Also it can be seen that the magnitude probabilities are rarely higher than 0.5. This may be due to several aspects of the magnitude and surface density programs we would hope to refine. These include making the magnitude bin size reflect the range one would expect a cluster to show; running the magnitude program several times and offseting the bins so that we can catch clusters that straddle the bins; and running the bootstrapping part of the surface density program more times to get better statistics.
Circled below are galaxies in the field that had good color and magnitude probabilities. How we defined "good" here was rather arbitrary because there was limited time. However, with more time it would make sense to average the two probabilities and then look at the data as a whole to decide what should be considered "good."
Red circles are "good" galaxies in z = .4 to .5, purple in z = .5 to .6, blue in z = .6 to .7
This of course cannot be all one cluster as the galaxies span too great a redshift range. There do appear to be one or more overdensities here, though. Also, it is important to consider the needed improvements mentioned above in the surface density and magnitude programs. A better cluster candidate is seen below.
Here, there are no good cluster candidates in this area at higher redshift, which suggests that these galaxies are at least isolated in redshift. They are too spread out to all be part of the core population of one cluster, but this looks like a good candidate nonetheless.
Overall, the CRS method seems a promising way of finding many clusters relatively easily. With more time, we could refine the programs as discussed and then run all the maps through the magnitude program. This would be a more thorough test of the method.
As the Deep Lens Survey is also searching for clusters, but using lensing as an indicator of overdensity, our results could also later be compared to those of the lensing search to see how the selection effects of the different methods affect the results.
References:
Gladders, M. D., Yee, H.K.C.. 2000, Astronomical Journal, 120: 2148.
Stanford, S.A., Eisenhardt, P.R., Dickinson, M. 1998, Astrophysical Journal, 492: 461.
Other sciency stuff I did at CTIO:
*Deep Lens Survey run: I looked for transients (stuff that changes in a field over time: mostly asteroids but also a few supernovae and some interesting unknown objects) in the data that was being collected. The transients numbered below 1000 are mostly mine. Check out 153 (sorry, they are not in order, but they are color-coded) for an interesting "unknown" object (perhaps the very beginning of a supernova), 41 & 117 for some nice supernovae, and take a look at a few of the variables and moving objects (rocks). If you click on a time series for an object, it will show you different pictures of the same field plus the difference image which makes the objects that have changed stand out.
*M83 images: cool!
CTIO REU/PIA 2003 motto: "El
burro sabe más que tú"
*UW Chile page featuring tons more photos (while it lasts)
*other 2003 student pages:
Katherine, Lara, Carey, Ryan, Abner, Rodrigo
I'm so gol-durn excited to be here!
