Euclid preparation - LXVI. Impact of line-of-sight projections on the covariance between galaxy cluster multi-wavelength observable properties: insights from hydrodynamic simulations

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Volume 695 (March 2025)

A&A, 695 (2025) A282

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Table B.2.

Scatter and correlation coefficient matrix between z = 0.9 log-residuals of scaling relations.

	c_NFW	$c_{NFW}^{2 D}$ $c^{\mathrm{2D}}_{\mathrm{NFW}}$	$M_{NFW}^{2 D}$ $M^{\mathrm{2D}}_{\mathrm{NFW}}$	n	n^2D	M_★	$M_{★}^{2 D}$ $M_{\bigstar}^{\mathrm{2D}}$	Y	Y^2D	M_g	M_g^2D	M_g, 500c	$M_{g, 500 c}^{2 D}$ $M^{\mathrm{2D}}_{g,\mathrm{500c}}$	L_X	L_X^2D	L_X, 500c	$L_{X, 500 c}^{2 D}$ $L^{\mathrm{2D}}_{X,\mathrm{500c}}$	$L_{X, c e 500 c}^{2 D}$ $L^{\mathrm{2D}}_{X,ce\mathrm{500c}}$	T	T^2D	T_500c	$T_{500 c}^{2 D}$ $T^{\mathrm{2D}}_{\mathrm{500c}}$
c_NFW	0.32
$c_{NFW}^{2 D}$ $c^{\mathrm{2D}}_{\mathrm{NFW}}$	0.51	0.44
$M_{NFW}^{2 D}$ $M^{\mathrm{2D}}_{\mathrm{NFW}}$	−−	−−	0.21
n	−0.28	−−	−−	0.26
n^2D	−0.22	−0.34	0.51	0.70	0.31
M_★	0.37	−−	−−	−−	−−	0.08
$M_{★}^{2 D}$ $M_{\bigstar}^{\mathrm{2D}}$	−−	−0.31	0.78	−−	0.57	0.47	0.15
Y	0.34	0.27	−−	−0.23	−−	−−	−−	0.08
Y^2D	−−	−0.30	0.63	−−	0.32	−−	0.64	0.41	0.17
M_g	−0.29	−−	−−	0.23	0.21	−0.30	−−	0.40	0.20	0.05
M_g^2D	−−	−0.38	0.78	−−	0.53	−−	0.71	−−	0.79	−−	0.20
M_g, 500c	−−	0.41	−−	−−	−−	−0.28	−0.25	0.52	−−	0.44	−−	0.15
$M_{g, 500 c}^{2 D}$ $M^{\mathrm{2D}}_{g,\mathrm{500c}}$	−−	−0.24	0.80	−−	0.49	−−	0.67	−−	0.77	−−	0.96	−−	0.18
L_X	−0.20	−−	−−	0.26	−−	−−	−−	−−	−−	0.51	−−	0.51	−−	0.25
L_X^2D	−−	−−	0.42	0.26	0.48	−−	0.32	−−	0.22	0.44	0.39	0.35	0.44	0.79	0.28
L_X, 500c	−−	0.26	−−	−−	−−	−−	−−	0.32	−−	0.45	−−	0.73	−−	0.89	0.67	0.30
$L_{X, 500 c}^{2 D}$ $L^{\mathrm{2D}}_{X,\mathrm{500c}}$	−−	−−	0.23	0.23	0.29	−0.23	−−	0.23	−−	0.50	−−	0.59	0.22	0.87	0.86	0.87	0.28
$L_{X, c e 500 c}^{2 D}$ $L^{\mathrm{2D}}_{X,ce\mathrm{500c}}$	−0.31	−−	0.25	0.22	0.31	−0.30	−−	−−	−−	0.49	−−	0.58	0.24	0.69	0.75	0.65	0.85	0.31
T	0.52	0.40	−−	−0.22	−−	−−	−−	0.52	−−	−−	−−	0.33	−−	−−	−−	−−	−−	−−	0.22
T^2D	0.47	0.43	−−	−0.22	−0.28	−−	−−	0.50	−−	−−	−0.20	0.37	−−	−−	−0.28	−−	−−	−−	0.90	0.24
T_500c	0.52	0.35	−−	−0.21	−−	−−	−−	0.45	−−	−−	−−	0.21	−−	−−	−−	−−	−−	−−	0.95	0.84	0.22
$T_{500 c}^{2 D}$ $T^{\mathrm{2D}}_{\mathrm{500c}}$	0.48	0.41	−−	−0.21	−0.27	−−	−−	0.49	−−	−−	−−	0.34	−−	−−	−0.27	−−	−−	−−	0.90	0.98	0.86	0.23

Notes. Rows and columns are as in Table B.1.

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