Constraining Solar Position and Velocity with a nearby Hypervelocity Star

Gravitational three-body interaction among binary stars and the supermassive black hole at the center of the Milky Way occasionally ejects a hypervelocity star (HVS) with a velocity of ∼ 1000 {km} {{{s}}}^-1. Due to the ejection location, such an HVS initially has negligible azimuthal angular momentum {L}_z≃ 0 {kpc} {km} {{{s}}}^-1. Even if the halo is mildly triaxial, L _z of a recently ejected nearby HVS remains negligible, since its flight time from the Galactic center is too short to accumulate noticeable torque. However, if we make a wrong assumption about the solar position and velocity, such an HVS would apparently have noticeable nonzero azimuthal angular momentum, due to the wrong reflex motion of the Sun. Conversely, with precise astrometric data for a nearby HVS, we can measure the solar position and velocity by assuming that the HVS has zero azimuthal angular momentum. Based on this idea, here we propose a method to estimate the Galactocentric distance of the Sun R ₀ and the Galactocentric solar azimuthal velocity V _⊙ by using an HVS. We demonstrate with mock data for a nearby HVS candidate that the Gaia astrometric data, along with the currently available constraint on V _⊙/R ₀ from the proper motion measurement of Sgr A*, can constrain R ₀ and V _⊙ with uncertainties of ∼0.27 kpc and ∼7.8 km s^-1 (or fractional uncertainties of 3%), respectively. Our method will be a promising tool to constrain (R ₀, V _⊙), given that Gaia is expected to discover many nearby HVSs in the near future.