Table 2.
Ranges of the p-values of the KS tests between the distribution of the HVS phase-space coordinates in a spherical DM halo and those in different spheroidal halos.
| Phase-space | p-value | p-value | ||||
|---|---|---|---|---|---|---|
| coordinate | (spherical vs. prolate) | (spherical vs. oblate) | ||||
| qz = 1.4 | qz = 1.1 | qz = 1.05 | qz = 0.7 | qz = 0.9 | qz = 0.95 | |
| x | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| y | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| z | [0.99–1.00] | 1.00 | 1.00 | [0.88–1.00] | 1.00 | 1.00 |
| r | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| ϑ | [0.94–1.00] | 1.00 | 1.00 | [0.71–0.99] | 1.00 | 1.00 |
| vx | [0.98–1.00] | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| vy | [0.98–1.00] | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| vz | [0.93–1.00] | 1.00 | 1.00 | [0.76–0.99] | 1.00 | 1.00 |
| vr | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| vt = |vϑ| | [6 × 10−22–5 × 10−14] | [2 × 10−4–0.01] | [0.06–0.44] | [7 × 10−21–6 × 10−11] | [8 × 10−4–0.04] | [0.11–0.47] |
Notes. Each entry shows the ranges of p-values obtained from a sample of 50 series of mock catalogs A. Each series is made of a spherical halo and spheroidal halos with axial symmetry about the z axis with six different values of the triaxiality parameter qz. Column (1): HVS phase-space coordinate in the galactocentric reference frame. Columns (2)–(4): p-value of the KS test for a spherical halo compared against a prolate halo (with qz = 1.4, qz = 1.1, qz = 1.05). Columns (5)–(7): p-value of the KS test for a spherical halo compared against an oblate halo (with qz = 0.7, qz = 0.9, qz = 0.95). A single p-value is shown instead of a p-value range when the relative difference between the limits of the p-value interval is smaller than 10−2. With the adopted 5% significance level, p-values smaller than 5% indicate that the compared distributions are not drawn from the same parent distribution, implying that the corresponding phase-space variable can be an indicator of the shape of the DM halo.
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