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Table 4:

Comparison of the mean orthogonal scatter of the substructure parameters from the analysis of the simulated clusters seen from different projection angles.

Parameter pair
X-Y X-Z Y-Z Mean

$\langle \Delta \widetilde{P_2}/\widetilde{P_2} \rangle /\sqrt{2}$
0.72 0.79 0.77 0.76
${\rm exp}\ {\langle \ln( \Delta \widetilde{P_2}/\widetilde{P_2}) \rangle} /\sqrt{2}$ 0.48 0.56 0.57 0.54
$\langle \Delta \widetilde{P_3}/\widetilde{P_3} \rangle /\sqrt{2}$ 0.99 1.85 0.91 1.25
${\rm exp}\ {\langle \ln( \Delta \widetilde{P_3}/\widetilde{P_3}) \rangle} /\sqrt{2}$ 0.63 0.83 0.72 0.73
$\langle \Delta \widetilde{P_4}/\widetilde{P_4} \rangle /\sqrt{2}$ 1.13 1.03 1.01 1.06
${\rm exp}\ {\langle \ln(\Delta \widetilde{P_4}/\widetilde{P_4}) \rangle} /\sqrt{2}$ 0.71 0.80 0.80 0.77
$\langle \Delta w/w \rangle /\sqrt{2}$ 0.50 0.49 0.48 0.49
${\rm exp}\ {\langle (\ln(\Delta w/w)) \rangle} /\sqrt{2}$ 0.32 0.29 0.26 0.29

Notes.  $\widetilde{P_2} = P_2/P_0$, etc. The orthogonal scatter is defined as the mean deviation from the diagonal in the plot and thus the algebraic expressions in the table contain an extra factor of $1/\sqrt{2}$. The mean is determined by both linear and logarithmic averaging. The means for the three projections and the total mean are given. The standard deviation of these parameters from the mean is slightly smaller than the means, but of the same order of magnitude.


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