On the frequencies of circumbinary discs in protostellar systems

We report the analysis of circumbinary discs formed in a radiation hydrodynamical simulation of star cluster formation. We consider both pure binary stars and pairs within triple and quadruple systems. The protostellar systems are all young (ages < $10^5$ yrs). We find that the systems that host a circumbinary disc have a median separation of $\approx 11$ au, and the median characteristic radius of the discs is $\approx 64$ au. We find that $89$ per cent of pure binaries with semi-major axes $a<1$ au have a circumbinary disc, and the occurrence rate of circumbinary discs is bimodal with log-separation in pure binaries with a second peak at $a \approx 50$ au. Systems with $a>100$ au almost never have a circumbinary disc. The median size of a circumbinary disc is between $\approx 5-6\ a$ depending on the order of the system, with higher order systems having larger discs relative to binary separation. We find the underlying distribution of mutual inclinations between circumbinary discs and binary orbit of both observed and simulated discs to not differ statistically.