Self-gravity in thin protoplanetary discs
- 1Leibniz-Institut für Astrophysik Potsdam (AIP)
Abstract
Context. Gravitational instability (GI) is a leading theory proposed to explain both angular momentum transport and early planet formation in young, massive discs. In the early 2010s, 3D smoothed particle hydrodynamics (SPH) simulations investigating GI failed to achieve convergence. Although this issue was initially addressed and attributed to resolution-dependent viscosity, it subsequently emerged in 2D SPH and 2D grid-based simulations – suggesting a numerical artefact inherent to the 2D approximation of gravity. Aims. Recently, we derived from first principles a much improved prescription for gravity in 2D discs (via a Bessel kernel). This prescription introduces a characteristic length, Hrms, below which gravity smoothly transitions from a 3D to a 2D scaling. This cannot be captured by standard smoothing length approaches, widely used in 2D simulations. My objective is to employ this new prescription to resolve the convergence issue of GI in 2D and compare the outcomes of the instability in runs using the Bessel kernel with those obtained using softening prescriptions at high resolution. Methods. I conducted numerical simulations with the FARGOCPT code, where the Bessel prescription was implemented. Results. The 2D Bessel formalism of gravity effectively resolves the convergence issues encountered in 2D simulations. When compared to simulations employing softened or unsoftened potentials, I observe that a softening parameter ϵ/H ≤ 0.3 overestimates gravitational effects. This may result in an artificially high number of fragments, potentially leading to final fragment masses that are overestimated by a factor of 2–3. Conversely, employing a softening parameter exceeding the scale height inhibits gravitational effects. Although my analysis initially suggests that a softening parameter of 0.6H might offer the best compromise, in reality, the resulting fragments fail to remain gravitationally bound – a limitation not observed when using the Bessel kernel. Conclusions. My findings on the Bessel kernel, coupled with its high numerical efficiency, strongly suggest its adoption in future studies to ensure a consistent and accurate treatment of gravity in thin discs.
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BibTeX
@article{restrepo2026selfgravity,
title = {{Self-gravity in thin protoplanetary discs}},
author = {Rendon Restrepo S.},
journal = {Astronomy \& Astrophysics},
year = {2026},
month = oct,
doi = {10.1051/0004-6361/202660974},
url = {https://doi.org/10.1051/0004-6361/202660974},
note = {CC BY},
}
RIS
TY - JOUR
TI - Self-gravity in thin protoplanetary discs
AU - Rendon Restrepo S.
PY - 2026
DA - 2026/10/24
JO - Astronomy & Astrophysics
DO - 10.1051/0004-6361/202660974
UR - https://doi.org/10.1051/0004-6361/202660974
AB - Context. Gravitational instability (GI) is a leading theory proposed to explain both angular momentum transport and early planet formation in young, massive discs. In the early 2010s, 3D smoothed particle hydrodynamics (SPH) simulations investigating GI failed to achieve convergence. Although this issue was initially addressed and attributed to resolution-dependent viscosity, it subsequently emerged in 2D SPH and 2D grid-based simulations – suggesting a numerical artefact inherent to the 2D approximation of gravity. Aims. Recently, we derived from first principles a much improved prescription for gravity in 2D discs (via a Bessel kernel). This prescription introduces a characteristic length, Hrms, below which gravity smoothly transitions from a 3D to a 2D scaling. This cannot be captured by standard smoothing length approaches, widely used in 2D simulations. My objective is to employ this new prescription to resolve the convergence issue of GI in 2D and compare the outcomes of the instability in runs using the Bessel kernel with those obtained using softening prescriptions at high resolution. Methods. I conducted numerical simulations with the FARGOCPT code, where the Bessel prescription was implemented. Results. The 2D Bessel formalism of gravity effectively resolves the convergence issues encountered in 2D simulations. When compared to simulations employing softened or unsoftened potentials, I observe that a softening parameter ϵ/H ≤ 0.3 overestimates gravitational effects. This may result in an artificially high number of fragments, potentially leading to final fragment masses that are overestimated by a factor of 2–3. Conversely, employing a softening parameter exceeding the scale height inhibits gravitational effects. Although my analysis initially suggests that a softening parameter of 0.6H might offer the best compromise, in reality, the resulting fragments fail to remain gravitationally bound – a limitation not observed when using the Bessel kernel. Conclusions. My findings on the Bessel kernel, coupled with its high numerical efficiency, strongly suggest its adoption in future studies to ensure a consistent and accurate treatment of gravity in thin discs.
SN - 0004-6361
SN - 1432-0746
ER -