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Context. The fraction of field binaries on retrograde orbits about the MilkyWay is significantly lower compared to its prograde counterpart. Chemical anddynamical evidence suggests that the retrograde stellar population originatesfrom $\omega$ Centauri, which is either the most massive globular cluster (GC)of the Milky Way or the putative core of a former dwarf galaxy. Aims. Starformation conditions required to produce the retrograde binary population areconstrained assuming that the retrograde stellar population originates from$\omega$ Centauri's progenitor. Methods. We match the observed low binaryfraction with dynamical population synthesis models, including a universalinitial binary population and dynamical processing in star clusters, making useof the publicly available binary population synthesis tool BiPoS1. Results. Itis found that either the GC progenitor of $\omega$ Centauri must have formedwith a stellar density of $\approx 10^8 \; M_{sun} \; pc^{-3}$ or the $\omega$Centauri dwarf galaxy's progenitor star cluster population must have formed inan extreme starburst with a star formation rate exceeding $1000 \; M_{sun} \;yr^{-1}$ and probably a top-heavy embedded-cluster mass function withsuppressed low-mass cluster formation. The separation and mass ratiodistribution for retrograde field binaries are predicted for comparison withfuture observations. Conclusions. A viable solution for the deficiency ofbinaries on retrograde orbits is presented, and star formation conditions for$\omega$ Centauri as well as orbital parameter distributions for the MilkyWay's retrograde binary population are predicted. The dwarf galaxy origin for$\omega$ Centauri is tentatively preferred within the present context.

astronomy and astrophysics

A possible solution to the Milky Way's binary-deficient retrograde  stellar population. Evidence that $\omega$ Centauri has formed in an extreme  starburst