An efficient spectral Poisson solver for NIRVANA-III: the shearing-box case with vertical vacuum boundary conditions

Description

Abstract

The Gravitational Instability (GI) is a dominant theory that explains angular momentum transport in young protoplanetary disks. Additionally, it is a key theory in planet formation, describing how a disk can fragment into clumps for efficient cooling. Most simulations characterizing GI have relied on a thin-disc (2D) approximation, employing either a zero or a finite smoothing length prescription for the gravitational potential. However, a finite smoothing length suppresses the Newtonian nature of gravity, potentially inhibiting gravitational collapse, and does not respect Newton's third law. Conversely, a vanishing smoothing length, or solving a 2D Poisson equation, artificially amplifies gravity.

In the first part of my talk, I will introduce an analytically derived, exact 2D self-gravity prescription (known as Bessel kernel) designed for use in 2D simulations. This prescription eliminates the need for smoothing length approximations. Specifically, I will demonstrate how it resolves the inherent issues of a Plummer potential, particularly the short-range suppression of Newtonian gravity. I will then discuss the broader implications of this work for the GI paradigm of planet formation, supported by 2D global simulations with the FARGO-CPT code.  Specifically, I will show how this approach may address the long-debated "convergence issue" in GI simulations with 2D grid-based codes.