Constraining the Tilt of the Milky Way's Dark Matter Halo with the Sagittarius Stream

Recent studies have suggested that the Milky Way (MW)'s Dark Matter (DM) halo may be significantly tilted with respect to its central stellar disk, a feature that might be linked to its formation history. In this work, we demonstrate a method of constraining the orientation of the minor axis of the DM halo using the angle and frequency variables. This method is complementary to other traditional techniques, such as orbit fitting. We first test the method using a simulated tidal stream evolving in a realistic environment inside an MW-mass host from the FIRE cosmological simulation, showing that the theoretical description of a stream in the action-angle-frequency formalism still holds for a realistic dwarf galaxy stream in a cosmological potential. Utilizing the slopes of the line in angle and frequency space, we show that the correct rotation frame yields a minimal slope difference, allowing us to put a constraint on the minor axis location. Finally, we apply this method to the Sagittarius stream's leading arm. We report that the MW's DM halo is oblate with the flattening parameter in the potential $q\sim0.7-0.9$ and the minor axis pointing toward $(\ell,b) = (42^{o},48^{o})$. Our constraint on the minor axis location is weak and disagrees with the estimates from other works; we argue that the inconsistency can be attributed in part to the observational uncertainties and in part to the influence of the Large Magellanic Cloud.