Elsevier

Icarus

Volume 183, Issue 2, August 2006, Pages 435-450
Icarus

On convection in ice I shells of outer Solar System bodies, with detailed application to Callisto

https://doi.org/10.1016/j.icarus.2006.03.004Get rights and content

Abstract

It has been argued that the dominant non-Newtonian creep mechanisms of water ice make the ice shell above Callisto's ocean, and by inference all radiogenically heated ice I shells in the outer Solar System, stable against solid-state convective overturn. Conductive heat transport and internal melting (oceans) are therefore predicted to be, or have been, widespread among midsize and larger icy satellites and Kuiper Belt objects. Alternatively, at low stresses (where non-Newtonian viscosities can be arbitrarily large), convective instabilities may arise in the diffusional creep regime for arbitrarily small temperature perturbations. For Callisto, ice viscosities are low enough that convection is expected over most of geologic time above the internal liquid layer for plausible ice grain sizes (⩽a few mm); the alternative for early Callisto, a conducting shell over a very deep ocean (>450 km), is not compatible with Callisto's present partially differentiated state. Moreover, if convection is occurring today, the stagnant lid would be quite thick (∼100 km) and compatible with the lack of active geology. Nevertheless, Callisto's steady-state heat flow may have fallen below the convective minimum for its ice I shell late in Solar System history. In this case convection ends, the ice shell melts back at its base, and the internal ocean widens considerably. The presence of such an ocean, of order 200 km thick, is compatible with Callisto's moment-of-inertia, but its formation would have caused an ∼0.25% radial expansion. The tectonic effects of such a late, slow expansion are not observed, so convection likely persists in Callisto, possibly subcritically. Ganymede, due to its greater size, rock fraction and full differentiation, has a substantially higher heat flow than Callisto and has not reached this tectonic end state. Titan, if differentiated, and Triton should be more similar to Ganymede in this regard. Pluto, like Callisto, may be near the tipping point for convective shutdown, but uncertainties in its size and rock fraction prevent a more definitive assessment.

Introduction

It has long been thought that the larger icy satellites of the outer Solar System could contain internal liquid water oceans (Lewis, 1971). Indeed, even smaller midsize (∼500–1500-km diameter) satellites could have had oceans earlier in their histories, if convective transport of internal heat through the ice did not occur (Lewis, 1971, Consolmago and Lewis, 1977). Nevertheless, it is the larger icy satellites (Ganymede, Callisto, Titan, Triton, and Europa) and Pluto that are the best candidates for possessing oceans, because the minimum melting temperature of ice (251 K) is attainable at 0.21 GPa within their icy outer layers, or nearly so in the case of Europa and Pluto (Friedson and Stevenson, 1983, McKinnon et al., 1997, Spohn and Schubert, 2003, Schubert et al., 2004). Dissolved salts, ammonia, or methanol further lower this minimum melting temperature. An icy satellite warming from an initially cold condition thus first melts at depth, and if this melt is denser than the ice I-rich layer above, an internal ocean or aquasphere may open up; conversely if the melt is buoyant, volcanism may result. For a satellite cooling and freezing from a largely molten state (such as due to accretional, tidal, or early radiogenic heating), the residual ocean will concentrate dissolved solutes, enhancing the freezing-point depression (e.g., Kirk and Stevenson, 1987, Grasset and Sotin, 1996). Europa is a special case in that its ice shell is not thick in the above sense (it is unlikely that pressures are high enough for ice II or III at the base of its water/ice shell), but strong tidal heating in the surface ice layer almost certainly maintains a subsurface ocean (Ojakangas and Stevenson, 1989, Greeley et al., 2004).1

The ocean detected by electromagnetic induction within Callisto (Zimmer et al., 2000) was one of the more surprising results of the Galileo mission. It was argued by Ruiz (2001) that the dominant non-Newtonian creep mechanisms of water ice, grain-boundary sliding (Goldsby and Kohlstedt, 2001) and dislocation creep (Durham and Stern, 2001), make the ice shell above the ocean stable against solid-state convective overturn, and stable over geologic time. His argument relied on newly developed scaling and stability relationships for heat transfer by non-Newtonian (or power-law) convection (Solomatov, 1995) that superceded earlier parameterized convection formulations (see McKinnon, 1998, for a review). Moreover, although unstated, his argument applied to all similarly radiogenically heated ice I shells in the outer Solar System, and by extrapolation to midsized icy satellites and large Kuiper Belt objects (in which ice I is stable throughout much or all of their interiors; e.g., Schubert et al., 1986) as well. Conductive heat transport and internal melting are thus predicted to be, or have been, widespread among large and midsize outer planet satellites (cf. Fairén and Ruiz, 2003) and the larger Kuiper Belt objects (McKinnon, 2002). Convection, and the tectonics that result, could then only occur in ice I shells whose viscosities are lowered, e.g., by tidal flexing (McKinnon, 1999).

