Transitions from one electronic state to a lower level will result in photo-emission
at visible or UV wavelengths (λ ⪅ 1 μm). Vibrational transitions occur in the near to
mid-infrared (λ ~ 1–100 μm) while rotational transitions result in emission in the
far-infrared and microwave (λ ⪆ 100 μm). In a first approximation, the BornOppenheimer approximation, these types of transitions can be treated separately
(Lopez-Puertas and Taylor 2001).
The interpretation of the resulting emissions requires knowledge of the processes
involved and the density regime that the emitting species find themselves in. These
processes can be separated into collisional excitation and radiative processes
(Bockelée-Morvan et al. 2004a). Coma gases have temperatures that are very
much less than ~1000 K so that electronic and vibrational excitations occur mainly
as a result of radiative processes (Combi 1996). Irradiance by the Sun is the main
source of the radiation in this case although other processes, such as electron impact
excitation, prompt emissions arising from dissociation reactions, and thermal collisional losses, are of importance.
In the innermost coma of an active comet, local thermal equilibrium (LTE) may
be reached when there are sufficient collisions to thermalize the rotational
populations of the ground vibrational states of the major species at the kinetic
temperature of the gas (Zakharov et al. 2007). The collisions lead to a Maxwellian
distribution for the velocity distribution function (VDF). We shall see in Sect. 3.4
that although the gas is tenuous, the VDF does indeed tend towards a Maxwellian
distribution within a few kilometres of the nucleus surface for an active comet.
However, with the gas density dropping rapidly with distance (Eq. 3.1) and the mean
free path increasing (Fig. 3.19), collisions become infrequent and the VDF can no
longer be described as a Maxwellian. Hence, with such low temperatures, all of the
vibrational bands are in non-LTE everywhere in the coma and the concept of LTE
also becomes meaningless for the rotational populations beyond a few tens of
kilometres even for an active nucleus.
For active comets, optical thickness effects need to be accounted for. In particular,
the rotational lines of H 2 O are subject to self-absorption effects in active comets and
are important in Rosetta observations of the innermost coma of 67P. Consequently, it
is necessary to make a short diversion and look at the radiative transfer equation for
an optically thick medium before going into more detail.
In the general case, light can be removed from a beam through both absorption
and scattering with extinction being the sum of the absorption and scattering crosssections. Let us begin by assuming that scattering can be ignored. The decrease in
radiance at a specific frequency when travelling along a path of interval, ds, through
an absorbing medium is given by
dI ϑ ¼ Àκ ϑ I ϑ ds
ð3:10Þ
where κ ϑ is the absorption coefficient in units of [m
À1 ]. The absorption coefficient
can be expressed in terms of the absorption cross-section, σ abs , which is frequency
dependent, through
3.2 Major Species and Their Emissions
185
at visible or UV wavelengths (λ ⪅ 1 μm). Vibrational transitions occur in the near to
mid-infrared (λ ~ 1–100 μm) while rotational transitions result in emission in the
far-infrared and microwave (λ ⪆ 100 μm). In a first approximation, the BornOppenheimer approximation, these types of transitions can be treated separately
(Lopez-Puertas and Taylor 2001).
The interpretation of the resulting emissions requires knowledge of the processes
involved and the density regime that the emitting species find themselves in. These
processes can be separated into collisional excitation and radiative processes
(Bockelée-Morvan et al. 2004a). Coma gases have temperatures that are very
much less than ~1000 K so that electronic and vibrational excitations occur mainly
as a result of radiative processes (Combi 1996). Irradiance by the Sun is the main
source of the radiation in this case although other processes, such as electron impact
excitation, prompt emissions arising from dissociation reactions, and thermal collisional losses, are of importance.
In the innermost coma of an active comet, local thermal equilibrium (LTE) may
be reached when there are sufficient collisions to thermalize the rotational
populations of the ground vibrational states of the major species at the kinetic
temperature of the gas (Zakharov et al. 2007). The collisions lead to a Maxwellian
distribution for the velocity distribution function (VDF). We shall see in Sect. 3.4
that although the gas is tenuous, the VDF does indeed tend towards a Maxwellian
distribution within a few kilometres of the nucleus surface for an active comet.
However, with the gas density dropping rapidly with distance (Eq. 3.1) and the mean
free path increasing (Fig. 3.19), collisions become infrequent and the VDF can no
longer be described as a Maxwellian. Hence, with such low temperatures, all of the
vibrational bands are in non-LTE everywhere in the coma and the concept of LTE
also becomes meaningless for the rotational populations beyond a few tens of
kilometres even for an active nucleus.
For active comets, optical thickness effects need to be accounted for. In particular,
the rotational lines of H 2 O are subject to self-absorption effects in active comets and
are important in Rosetta observations of the innermost coma of 67P. Consequently, it
is necessary to make a short diversion and look at the radiative transfer equation for
an optically thick medium before going into more detail.
In the general case, light can be removed from a beam through both absorption
and scattering with extinction being the sum of the absorption and scattering crosssections. Let us begin by assuming that scattering can be ignored. The decrease in
radiance at a specific frequency when travelling along a path of interval, ds, through
an absorbing medium is given by
dI ϑ ¼ Àκ ϑ I ϑ ds
ð3:10Þ
where κ ϑ is the absorption coefficient in units of [m
À1 ]. The absorption coefficient
can be expressed in terms of the absorption cross-section, σ abs , which is frequency
dependent, through
3.2 Major Species and Their Emissions
185