A method allowing for a simplified solution to the
→ radiative transfer equation
at frequencies of spectral lines in media moving with a high velocity gradient.
This method assumes that
the macroscopic velocity gradients are more important than local random variations
of thermal line width:
dv/dr > vth/l,
where dv/dr is the velocity gradient, vth is the
thermal broadening of the line, and l the length scale.
The Sobolev approximation
is only valid if the conditions of the gas do not change over the
→ Sobolev length.
Under the Sobolev approximation, each point in the medium is isolated from
other points, and the → radiative transfer
problem becomes a local one and therefore
much easier to solve.
See also: Named after the Russian astronomer Viktor Viktorovich Sobolev,
Moving Envelopes of Stars [in Russian], Leningr. Gos. Univ., Leningrad (1947)
[translated by S. Gaposchkin, Harvard Univ. Press, Cambridge, Mass. (1960)];
→ approximation.
