Very slowly deposited amorphous ice has a thermal conductivity about four orders of magnitude or more smaller than hitherto estimated. Using the exceedingly low value of the thermal conductivity of comets deduced from the properties of amorphous ice leads to the expectation that internal heating of comets is negligible below the outer several tens of centimeters

Greenberg, J. M.

Kouchi, Akira

Mukai, T.

Xing, Z. F.

Yamamoto, T.

English

NASA Technical Reports Server

Asteroicb, Comets, Meteors 1991, pp. 325-328
Lunar and Planetary Institute, Houston, 1992
N93  oI
A NEW MEASUREMENT OF THERMAL CONDUCTIVITY OF AMORPHOUS ICE AND
ITS IMPLICATIONS FOR THE THERMAL EVOLUTION OF COMETS
325
A. Kouchi(1), J. M. Greenberg(1), T. Yamamoto(2), T. Mukai(3),
and Z. F. Xing(1)
(i) Laboratory Astrophysics, University of Leiden, 2300RA
Leiden, The Netherlands
(2) Institute of Space and Astronautical Science, Yoshinodai,
Sagamihara, Kanagawa 229, Japan
(3) Department of Earth Sciences, Kobe University, Nada, Kobe
657, Japan
ft
ABSTRACT
Very slowly deposited amorphous ice has a thermal conductivity
about four orders of magnitude or more smaller than hitherto
estimated. Using the exceedingly low value of the thermal
conductivity of comets deduced from the properties of amorphous ice
leads to the expectation that internal heating of comets is
negligible below the outer several tens of centimeters.
INTRODUCTION
Although the importance of knowing the thermal conductivity, K, of
vapor-deposited amorphous ice (a-H20) for predicting the thermal
evolution of comets has been widely recognized (e.g., Klinger,
1980; Espinasse et al., 1991 and references therein), there has
been no direct measurement available. Therefore, most of the
discussions on comet evolution have been based on a theoretical
estimation of K by Klinger(1980). On the basis of our new
experimental results and a reanalysis of data found in literature,
we have arrived at a new estimate of the K for a-H20 (Kouchi et
al., 1991). We discuss the thermal evolution of comet using the
new value of K.
MEASUREMENT OF THERMAL CONDUCTIVITY
Kouchi et ai.(1991) investigated the thermal diffusion in ice thin
film during deposition, and gave the following relation:
h = (Th-Ts) KI [ (l-A) aT4-_aT$+VL] (i)
where h is the thickness of ice film, Th, T s and T R the temperature
of the surface of ice film, that of a substrate and that of the
1
ambient radiation field, respectively, A the Planck averaged albedo
of the sample at temperature TR, _ the Planck averaged emissivity
at temperature Th, a the Stefan-Boltzmann constant, V the
deposition rate, L the heat of deposition per unit volume, and
https://ntrs.nasa.gov/search.jsp?R=19930010002 2020-03-17T07:30:49+00:00Z
326 Asteroids, Comets, Meteors 1991
__ (Th_Ts) -I_T h K (T) dT,
S
the mean thermal conductivity between Ts and Th. If we obtain the
whole set of data: Ts, Th, TR, h and V, we can calculate the K of
a-H20 using eq. (i). However, it is very difficult or almost
impossible to measure the surface temperature Th because the
thickness of a-H20 is very small compared to the sxze of the
thermometer (e. g., thermocouples) , and because tRe thermal
conductivity of a-HzO xs smaller than that of any kT_owl_
thermometer.
105 , , , , i , , , , i , , , ,
10 4
o
10 3
E 10 2
l--
(J
r_
z
o
o
- 10
<
rr
UJ
X
F-
Z
< 1
UJ
=E
10-1i
0
I I I I 1 • I L I i ! I I i
50 100 150
MEAN TEMPERATURE (K)
z 7: "
Fig.l Mean thermal conductivities of amorphous ice obtained by
Kouchi et al. (1991) and that estimated by Klinger (1980).
|=
=-
_ =
Asteroids, Comets, Meteors 1991 327
Kouchi et ai.(1991) observed the structural change of ice films
during deposition at Ts=125-130 K using reflection electron
diffraction. At thicknesses smaller than h , deposition of a-H20
occurred, while at a thickness larger than _c, cubic ice (ice Ic)
was deposited. This clearly shows that the surface temperature of
the ice film at the thickness of h c corresponds to the temperature
of phase transition from a-H20 to ice Ic, which occurs at around 140
