Voyager 2 images of Miranda revealed a significant history of geological activity. Overlying an apparently ancient cratered terrain are assemblages of concentric ridges, scarps, and dark banded material. The problems that evolutionary thermal and structural modes of Miranda must face, to provide a convincing explanation for such topographic complexity, are examined

Cassen, P. M.

Reynolds, R. T.

Squyres, S. W.

Thomas, P. J.

English

NASA Technical Reports Server

The VJsceosiQ of Wiapanda 
P.J. Thomas, R.T. Reynolds, S. W. Squyres and P.M. Cassen 
Theoretical Studies Branch, NASA Ames Research Center, Moffett Field, CA 94035. 
Voyager 2 images of Miranda reveal a significant history of geological activity. Overlying an apparently 
ancient, cratered terrain are assemblages of concentric ridges, scarps and dark banded material. Three 
regions of complex terrain are visible in the Voyager images, which cover virtually an entire hemisphere. 
These regions are typically -- 2OOkm in diameter. 
Although the concentric ridges have some similarity to the regularity of the grooved terrain on 
Ganymede, they are also associated with what appear to be extensive flow regions possibly associated 
with internal melting) that, in some cases, have modified the geometry of the ridges. !F inally, widespread 
brittle behavior is observed in the form of large faults, scarps and graben up to 15km deep. 
We examine the problems that evolutionary thermal and structural models of Miranda must 
face, to provide an convincing explanation for such topographic complexity. The problems center around 
the requirement that such a small body ( R  - 242km) must have a sufficient heat generation mechanism 
to lower its viscosity substantially. It would generally be expected that a body of such size with such 
low ambient temperatures (.v 50 M) would have an extremely rigid surface. While the observed fault 
regions are consistent with a rigid surface, the high degree of sphericity of Miranda implies a low viscosity 
material, at least at some time in Miranda's past. 
For viscous relaxation on a scale of L - 100km to occur over a reasonable timescale (7,s logy), 
the dominant viscosity pr determining viscous motion is given by 
where for Miranda g = 0.09ms-~ and p = 1 2 0 0 k ~ m - ~  (Tyler e t  a!., 1986) yielding lrs 1 0 ~ ~ P a s .  As- 
suming a Newtonian viscosity law for ice (Weertman, 1970): 
with parameters appropriate to low-temperature ice A* = 25; T, = 273K; and yo = 10l~Pa3 (Reynolds 
and Cassen, l979), this is appropriate to a temperature T of 157K, or a temperature > 100K above the 
ambient temperature. 
The two reference models for Miranda that we consider are that (1 the complex terrain was 
g a period of reaccretion following a disruptive impact (Smit b e t  at., 1986 in thia c a e  
the energy required for resnrfacing is produced by the release of the potential energy of t b e reaccreted 
fkagments; or that (2) the complex terrain represents a disturbed region overlying a diapiric instabilit , 
similar to a mechanism proposed for the formation of palimpsests on Canymede (Hale e t  al., 1980f: 
In the second case the energy required for resurfacing must have an internal origin, such as radiogenic 
heating or tidal deformation. These two models represent exogenic and endogenic formation models 
for the complex terrain, respectively. They also permit estimates of dynamic viscosities and associated 
emergy inputs required by these models. 
If population statistics derived for the sizes of comet nuclei are valid for projectiles impacting on 
Miranda, it is conceivable that Miranda underwent a series of collisions with bodies of sufficient kinetic 
to disrupt it in the firat Gy after its initial formation (Shoemaker and Wolfe, 1982; Smith e t  at., 
1986 This model implies that the final stages of reaccretion may have produced the observed terrain enerY 
patterns by liberation of the gravitational potential energy of the disrupted fragments of the satellite. 
While both models must be able to account for Miranda's high degree of sphericity, the reac- 
cretion model faces a more stringent relaxation condition: that relaxation must remove all traces of the 
impact crater associated with the disruptive impact. Such a crater will have topographic harmonics 
associated with the rim with wavelenaths much smaller than lOOkm and thus much longer relaxation 
- ., 
times. For example, to relax crater rims with wavelengths on a scale of lOkm in logy would require a 
viscosity of 1 0 ~ ~ P a s .  
Unfortunately for this model, the energy that can be obtained from reaccretiond heating for 
