STATISTICAL STUDY OF SOME GROUPS OF GALAXIES

Introduction:The majority of the galaxies in the universe tend to aggregate in groups(Tully 1987). Groups of galaxies range from loose groups to compact groups. The loose groups of galaxies contain less number of galaxies than clusters. The compact groups of galaxies are so dense with separation distances of a galaxy’s diameter. The first observed compact groups were Stephan’s Quintet (1877) and Seyfert’s Sextet (1948).

Searching for compact groups has been started by Shakbazyan in 1973, after she has found a group of 17 faint red objects which were thought to be a cluster of stars (Shakbazyan1957). The first systematic search for compact groups of galaxies was held by Rose (1977) by setting criteria that the number of galaxies is 3 or more with a total surface equals or brighter than 17.5 mag arcsec -2 . He has found a total number of 205 compact groups of galaxies. The second systematic search was held by Hickson (1982) after adopting different criteria that the number of galaxies is 3 or more with 3 mag difference from the brightest member, the total surface brightness is equal to or brighter than 26.0 mag arcsec-2 and the isolation criterion by setting a large circle that is 3 times a small circle passing through the centers of the galaxies in the group to isolate the members of the same group from the field. He has found 100 compact groups of galaxies (HCGs). Studies on HCGs showed that 8 groups have galaxies with a discordant redshift (Hickson et al. 1992).
Other searching techniques were introduced using different criteria (Prandoni et al. 1992, Garcia et al. 1995, Barton et al. 1996, Iovino et al. 1999 The paper is organized as follows: section 2 describes the data used and method while section 3 describes the results obtained and discussion.

Data and Method:-
The Data:-In 2005, de Carvalho et al. searched the Digitalized Palomar Observatory sky survey (DPOSS) for compact groups of galaxies, within an area of 6260 deg. sq. including the northern and a part of the southern sky. They adopted the following criteria: 1. N ≥ 4 with magnitude difference ≤ 2 2. R isol ≥ 3R gr 3. gr µ < 24.0 mag arcsec -2 4. │b│ > 40° to avoid stars contamination Where N is the number of galaxies in a group, R gr is the angular diameter of the smallest circle, R isol is the angular diameter of the greatest circle, gr µ is the mean surface brightness in the r band and b is the galactic latitude.
They found a total of 459 groups of galaxies with 4 or more members.
The Method:-We applied the clustering technique which we choose because of its simplicity and direct calculations on the groups that contain 5 members from de Carvalho et al catalog (2005). Before we start, we assume that galaxies in the same group are not connected and we try to find if their physical attributes will show any similarity.
Galaxies in the same group are supposed to have similar properties that connect them together. The method uses the physical attributes of the galaxies in each group to testthe relation between all galaxies in the same group and knowing if galaxies are real member or should be discarded from the group. By calculating the astrophysical Euclidean separation coefficient between each two galaxies, one can find the similarities and dissimilarities between the galaxies.
We use a Hierarchical clustering method which is UPGMA (Unweighted Pair Group Method using Arithmetic Average) method, Romesburg(1984). The UPGMA method is an Agglomerative clustering that starts with galaxies as being individual clusters and merges galaxies with similar attributes by averaging similarities of each two galaxies and forms a tree-like structure in a bottom-up way which can be cut off at any level.
The method starts with a data matrix which contains the galaxies in one column and their attributesthat we think show similarities if the galaxies are from the same group in one row. The second step is to build the resemblance matrix by using a clustering method andcalculating the resemblance coefficienttofind if there is a similarity or dissimilarity between different galaxies' attributes.
We thencalculate theresemblance coefficient to obtain the value of dissimilarities between each two galaxies.The larger value of the Euclidean coefficient, the more dissimilar are the galaxies that means that they don't belong to the same group, and the smaller the value, the more similar and connected are the galaxies which concludes that they lie in the same group. The galaxies have a discordant attribute and are regarded as an Attribute Discordant (AD) We calculated the astrophysical Euclidean coefficient of each two members in the same group using the total magnitude of the group in the r band and the g-r color index.

Results:-
The following tables showthe results as follows: Column (1): the galaxy symbol (G), column (2): the total magnitude of the first galaxy in the r band, column (3): the total magnitude of the second galaxy in the r band, column (4): the g-r color index of the first galaxy, column (5): the g-r color index of the second galaxy, column (6): the Astrophysical Euclidean coefficient between every 2 galaxies in the group, column (7): the average astrophysical Euclidean coefficient in each group, column (8): the standard deviation in each group, column (9): the classification of every two galaxies regarding each otherand column ( Applying the UPGMA method on the 5 member groups showed that most of the galaxies are real members while23 groups has a discordant attribute and should be discarded from their groups.