Are exoplanets which are above escape velocity of particular interest? I was perusing the exoplanet database and looking for some of the more extreme orbits, when I happened upon HD 20782 B:

http://exoplanets.org/detail/HD_20782_b

Which is also listed (in two sentences) on wikipedia, so there's not a whole lot of information. However, the first thing I noticed was that it was almost at escape velocity!



I guess not much is known, but my overall question is:

Would an exoplanet on an escape trajectory offer us any opportunities for research that have yet to be performed? What would those opportunities be? The answer can be a justified no (E.G. once the planet leaves the host star, we can't observe the doppler shift anymore).



Imaginary Bonus Points: have there ever been any observed as escaping/becoming rogue planets?
The problem is that planet ejection is something that takes place over a very short timescale compared to the ages of the systems in question, so we're unlikely to see it actually take place. The main prospect of detection would be imaging of the ejected planets, for which you'd want a young giant planet as these retain enough heat from their formation to be sufficiently luminous in the infrared for detection even when not illuminated by a nearby star.

There has actually been a claim for the detection of a (proto)planet in the process of being ejected from a binary star system: the case of TMR-1C as reported by Terebey et al. (1998) "A Candidate Protoplanet in the Taurus Star-forming Region". Unfortunately the nature of the object is not confirmed, see Terebey et al. (2000) "The spectrum of TMR-1C is consistent with a background star". There has been some back-and-forth on this: Riaz &amp; Martín (2011) "Large-amplitude photometric variability of the candidate protoplanet TMR-1C
" reject the background star hypothesis, while Riaz et al. (2013) "A near-infrared variability campaign of TMR-1: New light on the nature of the candidate protoplanet TMR-1C" regard it as a strong candidate for being a young stellar object (YSO).

Another relevant case might be the circumbinary planet HD 106906 (AB) b, which may have been saved from ejection by a stellar flyby, see De Rosa &amp; Kalas (2019) "A Near-coplanar Stellar Flyby of the Planet Host Star HD 106906".

Ejected planets are of interest due to their contribution to the population of low-mass objects in star clusters and the field (this population may well contain both ejected planets and low-mass brown dwarfs), and the impacts on the orbital architecture of the surviving planets after episodes of planet-planet scattering. One example of the latter I found is Carrera et al. (2019) "Planet-planet scattering as the source of the highest eccentricity exoplanets", there are many other papers on this topic.