The oblateness of the Milky Way dark matter halo from the stellar streams of NGC 3201, M68, and Palomar 5

Abstract: We explore constraints on the Milky Way dark matter halo oblateness using three stellar streams from globular clusters NGC 3201, M68, and Palomar 5. Previous constraints on the gravitational potential from dynamical equilibrium of stellar populations and distant Milky Way satellites are included. We model the dark halo as axisymmetric with axis ratio $q_\rho^{\rm h}$ and four additional free parameters of a two power-law density profile. The halo axis ratio, while barely constrained by the NGC 3201 stream alone, is required to be close to spherical by the streams of Palomar 5 ($q_\rho^{\rm h}=1.01\pm0.09$) and M68 ($q_\rho^{\rm h}=1.14^{+0.21}_{-0.14}$), the latter allowing a more prolate shape. The three streams together are well fitted with a halo axis ratio $q_\rho^{\rm h}=1.06\pm0.06$ and core radius $\sim$ 20 kpc. Our estimate of the halo shape agrees with previous studies using other observational data and is in tension with cosmological simulations predicting that most spiral galaxies have oblate dark matter halos with the short axis perpendicular to the disc. We discuss why the impact of the Magellanic Clouds tide is too small to change our conclusion on the halo axis ratio. We note that dynamical equilibrium of a spherical halo in the oblate disk potential implies an anisotropic dark matter velocity dispersion, larger along the vertical direction than the horizontal ones, which should relate to the assembly history of the Milky Way.