Cloud tomography with proper-motion-based distances

Each dot is a star placed at a random phase on a randomly chosen x2 orbit in the nuclear stellar disc (nested ellipses elongated perpendicular to the Galactic bar; Nieuwmunster et al. 2024), with positions drawn from the NSD's actual measured radial density profile (circular by default). The "NSD ellipticity" slider flattens that density map — and, since the stars set the potential, the same axis ratio also sets how flattened the x2 orbits themselves are; the two aren't independent knobs. Color shows a velocity each star would have — toggle below between plane-of-sky (proper motion) and line-of-sight (radial velocity). On the right, the same stars are plotted the way you'd actually observe them: transverse sky position (∝ Galactic longitude l) vs. velocity. The open, parallelogram-like loop that traces out is the signature of the barred orbit family — and because it's a loop rather than a scatter, a star's (l, v) pair still tells you which single orbit and phase it sits on, hence its unique 3D location. Click a star in either panel to highlight it in both. Turn on the dust cloud below to see the flip side: stars behind a thick enough cloud along the line of sight are extinguished, just as real dust column density is read off from how stars are dimmed and reddened behind it (the technique behind Vasini et al. 2026). The icon at the panel's edge marks the direction back to the Sun, and dashed lines mark Galactic longitude l (this face-on plane is everywhere at b ≈ 0, so there's no b to grid). The panel is drawn as seen from the North Galactic Pole, matching the Milky Way's real (clockwise) sense of rotation, with the bar's near side correctly toward positive l. The cloud now has its own line-of-sight depth, independent of its size on the sky — drag it, resize it, and use "zoom to the cloud's sightline" to isolate just the stars along that one pencil beam, in front of and behind it. The two extra panels below are tomography diagnostics: a histogram of how many stars sit at each line-of-sight distance, stacked by how extinguished each one is (white = barely dimmed, black = nearly invisible), and an extinction (mag) vs. proper-motion plot — for a star at fractional depth d into the cloud, A = A_cloud × d. It's proper motion, not radial velocity, that does the work here: Vasini et al. 2026's actual method uses the NSD's rotation — near side moving toward +l, far side toward −l — as a proxy for distance, since a star's proper motion parallel to the plane barely depends on where along the line of sight it sits.