Characterising galaxy cluster scaling relations as cosmic isotropy tracers using FLAMINGO simulations

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Table 2.

Best-fit parameters of the scaling relations using the full lightcone sample.

Relation (Y − X)	A_YX	B_YX	σ_intr	$A_{YX}^{(s)}$ $A_{YX}^{(s)}$	$B_{YX}^{(s)}$ $B_{YX}^{(s)}$	σ_intr^(s)	σ_tot^(s)	Configuration
L_X − T	$1 . 770_{- 0.032}^{+ 0.041}$ $1.770^{+0.041}_{-0.032}$	$2 . 220_{- 0.078}^{+ 0.070}$ $2.220^{+0.070}_{-0.078}$	$0 . 164_{- 0.009}^{+ 0.012}$ $0.164^{+0.012}_{-0.009}$	$1 . 762_{- 0.040}^{+ 0.049}$ $1.762^{+0.049}_{-0.040}$	$2 . 215_{- 0.084}^{+ 0.081}$ $2.215^{+0.081}_{-0.084}$	$0 . 240_{- 0.018}^{+ 0.018}$ $0.240^{+0.018}_{-0.018}$	$0 . 251_{- 0.016}^{+ 0.018}$ $0.251^{+0.018}_{-0.016}$	M21
L_X − T	$1 . 754_{- 0.024}^{+ 0.016}$ $1.754^{+0.016}_{-0.024}$	$2 . 500_{- 0.069}^{+ 0.063}$ $2.500^{+0.063}_{-0.069}$	$0 . 154_{- 0.004}^{+ 0.012}$ $0.154^{+0.012}_{-0.004}$	$1 . 738_{- 0.040}^{+ 0.032}$ $1.738^{+0.032}_{-0.040}$	$2 . 506_{- 0.087}^{+ 0.069}$ $2.506^{+0.069}_{-0.087}$	$0 . 228_{- 0.018}^{+ 0.012}$ $0.228^{+0.012}_{-0.018}$	$0 . 243_{- 0.015}^{+ 0.012}$ $0.243^{+0.012}_{-0.015}$	MCMC

Y_SZ − T	$1 . 094_{- 0.020}^{+ 0.015}$ $1.094^{+0.015}_{-0.020}$	$2 . 441_{- 0.033}^{+ 0.030}$ $2.441^{+0.030}_{-0.033}$	$0 . 110_{- 0.006}^{+ 0.006}$ $0.110^{+0.006}_{-0.006}$	$1 . 081_{- 0.025}^{+ 0.030}$ $1.081^{+0.030}_{-0.025}$	$2 . 448_{- 0.054}^{+ 0.051}$ $2.448^{+0.051}_{-0.054}$	$0 . 156_{- 0.012}^{+ 0.012}$ $0.156^{+0.012}_{-0.012}$	$0 . 189_{- 0.009}^{+ 0.010}$ $0.189^{+0.010}_{-0.009}$	M21
Y_SZ − T	$1 . 102_{- 0.015}^{+ 0.015}$ $1.102^{+0.015}_{-0.015}$	$2 . 748_{- 0.029}^{+ 0.032}$ $2.748^{+0.032}_{-0.029}$	$0 . 108_{- 0.004}^{+ 0.004}$ $0.108^{+0.004}_{-0.004}$	$1 . 096_{- 0.020}^{+ 0.020}$ $1.096^{+0.020}_{-0.020}$	$2 . 763_{- 0.048}^{+ 0.048}$ $2.763^{+0.048}_{-0.048}$	$0 . 156_{- 0.006}^{+ 0.012}$ $0.156^{+0.012}_{-0.006}$	$0 . 195_{- 0.009}^{+ 0.009}$ $0.195^{+0.009}_{-0.009}$	MCMC

M_gas − T	$1 . 079_{- 0.010}^{+ 0.010}$ $1.079^{+0.010}_{-0.010}$	$1 . 827_{- 0.039}^{+ 0.039}$ $1.827^{+0.039}_{-0.039}$	$0 . 080_{- 0.006}^{+ 0.006}$ $0.080^{+0.006}_{-0.006}$	−	−	−	−	M21
M_gas − T	$1 . 086_{- 0.005}^{+ 0.010}$ $1.086^{+0.010}_{-0.005}$	$2 . 050_{- 0.039}^{+ 0.039}$ $2.050^{+0.039}_{-0.039}$	$0 . 078_{- 0.008}^{+ 0.004}$ $0.078^{+0.004}_{-0.008}$	−	−	−	−	MCMC

Notes. All fits are performed using the reduced χ² regression method (Sect. 3.1.1). The reported uncertainties in A, B, and σ_intr correspond to the 16th and 84th percentiles across all lightcones. Superscript ^(s) denotes fits after injecting scatter to match the M21 sample (Sect. 2.4). The ‘Configuration’ column indicates the number of clusters and fitting constants used, as defined in Table 1.

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