phenomenon 52.25 The Sun rings, and its interior can be inverted

open in the book · parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1948 · p. 1409

phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt

Rests on

depends_on equation 52.39 eq:stellar-duvall ¶
depends_on proposition 52.24 The p-mode cavity ¶
- depends_on equation 52.20 eq:stellar-brunt ¶
- depends_on theorem 31.12 Conservation of mass ¶
  - depends_on lemma 31.11 Transport theorem for a material volume ¶
    - depends_on definition 31.4 Material derivative ¶
      - depends_on equation 7.124 eq:ana-nabla-gradient ¶
      - depends_on proposition 7.104 Chain rule in several variables ¶
      - proves proof ch:14-fluid-dynamics@proof-1 ¶
    - depends_on theorem 7.133 Gauss ¶
      - depends_on definition 7.127 Simple regions ¶
      - depends_on remark 7.128 What the derivations below take as given ¶
      - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - proves proof ch:05-real-analysis@proof-79 ¶
    - proves proof ch:14-fluid-dynamics@proof-4 ¶
  - proves proof ch:14-fluid-dynamics@proof-5 ¶
- depends_on theorem 31.22 Euler's equations of motion ¶
  - depends_on definition 31.21 Ideal fluid ¶
    - depends_on definition 31.1 Fluid ¶
      - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
  - depends_on lemma 31.11 Transport theorem for a material volume ¶ ↺
  - depends_on theorem 30.21 Cauchy's equation of motion ¶
    - depends_on theorem 7.133 Gauss ¶ ↺
    - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶ ↺
    - proves proof ch:13-continuum-elasticity@proof-9 ¶
  - proves proof ch:14-fluid-dynamics@proof-11 ¶
- depends_on theorem 9.78 Semiclassical quantisation of a well ¶
  - depends_on corollary 9.62 The semiclassical wave ¶
    - depends_on equation 9.62 eq:slt-wkb-ansatz ¶
    - depends_on equation 9.61 eq:slt-wkb-kappa ¶
    - depends_on proposition 9.61 Eikonal and transport equations ¶
      - depends_on equation 9.64 eq:slt-wkb-series ¶
      - depends_on proposition 9.60 Exact Riccati form ¶
      - proves proof ch:07-odes-sturm-liouville@proof-31 ¶
    - proves proof ch:07-odes-sturm-liouville@proof-32 ¶
  - depends_on equation 9.59 eq:slt-wkb-schrodinger ¶
  - depends_on theorem 9.72 Connection formulae ¶
    - depends_on corollary 9.62 The semiclassical wave ¶ ↺
    - depends_on equation 9.79 eq:slt-wkb-airy-ai ¶
    - depends_on equation 9.80 eq:slt-wkb-airy-bi ¶
    - depends_on equation 9.76 eq:slt-wkb-airy-equation ¶
    - depends_on equation 9.74 eq:slt-wkb-airy-scale ¶
    - proves proof ch:07-odes-sturm-liouville@proof-37 ¶
  - proves proof ch:07-odes-sturm-liouville@proof-40 ¶
- proves proof ch:11-stellar-structure-nucleosynthesis@proof-20 ¶
proves proof ch:11-stellar-structure-nucleosynthesis@proof-21 ¶

Supports

depends_on phenomenon 52.22 The solar-neutrino deficit, and its resolution ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`cites`	→	The Chemical Composition of the Sun	derived	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1962
`cites`	→	New Solar Opacities, Abundances, Helioseismology, and Neutrino Fluxes	derived	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1962
`cites`	→	Helioseismology	derived	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1959
`cites`	→	Observations of low wavenumber nonradial eigenmodes of the sun	derived	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1955
`cites`	→	Velocity Fields in the Solar Atmosphere. I. Preliminary Report	derived	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1951
`cites`	→	The Five-Minute Oscillations on the Solar Surface	derived	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1954
`depends_on`	→	eq:stellar-duvall	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1963
`depends_on`	→	The p-mode cavity	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1963
`depends_on`	←	The solar-neutrino deficit, and its resolution	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1689
`proves`	←	ch:11-stellar-structure-nucleosynthesis@proof-21	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1966