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Interpreting Emission-Line Spectra
Because various emission lines sample different regimes of temperature, density, and ionization, emission spectra
are uniquely powerful probes of conditions around active nuclei. Remember, though, that they do sample
conditions
around
the central engine, which we can study only as it affects the surrounding gas.
Important references on emission-line processes are Osterbrock,
Astrophysics of Gaseous Nebulae and
Active Galactic Nuclei
(University Science Books); Spitzer,
Physical Processes in the Interstellar Medium
(Wiley-Interscience); Aller,
Physics of Thermal Gaseous Nebulae
, and for specifics of AGN applications,
Davidson and Netzer 1979 (Rev. Mod. Phys. 51, 715) and
Peterson's
AGN textbook
.
Review of the recombination theory in
the star-formation lecture
will be helpful. Every state of an atom or ion has
quantum numbers of importance here as follows:
Each (
l,s
) pair has multiplicity
g = 2s+1
- the number of energy levels with distinct
j
. For historical reasons,
different values of
l=0,1,2,3
are denoted in spectroscopic notation by S,P,D,F (strong, principal, diffuse, faint),
then G,H,.
.. A spectroscopic term (atomic state) is denoted by
n
g
L
J
.
For any possible transition between two states
m,n
there exist the Einstein transition coefficients
A
mn
, B
mn
, B
nm
.
These give the probabilities of transition between these two states.
A
mn
is the spontaneous transition rate per unit
time per atom, formally given by
in the first-order (electric dipole) expansion. The
B
values - the stimulated emission coefficient and the absorption
coefficient - are related as may be shown by considering thermodynamic equilibrium and detailed balance:
Here, for incident radiation intensity at the frequency Ȟ
mn
equal to U
Ȟ
, the probability of an induced downward
transition, or stimulated emission, is
B
mn
U
Ȟ
. Transitions with Δ
l
= ± 1 or Δ
s
= ± 1 are dipole (permitted)
transitions. Other kinds, via electric quadrupole or magnetic dipole moment, are possible but have generally
much lower
A
mn
; hence the term forbidden transitions. The upper levels in these cases are said to be metastable