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

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Table 4.

Summary of bulk flow results from the FLAMINGO lightcones for different scaling relations and redshift ranges in direct comparison with the observed values from M21.

Relation	Redshift Range	No scatter u_bf (km s⁻¹)	Matched scatter u_bf (km s⁻¹)	FLAMINGO \|⟨v⟩\| (km s⁻¹)	M21 observed u_bf (km s⁻¹)	p-value of M21 (σ)	p-value of M21 (σ) matched scatter
L_X − T	z < 0.07	$315_{- 131}^{+ 262}$ $315^{+262}_{-131}$	$414_{- 169}^{+ 263}$ $414^{+263}_{-169}$	$86_{- 35}^{+ 40}$ $86^{+40}_{-35}$	$1100_{- 410}^{+ 410}$ $1100_{-410}^{+410}$	^a 0.0067 (2.71σ)	^a 0.0081 (2.65σ)
	z < 0.10	$315_{- 131}^{+ 260}$ $315^{+260}_{-131}$	$415_{- 172}^{+ 260}$ $415^{+260}_{-172}$	$75_{- 30}^{+ 36}$ $75^{+36}_{-30}$	$1080_{- 380}^{+ 380}$ $1080^{+380}_{-380}$	0.0082 (2.64σ)	0.0067 (2.72σ)
	z < 0.13	$313_{- 130}^{+ 263}$ $313^{+263}_{-130}$	$417_{- 172}^{+ 261}$ $417^{+261}_{-172}$	$68_{- 27}^{+ 34}$ $68^{+34}_{-27}$	–	–	–

Y_SZ − T	z < 0.07	$164_{- 56}^{+ 119}$ $164^{+119}_{-56}$	$264_{- 83}^{+ 170}$ $264^{+170}_{-83}$	$86_{- 35}^{+ 40}$ $86^{+40}_{-35}$	$1060_{- 390}^{+ 390}$ $1060^{+390}_{-390}$	3.2 × 10⁻⁶ (4.66σ)	5.8 × 10⁻⁴ (3.44σ)
	z < 0.10	$164_{- 56}^{+ 119}$ $164^{+119}_{-56}$	$264_{- 81}^{+ 166}$ $264^{+166}_{-81}$	$75_{- 30}^{+ 36}$ $75^{+36}_{-30}$	$1020_{- 380}^{+ 380}$ $1020^{+380}_{-380}$	3.5 × 10⁻⁶ (4.64σ)	0.0011 (3.26σ)
	z < 0.13	$164_{- 56}^{+ 117}$ $164^{+117}_{-56}$	$264_{- 82}^{+ 172}$ $264^{+172}_{-82}$	$68_{- 27}^{+ 34}$ $68^{+34}_{-27}$	–	–	–

M_gas − T	z < 0.07	$158_{- 73}^{+ 129}$ $158^{+129}_{-73}$	–	$86_{- 35}^{+ 40}$ $86^{+40}_{-35}$	–	–	–
	z < 0.10	$158_{- 73}^{+ 130}$ $158^{+130}_{-73}$	–	$75_{- 30}^{+ 36}$ $75^{+36}_{-30}$	–	–	–
	z < 0.13	$158_{- 72}^{+ 130}$ $158^{+130}_{-72}$	–	$68_{- 27}^{+ 34}$ $68^{+34}_{-27}$	–	–	–

L_X − T + Y_SZ − T	z < 0.07	–	–	–	–	^a 5.0 × 10⁻⁵ (4.05σ)	^a 3.6 × 10⁻⁴ (3.57σ)
Combined	z < 0.10	–	–	–	–	4.5 × 10⁻⁵ (4.08σ)	3.8 × 10⁻⁴ (3.56σ)

Notes.

^(a)

The columns show the fitted bulk flow amplitudes, u_bf (with and without matched scatter), the actual bulk peculiar velocity in FLAMINGO (|⟨v⟩|), the observed M21 values, and the resulting p-values (with Gaussian-equivalent significance in parentheses). Results are reported for three redshift shells and for the combined L_X − T + Y_SZ − T analysis. Dashes indicate configurations not evaluated. Precisely, the L_X − T bulk flow in M21 is measured in z < 0.06; however, this difference is negligible.

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