The galactic rate of second- and third-generation disc and planet formation

We investigate the formation of discs within binary systems where at least one component has left the main sequence. In particular, we calculate the occurrence rates of systems that can host long-lived, massive discs that may be able to support the formation of planets. We synthesize a population based on Milky Way properties, using both theoretical and observational inputs to constrain key properties, such as the shape of the initial mass function, binary fraction, and mass-transfer physics. We predict 0.26 per cent of binary systems will host second-generation discs (where the primary has evolved), and 0.13 per cent of systems will host third-generation discs (where the secondary also evolves). For the Milky Way, this translates into 130 million and 90 million second- and third-generation systems, respectively, from an estimated total of 50 billion binary systems. Of these systems that form discs, we estimate approximately 20 per cent of second-generation and 3.8 per cent of third-generation discs have enough mass to form a planetary system. We speculate on how the process of planet formation differs in these systems from conventional planet formation in protostellar discs.