Ultrafast Stars Discovered Racing Through Milky Way

The basic idea here is the boost a smaller body can get when interacting with larger ones. This is/was used for space probes to get to the outer solar system, which would otherwise be prohibitive on fuel grounds. 'Gravity assist' or 'slingshot' are common phrases for this.

It has to be a 3+ body system. So you have the Earth traveling around the Sun. A much smaller object comes into the near Earth space and thus descends significantly into it's gravity 'well'. But the Earth is in turn attracted by the Sun ( that's why it's orbiting ) so that 'well' is in turn on the move. From the point of view of the nett pull felt by the spacecraft - from both Earth and Sun - it's path into closest approach with Earth is not time symmetric compared to it's path outward from that point ( and if you get the approach wrong you may get 'gravity retardation' instead ). The transfer of kinetic energy to the craft is large, relatively, but tiny for the Earth, relatively. So the craft shoots on outwards from the Sun and the Earth moves ever so slightly inwards. Indeed for some missions there were several loops ( timing is everything here ) around the inner solar system bodies to achieve enough energy to go to some target way further out.

Similar principles apply to 'ordinary' boosting in gravity wells with only two bodies though. So a craft with fuel aboard can descend into, say, Jupiter's near space. If you burn the fuel outbound rather than inbound you will ( for the sake of the craft ) get the energy benefit of descent down the well of some given mass of fuel. But it's really a three plus body problem - you just consider the fuel as temporarily attached. In any case it's better to throw the fuel behind you when you are leaving, compared to when you are coming in.

The benefit to be gained depends on the well of the primary body, plus how much mass you 'sacrifice' by throwing it inwards vs how much is preserved to continue outwards. So these very fast stars are presumed to have quite energetic trajectories as a result of pairs of stars interacting with the central black hole of our galaxy. One star of a pair loses kinetic energy - thus falling closer in towards ( or entirely into ) the hole - by giving it to the other to race off elsewhere. Such high speeds indicate quite a massive slingshot effect. Cosmic billiards anyone ?! :-)

Cheers, Mike.

( edit ) Actually for a black hole the 'surface' gravity or field strength at the event horizon diminishes with size. So a multi-million solar mass hole as considered here will have a gentler ( than you might have first thought ) change of field strength in the regions where you can have a near miss and yet survive. Or put another way you have to stay well away from the centre of such a thing. Even so, it might be the case that several encounters are required to get the magnitude of boost these observations imply ... interesting ....

( edit ) In the fuel burn case described above I'm referring to the gravitational benefit of keeping the fuel onboard until closest approach, which is separate from whatever you get by converting the chemical energy content of the fuel.