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.
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
NERFINISHED
ⓘ
Karl Schwarzschild NERFINISHED ⓘ |
| provides | analytic solution for radiative transfer in idealized atmospheres ⓘ |
| relatedTo |
Eddington approximation
NERFINISHED
ⓘ
Milne–Eddington atmosphere NERFINISHED ⓘ 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 ⓘ |
Referenced by (1)
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