Investigating the origin of the Milky Way streams - A revised look at their orbital pole distribution in light of precession effects

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Volume 702 (October 2025)

A&A, 702 (2025) A62

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Table 2.

Bernoulli probability for the simulation sample.

Distance cut	P (N = 100)	P (N = 300)	P (N = 500)
d < 100 kpc	$0 . 92_{- 0.19}^{+ 0.00}$ $0.92^{+0.00}_{-0.19}$ ( $(0 . 09_{- 0.00}^{+ 0.24}) σ$ $(0.09^{+0.24}_{-0.00})\sigma$ )	$0 . 98_{- 0.19}^{+ 0.00}$ $0.98^{+0.00}_{-0.19}$ ( $(0 . 03_{- 0.00}^{+ 0.24}) σ$ $(0.03^{+0.24}_{-0.00})\sigma$ )	$0 . 98_{- 0.01}^{+ 0.00}$ $0.98^{+0.00}_{-0.01}$ ( $(0 . 02_{- 0.00}^{+ 0.02}) σ$ $(0.02^{+0.02}_{-0.00})\sigma$ )
d < 150 kpc	$(2 . 41_{- 0.00}^{+ 14.80}) \times 10^{- 2}$ $(2.41^{+14.80}_{-0.00})\times 10^{-2}$ ( $(2 . 26_{- 0.89}^{+ 0.00}) σ$ $(2.26^{+0.00}_{-0.89})\sigma$ )	$(3 . 74_{- 0.00}^{+ 13.39}) \times 10^{- 3}$ $(3.74^{+13.39}_{-0.00})\times 10^{-3}$ ( $(2 . 90_{- 0.52}^{+ 0.00}) σ$ $(2.90^{+0.00}_{-0.52})\sigma$ )	$(5 . 08_{- 0.00}^{+ 15.01}) \times 10^{- 4}$ $(5.08^{+15.01}_{-0.00})\times 10^{-4}$ ( $(3 . 48_{- 0.39}^{+ 0.00}) σ$ $(3.48^{+0.00}_{-0.39})\sigma$ )
d < 200 kpc	$(1 . 78_{- 0.00}^{+ 10.72}) \times 10^{- 2}$ $(1.78^{+10.72}_{-0.00})\times 10^{-2}$ ( $(2 . 37_{- 0.83}^{+ 0.00}) σ$ $(2.37^{+0.00}_{-0.83})\sigma$ )	$(1 . 99_{- 0.00}^{+ 7.81}) \times 10^{- 3}$ $(1.99^{+7.81}_{-0.00})\times 10^{-3}$ ( $(3 . 09_{- 0.51}^{+ 0.00}) σ$ $(3.09^{+0.00}_{-0.51})\sigma$ )	$(2 . 70_{- 0.00}^{+ 8.60}) \times 10^{- 4}$ $(2.70^{+8.60}_{-0.00})\times 10^{-4}$ ( $(3 . 64_{- 0.39}^{+ 0.00}) σ$ $(3.64^{+0.00}_{-0.39})\sigma$ )
d < 350 kpc	$(8 . 43_{- 0.00}^{+ 31.07}) \times 10^{- 3}$ $(8.43^{+31.07}_{-0.00})\times 10^{-3}$ ( $(2 . 63_{- 0.58}^{+ 0.00}) σ$ $(2.63^{+0.00}_{-0.58})\sigma$ )	$(1 . 36_{- 0.00}^{+ 7.34}) \times 10^{- 4}$ $(1.36^{+7.34}_{-0.00})\times 10^{-4}$ ( $(3 . 82_{- 0.49}^{+ 0.00}) σ$ $(3.82^{+0.00}_{-0.49})\sigma$ )	$(1 . 74_{- 0.00}^{+ 3.45}) \times 10^{- 6}$ $(1.74^{+3.45}_{-0.00})\times 10^{-6}$ ( $(4 . 78_{- 0.22}^{+ 0.00}) σ$ $(4.78^{+0.00}_{-0.22})\sigma$ )

Notes. The P values represent the probability that, for a randomly selected sample, a homogeneous pole distribution provides the same (or higher) fraction of VPOS members as the pole distribution of the Banik et al. (2022) simulation. For example, according to this method, there is a $(0 . 84_{- 0.00}^{+ 3.11}) %$ $(0.84^{+3.11}_{-0.00})\%$ chance that, if 100 elements are randomly drawn from a homogeneous distribution with d < 350 kpc, these have the same or a higher fraction of VPOS members than 100 elements drawn from the anisotropic distribution of Banik et al. (2022) at this distance. The corresponding number of standard deviations is also indicated in parentheses. This probability was obtained at different upper distance cuts (d< ) and for different sample sizes (N), considering only one possible orbital sense (half l-parameter space). In these simulations, a lower distance cut in the z direction of z > 50 kpc was imposed to remove the disc contamination.

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