A Vertically Orientated Dark Matter Halo Marks a Flip of the Galactic Disk

TL;DR

The paper addresses how the Milky Way's dark-matter halo is shaped and oriented in 3D, and how this relates to the planetesimal satellite plane. It introduces a data-driven empirical triaxial orbit-superposition method that allows the DM halo axis ratios to vary with radius, and applies it to 6D phase-space data from 14,497 LAMOST+Gaia halo K-giants out to ~50 kpc. The authors find a triaxial, nearly oblate halo with $q_{ m DM}=0.92\\pm0.08$ and $p_{ m DM}=0.80\pm0.20$, and present tentative evidence for a radial twist in which the inner halo aligns with the disk while the outer halo becomes vertically oriented, consistent with a disk flip driven by minor mergers. By comparing to MW-like systems in TNG50 and Auriga simulations, they show that the MW configuration, including a vertically aligned halo and a plane of satellites, can arise from disk tilts and minor-merger histories under ΛCDM, though it is a relatively rare outcome. The study provides a coherent framework linking halo orientation, satellite planes, and disk evolution, with significant implications for MW formation and dynamical modelling.

Abstract

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 with minimal assumptions on 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 determine the 3D dark-matter distribution of the Milky Way out to approximately $50$ kpc. We discover a triaxial, nearly oblate dark-matter halo with $q_{\rm DM} = Z/X= 0.92\pm0.08$, $p_{\rm DM} = Y/X= 0.8\pm0.2$ averagely within 50 kpc, where $Z$ axis is defined perpendicular to the stellar disk. The axes ratio $q_{\rm DM} > p_{\rm DM}$ is strongly preferred; the long-intermediate axis plane of the dark-matter halo is unexpectedly vertical to the Galactic disk, yet aligned with the `plane of satellites'. This striking configuration suggests that the Galactic disk (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 supported by Milky Way analogues from Auriga and TNG50. By allowing $q_{\rm DM}(r)$ and $p_{\rm DM}(r)$ vary with radii, we find tentative evidence that the dark-matter halo is twisted, that it agrees alignment with the disk in the inner regions and transitions to a vertical orientation at $r\gtrsim 20$ kpc, supporting the disk flip scenario prediction. Such disk 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 disk evolution, reinforcing the internal consistency of the Milky Way in $Λ$CDM model.

Figures (17)

• Figure 1: The density of stars in the parameter phase of circularity $\lambda_z$ versus metallicity [Fe/H]. We first remove the disk stars with circularity $\lambda_z > 0.8$, then also remove the group of stars with $\lambda_z>0.3$ and $[\rm Fe/H]>-1.2$. The rest is kept as halo stars in our sample.
• Figure 2: The K giants in our final sample of smooth halo in the northern hemisphere, colored by the weights of particles obtained by correction of selection function. The sample can be taken as complete in the $R_{\rm gc}-z_{\rm gc}$ space after correction of selection function.
• Figure 3: The spatial binning scheme we used for comparing the velocity distributions of the model and data. We divide the model into $7\times 5$ spatial bins along $r\times \theta$, and calculate the likelihood of stars located within each bin by comparing to the velocity distributions of the model in the corresponding bin.
• Figure 4: The model constraints on the parameters of the underlying DM distribution $\rho_0$, $r_s$, $\gamma$, $q_{\rm DM}$, and $p_{\rm DM}$. The three parameters determining the radial distribution, $\rho_0$, $r_s$, $\gamma$, are degenerate due to the lack of data points at $r<8$ kpc and $r>50$ kpc. However the 3D DM distribution within our data coverage ($r\lesssim 50$ kpc) are well constrained by our model, with a significant role played by the density distribution $\chi^2_{\rm den}$.
• Figure 5: The enclosed mass profiles and rotation curve we obtained for the Milky Way. The solid line is the average of models within the $1\sigma$ confidence level, while the dashed curves are the upper and lower boundary.