Compilation and Identification of Galaxy Clusters and Groups

3.1 Compilation and Identification of Galaxy Clusters and Groups

3.1.1 Galaxy clusters and groups compiled from the NED

The galaxy cluster/group catalogue of the SSC used in this study is based on those com-piled from the NED. However, since the galaxy clusters and groups comcom-piled from the NED include results from different observations and detection algorithms, and thus one cluster/group may be detected by different observations more than one time, or it is just a substructure of one larger cluster. We therefore discard those detected as substructures first. In addition, previous cluster/group identifications based on the optical images may lacked galaxy redshift data, therefore the centers of clusters might be defined by foreground or background bright galaxies and lead to the bias in cluster centers and redshifts. There-fore, in order to confirm the cluster/group uniqueness and calculate the basic properties of clusters/groups such as virial radius and mass, all galaxies with measured velocity (∼ 5000 galaxies in the SSC) as well as X-ray observations in this region are used to establish the cluster/group catalogue used in this study.

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3.1.2 X-ray detected galaxy clusters and groups

The X-ray detections of clusters/groups in the SSC are compiled from the REFLEX cluster catalogue (Böhringer et al. 2004) and the study of de Filippis et al. (2005). A total of 16 clusters from the REFLEX cluster catalogue with X-ray flux (0.1 − 2.4 keV) above 3 × 10⁻¹²erg s⁻¹cm⁻² and the additional 6 clusters from de Filippis et al. (2005) with X-ray flux (0.1 − 2.4 keV) above 1.55 ×10⁻¹² erg cm⁻² s⁻¹ are compiled. The measured and estimated X-ray flux, luminosity and temperature of clusters are listed in 3.1. The X-ray flux and luminosity are quoted from the REFLEX catalogue and the Table 4 of de Filippis et al. (2005), while the cluster temperature is surveyed through “BAX” (The X-Ray Galaxy Clusters Database, http://bax.ast.obs-mip.fr/). For those with temperature estimated from the spectroscopic data, the temperature is quoted from the related literatures, as to those without spectroscopic data, the cluster temperature is derived through the L_x− T relation from Markevitch (1998):

To identify galaxy systems which have not yet been detected before, the galaxy distribution in the SSC is binned with a pixel size of 3 × 3 arcmin²by using equations 2.1 and 2.2. These binned pixels are further smoothed by convolving with a 3 × 3 Gaussian kernel with FWHM of 6 arcmins. The galaxy density fluctuation σ is estimated by the standard deviation of background galaxy density distribution. The overdensity regions are defined as groups of pixels which have density greater than 3σ . These pixels above the threshold are linked with each other in case of i ± 1 or j ± 1, where i and j are pixel index number in RA and Dec directions, respectively. It is similar to the method of friend-of-friend, all linked pixels are belonged to the same overdensity region, that is, one galaxy system candidate. The centers of galaxy system candidates are defined by the density peak of overdensity regions, and the redshifts are determined preliminarily by the mean velocity of galaxies in overdensity regions.

3.1 Compilation and Identification of Galaxy Clusters and Groups 23

Table 3.1 Properties of X-ray detected clusters in the SSC

Name RA Dec z fx(0.1-2.4 keV) Lx(0.1-2.4 keV) kT Ref.

10⁻¹²erg cm⁻²s⁻¹ 10⁴⁴erg s⁻¹ keV

* RBS1175 193.1421 -31.2678 0.0535 12.91 1.013 3.65

* A3528N 193.5979 -29.0228 0.0542 8.801 0.727 4.65 b

* A3528S 193.6725 -29.2233 0.0544 15.402 1.196 4.94 a

* A3530 193.8938 -30.3306 0.0541 10.314 0.741 3.68 b

* BS(RXCJ1256.9-3119) 194.2492 -31.3219 0.0561 5.378 0.422 2.41

* A3532 194.3204 -30.3769 0.0554 18.733 1.457 4.34 b

* S0721 196.4771 -37.6614 0.0497 8.181 0.495 2.6

* A1736 201.7061 -27.1634 0.0458 36.893 1.796 2.95 c

* A3558 201.9896 -31.5025 0.0480 58.526 3.518 5.51 a

* A3558(B)(SC1327-312) 202.4288 -31.6025 0.0488 14.434 0.865 3.53 a

* A3558(C)(SC1329-314) 202.885 -31.8153 0.0448 4.901 0.257 1.9

* A3560 203.0942 -33.1394 0.0487 14.129 0.833 3.3 d

* A3562 203.4012 -31.6611 0.0490 24.485 1.475 3.8 a

* A3570 206.7188 -37.8744 0.0377 5.527 0.191 2.3 b

* A3571 206.8683 -32.8497 0.0391 115.471 4.206 7.6 a

* BS(A3577) 208.3721 -27.8886 0.0468 4.993 0.281 1.98

+ S0718 194.963 -33.661 0.0478 1.43 0.073 1.1

+ S0724 198.286 -32.994 0.0493 2.05 0.111 1.3

+ A3553 199.805 -37.179 0.0487 1.35 0.071 1.1

+ A3554 199.865 -33.497 0.0470 2.91 0.143 1.5

+ S0729 200.358 -35.816 0.0499 1.27 0.071 1.1

+ A3556 201.001 -31.656 0.0479 1.72 0.088 3.8 b

“*” : X-ray detection by REFLEX; “+”: X-ray detection by de Filippis et al. (2005).

