# Hills' mechanism for making Hypervelocity Stars

In Hill’s mechanism, the gravitational tidal force of a single MBH disrupts an approaching binary. One star is captured on an eccentric orbit around the MBH and, by conservation of energy, the other star escapes with a final velocity equal to the geometric mean of the ∼$$10^4$$ km/s infall velocity and the ∼$$10^2$$ km/s binary orbital velocity.
Hypervelocity Stars and the Galactic Center, Warren R. Brown, p.3

I don't understand how the high energy/velocity can be transferred to the star.

(Hills' 1988 Nature paper is still paywalled.)

• Ever try throwing two rubber balls, stacked, at the ground. If you do it right, almost all the combined energy will go into the upper ball, which will rebound to an amazing height, while the lower ball will stay near the ground. Nov 14 '19 at 17:07
• – uhoh
Nov 14 '19 at 22:23
• @uhoh I found an explanation in Ejection of Hypervelocity Stars by the (Binary) Black Hole in the Galactic Center. It looks like the same principle as the Oberth effect. Nov 14 '19 at 23:31
• That's really cool! Write it up?
– uhoh
Nov 15 '19 at 0:28
• @PM2Ring Thanks, fixed. Nov 18 '19 at 15:23

Consider two unit masses with velocity $$V$$. Give them a small push apart so they have velocities $$V+v$$ and $$V-v$$ with $$v\ll V$$ . Their kinetic energies are then $$\frac{(V+v)^2}{2} \approx \frac{(V)^2}{2} +vV$$ and $$\frac{(V-v)^2}{2} \approx \frac{(V)^2}{2} -vV$$ We have transferred energy $$\approx vV$$ from one mass to the other with the expenditure of a much smaller energy $$v^2$$.
Now suppose the masses are initially moving with some tiny velocity and then travel into a potential well where they have velocity $$V$$. If we push while they are in the well then one will have enough kinetic energy to escape the well plus $$vV$$, while the other will be trapped in the well.