# Concerning a binary system of stars/planets/black holes could one of them be ejected before eventually merging or colliding?

I was having a discussion with an undergraduate student of physics about binaries and their interactions with external celestial bodies (which could cause the ejection of one of the members in the binary).

He told me that you don't even need a third body, was one of the members of the binary can kick the other to high speeds. He mentioned Mass Transfer Instability as one mechanism, but I am not sure how does this work.

Are there any other mechanisms where one of the members of the binary can expel the other from the system at high speeds? Are there any mechanisms where any celestial body that is part of a binary (planets, stars, black holes...) can eject the other member of the system at very high speeds?

Not in Newtonian gravity with particles. This situation is soluble with stable elliptical orbits, so any examples would have to depend on either Relativity, or that the bodies are not particles.

If the bodies are not rigid, then tides can cause the bodies to separate, this is happening with our moon, but in general, if one of the bodies is rotating rapidly, then tides can transfer angular momentum from the rotating body to the orbit, however as the two get further away, the tidal effect reduces. This can't cause one body to be rapidly ejected.

So looking at relativity, there is a possibility. First you need a (rapidly) rotating black hole. This has a region, called the ergosphere, from which an orbiting body can extract mass/energy from the black hole. A process to do this was described by Roger Penrose. An orbiting body must enter the ergosphere (but not fall to the event horizon), split up, with one part falling into the black hole, and the other part being pushed forward. The net result would be that the rate of rotation of the black hole would lessen, and the part of the body that didn't fall into the black hole would gain energy. Potentially it could gain a lot of energy. (more than 20% of its rest-mass energy)

This is quite an exceptional situation, and you don't get the whole body back, some must necessarily be left behind. It could be used to eject one member of a binary system

The final category in which a binary can eject a member, is when one part of the pair does something fundamentally non-gravitational such as "explode". The physical push from an asymmetric supernova can eject it from a binary system, but I don't think that this is what you quite mean.

• Could one of the members of the binary be ejected if it interacted with gas bodies in the galaxy as it is suggested here (but in this case, with black holes)?: physicsworld.com/a/… @JamesK Commented Jul 31, 2023 at 16:36
• If it intteracts with a third mass, then it's not a "binary" now is it? Commented Jul 31, 2023 at 22:07

When a binary star goes supernova, not only can they get separated, but one of them or both may be even ejected from the galaxy they are in. See https://www.nasa.gov/mission_pages/chandra/images/binary-stars-ejected-from-fornax-cluster.html

Simple mass loss from a binary system can result in unbinding the system and one of the stars shooting off at relatively high speed.

An example:

Take a binary with a massive primary star, say $$M_1=50 M_\odot$$, and a companion of mass $$M_2=1M_\odot$$, and give them a circular orbit with an orbital separation of $$a=0.1$$ au.

To first order we can take the orbital speed of the companion as $$(GM_1/a)^{1/2} = 667$$ km/s.

Now let the $$50M_\odot$$ star lose lots of mass. For simplicity let's assume this happens impulsively - so could be a supernova - and it loses $$40M_\odot$$ of mass.

The escape velocity of the new system - a $$M_1=10M_\odot$$ object and a $$M_2=1M_{\odot}$$ star separated by $$a=0.1$$ au - is roughly $$\sqrt{2G(M_1+M_2)/a} = 442$$ km/s.

Since the instantaneous orbital speed of $$M_2$$ is higher than this, then it will escape and will have a speed of roughly $$500$$ km/s as it exits.

This is an extreme example, but so-called runaway stars that might result from this mechanism have been known about for decades.

• could one of the members of the binary be ejected if it interacted with gas bodies in the galaxy as it is suggested here (but in this case, with black holes)?: physicsworld.com/a/… @ProfRob Commented Jul 31, 2023 at 16:35