The arguments of Ruiz (2001) are compromised by a mathematical error (see Appendix A). Nevertheless, if power-law creep is suppressed, then it is important to consider Newtonian alternatives. Indeed, at very low stresses, it can be easily shown that convective instabilities may arise by means of diffusion creep (McKinnon, 2001), specifically lattice diffusion or Nabarro–Herring creep (Poirier, 1985, ch. 7). Lattice diffusion creep has not been observed in water ice (Frost and Ashby, 1982, ch. 16; Goldsby and Kohlstedt, 2001), but I will show that measurements of diffusion coefficients imply Newtonian viscosities low enough that solid-state convection is expected above Callisto's internal liquid layer over most of geologic time for plausible ice grain sizes. Ruiz (2001) offered that a thick, conductive icy shell would explain the lack of active geology on Callisto (e.g., Moore et al., 2004). Even with convection, however, the cold stagnant lid should be quite thick today (about 100 km), and thus also compatible with the lack of active geology. The question of surface geological effects in the past, when the stagnant lid must have been much thinner, is addressed herein.

More recently, Barr et al. (2004) have examined the question of non-Newtonian convective instability when a long wavelength, finite temperature perturbation is applied to basally heated ice shells. Barr and Pappalardo (2005) further compared such non-Newtonian instabilities against the possibility of convection arising through diffusion creep. The present paper addresses the general question of convective instability for temperature perturbations of arbitrarily small amplitude and of any wavelength, and elaborates on the consequences.

I first review the present-day picture for Callisto and the arguments that have been made concerning convection within it (Section 2). This is followed by a detailed examination of the applicability of diffusion creep to ice I (Section 3) and its implications for convection (Section 4). Results are presented in Section 5, first in simple form, and then with increasing levels of detail regarding convective characteristics and heat flow. Inferences are drawn for Callisto's evolutionary history, including the formation of its ocean and whether convection is occurring today. This is followed by an extended discussion (Section 6), which considers the implications of these results for Ganymede, Titan, Triton, Pluto, and other bodies. The question of likely ice grain size is addressed, as are the implications for convective start-up and shut-down for Callisto. The section finishes with an examination of convective stress levels, both in terms of potential tectonic effects and the likely role of multiple deformation mechanisms in icy satellite convection. Section 7 concludes with a brief summary and outline of future work.

Section snippets

The case for Callisto

The post-Galileo view of Callisto's internal structure is rather surprising (Fig. 1). Beneath an ancient, heavily cratered, mass wasted, and rather dirt-rich surface (Moore et al., 2004) lies a relatively clean water-ice I dominated layer, which in turn floats on a aqueous layer (or ocean) whose precise composition is unknown. Below the ocean are layers of higher-pressure ice phases and admixed rock, and possibly, a modest rock (i.e., metal + silicate) core (Schubert et al., 2004). These

Diffusional flow

An important aspect of the convective initiation problem that has been generally left out (at least until recently) is the role of diffusion creep. One reason for its neglect is that it has never been reliably measured in the laboratory for ice (due to experimental difficulties in obtaining measurements on sufficiently fine grained ice at low enough stresses; Frost and Ashby, 1982, Duval et al., 1983, Goldsby and Kohlstedt, 2001). Volume or lattice diffusion is very well understood

Convection on Callisto

Because diffusional flow is temperature-dependent but Newtonian and Callisto's floating shell is bottom heated, the well-understood stagnant lid scaling of Solomatov (1995) can be used with some confidence. Here I adapt the analysis in McKinnon (1999). The temperature drop across the bottom boundary layer, TbTad, is of order RTad2/Q, where Tad is the ≈adiabatic temperature of the convecting sublayer and Tb is the (pressure-dependent melting) temperature at the base of the shell (Fig. 2). In

Results

The critical basal viscosity for convection to occur by diffusional creep is plotted in Fig. 4 as a function of true shell thickness. Equation (2) is inverted in the manner of Eq. (3), but ΔT is now an explicit function of depth through dTm/dP=22.3°C/209MPa (Petrenko and Whitworth, 1999, Table 11.1), and α and k are evaluated at Tad. The latter varies linearly between Tb10K at P=0 and Tb8K at P=209MPa. Density (ρ) is more sensitive to pressure than temperature in this situation, and an

Discussion

Ruiz (2001) argued that Callisto's ice I shell could not convect, citing the theoretical stability criteria for non-Newtonian convection. Although incorrect in detail, the stakes are still high because of the finite amplitude nature of the non-Newtonian instability. The latter applies to all radiogenically heated, separately convecting, ice I shells, not just Callisto's.

