Bulletin of Glaciological Research ,0 (,**2) ,-ῌ-,ῌJapanese Society of Snow and Ice

Simulation of cryovolcanism on Saturn’s moon Enceladus with the Green-Naghdi
theory of thermoelasticity
Swantje BARGMANN+*, Ralf GREVE, and Paul STEINMANN+**+ Chair of Applied Mechanics, University of Kaiserslautern, P.O. Box -*.3, 010/- Kaiserslautern, Germany, Institute of Low Temperature Science, Hokkaido University, Kita-+3, Nishi-2, Kita-ku, Sapporo *0*ῌ*2+3, Japan(Received April 1, ,**2; Revised manuscript accepted August +*, ,**2)

Abstract
In ,**/, the Cassini spacecraft proved the existence of cryovolcanism, i.e., the icy counterpart ofvolcanism on Earth, on Saturn’s moon Enceladus during its close ﬂy-bys. In particular, water-richplume venting was discovered in the south polar region. Thus, Enceladus was found to be one out of
three outer solar bodies to be geologically active. This contribution is concerned with the modellingand computation of this phenomenon. For the underlying thermoelastic description of ice at cryogenic temperatures, we resort to the Green-Naghdi approach. The Green-Naghdi theory includes theclassical Fourier approach, but, in addition to that, it is a lot more general as it also allows for othertypes of heat propagation. The numerical implementation is carried out with the help of the ﬁnite
element method. Results show that lateral spreading of internal and surface warming away from anactive volcanic vent increases strongly with increasing contribution of the non-classical heat ﬂux.
Agreement with available high-resolution surface temperature data based on infrared spectrometry
seems to be best if the non-classical heat ﬂux contributes signiﬁcantly to the total heat transport.
Complementary laboratory studies would be required in order to strengthen this speculative, yetpromising idea.

+.

Introduction

Enceladus is one of Saturn’s inner satellites. It
was discovered in +123 and orbits Saturn in an almost
circular orbit with a semi-major axis of ,-1,3.2 km anda period of +.-1 days. Enceladus has the shape of a
ﬂattened ellipsoid with a mean diameter of /*. km,
which makes it the sixth-largest Saturnian moon. It
consists of a rocky core and an icy mantle and surface,
the mean surface temperature being at a cryogenic
value of 11 K. In many ways, the general propertiesof Enceladus are very di#erent from those of othersatellites, and thus, it is a very active research topic.
With an albedo of *.33, it has the most reﬂective
surface of any body in the solar system. Moreover, it
shows recent geological activity, which is very unusual for such a small body.
Of particular interest is Enceladus’ south polar
region. Active cryovolcanism was found there in ,**/
during a ﬂy-by of the Cassini spacecraft (Porco et al.
,**0), which makes Enceladus the fourth body in thesolar system (along with the Earth, Jupiter’s moon Ioand Neptune’s moon Triton) where volcanic eruptions
have been observed. This ﬁnding goes along withthe spectrometric detection of a distinctive warm spot
centered on the south pole with a temperature of
approximately 2/ K, which is +/ K more than expectedfrom a simple radiation balance (Fig. +; Spencer et al.
,**0).
Cryovolcanoes are icy equivalents of the wellknown terrestrial volcanoes. Their main features areillustrated in Fig. ,. Instead of magma, Enceladus’cryovolcanoes erupt water, which has its source inpressurized sub-surface water chambers (Porco et al.
,**0). No ammonia, which would lower the melting
point, was found (Buratti et al. +33*), suggesting thatthe cryomagma is pure H, O. Cryovolcanoes on othericy moons may also erupt a mixture of water and, forexample, ammonia or methane.
The exact source which produces the cryovolcanic water plumes is still subject to research. In theliterature, di#erent mechanisms have been proposed
to explain the plume origin. Collins and Goodman* Now at Department of Applied Mechanics, Chalmers University of Technology, .+,30 Gothenburg, Sweden** Now at Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstraße /, 3+*/2 Erlangen, Germany