A million orbits: the same score. Nine dark matter halos: nine orchestras without a conductor. All musicians play from the same notes, but in each hall the music sounds different: sometimes in tune, sometimes out of sync. Likewise, satellite galaxies falling into a host halo follow orbits that depend not only on mass but also on the shape of the invisible stage.
Most satellite orbit calculations assume spherical potentials because it is simpler: energy and angular momentum fully determine the orbit, and turning points are found analytically. But cosmological simulations show that dark matter halos are typically triaxial, with the minor-to-major axis ratio around 2/3. The authors constructed nine static halos with the same virial mass of $10^{12}$ solar masses and the same spherically averaged density profile, but different triaxiality and oblateness. Through each halo, they ran the same million satellite orbits drawn from a cosmological infall distribution.
The result was twofold. The median distributions of pericenters, apocenters, and periods barely change with halo shape: the shift does not exceed 2% for typical shapes. But the scatter of successive pericenters of a single orbit is 5–23% depending on shape, and it does not depend on orbital energy. The minimum pericenter over a Hubble time decreases systematically: on average by 5–12%, and in the most flattened halos by up to 21%. In strongly flattened halos, the distribution of minimum pericenters shows a peak near 0.1 virial radius.
Reconstructing the orbit using a spherical potential instead of the true triaxial one yields a median position error of 0.1 virial radius within 2–4 billion years. For the dwarf galaxy Triangulum II, the pericenter uncertainty due to unknown halo shape and orientation reaches ~50%, which is five times larger than the stated error and an order of magnitude larger than the shift caused by the Large Magellanic Cloud.
Now the score has been reread. The average notes have not changed, but each musician hears them differently. Ignoring the halo shape means systematically underestimating how deep satellites dive toward the center, and thus making errors in their disruption rates and star formation quenching. An orchestra without a conductor plays the same symphony, but each time with new accents.
In the most flattened halos, the distribution of minimum pericenters forms a peak near 0.1 virial radius, although no such peak exists in the spherical case. This peak arises from chaotic orbits that dive deeper toward the center.