In search of the Local Universe dynamical homogeneity scale with CF4++ peculiar velocities

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Volume 701 (September 2025)

A&A, 701 (2025) A187

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Table 1.

Bulk flow measurements in the literature using supernovae or galaxy peculiar velocity datasets.

Work: Selection function	Dataset(s)	Measurement within distance range [km s⁻¹]:
0−50 h⁻¹ Mpc	51−100 h⁻¹ Mpc	101−150 h⁻¹ Mpc	151−200 h⁻¹ Mpc

ΛCDM prediction (σ_BF)		$476_{- 220}^{+ 258} - 258_{- 112}^{+ 133}$ $476^{+258}_{-220}{-}258^{+133}_{-112}$	$256_{- 112}^{+ 132} - 184_{- 80}^{+ 94}$ $256^{+132}_{-112}{-}184^{+94}_{-80}$	$183_{- 80}^{+ 94} - 142_{- 62}^{+ 73}$ $183^{+94}_{-80}{-}142^{+73}_{-62}$	$141_{- 62}^{+ 72} - 115_{- 36}^{+ 43}$ $141^{+72}_{-62}{-}115^{+43}_{-36}$
W09: Gaussian	SFI++, SN, etc.	407 ± 81 (50)
C11: Top-Hat	Union 2 SN		250 ± 190 (100)
D11: Top-Hat	Union 2 SN			188 ± 119 (150)
N11: Top-Hat	SFI++	333 ± 38 (40)
T12: Gaussian	A1SN	249 ± 76 (50)
M13: Top-Hat	SFI++, A1SN, etc.	310 (50)
H14: Gaussian	2MTF	292 ± 28 (40)
C15: Gaussian	2M++	227 ± 25 (50)
H15: Top-Hat	CF2	250 ± 21 (50)		239 ± 38 (150)
S16: Hemisphere	6dFGSv	248 ± 58 (50)	243 ± 58 (70)
Q19: Top-Hat	2MTF, CF3	259 ± 15 (37)
B20: Gaussian	A2SN, SFI++	252 ± 11 (40)
S21: Top-Hat	DSS	245 ± 32 (30)
Q21: Top-Hat	2MTF	332 ± 27 (30)
QP21: Top-Hat	CF4TF	376 ± 23 (35)
A23: Top-Hat	ALFAFA	401 ± 151 (21)
W23: –	CF4			395 ± 29 (150)	427 ± 37 (200)
WH23: Top-Hat	CF4	408 ± 165 (49)			428 ± 108 (173)
B24: –	CF4				227 ± 11 (175)
L24: –	SN-Pantheon+		268 ± 119 (61)
This work: Top-Hat	CF4++	152 ± 15 (50)	254 ± 16 (100)	315 ± 40 (150)	351 ± 109 (200)

Average bulk flow and		324 ± 28 (37)	275 ± 87 (84)	264 ± 70 (140)	355 ± 66 (183)
Deviation from ΛCDM		0.21 σ	0.53σ	1.12σ	2.54σ
Average CF4++ and		298 ± 20 (30)	191 ± 16 (80)	301 ± 28 (130)	326 ± 83 (180)
Deviation from ΛCDM		0.07 σ	0.16σ	1.70σ	1.93σ

Notes. The radii, listed in brackets, are the stated values of their respective articles in units of h⁻¹ Mpc. Those with selection functions that are non top-hat, when plotted in Figure 9, are modified using the methodology described in Section 4. The ΛCDM and 1σ confidence values quoted at the top of the table are the measurement ranges expected in their stated distance intervals. The bottom four rows of this table, respectively, calculate within each 50 h⁻¹ Mpc interval: (1) the average bulk flow measurement across the literature (BF_lit) (assuming top-hat radii); (3) the average CF4++ measurement (BF_CF4 + +); respectively, the tension of (2) the BF_lit and (4) the BF_CF4 + + measurement with the ΛCDM prediction at the listed effective radius.

References: (W09) Watkins et al. (2009); (C11) Colin et al. (2011); (D11) Dai et al. (2011); (N11) Nusser & Davis (2011); (T12) Turnbull et al. (2012); (M13) Ma & Scott (2013); (H14) Hong et al. (2014); (C15) Carrick et al. (2015); (H15) Hoffman et al. (2015); (S16) Scrimgeour et al. (2016); (Q19) Qin et al. (2019); (B20) Boruah et al. (2020); (S21) Stahl et al. (2021); (Q21) Qin (2021); (QP21) Qin et al. (2021); (A23) Avila et al. (2023); (W23) Watkins et al. (2023); (WH23) Whitford et al. (2023); (B24) Boubel et al. (2024); (L24) Lopes et al. (2024).

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