Euclid preparation - LXV. Determining the weak lensing mass accuracy and precision for galaxy clusters

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Volume 695 (March 2025)

A&A, 695 (2025) A280

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Table B.1.

Fitted parameters of the log M_WL − log M_sim relation.

Data Set	Median	CBI	Mean	ML
LSS + shape noise (4)	${\begin{matrix} α = - 0.070 \pm 0.006 \\ β = 0.920 \pm 0.022 \\ σ = 0.202 \pm 0.005 \end{matrix}$ $\left\{\begin{array}{l} \alpha = -0.070 \pm 0.006 \\ \beta = 0.920 \pm 0.022 \\ \sigma = 0.202 \pm 0.005 \end{array}\right.$	$\begin{matrix} - 0.082 \pm 0.006 \\ 0.904 \pm 0.021 \\ 0.194 \pm 0.005 \end{matrix}$ $\begin{array}{c} -0.082 \pm 0.006\\ 0.904 \pm 0.021 \\ 0.194 \pm 0.005\end{array}$	$\begin{matrix} - 0.097 \pm 0.005 \\ 0.875 \pm 0.021 \\ 0.169 \pm 0.005 \end{matrix}$ $\begin{array}{c} -0.097 \pm 0.005 \\ 0.875 \pm 0.021 \\ 0.169 \pm 0.005 \end{array}$	$\begin{matrix} - 0.098 \pm 0.007 \\ 1.027 \pm 0.030 \\ 0.382 \pm 0.006 \end{matrix}$ $\begin{array}{c}-0.098 \pm 0.007 \\ 1.027 \pm 0.030 \\ 0.382 \pm 0.006\end{array}$
Three Hundred (ECG)	${\begin{matrix} α = - 0.114 \pm 0.046 \\ β = 1.081 \pm 0.044 \\ σ = 0.064 \pm 0.003 \end{matrix}$ $\left\{ \begin{array}{l} \alpha = -0.114 \pm 0.046\\ \beta = 1.081 \pm 0.044\\ \sigma = 0.064 \pm 0.003 \end{array}\right.$	-	-	-
photo-z non-conservative (5.1.1)	${\begin{matrix} α = - 0.150 \pm 0.005 \\ β = 0.855 \pm 0.020 \\ σ = 0.170 \pm 0.005 \end{matrix}$ $\left\{ \begin{array}{l} \alpha = -0.150 \pm 0.005\\ \beta = 0.855 \pm 0.020\\ \sigma = 0.170 \pm 0.005\end{array}\right.$	$\begin{matrix} - 0.158 \pm 0.005 \\ 0.835 \pm 0.021 \\ 0.160 \pm 0.005 \end{matrix}$ $\begin{array}{c} -0.158 \pm 0.005\\ 0.835 \pm 0.021\\ 0.160 \pm 0.005\end{array}$	$\begin{matrix} - 0.167 \pm 0.005 \\ 0.807 \pm 0.020 \\ 0.135 \pm 0.005 \end{matrix}$ $\begin{array}{c} -0.167 \pm 0.005\\ 0.807 \pm 0.020\\ 0.135 \pm 0.005\end{array}$	$\begin{matrix} - 0.216 \pm 0.007 \\ 0.977 \pm 0.029 \\ 0.365 \pm 0.006 \end{matrix}$ $\begin{array}{c}-0.216 \pm 0.007\\ 0.977 \pm 0.029\\ 0.365 \pm 0.006\end{array}$
