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Where can I find the observed frequency of triple star systems where the outer star is in a retrograde orbit?

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  • $\begingroup$ Wow, I'm not aware of even one such star system, though I'm sure they exist. $\endgroup$ – barrycarter Apr 17 '16 at 20:09
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The usual recipe used in the population synthesis literature is that triple stars comprise ~10% of all stellar systems and the mutual inclination is uniform in the cosine. Most of these systems have a large enough semi-major axis ratio that the inner binary is dynamically decoupled from the outer binary, so retrograde orbits will be just as likely as prograde orbits. So, to an order of magnitude, ~5% of stellar systems should be triples with retrograde orbits.

Things get more complicated if you are interested in more details. More massive stars have higher multiplicities, so the fraction is probably somewhat higher for them. For more compact systems, dynamical effects like the Kozai-Lidov mechanism will become important and can lead to prograde orbits becoming retrograde and vice versa. Moreover, in compact systems, retrograde orbits are slightly more stable than prograde orbits, so they are likely to be a little more overrepresented, though I'm not aware of any observational evidence that there is any great difference between the two.

If you want more details on the observations of multiple stellar systems you should read Raghavan et al. (2010). However, I don't think that they measured mutual inclinations. In general those measurements are very difficult to do. Andrei Tokovinin has done a lot of great observational work on triple stars as well, so you might want to look at Tokovinin (2014) and Tokovinin (2008) among other papers. There's also a good review by Duchene & Kraus (2013).

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I would say that this sort of system would be near impossible. Both the mechanics of triple star systems being very complicated and the fact that have the outermost star would have to be captured, not from the original local stellar material, no easy feat.

Basically, the system would be virtually non existent, especially in the long term due to large gravitational wave energy decay (thanks LIGO) and general instability.

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