{"paper":{"title":"Self-gravity in thin protoplanetary discs: 2. Numerical convergence solved and revealing the overestimation in mass of formed planets with softening","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The 2D Bessel kernel for self-gravity resolves numerical convergence in thin disc simulations and shows that softening overestimates planet masses by a factor of two to three.","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"S. Rendon Restrepo","submitted_at":"2026-05-13T12:53:08Z","abstract_excerpt":"The Gravitational Instability (GI) is a leading theory for explaining early planet formation in massive discs. In the early 2010s, 3D SPH simulations of GI failed to converge, initially attributed to resolution-dependent viscosity but later appearing in 2D SPH and grid-based simulations, suggesting a numerical artifact inherent to the 2D approximation of gravity. 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 below which gravity smoothly transitions from a 3D to a 2D sca"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The 2D Bessel formalism of gravity effectively resolves the convergence issues encountered in 2D simulations. When compared to simulations employing softened or unsoftened potentials, a small softening parameter tends to overestimate gravitational effects. This results in an artificially high number of fragments, leading to final fragment masses that are overestimated by a factor of 2-3.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the first-principles Bessel kernel accurately represents the vertical structure and 3D-to-2D transition in real thin discs without requiring direct validation against full 3D simulations.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new Bessel kernel for 2D disc gravity fixes convergence in GI simulations and reveals that softening prescriptions overestimate formed planet masses by a factor of 2-3.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The 2D Bessel kernel for self-gravity resolves numerical convergence in thin disc simulations and shows that softening overestimates planet masses by a factor of two to three.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f54bdb927d4d516079302170ba3dba50225b9969e1fd94c19b17f8788885527c"},"source":{"id":"2605.13461","kind":"arxiv","version":1},"verdict":{"id":"1ace4495-0186-4aed-8748-82579b2f810b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:13:45.099541Z","strongest_claim":"The 2D Bessel formalism of gravity effectively resolves the convergence issues encountered in 2D simulations. When compared to simulations employing softened or unsoftened potentials, a small softening parameter tends to overestimate gravitational effects. This results in an artificially high number of fragments, leading to final fragment masses that are overestimated by a factor of 2-3.","one_line_summary":"A new Bessel kernel for 2D disc gravity fixes convergence in GI simulations and reveals that softening prescriptions overestimate formed planet masses by a factor of 2-3.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the first-principles Bessel kernel accurately represents the vertical structure and 3D-to-2D transition in real thin discs without requiring direct validation against full 3D simulations.","pith_extraction_headline":"The 2D Bessel kernel for self-gravity resolves numerical convergence in thin disc simulations and shows that softening overestimates planet masses by a factor of two to three."},"references":{"count":57,"sample":[{"doi":"","year":1989,"title":"Adams, F. C., Ruden, S. P., & Shu, F. H. 1989, ApJ, 347, 959","work_id":"67701dc0-4e37-4b73-af6f-860b8179a960","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"2011, in Advances in Imaging and Electron Physics, V ol","work_id":"57c5d3d5-504c-4819-9d94-ea956f5ac02f","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"Baehr, H. & Klahr, H. 2015, The Astrophysical Journal, 814, 155","work_id":"f7c539d9-1cdd-42b2-9e93-259b0150f85e","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Baehr, H., Klahr, H., & Kratter, K. M. 2017, ApJ, 848, 40","work_id":"1c07fb0f-44a7-4d76-a82f-a3c585fd2363","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"Baruteau, C. & Masset, F. 2008, ApJ, 678, 483","work_id":"12521411-d8e0-4b4d-a5bf-463f300c0857","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":57,"snapshot_sha256":"544253bb7ddab5142c31db9217e983b3db45dd45d494f99783d05d4f276094fe","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"978738785edbcdcbf76646da6421c64e30bc797dc5e4abe99fd88f7ec7322f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}