Studying Binary Systems in Omega Centauri with MUSE: II. Observational constraints on the orbital period distribution

Omega Centauri ($\omega$ Cen) is one of the most complex star clusters in the Milky Way, and likely the stripped nucleus of an accreted dwarf galaxy. Being the subject of debate between it hosting an intermediate-mass black hole (IMBH) or a collection of stellar-mass black holes (BHs) in its center, $\omega$ Cen has been intensively studied over the past decades. Our work focuses on characterizing the properties of binary systems in $\omega$ Cen via multi-epoch MUSE spectroscopic observations spanning over eight years and covering much of its central regions (i.e. core radius). We did not detect any stellar-mass BHs candidates orbiting luminous stars, although mock samples indicate a high sensitivity of our survey to such systems. This suggests that BHs orbiting stars may be rare in $\omega$ Cen or in wide orbits around low-mass companions (where our survey is 50% complete) or that the periods of such systems are longer than expected from cluster dynamics. Additionally, we constrained the orbital properties of 19 binary systems in the cluster, with periods ranging from fractions of a day up to several hundred days. We observe an excess of binaries with P $\ge$ 10 d and find evidence that the intrinsic period distribution of binaries in $\omega$ Cen differs from those predicted by cluster evolutionary models.