vik dhillon: phy213 - the physics of stellar interiors - opacity
We first introduced the concept of opacity when deriving the
equation of radiative transport.
Opacity is the resistance of material to the flow of heat, which
in most stellar interiors is determined by all the processes which
scatter and absorb photons. We will now look at each of these
processes in turn, of which there are four:
The first three are known as true absorption processes because
they involve the disappearance of a photon, whereas the fourth
process only alters the direction of a photon. All four processes
are described below and are shown pictorially in
Schematic energy level diagram showing the four microscopic
processes which contribute to opacity in stellar interiors.
Bound-bound absorptions occur when an electron is moved from one orbit
in an atom or ion into another orbit of higher energy due to the
absorption of a photon. If the energy of the two orbits is
E1 and E2, a photon of
frequency bb will produce a
E2 - E1 =
Bound-bound processes are responsible for the spectral lines visible in
stellar spectra, which are formed in the atmospheres of stars. In
stellar interiors, however, bound-bound processes are not of great
importance as most of the atoms are highly ionised and only a small
fraction contain electrons in bound orbits. In addition, most of
the photons in stellar interiors are so energetic that they are more
likely to cause bound-free absorptions, as described below.
Bound-free absorptions involve the ejection of an electron from a
bound orbit around an atom or ion into a free hyperbolic orbit due
to the absorption of a photon. A photon of
frequency bf will convert a
bound electron of energy E1 into a free
electron of energy E3 if
E3 - E1 =
Provided the photon has sufficient energy to remove the electron from
the atom or ion, any value of energy can lead to a bound-free process. Bound-free
processes hence lead to continuous absorption in stellar atmospheres.
In stellar interiors, however, the importance of bound-free processes
is reduced due to the rarity of bound electrons.
Free-free absorption occurs when a free electron of energy
E3 absorbs a photon of frequency
ff and moves to a state
with energy E4, where
E4 - E3 =
There is no restriction on the energy of a photon which can induce
a free-free transition and hence free-free absorption is a
continuous absorption process which operates in both stellar
atmospheres and stellar interiors. Note that, in both
free-free and bound-free absorption, low energy photons are more
likely to be absorbed than high energy photons.
In addition to the above absorption processes, it is also possible for
a photon to be scattered by an electron or an atom. One can think of
scattering as a collision between two particles which bounce of one
another. If the energy of the photon satisfies
h << mc2,
where m is the mass of the particle doing the scattering, the
particle is scarcely moved by the collision. In this case the photon can
be imagined to be bounced off a stationary particle.
Although this process does not lead to the true absorption
of radiation, it does slow the rate at which energy escapes from a star
because it continually changes the direction of the photons.