Caltech: Geological and Planetary Sciences

David J. (Dave) Stevenson

Research

1. Earth and Moon Formation

In our current understanding of the formation of the terrestrial planets, giant impacts play a central role and the formation of the Moon is a late stage consequence of a particularly large oblique impact. Following such a large impact, a molten silicate disk forms in Earth orbit, evolving quickly to form the Moon, perhaps on a timescale of 100 to 1000 years (Thompson and Stevenson, 1988) or perhaps even faster (Machida and Abe, 2004). This part of the evolution is not well understood (it cannot be modeled by planetesimal evolution). During this phase, the disk has a massive silicate vapor atmosphere that is continuously joined to the silicate atmosphere of the post-giant impact Earth. The goal of this work is to explain the geochemical characteristics of the Moon as the result of processes occurring immediately after the giant impact. This model has the potential to explain both the Earth-Moon similarities and differences.

Figure 1. Standard oxygen isotope plot showing the remarkable similarity of Earth & Moon compared to Mars Figure

2. Cross-sectional view of the silicate melt & vapor disk within which mixing may take place between earth and Moon-forming material during a time ~100yrs after disk formation.

Contrary to the corresponding solar nebula problem (which is quasi-steady state) this rapidly evolving system is expected to have vigorous turbulent convection and therefore turbulent mixing far greater than that commonly attributed to the planet-forming disk. As a result, we believe this model offers the prospect of explaining the Earth-Moon similarity in oxygen isotopes shown in Fig 1. In our scenario, the incoming giant impactor has a different oxygen isotopic character, as one would expect based on current accretion models (Chambers, 2001). However, convective mixing through the common massive silicate atmosphere dilutes the moon-forming isotopic distinctiveness and reduces (though perhaps not completely eliminates) the isotopic difference. Because we do not have a full understanding of the relevant dynamics, our approach is to emphasize observational tests. However, simple estimates of turbulent mixing suggest that it is possible to explain the Earth-Moon similarity by this model.

To the extent that this model is successful in explaining the difference in composition between the Moon and silicate Earth, it may be possible to place constraints on the T, P of last equilibration with the Moon. The goal here is to quantify this effect using equilibrium thermodynamics and use this prediction as a test of the mixing model. We also look at the behavior of water and of other isotopic systems.

In a related effort, we have been studying the fluid dynamic of mixing between the cores of massive projectiles and the partially molten mantle of Earth, immediately after a giant impact. This is relevant to the question of how to best interpret Hf-W isotopic data that are used to explain the timing of earth formation and core formation. We find that there is incomplete re-equilibration of core and mantle during and immediately after a giant impact (i.e., some of the iron finds it way to the core without the opportunity to pick up the siderophilic tungsten made by hafnium decay in Earth’s mantle during the millions of years prior to the giant impact.) This suggests problems for the connection between Hf-W chronologies and the precise timing of events during Earth and Moon formation. See also Stevenson (1990).

2. Giant Planet Zonal Flows

The giant planets exhibit strong east-west winds in the observable atmosphere. It has been argued, most notably by Busse (1983), that this flow is deep-seated, i.e., it extends down into the interior on cylinders, as shown in this figure for Jupiter.

Figure 3. The relationship between atmospheric and interior flows proposed by Busse. Our work suggests that this picture must be incorrect.

However, these cylinders may reach to levels where the electrical conductivity is sufficient to allow coupling of the flow to the magnetic field. Even a magnetic Reynolds number somewhat less than unity can correspond to a significant current generation. Our result for Jupiter is that a deep-seated zonal flow is in fact highly unlikely and certainly very restricted in radial extent. The main difficulty is that such a flow will create large electrical currents in a low conductivity region. The associated Ohmic dissipation then exceeds the luminosity of Jupiter. The zonal flow must be confined to the outermost 4% of the planetary radius in Jupiter (and a somewhat thicker layer in the other giant planets). This is the rigorous part of the analysis. But in addition, the hypothesized flow has no force acting on it seems capable of providing the shear needed to reduce its amplitude from ~100m/s to a tolerable fraction of a meter per second if this shear exists in the high density region where the conductivity begins to be important. In particular, Lorentz forces are grossly insufficient.

It seems likely that the flow seen in the atmosphere of Jupiter is mostly “meteorological” (i.e., it is a shallow layer flow). These results are testable because deep seated flows yield gravitational signals that are detectable by the JUNO spacecraft, scheduled for launch in 2011.

3. Planetary Magnetic Fields

Work continues on the puzzle of how to explain the pattern of magnetic fields in the solar system. Why do some planets have large magnetic fields now or only had them in the distant past? Why does Ganymede have a dynamo while Mars and Titan do not? Although the answers to these puzzles may depend in part on a better understanding of dynamo theory, many of these issues require an understanding of whether these bodies have liquid, convective cores. The main issue here is energy sources (cooling, presence of an inner core, etc.) Here is a recent review on this problem, published as Stevenson(2003b).

It is possible (though far from certain) that these models might also shed light on the puzzling question presented by the new “observation” of Saturn’s spin (Giampieri, 2006; Stevenson, 2006). For example, there may be choices of the forcing (i.e., of the zonal flow) for which a high latitude non-dipole field “anomaly” naturally emerges. This would not directly explain the observations but might provide a magnetic anomaly that guides the magnetospheric or ionospheric anomaly responsible for the observed field disturbance. Here is a recently published discussion of Saturn’s spin, published as Stevenson(2006).

