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Gravitational instability (GI) is a key physical process in which a disc becomes unstable to its own gravity, driving
outward angular momentum transport, mass accretion onto the central star, and even the amplification of magnetic
fields through a dynamo effect. Most importantly, it is a leading theory of planet formation, describing how a disc
can fragment into bound clumps when cooling is efficient.
Most simulations characterising GI have relied on a thin-disc (2D) approximation, employing either a zero or a
finite smoothing length for the self-gravity potential. A finite smoothing length, however, suppresses the genuinely Newtonian nature of gravity and violates Newton’s third law, potentially inhibiting gravitational collapse.
Conversely, a vanishing smoothing length, or solving a 2D Poisson equation, artificially amplifies gravity.
In this seminar, I will first introduce the analytically derived, exact 2D self-gravity prescription (the so-called
Bessel kernel) designed for use in 2D simulations, and discuss its implications for the GI paradigm of planet
formation, as supported by global 2D simulations. Specifically, I will show how this approach resolves the
long-debated “convergence issue” in GI simulations with 2D SPH and grid-based codes, and demonstrate that
simulations employing small smoothing lengths—a practice still common in the field—tend to overestimate both
the mass and the number of objects formed. Finally, I will present preliminary results suggesting that a more
realistic gravity prescription may suppress stochastic fragmentation.