Constraining Solar position and velocity with a Nearby Hypervelocity
  Star
  Gravitational 3-body interaction among binary stars and the supermassive
black hole (SMBH) at the center of the Milky Way occasionally ejects a
hypervelocity star (HVS) with a velocity of ~1000 km/s. Due to the ejection
location, such a HVS initially has negligible azimuthal angular momentum Lz ~ 0
kpc km/s. Even if the halo is mildly triaxial, Lz 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 a HVS would apparently have
noticeable non-zero 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 R0 and the Galactocentric Solar
azimuthal velocity Vsun by using a HVS. We demonstrate with mock data for a
nearby HVS candidate that the Gaia astrometric data, along with the currently
available constraint on Vsun/R0 from the proper motion measurement of Sgr A*,
can constrain R0 and Vsun with uncertainties of ~0.27 kpc and ~7.8 km/s (or
fractional uncertainties of 3 percent), respectively. Our method will be a
promising tool to constrain (R0, Vsun), given that Gaia is expected to discover
many nearby HVSs in the near future.
