A vertically orientated dark matter halo marks a flip of the Galactic disc

Unveiling the 3D shape of the Milky Way’s dark-matter halo is critical to understanding its formation history. We created an innovative dynamical model that makes minimal assumptions about the internal dynamical structures and accommodates a highly flexible triaxial DM halo. By applying the method to 6D phase-space data of K-giant stars from LAMOST + Gaia, we robustly determined the 3D dark-matter distribution of the Milky Way out to approximately 50 kpc. We discovered a triaxial, nearly oblate dark-matter halo with q DM = Z / X = 0.92 ± 0.08, p DM = Y / X = 0.8 ± 0.2 on average within 50 kpc, where the Z -axis is defined perpendicular to the stellar disc. The axes ratio q DM > p DM is strongly preferred; the long-intermediate axis plane of the dark-matter halo is unexpectedly vertical to the Galactic disc, yet aligned with the ‘plane of satellites’. This striking configuration suggests that the Galactic disc (and the inner halo) has flipped, likely torqued by minor mergers, from an original alignment with the outer dark-matter halo and satellite plane, as is supported by Milky Way analogues from Auriga and TNG50. By allowing q DM ( r ) and p DM ( r ) to vary with radii, we find tentative evidence that the dark-matter halo is twisted. This agrees alignment with the disc in the inner regions and transitions to a vertical orientation at r > 20 kpc, supporting the disc flip scenario prediction. Such disc reorientation is non-trivial, yet its physical mechanism is straightforward to comprehend and naturally originates a vertical satellite plane. Our findings offer a unified framework that links dark-matter halo orientation, satellite alignment, and disc evolution, reinforcing the internal consistency of the Milky Way in the Λ cold dark matter model.