The link between infall location, early disc size, and the fraction of self-gravitationally fragmenting discs

Many protoplanetary discs are self-gravitating early in their lives. If they fragment under their own gravity, they form bound gaseous clumps which may evolve to become giant planets. Today, the fraction of discs that undergo fragmentation, and the frequency of conditions that may lead to giant planet formation via gravitational instability, is still unknown. We perform a population synthesis of discs from formation to dispersal. In varying the infall radius, we study the relationship of the early disc size with fragmentation. Furthermore, we investigate how stellar accretion heating affects the fragmentation fraction. We find that discs fragment only if they become sufficiently large early in their lives. This size depends sensitively on where mass is added to the discs during the collapse of their parent molecular cloud core. By choosing intermediate infall locations leading to a synthetic disc size distribution that is in agreement with the observed one, we find a fragmentation fraction between 0.1 and 11 %, depending on the efficiency of stellar accretion heating of the discs. We conclude that the early disc size is mainly determined by the infall location during the collapse of the molecular cloud core and controls the population-wide frequency of fragmentation. Stellar accretion heating plays an important role for fragmentation and must be studied further. Our work is an observationally-informed step towards a prediction of the frequency of giant planet formation by gravitational instability. Upcoming observations and theoretical studies will deepen our understanding of the formation and early evolution of discs, eventually allowing to understand how infall, disc morphology, giant planet formation via gravitational instability, and the observed extrasolar planet population are linked.
Comment: Accepted for publication in A&A