3.5.3 The Swings and Greenstein Effects
CN, C 3 and C 2 all have emissions at visible wavelengths (Fig. 3.44). As in the case
of infrared emissions, beyond a few hundred kilometres from the nucleus, collisions
are rare and so resonant fluorescence of sunlight by these species at discrete
wavelengths dominates.
As with the infrared vibrational bands (Eq. 3.38), the observed intensity scattered
by an optically thin column illuminated by the Sun is given by
I ¼
hϑ
4π
g f
r 2
h
N g p α
ð Þ
ð3:118Þ
where a phase function for single scattering by gas at a phase angle, α, has now
been included. p(α) is normalized to 1 and is usually taken to be independent
of α. However, there may be some effect on p(α) as a result of polarization (see
Chamberlain and Hunten 1987). As before, g f is referred to as the “g-factor” and
is given by
g f J
0 , J i
ð
Þ¼F
πq
2
c
mc
f osc J
0 , J i
ð
Þ
A J
0 , J i
ð
Þ
P
i
J
0 , J i
ð
Þ
ð3:119Þ
where f osc is the oscillator strength for the particular transition and A(J’,J i ) is the
transition probability. (Caution should be exercised with this equation as most
authors define the solar flux to be equal to πF ⨀ rather than simply F ⨀ as we have
done here.) This value (normalized to 1 AU from the Sun) can be tabulated for
important transitions. However, for cometary radicals with near-UV and visible
transitions, the Doppler shift with respect to the Sun, caused primarily by the orbital
speed, is of significance. The expected wavelength shift is given by
Δλ
λ
¼
v h
c
ð3:120Þ
where v h is the heliocentric velocity and hence species moving with respect to the
Sun “see” the solar flux at a Doppler-shifted wavelength. A simple example of this
with just two transitions within a wavelength range is sodium D-line emission.
Figure 3.50 shows the solar spectrum around the 589.0 and 589.6 nm lines.
Absorptions by elements in the solar photosphere are sometimes referred to as the
Fraunhofer absorptions and, in the case of sodium, are very deep. A sodium atom
with a zero radial velocity component with respect to the Sun, will see a low solar
flux in the bottom of this absorption line. However, radial velocities of the order of
15–20 km s
À1 are sufficient to almost double the incident flux and hence the same
column density will appear brighter to an observer. In the case of sodium, this effect
has been seen prominently in the Jupiter system associated with sodium emitted
from the innermost Galilean moon, Io (e.g. Goldberg et al. 1984; Thomas 1992).
3.5 Reaction Chemistry and the Extended Coma
263
CN, C 3 and C 2 all have emissions at visible wavelengths (Fig. 3.44). As in the case
of infrared emissions, beyond a few hundred kilometres from the nucleus, collisions
are rare and so resonant fluorescence of sunlight by these species at discrete
wavelengths dominates.
As with the infrared vibrational bands (Eq. 3.38), the observed intensity scattered
by an optically thin column illuminated by the Sun is given by
I ¼
hϑ
4π
g f
r 2
h
N g p α
ð Þ
ð3:118Þ
where a phase function for single scattering by gas at a phase angle, α, has now
been included. p(α) is normalized to 1 and is usually taken to be independent
of α. However, there may be some effect on p(α) as a result of polarization (see
Chamberlain and Hunten 1987). As before, g f is referred to as the “g-factor” and
is given by
g f J
0 , J i
ð
Þ¼F
πq
2
c
mc
f osc J
0 , J i
ð
Þ
A J
0 , J i
ð
Þ
P
i
J
0 , J i
ð
Þ
ð3:119Þ
where f osc is the oscillator strength for the particular transition and A(J’,J i ) is the
transition probability. (Caution should be exercised with this equation as most
authors define the solar flux to be equal to πF ⨀ rather than simply F ⨀ as we have
done here.) This value (normalized to 1 AU from the Sun) can be tabulated for
important transitions. However, for cometary radicals with near-UV and visible
transitions, the Doppler shift with respect to the Sun, caused primarily by the orbital
speed, is of significance. The expected wavelength shift is given by
Δλ
λ
¼
v h
c
ð3:120Þ
where v h is the heliocentric velocity and hence species moving with respect to the
Sun “see” the solar flux at a Doppler-shifted wavelength. A simple example of this
with just two transitions within a wavelength range is sodium D-line emission.
Figure 3.50 shows the solar spectrum around the 589.0 and 589.6 nm lines.
Absorptions by elements in the solar photosphere are sometimes referred to as the
Fraunhofer absorptions and, in the case of sodium, are very deep. A sodium atom
with a zero radial velocity component with respect to the Sun, will see a low solar
flux in the bottom of this absorption line. However, radial velocities of the order of
15–20 km s
À1 are sufficient to almost double the incident flux and hence the same
column density will appear brighter to an observer. In the case of sodium, this effect
has been seen prominently in the Jupiter system associated with sodium emitted
from the innermost Galilean moon, Io (e.g. Goldberg et al. 1984; Thomas 1992).
3.5 Reaction Chemistry and the Extended Coma
263