the vectorial model (e.g. Fig. 3.47) and appropriate g-factors for the emission rate
(taking into account phenomena such as the Swings effect for near-UV bands of
OH). The total volatile production rate also includes the other major species, CO 2
and CO. Their contribution is less easily established but assuming that water
contributes roughly 90% to the total volatile loss (Sect. 3.2) seems to be a reasonable
assumption. Consequently, the volatile emission from the nucleus at any one time
can be obtained reasonably well. However, variability is significant. The ROSINA
data provide by far the most comprehensive measurements of local gas densities at
the spacecraft that can be extrapolated to gas production rates over the mission
(Hansen et al. 2016). Integration of Hansen’s fit to the Rosetta data sets and
assuming water as the dominant species leads a volatile loss of 6.3 10
9 kg which
in combination with the total mass lost (Pätzold et al. 2019; Sect. 2.3) leads to a Q d /
Q g (integrated over the orbit) of ~0.7 Æ 0.5 where we have used Pätzold’s error
estimate alone. There are clearly assumptions needed to produce the gas production
rates and Hansen’s model is also somewhat artificial but this is probably one of the
most reliable approaches to determine the gas mass loss.
Biver et al. (2019) arrived at a total water production for the apparition in the
range of 4.0–5.8 10
9 kg (see Choukroun et al. 2020 for a review) which would place
Q d /Q g at between 0.7 and 2.3 using the nominal value of Pätzold et al. (2019).
For the non-volatile component, an independent measurement of the total production is far more difficult to establish because the mass loss seems to be dominated
by the largest particles emitted by the nucleus. Potentially, the loss of a few
individual particles (perhaps better described as boulders) that are unseen from the
ground (because of resolution) or from in situ observation (because of instrumental
measurement limits on detection and outflow velocity) dominate the mass loss.
Nonetheless, it is instructive to see if the values of Afρ are consistent with the
estimated total mass loss while keeping in mind the caveats.
Using Table 4.1, we can set the dust size distribution power law exponent to 2.8
which encompasses values for both 1P/Halley and 67P. Figure 4.18 indicates Afρ
through the Rosetta mission and we have seen in Fig. 4.32 that individual points can
be converted to obtain a dust mass production rate depending upon the scattering
properties such as the use of Mie theory, the refractive index for the Mie equations,
and an assumed particle size dependent velocity distribution, v d (a), using Eq. 4.105.
We have also seen Eq. 4.101 that v d (a) is a straightforward function of the gas
production rate. Hence, we can use the gas production rate of Hansen et al. (2016) to
support interpolation of the values of v d (a) derived by Marschall (2017) from gas
dynamics simulations. Inversion of Eq. 4.105 for each measured Afρ value of Gerig
et al. (2018) then provides a function that can be integrated to give a total dust mass
loss. This is novel because all other measurements for dust mass loss are either
derived from the difference between the total mass loss and the gas mass lost or they
are extrapolations from in situ dust measurements obtained mostly at the terminator
in the case of Rosetta. Here, 2D remote-sensing provides a more global estimate.
The result of this procedure gives 12.3 10
9 kg. Taken at face value, this is
inconsistent with other measurements because it is close to Pätzold et al.’s upper
limit for the total mass loss including gas. However, two assumptions have been
4.15 Refractory to Volatile Ratios
393
(taking into account phenomena such as the Swings effect for near-UV bands of
OH). The total volatile production rate also includes the other major species, CO 2
and CO. Their contribution is less easily established but assuming that water
contributes roughly 90% to the total volatile loss (Sect. 3.2) seems to be a reasonable
assumption. Consequently, the volatile emission from the nucleus at any one time
can be obtained reasonably well. However, variability is significant. The ROSINA
data provide by far the most comprehensive measurements of local gas densities at
the spacecraft that can be extrapolated to gas production rates over the mission
(Hansen et al. 2016). Integration of Hansen’s fit to the Rosetta data sets and
assuming water as the dominant species leads a volatile loss of 6.3 10
9 kg which
in combination with the total mass lost (Pätzold et al. 2019; Sect. 2.3) leads to a Q d /
Q g (integrated over the orbit) of ~0.7 Æ 0.5 where we have used Pätzold’s error
estimate alone. There are clearly assumptions needed to produce the gas production
rates and Hansen’s model is also somewhat artificial but this is probably one of the
most reliable approaches to determine the gas mass loss.
Biver et al. (2019) arrived at a total water production for the apparition in the
range of 4.0–5.8 10
9 kg (see Choukroun et al. 2020 for a review) which would place
Q d /Q g at between 0.7 and 2.3 using the nominal value of Pätzold et al. (2019).
For the non-volatile component, an independent measurement of the total production is far more difficult to establish because the mass loss seems to be dominated
by the largest particles emitted by the nucleus. Potentially, the loss of a few
individual particles (perhaps better described as boulders) that are unseen from the
ground (because of resolution) or from in situ observation (because of instrumental
measurement limits on detection and outflow velocity) dominate the mass loss.
Nonetheless, it is instructive to see if the values of Afρ are consistent with the
estimated total mass loss while keeping in mind the caveats.
Using Table 4.1, we can set the dust size distribution power law exponent to 2.8
which encompasses values for both 1P/Halley and 67P. Figure 4.18 indicates Afρ
through the Rosetta mission and we have seen in Fig. 4.32 that individual points can
be converted to obtain a dust mass production rate depending upon the scattering
properties such as the use of Mie theory, the refractive index for the Mie equations,
and an assumed particle size dependent velocity distribution, v d (a), using Eq. 4.105.
We have also seen Eq. 4.101 that v d (a) is a straightforward function of the gas
production rate. Hence, we can use the gas production rate of Hansen et al. (2016) to
support interpolation of the values of v d (a) derived by Marschall (2017) from gas
dynamics simulations. Inversion of Eq. 4.105 for each measured Afρ value of Gerig
et al. (2018) then provides a function that can be integrated to give a total dust mass
loss. This is novel because all other measurements for dust mass loss are either
derived from the difference between the total mass loss and the gas mass lost or they
are extrapolations from in situ dust measurements obtained mostly at the terminator
in the case of Rosetta. Here, 2D remote-sensing provides a more global estimate.
The result of this procedure gives 12.3 10
9 kg. Taken at face value, this is
inconsistent with other measurements because it is close to Pätzold et al.’s upper
limit for the total mass loss including gas. However, two assumptions have been
4.15 Refractory to Volatile Ratios
393