R. Ignace et Ma. Hendry, Analytic inversion of emission lines of arbitrary optical depth for the structure of supernova ejecta, ASTROPHYS J, 537(2), 2000, pp. L131-L134
We derive a method for inverting emission-line profiles formed in supernova
ejecta. The derivation assumes spherical symmetry and homologous expansion
[i.e., nu(r) proportional to r], is analytic, and even takes account of oc
cultation by a pseudophotosphere. Previous inversion methods have been deve
loped that are restricted to optically thin lines, but the particular case
of homologous expansion permits an analytic result for lines of arbitrary o
ptical depth. In fact, we show that the quantity that is generically retrie
ved is the run of line intensity I-lambda with radius in the ejecta. This r
esult is quite general and so could be applied to resonance lines, recombin
ation lines, etc. As a specific example, we show how to derive the run of (
Sobolev) optical depth tau(lambda) with radius in the case of a pure resona
nce scattering emission line.