DIPSY: A new Disc Instability Population SYnthesis

I. Modelling, evolution of individual systems, and tests

¹ Space Research and Planetary Sciences, Physics Institute, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
² Center for Space and Habitability, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
³ Department of Astrophysics, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland

^★ Corresponding author: oliver.schib@unibe.ch

Received: 4 July 2025
Accepted: 10 September 2025

Abstract

Context. Disc instability (DI) is a model aimed at explaining the formation of companions through the fragmentation of the circum-stellar gas disc. Furthermore, DI could explain the formation of part of the observed exoplanetary population. Our understanding of DI is still incomplete given the complex nature of the process and challenges related to its modelling.

Aims. We aim to provide a new comprehensive global model for the formation of companions via DI. The model includes the formation of the star-and-disc system through infall from the molecular cloud core (MCC) as well as the evolution of companions that might emerge via fragmentation in it. This approach allows us to study a large parameter space, perform population synthesis calculations, and make predictions that can be compared with observations. This makes it possible to put the models for the different sub-processes included in the global model to the observational test.

Methods. We have developed a global formation and evolution model for companions formed via DI: DIPSY. The model solves the 1D vertically integrated viscous evolution equation of the protostellar and protoplanetary disc with a variable α viscosity. It includes infall from the MCC, stellar irradiation, internal and external photoevaporation, and exchange of both mass and angular momentum between disc and companions. The latter leads for the companions to orbital migration and damping of the eccentricities and inclinations. As it evolves, the disc is continuously monitored for self-gravity and fragmentation. When the conditions are satisfied, one (or several) clumps are inserted. The evolution of the clumps is then followed in detail. Clump contraction, including the second collapse is considered by using interior evolution tracks. Thermal irradiation by the disc, mass growth by gas accretion, and mass loss via Roche lobe overflow are also included. The interaction of clumps with each other is included with a full N-body integrator which can lead to collisions, scattering, or ejections.

Results. We showcased the model by performing a number of simulations for various initial conditions, from simple non-fragmenting systems to complex systems with many fragments.

Conclusions. We confirm that the DIPSY model is a comprehensive and versatile global model of companion formation via DI. It enables studies of the formation of companions with planetary to low stellar masses around primaries with final masses that range from the brown dwarf to the B-star regime. We conclude that it is necessary to consider the many interconnected processes such as gas accretion, orbital migration, and N-body interactions, as they strongly influence the inferred population of forming objects. It is also clear that model assumptions play a key role in the determination of the systems undergoing formation.