Table A.1
Phase-space hypervolume of each dynamical family in standardised action–energy space.
| Family | N | log10 V | V | Condition number |
|---|---|---|---|---|
| Sgr | 5 | −10.25 | 5.67 × 10−11 | 3.3 × 1016 |
| lowE | 11 | −4.16 | 6.86 × 10−5 | 2.2 × 102 |
| inSitu | 20 | −3.62 | 2.40 × 10−4 | 1.6 × 102 |
| H99 | 7 | −2.53 | 2.93 × 10−3 | 6.2 × 102 |
| GSE | 19 | −2.14 | 7.20 × 10−3 | 2.4 × 102 |
| Seq | 7 | −1.91 | 1.24 × 10−2 | 2.1 × 104 |
The volume is defined as ![Mathematical equation: $\[\sqrt{\operatorname{det}(\Sigma)}\]$](/articles/aa/full_html/2026/05/aa59820-26/aa59820-26-eq65.png)
, where Σ is the covariance matrix of (EJ,int, Lz, L⊥, Jr, [Fe/H]). The extreme condition number for Sagittarius reflects the small sample size and near-linear alignment of its debris in action space; the volume estimate should therefore be interpreted qualitatively rather than as a precise geometric measurement.
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