A slightly oblate dark matter halo revealed by a retrograde precessing Galactic disk warp

The shape of the dark matter (DM) halo is key to understanding the hierarchical formation of the Galaxy. Despite extensive efforts in recent decades, however, its shape remains a matter of debate, with suggestions ranging from strongly oblate to prolate. Here, we present a new constraint on its present shape by directly measuring the evolution of the Galactic disk warp with time, as traced by accurate distance estimates and precise age determinations for about 2,600 classical Cepheids. We show that the Galactic warp is mildly precessing in a retrograde direction at a rate of $\omega = -2.1 \pm 0.5 ({\rm statistical}) \pm 0.6 ({\rm systematic})$ km s$^{-1}$ kpc$^{-1}$ for the outer disk over the Galactocentric radius [$7.5, 25$] kpc, decreasing with radius. This constrains the shape of the DM halo to be slightly oblate with a flattening (minor axis to major axis ratio) in the range $0.84 \le q_{\Phi} \le 0.96$. Given the young nature of the disk warp traced by Cepheids (less than 200 Myr), our approach directly measures the shape of the present-day DM halo. This measurement, combined with other measurements from older tracers, could provide vital constraints on the evolution of the DM halo and the assembly history of the Galaxy.