Sublimation of Ices
Notice: These pages were updated on 12 July 2004 to correct an
error of a factor 2 in the calclations of the rapidly rotating
model. The other calculations were correct. The web forms were
disabled temporarily because they were leaving processes running.
These web pages provide a simple tool to calculate the sublimation
of ices under various circumstances. The calculations are all
based on the methods described by Cowan and A'Hearn (1979
Moon and Planets 21, 155-171), which in turn are based
on earlier work by Delsemme and others. These calculations are the
basis, e.g., for the "active areas" of cometary nuclei
discussed by A'Hearn et al. (1995 Icarus
118, 223-270). The calculations have not been substantially
altered from the original publication and use essentially the same
code. We note, as pointed out to us by W. Huebner and D. Boice, that
our use of empirical results for heat of sublimation
and vapor pressure leads our result to be inconsistent with the
Clausius-Clapeyron equation, but this has negligible effect on the
results for most (but not all) physical situations. These pages
are posted largely as a convenience for the people who ask us for
various results. Results are available for pure water, pure CO,
pure CO2, and for water clathrates (assumed to release
caged molecules as the water itself evaporates; this calculates
the rate of water sublimation and the rate of caged molecule
sublimation is obtained by multiplying by the clathrate abundance
ratio).
Normal Surfaces and Isothermal Spheres
Sublimation from a surface normal to the sun and from an isothermal
sphere are relatively straightforward to calculate. We note that
the isothermal sphere is sometimes incorrectly referred to as a
fast-rotator (see below). When averaging over a real cometary
nucleus, at least for simple, convex geometries, the normal surface
represents the highest possible sublimation, while the isothermal
sphere represents the lowest possible sublimation (all other
parameters being equal). Tabulated results, for Bond albedo 5%
and infrared emissivity 100%, are available for
H2O, for
CO2, and for
CO. For results with other albedo,
other infrared emissivity, or other heliocentric distance, the
web-form is being updated.
Rapid Rotators
A rapidly rotating nucleus is one for which the thermal inertia is
large enough that parallels of latitude become isotherms. The
average sublimation over the nucleus is then a function of the
obliquity, i.e., of the orientation of the rotation axis.
The sublimation is relatively high if the
nucleus is pole-on toward the sun (obliquity = 0) and much
smaller if the axis is perpendicular to the comet-sun line
(obliquity = 90). All calculations assume a spherical body.
Note that a non-rotating comet is thus identical to a comet that
is pole-on toward the sun. Our approach calculates the
sublimation separately at each latitude
(and for a rapid rotator the sublimation is constant
all the way around the parallel of latitude, even on the night
side) and then calculates the appropriate average over the
entire surface, i.e., the average over all 4*pi*R2
of the surface, including areas where the actual sublimation
is zero. Tabulated results are available for the pole-on case,
which is identical both to the non-rotating case and to the case
of zero thermal inertia, for
H2O, for
CO2, and for
CO. As for the tables above,
the visual Bond albedo is 5% and the thermal emissivity is 100%.
The active areas of cometary nuclei calculated by A'Hearn
et al. are based on this table. To calculate average
sublimation for other obliquities (angles between equatorial plane and the comet-sun line), other values
of the albedo and emissivity, or other heliocentric distances,
the web-form is being updated.
Created: 10 October 2003, mfa using cgi scripts by Jeff Hahn
Updated: Saturday, 17-Jul-2004 11:45:01 EDT, mfa