{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"368b0a3ff06cd1eac070e82ba0eca54145e4572b0ebfd28f324c99e9df7558ae","created":"2026-10-03T07:17:55Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","575381764f0952e6e35971a61db7d04d95345419df4465f7e11d2e986e927dab"],"salt":"6627291752206c497a6333914b9c55f3be4cc4d8e1f92c4e9e583877c138399d","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"astro.planetesimal-formation.si-threshold","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[{"note":"","parent_revision":"575381764f0952e6e35971a61db7d04d95345419df4465f7e11d2e986e927dab","relation":"special_case"}],"plain":"Pebbles drifting through gas can bunch up through a feedback between their drag and the gas flow (the streaming instability), and dense bunches collapse under gravity. This only works if there are enough pebbles and the gas is calm enough, and the exact conditions are uncertain.","posed_since":"2005","precise":"Determine the critical solid-to-gas surface density ratio $Z_{\\mathrm{crit}}(\\mathrm{St}, \\Pi, \\alpha)$ above which the streaming instability produces gravitationally bound clumps in a stratified disk, where $\\Pi = \\eta v_{K}/c_{s}$ and $\\alpha$ is the turbulence parameter, including MRI or vertical shear instability turbulence with $\\alpha \\sim 10^{-4}-10^{-3}$ and a size distribution of particles. The answer is a calibrated threshold function verified at converged resolution.","problem_ref":null,"references":"","settled_by":"Converged three-dimensional stratified shearing-box simulations with self-gravity, realistic turbulence and particle size distributions.","status_note":"Laminar thresholds were mapped by 2021 (Li and Youdin: $Z_{\\mathrm{crit}}$ as low as $\\sim 0.004$ for $\\mathrm{St} \\sim 0.1-0.3$, rising steeply for $\\mathrm{St} \\le 0.01$); how MRI or vertical-shear turbulence and particle size distributions shift $Z_{\\mathrm{crit}}$ is not settled as of 2026.","title":"When does the streaming instability collapse pebbles into planetesimals?","topic_ref":"31e036d86c734de67f0897bf2bb6f507ef858098857fb27d31ab4bb1d62da4e6"},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"00c0ce771752d8d74169a2f64aa37642543605dfbaed0ed004cbea2d9caf3efb","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"1d06ea96bb3b92febe19e2d0a23deba6af557bfd46064bf62a010cacb6a2f53e","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"qmjP4VjlImHX73UBuwYUtjb9K9dsg-ZIjwT3ct_RSswV6xE_f02p2mwFz3HFs86rEts3K7s9MAy_m8FWueBcDA"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIHQbqlrs7kv6-GeLQoj3rpq9Ve_1GBkv2KgEMrLai9T7xIBzgCXQhHwuR5JpH_Y68wWGnIcKyTUty7r7_F1ubS4WUCPAg4w-h5jkA6lj7kgvuPnfOvJJM36fOsAjUqB8U2EQzzP0I8SABVsikJTSAPCqRRDxvJIYRSUKgzDQBeVMtGcl2ZCUG7AjxIBNmpxZJBdi5XlvTTQJ1Quhmki_NZ4T7QZwC5SFmZANiCPEgIljE_01ZCsc18FpxlHjtfm364IXk1mn2gJO72jYzORAI8CB2kH4vNb7kV3Xaw5m-11iwgeNNw3HUxZTGzNhBGZGQAgjxILsjqRZq9WrFGbMMlciq-haEUPJ-vZn5OLpxdYOWip-kCPEgwbGZZS6QTbBEHqDWogFFI_MwwxJDJWE6c9zC5dsbY-MI8SByOXFSMcZPx-OI54voF1A1KoKCW2ZGWFJKc0hkOGWyGQjwIMIc4xq7iJ2YP27EtWYUvEm4-TQD7cayDq2XvZh74n3BCPAg3v2QXfNkDO6Xzu9061umH0rhjRfHBKza3uG2nPQbpd8I8CCtNZgmApuKULvPC9nsMCaM05arV-F3o5FTlnJCnRvdMgjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7Pmby5WLyI-A0I8QRqwKw78AhITF7Tr3a1xP8Ag9_jDS75DI4sK2h0dHBzOi8vYm9iLmJ0