Probing the shape of the Milky Way dark matter halo with hypervelocity stars: A new method

We propose a new method for determining the shape of the gravitational potential of the dark matter (DM) halo of the Milky Way (MW) with the galactocentric tangential velocities of a sample of hypervelocity stars (HVSs). We compute the trajectories of different samples of HVSs in a MW where the baryon distribution is axisymmetric and the DM potential either is spherical or is spheroidal or triaxial with radial-dependent axis ratios. We create ideal observed samples of HVSs with known latitudinal components of the tangential velocity, v(theta), and azimuthal component of the tangential velocity, v(theta). We determine the shape of the DM potential with the distribution of vertical bar v(theta)vertical bar when the Galactic potential is axisymmetric, or with the distribution of vertical bar v(theta)vertical bar and of a function, (v) over bar (phi), of v(phi) when the Galactic potential is non-axisymmetric. We recover the correct shape of the DM potential by comparing the distribution of vertical bar v(theta)vertical bar and (v) over bar (phi) of the ideal observed sample against the corresponding distributions of mock samples of HVSs that traveled in DM halos of different shapes. We use ideal observed samples of similar to 800 HVSs, which are the largest samples of 4 M-circle dot HVSs ejected with the Hills mechanism at a rate similar to 10(-4) yr(-1), currently outgoing, and located at more than 10 kpc from the Galactic Center. In our ideal case of galactocentric velocities with null uncertainties and no observational limitations, the method recovers the correct shape of the DM potential with a success rate S greater than or similar to 89% when the Galactic potential is axisymmetric, and S > 96% in the explored non-axisymmetric cases. The unsuccessful cases yield axis ratios of the DM potential that are off by +/- 0.1. The success rate decreases with decreasing size of the HVS sample: for example, for a spherical DM halo, S drops from similar to 98% to similar to 38% when the sample size decreases from similar to 800 to similar to 40 HVSs. Accurate estimates of the success rate of our method applied to real data require more realistic samples of mock observed HVSs. Nevertheless, our analysis suggests that a robust determination of the shape of the DM potential requires the measure of the galactocentric velocity of a few hundred HVSs of robustly confirmed galactocentric origin