photo-z robust (5.1.2)	${\begin{matrix} α = - 0.066 \pm 0.006 \\ β = 0.881 \pm 0.023 \\ σ = 0.220 \pm 0.005 \end{matrix}$ $\left\{ \begin{array}{l} \alpha = -0.066 \pm 0.006\\ \beta = 0.881 \pm 0.023\\ \sigma = 0.220 \pm 0.005\end{array}\right.$	$\begin{matrix} - 0.094 \pm 0.006 \\ 0.843 \pm 0.021 \\ 0.178 \pm 0.005 \end{matrix}$ $\begin{array}{c} -0.094 \pm 0.006\\ 0.843 \pm 0.021\\ 0.178 \pm 0.005\end{array}$	$\begin{matrix} - 0.094 \pm 0.006 \\ 0.843 \pm 0.021 \\ 0.178 \pm 0.005 \end{matrix}$ $\begin{array}{c} -0.094 \pm 0.006\\ 0.843 \pm 0.021\\ 0.178 \pm 0.005\end{array}$	$\begin{matrix} - 0.099 \pm 0.008 \\ 1.008 \pm 0.031 \\ 0.418 \pm 0.007 \end{matrix}$ $\begin{array}{c} -0.099 \pm 0.008\\ 1.008 \pm 0.031\\ 0.418 \pm 0.007\end{array}$
`AMICO`-like (5.2)	${\begin{matrix} α = - 0.086 \pm 0.007 \\ β = 0.897 \pm 0.024 \\ σ = 0.206 \pm 0.006 \end{matrix}$ $\left\{ \begin{array}{l} \alpha = -0.086 \pm 0.007\\ \beta = 0.897 \pm 0.024\\ \sigma = 0.206 \pm 0.006\end{array}\right.$	$\begin{matrix} - 0.098 \pm 0.006 \\ 0.883 \pm 0.024 \\ 0.199 \pm 0.006 \end{matrix}$ $\begin{array}{c} -0.098 \pm 0.006\\ 0.883 \pm 0.024\\ 0.199 \pm 0.006\end{array}$	$\begin{matrix} - 0.111 \pm 0.006 \\ 0.864 \pm 0.023 \\ 0.172 \pm 0.006 \end{matrix}$ $\begin{array}{c} -0.111 \pm 0.006\\ 0.864 \pm 0.023\\ 0.172 \pm 0.006\end{array}$	$\begin{matrix} - 0.118 \pm 0.008 \\ 0.988 \pm 0.034 \\ 0.394 \pm 0.007 \end{matrix}$ $\begin{array}{c} -0.118 \pm 0.008\\ 0.988 \pm 0.034\\ 0.394 \pm 0.007\end{array}$
`PZWav`-like (5.2)	${\begin{matrix} α = - 0.091 \pm 0.006 \\ β = 0.877 \pm 0.025 \\ σ = 0.213 \pm 0.006 \end{matrix}$ $\left\{\begin{array}{l} \alpha = -0.091 \pm 0.006\\ \beta = 0.877 \pm 0.025\\ \sigma = 0.213 \pm 0.006\end{array} \right.$	$\begin{matrix} - 0.102 \pm 0.006 \\ 0.859 \pm 0.024 \\ 0.205 \pm 0.005 \end{matrix}$ $\begin{array}{c} -0.102 \pm 0.006\\ 0.859 \pm 0.024\\ 0.205 \pm 0.005\end{array}$	$\begin{matrix} - 0.102 \pm 0.006 \\ 0.861 \pm 0.024 \\ 0.205 \pm 0.006 \end{matrix}$ $\begin{array}{c} -0.102 \pm 0.006\\ 0.861 \pm 0.024\\ 0.205 \pm 0.006\end{array}$	$\begin{matrix} - 0.127 \pm 0.008 \\ 0.983 \pm 0.033 \\ 0.397 \pm 0.007 \end{matrix}$ $\begin{array}{c} -0.127 \pm 0.008\\ 0.983 \pm 0.033\\ 0.397 \pm 0.007\end{array}$
masks (5.3)	${\begin{matrix} α = - 0.070 \pm 0.007 \\ β = 0.906 \pm 0.025 \\ σ = 0.212 \pm 0.006 \end{matrix}$ $\left\{ \begin{array}{l} \alpha = -0.070 \pm 0.007\\ \beta = 0.906 \pm 0.025\\ \sigma = 0.212 \pm 0.006\end{array}\right.$	$\begin{matrix} - 0.081 \pm 0.006 \\ 0.887 \pm 0.026 \\ 0.203 \pm 0.006 \end{matrix}$ $\begin{array}{c}-0.081 \pm 0.006\\ 0.887 \pm 0.026 \\ 0.203 \pm 0.006\end{array}$	$\begin{matrix} - 0.094 \pm 0.006 \\ 0.860 \pm 0.024 \\ 0.177 \pm 0.005 \end{matrix}$ $\begin{array}{c} -0.094 \pm 0.006\\ 0.860 \pm 0.024\\ 0.177 \pm 0.005\end{array}$	$\begin{matrix} - 0.095 \pm 0.008 \\ 1.020 \pm 0.033 \\ 0.393 \pm 0.008 \end{matrix}$ $\begin{array}{c}-0.095 \pm 0.008\\ 1.020 \pm 0.033\\ 0.393 \pm 0.008\end{array}$