Yy5jYWxlbmRhci5vcGVudGltZXN0YW1wcy5vcmcI8CBXWeNiWFWltfHE0nkDXsVKIykUUwuObhsnN-2fvBt98gjwIM5Vf7j68sOFgVysYMc5S09Hho-fqxYW3oQ4oKUX7JpPCPAgaKHHQB3sdd9w1hu4NMh7vmb-p0X2r4uyVKKCj1G7S28I8SAW2Mg6Bzi9ygjrrjIYB7w90fwMcxH24SsqLmzPyAMGfwjwIMQ863zlveYIpNKWVrZaDOa4vowwoOg2CcTW8gXtxK3dCPEgrZxGGAf-t8jhz_eLMUyBN1IhNrdYDRcNHWvQcwNG9woI8CCVOUHG1YXudbaFIgUYvrCIevRWvb2ubhQAo-z0duD0rQjxIDBeKerVGkO3J2eXDwdraSioXbIWsdIPEN1s8pIwJIS2CPAgV2kB3n3JZ5HwBQjpRL1CWKnqvdCjZk3RcALk6N2wHigI8CB-wbljNlfqElD25uZkNg6taS81YDRU2vfMqGVQ420O9AjxWQEAAAABJM43UU6MLMRrPlCUqossvu1q_knons5yylyWTgxZzWUAAAAAAP7___8CLgABAAAAAAAWABQrYt3E7OllKRCEmL3FL589l78_5wAAAAAAAAAAImog8ATiyw4ACAjxILmbcIO7ixv3pCtwUMZ1VQGKus54F9lZ8-w5ECD5ZuiICAjwIG6ynCyFTLPE7Rgk-0ZGCtBDyqNQx8YvaSZNHy8D8p8jCAjwIMX8zoD2Be1YWvcx_bexVPRmBX0hK-do8b8t9SarimQVCAjxIG6XtpqIEclLlhzcK1LVjqoPGrjjmLnyno8tcETMzECECAjwIF6mlfXOFY51JhrK4eze8zQlKV75OYZYqbtyi8BWxmAsCAjwIKKUcJmVoz-u-geiRV_-ZHdF0VEPXaEPFWf_JX_0e7G2CAjxIGMeD0Z5QWNKBcAEpHht007FFIILW6aSJ8f3CMkKNsneCAjwIBFr6Je8rkB7kwhPGbq0yRgFwZsvW9JhY5sXDRtrq0QwCAjwIAHAwXaus-yUgKICJB5mVvx8VZuJgjwnpb0qWPg1pi6DCAjxIAJhb8cefkVHTAMymdsxa-_i-tUua62LcpALQnPG7R9_CAjwIDvsFqBhPfAL6TCtXZd7gBWmMpx6iiZ-Ug0Jf_LlcstgCAjwIDJRBX6Q0Vge-ra-k1_g76yJWTEp6WWF13I3JpTnsZPJCAjwILykZCbkC9VQgl5gytPKKir6T9nTvKR6y05iWSHBTQgzCAgABYiWDXPXGQED45c78Ah-sGbmQAwfZwjwEAYqxtHnZiPZnJEGPx_JvKsI8SDXkqDg17YsZIrEz5acRx7mBXCKW5mKNgRYnw_-U2cpDgjxBGrArDrwCEfK6Mono428_wCD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3JnCPAg10nyJ6Jn4kshQQQCKE0Lvj3hBC6nLRBVIzaPV4eh8VwI8CCQaAqWlxEbac_XOq1MOlf9iOKHEsxXspzbjK0vLpy8BwjwII3iRbRXUcDxrhAdkZmFlI15nySCSEZ7g922tF1Xln5DCPEgYYvZ1L4v4rPu_UqLfcHPtwSb2OH2GhPgVcVhhH6DpkQI8CDZCIoR20sC-uchP40oAmcLm9EJFV7xzwplj54AeVadXQjxILvLBjPFpCoz29m9Yf2qRnV7PI9GqxE8ozVQfk9QwCqrCPEgZXcMudvEoB_MJ8tqOW2PLTKAIeQBnE-1bfzptRc2gR8I8VkBAAAAAfXq-bmxWqOz7B5wKkwjzHGv2R4s7Y0Z76LqXWYNhmz0AAAAAAD-____Av0cAAAAAAAAFgAUl-skmdZDtn7Hnub6mF4HP2uVn7oAAAAAAAAAACJqIPAE4MsOAAgI8CBDmQsbEXc46Hu8DivhCBM1LGExa4TTM-wo7HpoCVjBTQgI8CCty5vkQtPHzzs8xqArOYhVSjgaDoG1ou3cojv5_P7wQQgI8SDQWB0kdXCTwbk-TqTt0QfRMyzDNLOtU1XXFgvGSRlW8wgI8CC2PKa_QCIBZtrXodq1GdEzppISMsMRDOnzr2gFjLKOAAgI8CCwQ_QF67bcFk_uJ2s0VCZmf5PGIjTmTCpt_qnVY5p_8AgI8SAbzyx7z-oxPMju6PvtQhzrJIQyH2ZAc9oyLuYemzbmZQgI8CC5bh7J74uUk91r8LwybHQFCNBC3PWeuwtMCCNFKWj19AgI8SAf4R2TUNPjaX_PWDUImpoITK0JoW89zaMKnD1wlEEi8AgI8SC2vNmdm7eyP5Ytl1yTzT0njliMdALl1ViKG-s3bG2zswgI8CCpbIVNz1GFVXdJk2zd82hBUoNFFemUPBt7IJdWEOciPwgI8CBtYdRQcrtX1FtCm1SxF7sx-5cO04U8KzbJh8fqBkyReAgI8CBHs2LGmX6gI-lV7yp1RrV7_tGfdiBAwnEFF6B6yXHzAQgI8CATotVmbXBMAixhZ-QKy5Q4lR0FusdA_wcIC1TbB7GmxAgIAAWIlg1z1xkBA-KXOw"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIzPN5NNRHIL3J2AEvJNwrznDJozi1ph2RdYtvGumre2rwIMz9e1IGtKJjB41a1bsCCi09KaZAvZFqFVKabI2dTn5zCPAgh1ahP8TWlRlldpGvlv_0eGcX3Ze5XdTSEvKWxxQQOk4I8SA-vpAFw-MG71WGHFqcbC-qMoCU7MwQoTY5BcazWighqQjwIEUbCaHh46-yDn-AGtSJkBDKzDnFbAY1gTXdpbc17gZZCPAg2PPrC4pqSqkjNMQ3tuI8A19v3sN2YkVdtBWKtLKuL4UI8CCT1ECzb5L0CSgTbYAbDrdoxCHBFA8XhmhHX3-4V7McMgjxILZHRWGZ2EbauVWb2Z-uhmX3p0OpttMODdo-XbuFB1TQCPAgrGIpQ0CZF7I2nODzSAkfB7ntmI6Mbb3vJr0ZuU9dTawI8SDw6LQ-RfhPE_v83K9oKkOzbHhdxc-f1_76FJQHtj9gCwjwIG_qk_muz-jg8UolhZs34aKKg3vvCTOQfEn-hyT2gbIDCPEgUZCxxJx-baWw4JFRfzCCtSjPn4ATBx_3FQi1O2Yo4-8I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3Wab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