While this might sound pleasing, there are numerous assumptions leading to large
uncertainties. The scattering model used here is Mie theory which produces phase
functions that are strongly forward scattering for larger particles. This forces the fits
to lower particle sizes which scatter more isotropically. Other scattering models can
produce significantly different (usually larger) values for the phase curve at 90
phase angle and would change the fit parameters. The assumption of a single size is
not tenable but introduction of a size distribution implies at least 1 more free
parameter. (The use of a single size in combination with Mie theory actually
complicates the inversion because of the oscillations we have seen in, for example,
Fig. 4.5 affect the numerical search for minima.) Also, as discussed above and
evident in Fig. 4.5, m ref is a function of wavelength but has been assumed constant.
It should be noted that although we have spectra, there are de facto only three data
points to fit; the temperature and amplitude of the Planck function of the thermal
emission and the amplitude of the Planck function corresponding to the reflected
sunlight. As we have at least five free parameters here (m ref,i , m ref,r , ε, x, and a scaling
factor corresponding to the column density) as well as a choice of scattering model,
some degeneracy in the solutions cannot be avoided.
Bockelée-Morvan et al. (2019) performed a more sophisticated fitting by incorporating dust colour into the fit (although the magnitude of the colour gradient was
small as can also be seen by the rather good fit to the reflected continuum seen in
Fig. 4.65 which does not include this term) and limiting the free parameters by using
a bolometric albedo to avoid specifying a particle size. However, in all cases, one
obtains a dust temperature fairly accurately. The derived temperature here is above
the free sublimation temperature of water ice suggesting that sublimation cooling of
the particles is not a dominant process even in the innermost coma.
The VIRTIS-H data for this analysis were line of sight integrations above the limb
of the nucleus. Motion of the spacecraft pointing allowed study of the variation in
dust properties with the impact parameter. Bockelée-Morvan et al. (2019) concluded
that there were variations in colour temperature with impact parameter with the
computed albedo increasing with distance above the limb (from 0 km to ~8 km). It
needs to be noted that this region is extremely dynamic with large changes in the dust
size distribution with cometocentric distance occurring because of the acceleration
gradient between small and large particles. Hence, the interpretation of this result is
by no means straightforward.
4.12.3 The Polarization of the Scattered Light
In the discussion of the Stokes vector (Eq. 4.6), we saw how the linear polarization is
defined. Sunlight scattered from comets is partially polarized. The plane of linear
polarization is either perpendicular or parallel to the scattering plane that is defined
by the Sun, Earth, and the comet (Zubko et al. 2016). The degree of linear polarization can then be expressed as
380
4 Dust Emission from the Surface
uncertainties. The scattering model used here is Mie theory which produces phase
functions that are strongly forward scattering for larger particles. This forces the fits
to lower particle sizes which scatter more isotropically. Other scattering models can
produce significantly different (usually larger) values for the phase curve at 90
phase angle and would change the fit parameters. The assumption of a single size is
not tenable but introduction of a size distribution implies at least 1 more free
parameter. (The use of a single size in combination with Mie theory actually
complicates the inversion because of the oscillations we have seen in, for example,
Fig. 4.5 affect the numerical search for minima.) Also, as discussed above and
evident in Fig. 4.5, m ref is a function of wavelength but has been assumed constant.
It should be noted that although we have spectra, there are de facto only three data
points to fit; the temperature and amplitude of the Planck function of the thermal
emission and the amplitude of the Planck function corresponding to the reflected
sunlight. As we have at least five free parameters here (m ref,i , m ref,r , ε, x, and a scaling
factor corresponding to the column density) as well as a choice of scattering model,
some degeneracy in the solutions cannot be avoided.
Bockelée-Morvan et al. (2019) performed a more sophisticated fitting by incorporating dust colour into the fit (although the magnitude of the colour gradient was
small as can also be seen by the rather good fit to the reflected continuum seen in
Fig. 4.65 which does not include this term) and limiting the free parameters by using
a bolometric albedo to avoid specifying a particle size. However, in all cases, one
obtains a dust temperature fairly accurately. The derived temperature here is above
the free sublimation temperature of water ice suggesting that sublimation cooling of
the particles is not a dominant process even in the innermost coma.
The VIRTIS-H data for this analysis were line of sight integrations above the limb
of the nucleus. Motion of the spacecraft pointing allowed study of the variation in
dust properties with the impact parameter. Bockelée-Morvan et al. (2019) concluded
that there were variations in colour temperature with impact parameter with the
computed albedo increasing with distance above the limb (from 0 km to ~8 km). It
needs to be noted that this region is extremely dynamic with large changes in the dust
size distribution with cometocentric distance occurring because of the acceleration
gradient between small and large particles. Hence, the interpretation of this result is
by no means straightforward.
4.12.3 The Polarization of the Scattered Light
In the discussion of the Stokes vector (Eq. 4.6), we saw how the linear polarization is
defined. Sunlight scattered from comets is partially polarized. The plane of linear
polarization is either perpendicular or parallel to the scattering plane that is defined
by the Sun, Earth, and the comet (Zubko et al. 2016). The degree of linear polarization can then be expressed as
380
4 Dust Emission from the Surface