Probing modified Newtonian dynamics with hypervelocity stars

We show that measuring the velocity components of hypervelocity stars (HVSs) can discriminate between modified Newtonian dynamics (MOND) and Newtonian gravity. HVSs are ejected from the Galactic center on radial trajectories with a null tangential velocity component in the reference frame of the Galaxy. They acquire tangential components due to the nonspherical components of the Galactic gravitational potential. Axisymmetric potentials only affect the latitudinal components, $v_\theta$, and non-null azimuthal components, $v_\phi$, originate from non-axisymmetric matter distributions. For HVSs with sufficiently high ejection speed, $v_\phi$ is proportionate to the deviation of the gravitational potential from axial symmetry. The ejection velocity threshold is $\sim$ 750 km/s for 4 $M_{\odot}$ stars and increases with decreasing HVS mass. We determine the upper limit of $v_\phi$ as a function of the galactocentric distance for these high-speed HVSs if QUMOND, the quasi-linear formulation of MOND, is the correct theory of gravity and either the triaxial Galactic bulge or a nonspherical hot gaseous halo is the primary source of $v_\phi$. In Newtonian gravity, the HVSs within 60 kpc of the Galactic center may easily have $v_\phi$ values higher than the QUMOND upper limit if the dark matter (DM) halo is triaxial or if the DM halo and the baryonic components are axisymmetric but their two axes of symmetry are misaligned. Therefore, even a limited sample of high-speed HVSs could distinguish between QUMOND and the DM model. This test is currently limited by (i) the lack of a proper procedure to assess the HVS nature of a star in the model to be constrained; and (ii) the present uncertainties on $v_\phi$, which are a factor of $\sim 10$ too large. A proper procedure to assess the HVS nature of the stars and astrometric measurements with microarcsecond precision would make this test feasible.