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Hyper velocity stars are starts that travel at a much faster rate then the Galactic keplerian velocity. Each HVS is thought to have started out as a member of a binary, which approaches a black hole and was tidally torn apart. We will first calculate the distance from the black hole at which the rapture occurs. Suppose we have a symmetric binary, i.e. two equal mass stars (both of mass  m ) in a circular orbit around each other, separated by a distance  a . The distance at which the force between the two stars is the same order of magnitude as the shear from the black hole is

 \frac{G M m}{r^2} \frac{a}{r} \approx \frac{G m^2}{a^3} \Rightarrow r = a \left( \frac{M}{m} \right)^{1/3}

The difference in potential energies between the two stars is

 \Delta E \approx v^2 \approx \frac{G M}{r} \frac{a}{r} \approx \frac{G M}{r} \left( \frac{M}{m} \right)^{1/3}

Hence the terminal velocity of the escaping companion is

 v \approx \sqrt{\frac{G M}{r}} \left(\frac{M}{m} \right)^{1/6}

For two solar mass stars approaching a  10^6 solar mass black hole, the terminal velocity can be 10 times higher than the escape velocity.