K. Furthermore, this enables us to measure the TL and, by assuming
A-0, _~I in eq. (i), to determine upper boun_ of _ of a-H20.
Figure 1 shows the _ of a-HzO obtained by Kouchi et al. (1991). It
is clear that the _ is at least one to four orders of magnitude
smaller than that estimated by Klinger (1980).
HEAT TRANSFER IN A COMET NUCLEUS
Since the cometary nucleus is very porous, the thermal conductivity
of the nucleus may be one to two orders of magnitude smaller than
that of constituent icy grains. This suggests that the thermal
conductivity of the comet nucleus is certainly smaller than 1 erg
cm "I s "I K "I and possibly as low as 10 .2, a quite shocking result.
With such a small value of K, the major mechanism of heat transfer
in the comet nucleus on short time scales may not be only by
conduction. However, radiation transport both by visual and
infrared and diffusive heat transport by evaporated water molecules
are also negligible (Kouchi et al., 1991). The more volatile
molecules like CO, CO 2 may be expected to play a more important
role in diffusive heat transport than H20 (Espinasse et al., 1991).
THERMAL EVOLUTION OF COMETS
Greenberg et ai.(1991) investigated the pre-history of a new comet:
from the protosolar nebula to the Oort cloud, then in the Oort
cloud, and from the Oort cloud to the inner sola_ system. They
found that all new comets return to the inner solar system at a
temperature lower than their formation temperature in the
protosolar nebula and 9 rough estimate is that it is reduced by
about 1/2.
Greenberg et al. (1991) also investigated how little the solar
heating affects the interior of a periodic comet. Table 1 shows
some typical results for a comet of any size with the initial
temperature of 16 K. It appears unlikely that below 25 cm, or even
less, the temperature in a periodic comet will rise enough to
evaporate CO and will certainly not be enough to evaporate or
crystallize water ice.
The conclusion that even periodic comets preserve pristine
interstellar matter in cold storage at relatively shallow depth
mandates that a greater effort be made to provide the lowest
possible return temperature--preferably less than 20 K--than to
require probe depth to some meters.
328 Asteroids, Comets, Meteors 1991
Table i. Illustrative examples of limitted heat penetration (AT)
below the surface of a periodic comet nucleus. AT=T-16 K, T o is
the surface temperature, and K=I0 -2 erg cm "I s "I K "I.
a To=300 K (-!_AV!
Ar (cm)
5
i0
20
50
75
time (yr)
1 3 i0 30 I00 i000
0 7 61 135 197 256
0 0 4 43 123 228
0 0 0 1 33 176
0 0 0 0 0 61
0 0 0 0 0 18
b T0=130 K (~SAU)
Ar (cm)
5
i0
20
5O
75
time (yr)
1 i0 i00 I000
0 25 79 103
0 2 49 92
0 0 13 71
0 0 0 25
0 0 0 7
: ACKNOWLEDGEMENTS
The authors would like to thank the Netherlands Organization for
Scientific Research and the Japan Society for the Promotion of
Science for their support. Part of this research was supported by
NASA grant(# NGR 33-018-148). ....Pn_ of the authors (T.Y.)
acknowledges the support from the University 0 f_ Tsukuba i Japan.
one of the authors (A.K.) was supported by the Yamada Science
Foundation, Japan.
REFERENCES
Espinasse S., Klinger J., Ritz C., and Schmitt B. (1991) Modeling
of the Thermal Behavior and of the Chemical Differentiation of
Cometary Nuclei. Icarus, 92, 350-365.
Greenberg J. M., Yamamoto T., and Xing Z. F. (1991) The Peter Pan
of the Solar System:PreservatiQn of protoso!ar Nebula Matter in
Comets by thelr ExceedingiYL0_ Th@rmal C0ndUctivi_y' submitted
Klinger J. (1980) Influence of a Phase Transition of ice on the _
Heat and Mass Balance of Comets. Science, 20__99, 271-272.
Kouchi A., Greenberg J. M., Yamamoto T., and Mukai T. (1991) ....
Extremely Low Thermal Conductivity of Amorphous Ice:Relevance to
Comet Evolution. submitted to Ap. J. Lett..


A new measurement of thermal conductivity of amorphous ice and its implications for the thermal evolution of comets

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