Callisto is one of the “big three” icy satellites, with Ganymede and Titan. Furthermore, from Solomatov (1995), Rag(D)(2+n)/n

Summary and prospectus

I have shown that Callisto's floating ice I shell, and by implication similar shells in the outer Solar System, are susceptible to convective overturn for sufficiently small grain size. The deformation mechanism responsible is Newtonian, volume diffusion. This is in itself not a remarkable result, and was given in outline form by McKinnon (2001). It relaxes the argument against convection in Callisto of Ruiz (2001), to the extent that it needed relaxing. It complements the numerical results of

Acknowledgements

This research was supported by grants from the NASA Planetary Geology and Geophysics and Jovian System Data Analysis Programs. I thank J.D. Anderson and A.P. Showman for constructive reviews, F. Nimmo for useful comments, and A.C. Barr for discussions.

References (73)

  • S. Mueller et al.

    Three-layered models of Ganymede and Callisto: Compositions, structures, and aspects of evolution

    Icarus

    (1988)
  • K. Nagel et al.

    A model for the interior structure, evolution, and differentiation of Callisto

    Icarus

    (2004)
  • G.W. Ojakangas et al.

    Thermal state of an ice shell on Europa

    Icarus

    (1989)
  • C.C. Reese et al.

    Non-Newtonian stagnant lid convection and magmatic resurfacing on Venus

    Icarus

    (1999)
  • M.N. Ross et al.

    Viscoelastic models of tidal heating in Encedalus

    Icarus

    (1989)
  • A.P. Showman et al.

    Coupled orbital and thermal evolution of Ganymede

    Icarus

    (1997)
  • F. Sohl et al.

    Implications from Galileo observations on the interior structure and chemistry of the Galilean satellites

    Icarus

    (2002)
  • T. Spohn et al.

    Oceans in the icy Galilean satellites of Jupiter?

    Icarus

    (2003)
  • C. Zimmer et al.

    Subsurface oceans on Europa and Callisto: Constraints from Galileo magnetometer observations

    Icarus

    (2000)
  • A.C. Barr et al.

    Does grain growth stop convection in the icy satellites?

    Bull. Am. Astron. Soc.

    (2005)
  • A.C. Barr et al.

    Onset of convection in the icy Galilean satellites: Influence of rheology

    J. Geophys. Res.

    (2005)
  • A.C. Barr et al.

    Convective instability in ice I with non-Newtonian rheology: Application to the ice Galilean satellites

    J. Geophys. Res.

    (2004)
  • M. Beeman et al.

    Friction of ice

    J. Geophys. Res.

    (1988)
  • W. Blum et al.

    Harper–Dorn creep—A Myth?

    Phys. Status Solidi A

    (1999)
  • D.M. Cole

    Observations of pressure effects on the creep of ice single crystals

    J. Glaciol.

    (1996)
  • G.J. Consolmago et al.

    Preliminary thermal history models of icy satellites

  • S. De La Chapelle et al.

    Dynamic recrystallization and texture development in ice as revealed by the study of deep ice cores in Antarctica and Greenland

    J. Geophys. Res.

    (1998)
  • C. Dumoulin et al.

    Heat transport in stagnant lid convection with temperature- and pressure-dependent Newtonian and non-Newtonian rheology

    J. Geophys. Res.

    (1999)
  • W.B. Durham et al.

    Rheological properties of water ice—Applications to the satellites of the outer planet

    Annu. Rev. Earth Planet. Sci.

    (2001)
  • P. Duval et al.

    Comment on “Superplastic deformation of ice: Experimental observations” by D.L. Goldsby and D.L. Kohlstedt

    J. Geophys. Res.

    (2002)
  • P. Duval et al.

    Rate-controlling processes in the creep of polycrystalline ice

    J. Phys. Chem.

    (1983)
  • A.G. Fairén et al.

    Seas under ice: Stability of liquid-water oceans within icy worlds

    Lunar Planet. Sci.

    (2003)
  • H.J. Frost et al.

    Deformation-Mechanism Maps: The Plasticity and Creep of Metals and Ceramics

    (1982)
  • P. Gabrielli et al.

    Meteoric smoke fallout over the Holocene epoch revealed by iridium and platinum in Greenland ice

    Nature

    (2004)
  • D.L. Goldsby et al.

    Superplastic deformation of ice: Experimental observations

    J. Geophys. Res.

    (2001)
  • D.L. Goldsby et al.

    Reply to comment by P. Duval and M. Montagnat on “Superplastic deformation of ice: Experimental observations”

    J. Geophys. Res.

    (2002)
  • Cited by (71)

    • The tidal–thermal evolution of the Pluto–Charon system

      2022, Icarus
      Citation Excerpt :

      For an ocean to form and remain liquid, the presence of long-lived heat sources is required, of which radioactive and tidal heating are the most significant contributors (McKinnon et al., 1997; Hussmann and Spohn, 2004; Schubert et al., 2010; Robuchon and Nimmo, 2011; Saxena et al., 2018). Consequently, understanding the long-term thermal and tidal evolution of planetary systems is a central tenet in evaluating the possibility for the existence of a present-day subsurface ocean and, in turn, the astrobiological potential of the outer Solar System (McKinnon, 2006; Mottl et al., 2007; Vance et al., 2007). The manuscript is arranged as follows.

    View all citing articles on Scopus
    View full text