Schuster–Schwarzschild theorem

E1018069

The Schuster–Schwarzschild theorem is a fundamental result in astrophysics that describes radiative transfer and the formation of spectral lines in stellar atmospheres under conditions of radiative equilibrium.

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Schuster–Schwarzschild theorem canonical 1

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Statements (46)

Predicate Object
instanceOf astrophysics theorem ⓘ
theorem in radiative transfer ⓘ
appliesTo stellar atmospheres ⓘ
approximationType two-layer or multi-layer idealized atmosphere model ⓘ
assumes no scattering or simplified scattering treatment ⓘ
plane-parallel atmosphere ⓘ
radiative equilibrium ⓘ
static atmosphere ⓘ
boundaryCondition diffusion approximation at large optical depth ⓘ
specified incident radiation at the top of the atmosphere ⓘ
category theorems in astrophysics ⓘ
theorems in physics ⓘ
concerns depth of formation of spectral lines ⓘ
intensity distribution emerging from a stellar atmosphere ⓘ
context classical theory of stellar atmospheres ⓘ
describes formation of spectral lines ⓘ
radiative transfer in stellar atmospheres ⓘ
field astrophysics ⓘ
radiative transfer ⓘ
stellar astrophysics ⓘ
goal connect emergent intensity with physical conditions in the atmosphere ⓘ
historicalImportance early foundation of quantitative stellar atmosphere theory ⓘ
impact clarified role of optical depth in line formation ⓘ
provided basis for interpreting stellar spectra quantitatively ⓘ
influenced development of line-blanketed atmosphere calculations ⓘ
later stellar atmosphere models ⓘ
involves Eddington-type approximations ⓘ
radiative equilibrium condition ⓘ
mathematicalForm solution of the radiative transfer equation with simplified boundary conditions ⓘ
namedAfter Arthur Schuster ⓘ
Karl Schwarzschild ⓘ
provides analytic solution for radiative transfer in idealized atmospheres ⓘ
relatedTo Eddington approximation ⓘ
Milne–Eddington atmosphere ⓘ
radiative transfer equation ⓘ
source function in LTE ⓘ
relates mean intensity of radiation ⓘ
optical depth ⓘ
source function ⓘ
status classical approximation, not a full numerical model ⓘ
typicalAssumption local thermodynamic equilibrium (LTE) ⓘ
usedFor deriving approximate line profiles ⓘ
modeling stellar spectral line formation ⓘ
understanding continuum and line formation layers ⓘ
usedIn introductory treatments of stellar atmospheres ⓘ
pedagogical derivations of line formation theory ⓘ

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Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Arthur Schuster → knownFor → Schuster–Schwarzschild theorem ⓘ