related to the energy input while the gas loss rate is related to the gas diffusion
coefficient, D g . In the simplest case of fluid diffusion in one dimension, this can be
represented by Fick’s law
j x ¼ ÀD g
dn g
dx
ð2:136Þ
where j x is the gas flux. If the flux away from the source is slower than the source
rate, then pressure must increase at the source. The source rate is related to the
thermal conductivity and hence the source and loss rates are not entirely independent
of each other. (A lower diffusion rate will, in general, result from good thermal
contact.)
Assuming steady-state and a constant temperature across the porous layer, the 1D
diffusion equation can be inverted to give the gradient in number density across a
porous medium of depth. This allows us to calculate a pressure difference using the
constant temperature assumption if the diffusion coefficient can be estimated.
Typical values would be of the order of 10
À5 m
2 s
À1 and, in simplified cases, is
directly proportional to the porosity (Huebner et al. 2006). For a gas emission rate of
3 Â 10
19 molecule m
À2 s
À1 at a depth of 5 cm (cf. Fig. 2.32), the pressure difference
is over 400 Pa and therefore exceeds most estimates of the structural (tensile)
strength of cometary material.
While this is a crude estimate with numerous simplifying assumptions, it illustrates that pressure can be built up under the right conditions to allow explosive
events and could be a viable explanation for dust pit production and other surface
disruption phenomena.
2.10.15 Ice Exposures
The search for exposed ice on the nuclei of comets has been somewhat frustrating. It
was recognized at the time of the 1P/Halley fly-by that local variations in brightness
on the nucleus were small and probably less than 50% at resolutions of ~100 m.
Given the low overall albedo, it was clear at this time that pure, highly reflecting,
large area, ice surfaces could not be present on the nucleus. Variations in brightness
alone would, in any case, not have been sufficient to demonstrate the presence of
surficial water ice. The first clear detection of exposed water ice (Fig. 2.103) was
made by the Deep Impact spacecraft at 9P/Tempel 1 (Sunshine et al. 2006) using the
strong infrared absorptions at 1.5 and 2.0 μm (Fig. 2.40). The total area of exposed
water ice was far below that required to produce the observed water production rate
and the visible brightness ratio of icy areas to non-icy areas was small. Hence other
sources of subliming water ice were “hidden” from the remote sensing
investigations.
Water ice was equally difficult to detect with the infrared spectrometer (VIRTIS)
onboard Rosetta (Capaccioni et al. 2015) with first results noting the complete
2.10 Surface Appearance and Cometary “Geology”
169
coefficient, D g . In the simplest case of fluid diffusion in one dimension, this can be
represented by Fick’s law
j x ¼ ÀD g
dn g
dx
ð2:136Þ
where j x is the gas flux. If the flux away from the source is slower than the source
rate, then pressure must increase at the source. The source rate is related to the
thermal conductivity and hence the source and loss rates are not entirely independent
of each other. (A lower diffusion rate will, in general, result from good thermal
contact.)
Assuming steady-state and a constant temperature across the porous layer, the 1D
diffusion equation can be inverted to give the gradient in number density across a
porous medium of depth. This allows us to calculate a pressure difference using the
constant temperature assumption if the diffusion coefficient can be estimated.
Typical values would be of the order of 10
À5 m
2 s
À1 and, in simplified cases, is
directly proportional to the porosity (Huebner et al. 2006). For a gas emission rate of
3 Â 10
19 molecule m
À2 s
À1 at a depth of 5 cm (cf. Fig. 2.32), the pressure difference
is over 400 Pa and therefore exceeds most estimates of the structural (tensile)
strength of cometary material.
While this is a crude estimate with numerous simplifying assumptions, it illustrates that pressure can be built up under the right conditions to allow explosive
events and could be a viable explanation for dust pit production and other surface
disruption phenomena.
2.10.15 Ice Exposures
The search for exposed ice on the nuclei of comets has been somewhat frustrating. It
was recognized at the time of the 1P/Halley fly-by that local variations in brightness
on the nucleus were small and probably less than 50% at resolutions of ~100 m.
Given the low overall albedo, it was clear at this time that pure, highly reflecting,
large area, ice surfaces could not be present on the nucleus. Variations in brightness
alone would, in any case, not have been sufficient to demonstrate the presence of
surficial water ice. The first clear detection of exposed water ice (Fig. 2.103) was
made by the Deep Impact spacecraft at 9P/Tempel 1 (Sunshine et al. 2006) using the
strong infrared absorptions at 1.5 and 2.0 μm (Fig. 2.40). The total area of exposed
water ice was far below that required to produce the observed water production rate
and the visible brightness ratio of icy areas to non-icy areas was small. Hence other
sources of subliming water ice were “hidden” from the remote sensing
investigations.
Water ice was equally difficult to detect with the infrared spectrometer (VIRTIS)
onboard Rosetta (Capaccioni et al. 2015) with first results noting the complete
2.10 Surface Appearance and Cometary “Geology”
169