Gravitational interactions of stars with supermassive black hole
  binaries - II. Hypervelocity stars
  Supermassive black holes (SMBHs) in galactic nuclei can eject hypervelocity
stars (HVSs). Using restricted three-body integrations, we study the properties
of stars ejected by circular, binary SMBHs as a function of their mass ratios
$q = M_2 / M_1$ and separations $a$, focusing on the stellar velocity and
angular distributions. We find that the ejection probability is an increasing
function of $q$ and $a$, and that the mean ejected velocity scales with $q$ and
$a$ similar to previous work but with modified scaling constants. Binary SMBHs
tend to eject their fastest stars toward the binary orbital plane. We calculate
the ejection rates as the binary SMBHs inspiral, and find that they eject stars
with velocities $v_\infty > 1000$ km/s at rates of $\sim 4 \times 10^{-2} - 2
\times 10^{-1}$ yr$^{-1}$ for $q = 1$ ($\sim 10^{-4} - 10^{-3}$ yr$^{-1}$ for
$q = 0.01$) over their lifetimes, and can emit a burst of HVSs with $v_\infty >
3000$ km/s as they coalesce. We integrate the stellar distributions over the
binary SMBH inspiral and compare them to those produced by the "Hills
mechanism" (in which a single SMBH ejects a star after tidally separating a
binary star system), and find that $N \sim 100$ HVS velocity samples with
$v_\infty \gtrsim 200$ km/s are needed to confidently distinguish between a
binary and single SMBH origin.
