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Astron. Astrophys. 317, 670-675 (1997)

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3. Substructures

Ideally, substructure tests should be applied to galaxy samples which are complete in magnitude. Here, we will use all the available data without regard to the magnitudes, for different reasons. First, the small sample size makes any further restriction unreasonable. In addition, complete magnitude information is not available for all cluster fields. Nevertheless, in those fields where magnitudes were available from COSMOS, redshift completeness amounts to ca. 75% of the galaxies down to [FORMULA]. Given the small field of view and the extensive redshift coverage, we will concentrate on substructure analysis methods which make use of the velocity information. We chose the test of Dressler & Shectman (1988, hereafter DS-test), the Lee test (Fitchett 1988), and several tests that check for departures from normality of the galaxy velocity distribution. Note that:
a) For the DS-test we followed the same procedure as Bird (1994), using [FORMULA] galaxies to define the neighbourhood of each galaxy, where N is the total number of galaxies involved in the analysis.
b) To assess the significance of substructure detections for the Lee test we performed the same test on 100 cluster simulations. Modelling of the simulated clusters was done with an 1/r galaxy density profile (Fitchett & Webster 1987) and with the same velocity dispersion as in Table 2. Steps of 4 degrees have been used for the orientation of the projection axis in the X-Y-cz plane. Note that the simulations for field 9b were done with an offset of 0.05 h-1 Mpc between the peak of the 1/r density distribution and the center of the circular selection region. A higher likelihood for the presence of substructure would result if the offset was not accounted for (92% instead of 87%).
c) Three different tests for normality have been employed, i.e. the U2, W2 and A2 tests taken from the ROSTAT package (Beers et al. 1990), the resulting significance being the mean from these three tests, which agree very well.
Each of these substructure tests has its strengths and weaknesses. For example, the DS-test measures the deviation of the local from the global kinematics, allowing to detect efficiently small offcenter groups, but sometimes failing in cases where two clumps of equal size and different mean velocities overlap in projection. On the other side, the Lee test is designed to be a very general maximum-likelihood method, but computational constraints confine its use to detecting bimodal structures of comparable size, thus being unable to state about the presence or absence of multimodal structures. It is also trivial that testing the gaussianity of a velocity sample alone cannot give clues about substructures which have same means and dispersions but differing locations in the plane of the sky. We see that all of these tests are bound to miss some manifestations of substructure, each one being sensitive to some particular configuration. For these reasons, a combination of all methods should allow a better judgement to be made. Our statement about the existence of substructure relies upon the fact that at least one of the three detection methods could find significant signs for it. Results are shown in Table 3, which gives field number (column 1), name of the cluster (2), significance level for the tests mentioned above (3-5), and total significance level for substructure (6), which is the highest value of columns 3, 4, and 5. As can be seen from the analysis results, 50% of the clusters show clear signs of substructure (5% significance level). This frequency of substructure in cluster cores has to be considered a lower level because of the intrinsic property of individual tests to miss some manifestations of substructure. It should be noted that the same order of magnitude for substructure frequency has been found by other authors (e.g. Escalera et al. 1994; West 1994), in particular also involving comparable spatial resolution but without redshift information (Salvador-Solé et al. 1993).


Table 3. Substructure analysis. Column 6 is the highest value of columns 3,4,5 and gives the final likelihood for the presence of substructure

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998