BMO + prior (6)	${\begin{matrix} α = - 0.116 \pm 0.005 \\ β = 0.732 \pm 0.017 \\ σ = 0.094 \pm 0.005 \end{matrix}$ $\left\{ \begin{array}{l} \alpha = -0.116 \pm 0.005\\ \beta = 0.732 \pm 0.017\\ \sigma = 0.094 \pm 0.005\end{array}\right.$	$\begin{matrix} - 0.124 \pm 0.004 \\ 0.727 \pm 0.017 \\ 0.092 \pm 0.005 \end{matrix}$ $\begin{array}{c} -0.124 \pm 0.004\\ 0.727 \pm 0.017\\ 0.092 \pm 0.005\end{array}$	$\begin{matrix} - 0.135 \pm 0.004 \\ 0.714 \pm 0.016 \\ 0.082 \pm 0.006 \end{matrix}$ $\begin{array}{c} -0.135 \pm 0.004\\ 0.714 \pm 0.016 \\ 0.082 \pm 0.006\end{array}$	$\begin{matrix} - 0.091 \pm 0.007 \\ 0.953 \pm 0.030 \\ 0.414 \pm 0.006 \end{matrix}$ $\begin{array}{c} -0.091 \pm 0.007\\ 0.953 \pm 0.030\\ 0.414 \pm 0.006\end{array}$
$\begin{matrix} photo- z robust + \\ AMICO -like + \\ masks + (7) \\ BMO + prior \end{matrix}$ $\begin{array}{l} \text{ photo-}z \text{ robust} \,+\\ {\mathtt{AMICO}}\text{-like} \,+ \\ \text{ masks} + {\quad\quad\quad}(7)\\ \text{ BMO} + \text{ prior} \end{array}$	${\begin{matrix} α = - 0.135 \pm 0.006 \\ β = 0.696 \pm 0.022 \\ σ = 0.108 \pm 0.006 \end{matrix}$ $\left\{\begin{array}{l} \alpha = -0.135 \pm 0.006\\ \beta = 0.696 \pm 0.022\\ \sigma = 0.108 \pm 0.006 \end{array}\right.$	$\begin{matrix} - 0.154 \pm 0.005 \\ 0.673 \pm 0.023 \\ 0.099 \pm 0.006 \end{matrix}$ $\begin{array}{c} -0.154 \pm 0.005\\ 0.673 \pm 0.023 \\ 0.099 \pm 0.006\end{array}$	$\begin{matrix} - 0.154 \pm 0.006 \\ 0.672 \pm 0.023 \\ 0.099 \pm 0.006 \end{matrix}$ $\begin{array}{c} -0.154 \pm 0.006\\ 0.672 \pm 0.023\\ 0.099 \pm 0.006\end{array}$	$\begin{matrix} - 0.097 \pm 0.010 \\ 0.924 \pm 0.043 \\ 0.473 \pm 0.008 \end{matrix}$ $\begin{array}{c} -0.097 \pm 0.010\\ 0.924 \pm 0.043\\ 0.473 \pm 0.008 \end{array}$

Notes. The intercept α, slope β, and intrinsic scatter σ of the regression line (see Eq. (22)) are reported for the median, CBI, mean, or ML estimators. Uncertainties are reported as the standard deviation of the marginalised parameter distribution.

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