The math, step by step

Everything starts from the 6-dimensional Gaia solution: position, parallax, proper motion, and the RVS line-of-sight velocity. The parent selection (ADQL on gaiadr3.gaia_source) requires a measured radial velocity, $\varpi > 0$, $\varpi/\sigma_\varpi > 5$ and finite proper motions — about 33.8 million stars.

Gaia parallaxes carry a small colour-, magnitude- and position-dependent bias. The release applies the Lindegren et al. (2021) per-star correction $\varpi_{\rm corr} = \varpi - z_5(G,\ \nu_{\rm eff},\ \beta)$ inside its validity window (6 < G < 21).

Inverting a noisy parallax biases distances, so the release adopts the Bailer-Jones et al. (2021) photogeometric posterior where available (zero-point-corrected inverse parallax otherwise, and only as a sensitivity check). The stored 16th/84th percentiles drive asymmetric (split-normal) draws in the Monte Carlo.

The observables become a Cartesian position and velocity in the Galactocentric frame (astropy conventions):

where $\mathbf{R}$ rotates the galactic centre to $+\hat{\mathbf{x}}$, $\mathbf{H}$ tilts for the Sun's height $z_\odot$, and $\mathbf{v}_\odot = (U,\ V_c + V,\ W)$. The release's default frame: $R_0 = 8.178\ {\rm kpc}$ (GRAVITY 2019), $z_\odot = 25\ {\rm pc}$, $V_c = 229\ {\rm km\,s^{-1}}$(Eilers 2019, consistent with the adopted potential), Schönrich (2010) solar motion. Try the paper's sensitivity variants:

This is a total speed — not the azimuthal velocity used by low-$v_\phi$ selections (the paper finds zero overlap with Filion et al. 2025). A typical disc star near the Sun has $V_{\rm GRF} \approx 240$ km s⁻¹; the catalogue threshold of 25 km s⁻¹ is about 10% of the local circular speed.

A point estimate is not enough near a threshold. The release draws (ϖ, μα*, μδ) from the full Gaia covariance (Cholesky of the 3×3 submatrix), v_r from its Gaussian error, and distance from the asymmetric Bailer-Jones posterior — adaptively 500 / 5,000 / 10,000 realisations per star (seed 20260502) — and defines

Tiers: A P>0.95 · B 0.84<P≤0.95 · C 0.5<P≤0.84 · Dpoint-estimate < 25 but P≤0.5. The sum of (1−P) over a tier estimates its contamination: 30.8 ± 5.3 expected false positives among the 541 Tier A+B stars.

Energy conservation along an orbit in a static potential reads $E = \tfrac{1}{2}v^2 + \Phi(\mathbf{r})$. Catching a star with $v \approx 0$ means catching it at a turning point with specific angular momentum $L_z = x v_y - y v_x \approx 0$. In any centrally concentrated potential such a star must fall nearly radially toward the inner Galaxy: eccentricity $e = (R_{\rm apo}-R_{\rm peri})/(R_{\rm apo}+R_{\rm peri}) \to 1$. The paper is explicit that this is largely a kinematic corollary of the selection — the catalogue's value is which stars are in this state, with calibrated probabilities.

Watch this star's orbit in the 3D viewer →