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    "id": "bondi-spherical-polytropic-accretion-family-1952",
    "title": "Bondi: balance gravity and pressure in spherical gas accretion",
    "summary": "Bondi solves the steady spherical polytropic accretion problem, identifies subsonic and critical transonic branches, and derives the mass-rate scaling and critical coefficient under an explicit inner-domain assumption.\n\nHow quickly can a star collect gas that is initially at rest far away? Gravity pulls it inward, while gas pressure resists compression. Bondi combines mass conservation with the energy equation to describe this competition using dimensionless variables. The accretion rate scales as the square of the central mass and the ambient gas density, divided by the cube of the ambient sound speed. A dimensionless coefficient labels the possible steady flows. When the modeled domain reaches the critical radius, that coefficient cannot exceed a gamma-dependent limit. At the critical value, a smooth solution can pass from subsonic to supersonic flow; smaller values also permit steady subsonic flows. The steady equations therefore do not uniquely select the physically realized rate. Bondi proposes an energy-based preference for the critical flow but expressly notes difficulties for an open, infinitely extended system. The result became a widely used reference model, although rotating flows, relativistic gravity, feedback and non-steady gas require additional physics.",
    "boundary": "The family assumes steady spherical Newtonian flow onto a fixed central mass, a polytropic gas at rest at infinity and 1<=gamma<=5/3. Rotation, self-gravity and mass growth are omitted. The critical rate depends on the inner-boundary domain; steady equations alone do not select it. The isothermal and gamma=5/3 endpoints require their own limits. The source’s energy/stability selection and moving-star interpolation are provisional, not universal proven theorems.",
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        "description": "The family assumes steady spherical Newtonian flow onto a fixed central mass, a polytropic gas at rest at infinity and 1<=gamma<=5/3. Rotation, self-gravity and mass growth are omitted. The critical rate depends on the inner-boundary domain; steady equations alone do not select it. The isothermal and gamma=5/3 endpoints require their own limits. The source’s energy/stability selection and moving-star interpolation are provisional, not universal proven theorems.",
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      "statement": "# Bondi: balance gravity and pressure in spherical gas accretion\n\nBondi solves the steady spherical polytropic accretion problem, identifies subsonic and critical transonic branches, and derives the mass-rate scaling and critical coefficient under an explicit inner-domain assumption.\n\nHow quickly can a star collect gas that is initially at rest far away? Gravity pulls it inward, while gas pressure resists compression. Bondi combines mass conservation with the energy equation to describe this competition using dimensionless variables. The accretion rate scales as the square of the central mass and the ambient gas density, divided by the cube of the ambient sound speed. A dimensionless coefficient labels the possible steady flows. When the modeled domain reaches the critical radius, that coefficient cannot exceed a gamma-dependent limit. At the critical value, a smooth solution can pass from subsonic to supersonic flow; smaller values also permit steady subsonic flows. The steady equations therefore do not uniquely select the physically realized rate. Bondi proposes an energy-based preference for the critical flow but expressly notes difficulties for an open, infinitely extended system. The result became a widely used reference model, although rotating flows, relativistic gravity, feedback and non-steady gas require additional physics.\n\n## Scientific scope\n\nThe family assumes steady spherical Newtonian flow onto a fixed central mass, a polytropic gas at rest at infinity and 1<=gamma<=5/3. Rotation, self-gravity and mass growth are omitted. The critical rate depends on the inner-boundary domain; steady equations alone do not select it. The isothermal and gamma=5/3 endpoints require their own limits. The source’s energy/stability selection and moving-star interpolation are provisional, not universal proven theorems.\n\n## People and systems\n\nH. Bondi\n\n\n\n## Original sources\n\n- [H. Bondi1952, On spherically symmetrical accretion, completeoriginal195-204](https://adsabs.harvard.edu/pdf/1952MNRAS.112..195B)\n- [RAS/Oxford1952original bibliographicidentity/abstract](https://academic.oup.com/mnras/article/112/2/195/2601964)\n- [Philip J. Armitage2020: Bondi’s accretion model as a continuing astrophysical reference](https://arxiv.org/abs/2004.00203)\n",
      "summary": "Bondi solves the steady spherical polytropic accretion problem, identifies subsonic and critical transonic branches, and derives the mass-rate scaling and critical coefficient under an explicit inner-domain assumption.\n\nHow quickly can a star collect gas that is initially at rest far away? Gravity pulls it inward, while gas pressure resists compression. Bondi combines mass conservation with the energy equation to describe this competition using dimensionless variables. The accretion rate scales as the square of the central mass and the ambient gas density, divided by the cube of the ambient sound speed. A dimensionless coefficient labels the possible steady flows. When the modeled domain reaches the critical radius, that coefficient cannot exceed a gamma-dependent limit. At the critical value, a smooth solution can pass from subsonic to supersonic flow; smaller values also permit steady subsonic flows. The steady equations therefore do not uniquely select the physically realized rate. Bondi proposes an energy-based preference for the critical flow but expressly notes difficulties for an open, infinitely extended system. The result became a widely used reference model, although rotating flows, relativistic gravity, feedback and non-steady gas require additional physics.",
      "title": "Bondi: balance gravity and pressure in spherical gas accretion"
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    "what_changed": "Bondi solves the steady spherical polytropic accretion problem, identifies subsonic and critical transonic branches, and derives the mass-rate scaling and critical coefficient under an explicit inner-domain assumption.",
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        "title": "H. Bondi 1952, On spherically symmetrical accretion, completeoriginal 195-204",
        "url": "https://adsabs.harvard.edu/pdf/1952MNRAS.112..195B",
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