<p>Consider two unit masses with velocity <span class="math-container">$V$</span>. Give them a small push apart so they have velocities <span class="math-container">$V+v$</span> and <span class="math-container">$V-v$</span> with <span class="math-container">$v\ll V$</span> . Their kinetic energies are then <span class="math-container">$$\frac{(V+v)^2}{2} \approx \frac{(V)^2}{2} +vV$$</span> and <span class="math-container">$$\frac{(V-v)^2}{2} \approx \frac{(V)^2}{2} -vV$$</span>
We have transferred energy <span class="math-container">$\approx vV$</span> from one mass to the other with the expenditure of a much smaller  energy <span class="math-container">$v^2$</span>.</p>

<p>Now suppose the masses are initially moving with some tiny velocity and then travel into a potential well where they have velocity <span class="math-container">$V$</span>. If we push while they are in the well then one will have enough kinetic energy to escape the well plus <span class="math-container">$vV$</span>, while the other will be trapped in the well.</p>

<p>This is the same principle as the <a href="https://en.wikipedia.org/wiki/Oberth_effect" rel="nofollow noreferrer">Oberth effect</a>, where the ejected reaction mass plays the role of one of the masses.</p>

CC BY-SA 4.0
2020-02-23T03:21:55.810Z
just fyi it's always okay to accept your own answer.
uhoh
CC BY-SA 4.0
2019-11-18T16:33:24.227Z
2019-11-18T16:33:24.227Z
Keith McClary
<blockquote>
  <p>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 ∼<span class="math-container">$10^4$</span> km/s
  infall velocity and the ∼<span class="math-container">$10^2$</span> km/s binary orbital velocity.<br>
  <a href="https://www.cfa.harvard.edu/~wbrown/Files/hvs_review.pdf" rel="nofollow noreferrer">Hypervelocity Stars and the Galactic Center, 
  Warren R. Brown, p.3</a></p>
</blockquote>

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

<p>(<a href="https://www.nature.com/articles/331687a0" rel="nofollow noreferrer">Hills' 1988 Nature paper</a> is still paywalled.)</p>

CC BY-SA 4.0
2019-11-14T17:07:53.370Z
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.
antlersoft
CC BY-SA 4.0
2019-11-14T22:23:18.807Z
arXiv: [The Great Escape: Discovery of a nearby 1700 km/s star ejected from the Milky Way by Sgr A*](https://arxiv.org/abs/1907.11725) and [MNRAS](https://academic.oup.com/mnras/advance-article-abstract/doi/10.1093/mnras/stz3081/5612212) and [Space.com](https://www.space.com/hypervelocity-star-ejected-from-milky-way.html), [carnegiescience.edu](https://carnegiescience.edu/news/runaway-star-was-ejected-heart-darkness), [livescience.com](https://www.livescience.com/star-ejected-milky-way.html) and [NYTimes](https://www.nytimes.com/2019/11/14/science/stars-black-hole-milky-way.html)
uhoh
CC BY-SA 4.0
2019-11-14T23:31:50.193Z
@uhoh I found an explanation in [Ejection of Hypervelocity Stars by the (Binary) Black Hole in the Galactic Center](https://iopscience.iop.org/article/10.1086/379546/fulltext/58563.text.html). It looks like the same principle as the [Oberth effect](https://en.wikipedia.org/wiki/Oberth_effect).
Keith McClary
CC BY-SA 4.0
2019-11-15T00:28:30.470Z
That's really cool! Write it up?
uhoh
CC BY-SA 4.0
2019-11-18T15:23:39.113Z
@PM2Ring Thanks, fixed.
Keith McClary
CC BY-SA 4.0
2019-11-18T15:52:38.107Z
As I understand it, the tidal disruption of the binary system means one star can end up in a closer orbit around the MBH, and thus loses energy (more negative potential energy). The overall energy is balanced by the other star gaining a *lot* of kinetic energy.
Peter Erwin
CC BY-SA 4.0
2020-02-23T03:21:29.267Z
I just noticed [this answer](https://astronomy.stackexchange.com/a/34790/7982) and I really like it! Can I interest you in undeleting it, and if there's something that you don't like about it perhaps just editing a little bit? To sweeten the pot I've just added a bounty. Crossing 1k rep opens up new SE privileges ;-)
uhoh
<supermassive-black-hole><tidal-forces>
Hills' mechanism for making Hypervelocity Stars
Keith McClary
# Hills' mechanism for making Hypervelocity Stars

(Asked by: username_0 on 2019-11-14)

> 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](https://www.cfa.harvard.edu/~wbrown/Files/hvs_review.pdf)

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

([Hills' 1988 Nature paper](https://www.nature.com/articles/331687a0) is still paywalled.)

**Tags:** supermassive-black-hole, tidal-forces

> **Comments:**
> **username_1**: 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.  
> **username_2**: arXiv: [The Great Escape: Discovery of a nearby 1700 km/s star ejected from the Milky Way by Sgr A*](https://arxiv.org/abs/1907.11725) and [MNRAS](https://academic.oup.com/mnras/advance-article-abstract/doi/10.1093/mnras/stz3081/5612212) and [Space.com](https://www.space.com/hypervelocity-star-ejected-from-milky-way.html), [carnegiescience.edu](https://carnegiescience.edu/news/runaway-star-was-ejected-heart-darkness), [livescience.com](https://www.livescience.com/star-ejected-milky-way.html) and [NYTimes](https://www.nytimes.com/2019/11/14/science/stars-black-hole-milky-way.html)  
> **username_0**: @username_2 I found an explanation in [Ejection of Hypervelocity Stars by the (Binary) Black Hole in the Galactic Center](https://iopscience.iop.org/article/10.1086/379546/fulltext/58563.text.html). It looks like the same principle as the [Oberth effect](https://en.wikipedia.org/wiki/Oberth_effect).  
> **username_2**: That's really cool! Write it up?  
> **username_0**: @PM2Ring Thanks, fixed.  
> **username_3**: As I understand it, the tidal disruption of the binary system means one star can end up in a closer orbit around the MBH, and thus loses energy (more negative potential energy). The overall energy is balanced by the other star gaining a *lot* of kinetic energy.  
> **username_2**: I just noticed [this answer](https://astronomy.stackexchange.com/a/34790/7982) and I really like it! Can I interest you in undeleting it, and if there's something that you don't like about it perhaps just editing a little bit? To sweeten the pot I've just added a bounty. Crossing 1k rep opens up new SE privileges ;-)  

---

## 1 answers

### Answer by username_0 on 2019-11-18. Score: 4

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.

This is the same principle as the [Oberth effect](https://en.wikipedia.org/wiki/Oberth_effect), where the ejected reaction mass plays the role of one of the masses.

> **Comments:**
> **username_2**: just fyi it's always okay to accept your own answer.  

---

