Milne–Eddington approximation
E818289
The Milne–Eddington approximation is a simplified model of stellar atmospheres that assumes constant physical properties with depth to make the radiative transfer equations analytically tractable.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Eddington approximation for radiative transfer | 1 |
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
astrophysical approximation
ⓘ
radiative transfer model ⓘ stellar atmosphere model ⓘ |
| advantage |
analytic tractability
ⓘ
computational simplicity ⓘ |
| appliesTo | stellar atmospheres ⓘ |
| approximationOf | full depth-dependent radiative transfer solution ⓘ |
| assumes |
constant continuum opacity with depth
ⓘ
constant line absorption coefficient with depth ⓘ constant physical properties with depth ⓘ gray atmosphere in many applications ⓘ linear source function with optical depth ⓘ local thermodynamic equilibrium ⓘ plane-parallel atmosphere ⓘ static atmosphere ⓘ |
| basedOn | Eddington approximation NERFINISHED ⓘ |
| characteristic |
allows closed-form expressions for emergent intensity
ⓘ
allows closed-form expressions for emergent polarization ⓘ neglects depth variation of many atmospheric parameters ⓘ treats line and continuum opacities in a simplified way ⓘ |
| comparedTo | more realistic multi-layer atmosphere models ⓘ |
| field |
astrophysics
ⓘ
radiative transfer theory ⓘ stellar astrophysics ⓘ |
| historicalContext | developed in early 20th century ⓘ |
| involves |
constant line-to-continuum opacity ratio
ⓘ
solution of the radiative transfer equation for a two-level atom in simplified form ⓘ source function linear in optical depth ⓘ |
| limitation |
cannot accurately represent strongly stratified atmospheres
ⓘ
limited accuracy for lines formed over large height ranges ⓘ |
| namedAfter |
Arthur Stanley Eddington
NERFINISHED
ⓘ
Edward Arthur Milne NERFINISHED ⓘ |
| purpose |
to interpret solar spectra
ⓘ
to interpret stellar spectra ⓘ to model spectral line formation ⓘ to obtain analytic solutions for radiative transfer ⓘ to simplify the radiative transfer equation ⓘ |
| relatedTo |
polarized radiative transfer
ⓘ
radiative transfer equation ⓘ spectral line formation theory ⓘ stellar atmosphere theory ⓘ |
| typicalApplication |
quick inversion of large spectropolarimetric data sets
ⓘ
solar photospheric line modeling ⓘ |
| usedFor |
analytic treatment of polarized radiative transfer
ⓘ
inversion of spectropolarimetric data ⓘ magnetic field diagnostics in stellar atmospheres ⓘ modeling of Stokes profiles ⓘ solar magnetic field measurements ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Eddington approximation for radiative transfer