Statistics and implications of substructure detected in a representative sample of X-ray clusters

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Volume 548 (December 2012)

A&A, 548 (2012) A59

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Table 1

Correlation coefficients measured for various cluster and substructure parameters.

Correlation	τ	P _null	ρ	P _null	Figure
(1)	(2)	(3)	(4)	(5)	(6)


w − P₃	1.31	0.19	0.18	0.28	1
	2.74	0.006	0.41	0.01	1
P₂ − ϵ	4.70	0.00	0.74	0.00	6
w − luminosity ratio	4.87	0.00	–0.76	0.00	8
P₃ − luminosity ratio	2.46	0.01	–0.36	0.03	8
P₃ − luminosity ratio^*	2.97	0.003	–0.44	0.01	8
luminosity gap-P₃	1.10	0.26	–0.19	0.35	9
luminosity gap-P₃^*	2.25	0.02	–0.41	0.04	9
BCG ϵ − P₂	2.77	0.006	0.66	0.007	10
BCG ϵ−X-ray ϵ	2.39	0.01	0.63	0.009	10

Notes. (1) the correlation tested (2) the coefficients of Kendall’s τ test (3) the corresponding probability of a null-correlation (4) the coefficients of Spearman’s rank test, ρ (5) the corresponding null probability (6) the corresponding figure number that shows the correlation. We used the ASURV software package to calculate the coefficients.

^(*)

Denotes the same correlation as in the preceding row but excluding the three clusters, 3, 6, and 7 as for example shown in Fig. 1. For the correlation of the luminosity gap and P₃ the corresponding clusters, 2, 4, and 5 in Fig. 9, are excluded.

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