The velocity dispersion function of red galaxies in four Hubble Frontier Fields galaxy clusters

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Table 3.

Parameters of the best Schechter function fit of the velocity dispersion function for the red members of the four clusters.

Cluster	$\tilde{ϕ}$ $Mathematical equation: $ \tilde{\phi} $$	α	log σ^* [km s⁻¹]	$\tilde{N}$ $Mathematical equation: $ \tilde{N} $$
A2744	$101_{- 15}^{+ 13}$ $Mathematical equation: $ 101^{+13}_{-15} $$	$1 . 60_{- 0.33}^{+ 0.32}$ $Mathematical equation: $ 1.60^{+0.32}_{-0.33} $$	$2 . 18_{- 0.09}^{+ 0.11}$ $Mathematical equation: $ 2.18^{+0.11}_{-0.09} $$	2.14
AS1063	$30_{- 13}^{+ 14}$ $Mathematical equation: $ 30^{+14}_{-13} $$	$0 . 55_{- 0.34}^{+ 0.34}$ $Mathematical equation: $ 0.55^{+0.34}_{-0.34} $$	$2 . 47_{- 0.12}^{+ 0.18}$ $Mathematical equation: $ 2.47^{+0.18}_{-0.12} $$	2.55
M0416	$36_{- 20}^{+ 32}$ $Mathematical equation: $ 36^{+32}_{-20} $$	$0 . 80_{- 0.56}^{+ 1.01}$ $Mathematical equation: $ 0.80^{+1.01}_{-0.56} $$	$2 . 46_{- 0.34}^{+ 0.57}$ $Mathematical equation: $ 2.46^{+0.57}_{-0.34} $$	2.95
M1149	$73_{- 23}^{+ 22}$ $Mathematical equation: $ 73^{+22}_{-23} $$	$1 . 16_{- 0.39}^{+ 0.40}$ $Mathematical equation: $ 1.16^{+0.40}_{-0.39} $$	$2 . 43_{- 0.16}^{+ 0.22}$ $Mathematical equation: $ 2.43^{+0.22}_{-0.16} $$	2.54

Notes. We report, for each cluster, the values of the three Schechter function parameters, defined as in Eq. (10), with the uncertainty determined by the MCMC optimisation, and the normalisation $\tilde{N}$ $Mathematical equation: $ \tilde{N} $$ used for the velocity dispersion bins.

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