Ref: literature reference for the cluster temperature: a (Cavagnolo et al. 2009), b (Fukazawa et al. 2004), c (Vikhlinin et al. 2009), d (de Plaa et al. 2007).

All candidates are further cross-correlated with the known clusters/groups, for those without identified counterpart, they are suggested to be new identification candidates. All new identification candidates need to be examined by the iterative method described below.

3.1.4 Determination of velocity dispersion σ

, r

, M

, and cluster members

For clusters and groups compiled from the NED or our new identifications, the virial radius and virial mass are derived through the calculation of r₂₀₀ and M₂₀₀. The definition of r₂₀₀ is the radius inside which the density is 200 times the critical density, and M₂₀₀ is the total mass inside of r₂₀₀:

M₂₀₀= 200 ρc× 4/3 r³₂₀₀, (3.2)

where r₂₀₀ approximates the virial radius, and thus M₂₀₀approximates the virial mass.

In this study, the r₂₀₀ and M₂₀₀ of 22 X-ray detected clusters are derived through the relation of M₅₀₀− T_xfrom Vikhlinin et al. (2009):

M₅₀₀= (2.95 ± 0.10) × 10¹⁴ k_BT_x

As to the clusters/groups under X-ray detection, r₂₀₀ are estimated by cluster velocity dispersion σ_v of cluster members within r₂₀₀ and ±3σ_v of cluster redshift z_cl (Finn et al.

2005):

The determination of velocity dispersion σ_vand r₂₀₀ for one cluster is through an iter-ative algorithm :

1. For clusters/groups from the NED, the cluster centers and redshifts are first defined as those from the NED, and the initial searching radius is10 arcmins, all galaxies within this radius and have radial velocity within ±3000 km s⁻¹of the cluster redshift z_clare selected.

3.1 Compilation and Identification of Galaxy Clusters and Groups 25

2. The new redshift z_cl, velocity dispersion σ_v, and cluster virial radius r₂₀₀are estimated by the galaxies selected by step (1) through equation 3.4, where σ_vis limited to be less than 300 km s⁻¹ to exclude severe contamination from foreground and background galaxies.

3. By using the biweight estimator from Beers et al. (1990), the z_cl, σ_v, and r₂₀₀ are estimated by the member galaxies (at least 4 galaxies) within r₂₀₀ and ±3σ_v of z_cl iteratively until convergence is reached, i.e. subsequent iterations differ by less than 0.03 ×p0.5/(n − 1) in σv, where n is the total number of cluster members with n ≥ 4.

For each cluster/group has estimated z_cl, σv and r200 through these steps, it is further visually examined by the distribution of member radial velocities, and the image of galaxy density distribution. If one cluster/group has its members mostly lie within r₂₀₀ of other richer cluster, then it is taken as a substructure of this richer cluster and is discarded. Fur-thermore, we also find that the centers of A3537 and A3541 quoted from the NED were defined by foreground bright galaxies, therefore we redefined their centers by mean RA and Dec of the cluster members, where the center of A3537 is from (195.261, -32.436) to (195.506, -32.601), and that of A3541 is from (197.171, -34.567) to (197.161, -34.430 ).

In addition, for A3568, there have no cluster members within ∼ 12 arcmins of the center quoted from the NED, therefore the center of this cluster was redefined by a nearby over-density region at the similar redshift, from (205.296, -34.636) to (205.346, -34.388). For these clusters, the z_cl, σ_v and r₂₀₀ were estimated again by adopting the new centers. For X-ray detected cluster RBS 1175, we also found the estimated r₂₀₀and M₂₀₀from the X-ray luminosity is much larger than that estimated by the velocity dispersion σ_v, and is incon-sistent with the small total number of cluster members from both the velocity and 2MASS catalogues. The possible explanation for this inconsistence is that the X-ray flux of this cluster is contaminated by three faint X-ray point sources. Therefore, the r₂₀₀ and M₂₀₀ of this cluster was calculated through σ_v.

After removing the clusters/groups which have less than 4 members and those are taken as substructures, a total of 52 clusters and groups from the NED and 17 new identifications are adopted in this study. The galaxy density distribution and the adopted clusters/groups in

the SSC are shown in Figure 3.3, where the clusters/groups from the NED and new iden-tifications in this study are represented by the yellow and red circles with a radius of r₂₀₀, respectively.