a body as small as Miranda b limited. The thermal energy retained by Miranda cannot be significantly 
@eater than the binding energy, - 2 x lo4 Jkg'l which, given a specific heat for ice of - 10~.Jkg-'K-l, 
https://ntrs.nasa.gov/search.jsp?R=19870013912 2020-03-20T10:37:27+00:00Z
predicts a maximum global temperature increase as small as - 2011. This estimate is in good agreement 
with more detailed models (Squyres et al., 1986). Of course, local heating arising from point contacts 
between reaccreted fragments may much greater temperatures in small regions. Furthermore, disruption 
and reaccretion will dissipate much of this initial energy, tending to produce a more isothermal temper- 
ature profile (Ellsworth and Schubert, 1983). One final important problem that this mechanism must 
face is that, according to various evolutionary models of the icy satellites, radiogenic heating produces 
a maximum temperature profile for small satellites within the f is t  - 100My (Ellsworth and Schubert, 
1983; Federico and Lanciano, 1983). This heat will also be dissipated by a cycle of multiple disruption 
and accretion, if such exists. 
We can consider energy constraints on the endogenic model by calculating the ascent time 7, 
for a buoyant inviscid sphere (our diapir model) of radius a = 50km at low Reynolds number through a 
layer of thickness L = 100km: 
3c1L 
Ta = - 
Apga2 (3) 
we assume a density difference Ap of 300k~wa-~, appropriate to warm pure ice surrounded by material 
with the mean density of Miranda. Assuming ~ ~ 5 1 0 ~ ~  we obtain p51022Pas, consistent with the 
determination above. This value is, however, very much of an upper limit, because Miranda's surface 
gravitational acceleration was assumed for g. The cooling time for such a diapir is a2/tc - 3 x 1oSy 
(where IE - 1 0 - ~ m ~ s - ~ ) .  For this ascent time (more reasonable than 109y because of the presence of 
some cratering on the ridged terrain) we have p s  1o2'Pas which is appropriate, using the viscosity law 
above, to T = 166R, or - lOOX above Miranda's ambient temperature. 
It is possible that extinct radionuclides such as 26A1 may have had a significant energy input 
into Miranda in the past. However, the half life of such elements (typically 5 lo6 y) indicates that any 
resurfacing that occurred as a result would be substantially older than the observed, very lightly cratered 
terrain on parts of Miranda. 
It appears to be clear that some energy source other than accretional heating is required to 
provide both the spherical shape of Miranda and the evidence of substantial viscous flow activity. The 
exogenic model requires enhanced temperatures after the last reaccretion, placing serious constaints on 
short term heating processes. In addition, it has a serious problem in accounting for the absence of 
small-scale impact features on much of Miranda's surface. 
Given the difficulties in finding a suitable energy source capable of raising Miranda's global 
temperature to a sufficient extent to reduce the viscosity of pure ice adequately, it is possible that 
mobilization of ice clathrated with 60, N2 or CH4 by pressure-solution creep may be an important 
transport process. Under certain conditions, viscosities many orders of magnitude smaller than those 
calculated above may be produced by this mechanism (Stevenson and Lunine, 1986). 
Since the temperatures determined here lie above the H20.NH3 eutectic at 173K, internal 
melting may have occurred to some extent. If the flow features were emplaced significantly after the 
accretional period (2 10'~) then tidal heating alone remains as a plausible energy source. The energy 
required to produce increases in temperature of the extent calculated for the entire satellite is of the order 
of J. If this was expended over the period of 3 x 10'y mentioned above, a heating rate of 109W, 
which is - the heating rate associated with 10's tidal flexure. For Miranda no easily indenfiable 
orbital resonance can account for this enhanced heating (Squyres et al., 1985). However, the effects of 
mutual satellite pertubations have not yet been considered in full complexity (Dermott and Nicholson, 
1986). In conclusion, it should be emphasized that due to the inability of reaccretional heating to provide 
a important energy input for Miranda, any heating mechanism required by the endogenic model must 
also be required by the exogenic model. 
References 
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The viscosity of Miranda

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