On the evolution of giant radio halos and their connection with cluster mergers

Table 3:

Synchrotron dissipation time (in unit of Gyr) in galaxy clusters that allows to match observations (1 cluster in the ``empty'' region) in a fraction of Montecarlo trials = 10% (Col. 5), 5% (Col. 6), 1% (Col. 7) and 0.3% (Col. 8).
$\cal{N}$	${N}_{\rm corr}$	${N}_{\rm emp}$	${N}_{\rm ul}$	$\tau_{10\%}$	$\tau_{5\%}$	$\tau_{1\%}$	$\tau_{0.3 \%}$
				(Gyr)	(Gyr)	(Gyr)	(Gyr)
17	5	1	11	0.35	0.42	0.57	0.68
19	7	1	11	0.32	0.34	0.51	0.60
20	7	1	12	0.30	0.36	0.49	0.59
17	5	1	11	0.69	0.84	1.14	1.35
19	7	1	11	0.64	0.68	1.01	1.20
20	7	1	12	0.60	0.73	0.97	1.17

Montecarlo simulations are carried out for three configurations: GMRT clusters with $L_{0.1{-}2.4}>8.4 \times 10^{44}$ erg s^-1 excluding the two mini-halos (first line), GMRT clusters with $L_{0.1{-}2.4}>8.4 \times 10^{44}$ erg s^-1 (second line), GMRT clusters with $L_{0.1{-}2.4}>8 \times 10^{44}$ erg s^-1 excluding the two mini-halos (tirdth line); total number of observed clusters and their distribution are given in Col. 1-4. We perform 10⁵ random extractions of $\cal{N}$ synthetic clusters assuming a grid of extraction probability with f in the range 0-1 (see text). Upper part gives the case where clusters cross the ``empty'' region two times, lower part gives the case where clusters cross this region only one time.

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