Probing modified Newtonian dynamics with hypervelocity stars

Abstract

We show that measuring the velocity components of hypervelocity stars (HVSs) can discriminate between modified Newtonian dynamics (MOND) and Newtonian gravity. Hypervelocity stars 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, vθ, and non-null azimuthal components, vϕ, originate from non-axisymmetric matter distributions. For HVSs with sufficiently high ejection speed, the azimuthal velocity components are proportionate to the deviation of the gravitational potential from axial symmetry. The ejection velocity threshold is ∼750 km s−1 for 4 M⊙ stars and increases with decreasing HVS mass. We determine the upper limit of vϕ as a function of the galactocentric distance for these high-speed HVSs if MOND, in its quasi-linear formulation QUMOND, is the correct theory of gravity and either the triaxial Galactic bulge or a nonspherical hot gaseous halo is the primary source of the azimuthal component, vϕ. In Newtonian gravity, the HVSs within 60 kpc of the Galactic center may easily have vϕ values higher than the QUMOND upper limit if the dark matter halo is triaxial or if the dark matter 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 in principle allow us to distinguish between the QUMOND scenario and the dark matter model. This test is currently limited by (i) the lack of a proper procedure to assess whether a star originates from the Galactic center and thus is indeed an HVS in the model one wishes to constrain; and (ii) the large uncertainties on the galactocentric azimuthal velocity components, which should be reduced by at least a factor of ∼10 to make this test conclusive. A proper procedure to assess the HVS nature of the observed stars and astrometric measurements with microarcsecond precision would make this test feasible.