{
  "id": "1112.4223",
  "version": "v5",
  "published": "2011-12-19T02:54:03.000Z",
  "updated": "2012-11-07T02:50:02.000Z",
  "title": "Scaling Symmetry and Integrable Spherical Hydrostatics",
  "authors": [
    "Sidney Bludman",
    "Dallas C. Kennedy"
  ],
  "comment": "10 pages, 4 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1106.1222",
  "journal": "Journal of Modern Physics, Vol. 4 No. 4 (April 2013) 486-494",
  "categories": [
    "math-ph",
    "astro-ph.SR",
    "math.MP",
    "physics.class-ph",
    "physics.flu-dyn"
  ],
  "abstract": "Any symmetry reduces a second-order differential equation to a first integral: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion (exemplified by scale-invariant hydrostatics) yield first-order {\\em non-conservation laws} between invariants. We obtain these non-conservation laws by extending Noether's Theorem to non-variational symmetries and present an innovative variational formulation of spherical adiabatic hydrostatics. For the scale-invariant case, this novel synthesis of group theory, hydrostatics, and astrophysics allows us to recover all the known properties of polytropes and define a {\\em core radius}, inside which polytropes of index $n$ share a common core mass density structure, and outside of which their envelopes differ. The Emden solutions (regular solutions of the Lane-Emden equation) are obtained, along with useful approximations. An appendix discusses the $n=3$ polytrope in order to emphasize how the same mechanical structure allows different thermal structures in relativistic degenerate white dwarfs and zero age main sequence stars.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2012-11-07T02:50:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integrable spherical hydrostatics",
      "scaling symmetry",
      "zero age main sequence stars",
      "common core mass density structure",
      "non-conservation laws"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.4236/jmp.2013.44069"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1082085,
      "adsabs": "2011arXiv1112.4223B"
    }
  }
}