The Velocity Distribution of Hypervelocity Stars
  We consider the process of stellar binaries tidally disrupted by a
supermassive black hole. For highly eccentric orbits, as one star is ejected
from the three-body system, the companion remains bound to the black hole.
Hypervelocity stars (HVSs) observed in the Galactic halo and S-stars observed
orbiting the central black hole may originate from such mechanism. In this
paper, we predict the velocity distribution of the ejected stars of a given
mass, after they have travelled out of the Galactic potential. We use both
analytical methods and Monte Carlo simulations. We find that each part of the
velocity distribution encodes different information. At low velocities < 800
km/s, the Galactic Potential shapes universally the observed distribution,
which rises towards a peak, related to the Galactic escape velocity. Beyond the
peak, the velocity distribution depends on binary mass and separation
distributions. Finally, the finite star life introduces a break related to
their mass. A qualitative comparison of our models with current observations
shows the great potential of HVSs to constrain bulge and Galactic properties.
Standard choices for parameter distributions predict velocities below and above
~800 km/s with equal probability, while none are observed beyond ~700 km/s and
the current detections are more clustered at low velocities 300-400 km/s. These
features may indicate that the separation distribution of binaries that reach
the tidal sphere is not flat in logarithmic space, as observed in more local
massive binaries, but has more power towards larger separations, enhancing
smaller velocities. In addition, the binary formation/evolution process or the
injection mechanism might also induce a cut-off at ~ 10 solar radii in the
separation distribution.