4. Giant Planet Structure

In the case of Earth and Mars, it has been possible to obtain very accurate moments of inertia from measurements of precession. This technique can be used in principle for the giant planets but it is difficult. For decades, the standard approach to defining the internal structure of the giant planets has instead relied on the interpretation of the gravitational moments. In principle, these contain even more information than the moment of inertia (because we can measure J₂, J₄ and even J₆). However, the interpretation in terms of density structure and the presence or absence of a core is non-unique. The classic Radau-Darwin theory gives the following “recipe”:

C/MR² = 2{1-2/5[5/(Λ₂+1) -1]^1/2}/3

where C is the polar moment of inertia, M and R are the planet mass and radius respectively, and Λ₂ =J₂/_q where q=Ω²R³/GM, the ratio of centrifugal force to gravity at the equator. More by accident than by good theory, this equation predicts C/MR² ~0.25 for Jupiter, close to the value that is obtained by detailed models designed to fit the gravitational moments. A coreless n=1 polytrope yields C/MR² = 0.26. By contrast, a new dynamical model (Ward and Canup, 2006) proposes that Jupiter’s obliquity is primarily forced rather than free (i.e., not primordial) and there is empirical evidence in the current pole location compatible with this interpretation. For their theory, C/MR² =0.236, lower than most interior models, and potentially supportive of a core for Jupiter. The presence or absence of a core is central to our understanding of how the giant planets formed (e.g., Lissauer and Stevenson, 2006).

Aside from being an approximate theory, the Radau-Darwin equation is conceptually incorrect. It implies that there is a one-to-one correspondence between a particular value of Λ₂ (an easily measured quantity) and the value of C/MR². One way to appreciate this conceptual error is to look at the predicted C/MR² at constant Λ₂, for a parameterized set of models. This is shown in Fig 4.

Figure 4 C/MR² as a function of fractional core radius x at fixed J₂/_q=0.145 for the exactly solvable model of a core of density A and radius x, overlain by an envelope of density 1 between radius x and radius 1. Models to the left correspond to cores of extremely high density (but finite envelope density); models to the right end point correspond to models where the density of the envelope is going to zero. Models beyond x~0.78 are unphysical (they require negative core densities). These models are not physically relevant to realistic giant planet structures but they demonstrate nicely the non-uniqueness of the relationship between moment of inertia and J₂/_q. The total range of non-uniqueness is about 15%. This is large!

In our current work we are seeking to understand better the non-uniqueness of the relationship between gravitational moments and moment of inertia or density structure. As a related issue, we are also seeking to understand what the gravitational moments tell us about the coefficient k in the formula E_grav = -kGM²/R. This is important for understand the accretion process, especially for Uranus and Neptune.

Here is a recent review on Jupiter’s interior.

5. Icy Satellites

Recent results from Cassini (both in orbit and from Huygens probe) have motivated consideration of models for Titan that involve some form of volcanism. One viewpoint is that there has been geologically recent release of methane from the interior (“recent” could mean as much as a billion years ago). These models are motivated in part by the notion that because methane is continuously destroyed and because there are no oceans and only limited evidence for lakes of methane on the surface, suggesting we must have a deep-seated source. The alternative approach proposes that the methane is in fact primordial (or at least billions of years old) and stored in a regolith near surface (Stevenson, 1992). In such a model there is no difficulty explaining the total needed reservoir of methane and no requirement that this methane be readily observed as oceans or lakes. A model of this kind would necessarily give a “wet” surface because the timescale for transport between surface/atmosphere and subsurface is geologically short. (There can be a methane cycle just as Earth has a near –surface water cycle.) A model of this kind also raises the question of whether the claimed evidence for volcanic constructs on Titan is, in fact, compelling. It is far from clear how to get water–ammonia volcanism on a body like this, although tidal heating may certainly help, since there is a tendency for bodies without recycling to “run down” (i.e., once you have sweated out the water/ammonia, you no longer have the possibility to have more volcanism). There is of course still the opportunity for some intrusive activity including escape of argon-40, without the need to build volcanic structures.

In a related effort, we have also looked recently at the likely non-Newtonian aspect of the water ice rheology resulting from the fact that the so-called Newtonian viscosity is grain-size dependent and the grain size in turn depends on stress. We find that this enlarges the size range for which bodies are expected to have oceans, increasing the likelihood that the Galilean satellites (e.g., Ganymede) would have an ocean, even without the presence of antifreeze such as ammonia.

6. Deep Earth

In addition to an interest in the earliest history of earth, there is a continuing effort on understanding the nature of the core and the interaction of the core with the mantle. One example of this work concerns the possibility that a small amount of liquid iron finds its way into the lowermost mantle through a suction process provided by the deviatoric stress that mantle convection inevitably provides. if the mantle can develop permeability, then the penetration distance of the iron is of order a kilometer. This may have relevance to some aspects of core-mantle coupling and chemical interaction.

Here is a publication describing aspects of this work (Kanda and Stevenson, 2006).

7. Some Other Topics

Here is a recent review on the formation of giant planets (to be published as Lissauer and Stevenson. 2006, in Protostars and Planets V).

8. Missions

I am involved in Juno, a New Frontiers class mission (PI Scott Bolton, SWRI) currently scheduled for launch in 2010. We will place a polar orbiter around Jupiter and obtain very high accuracy gravity and magnetic field data as well as water abundance by microwave sounding.

9. Students and Collaborators: Past, Present and Future

Jun-jun Liu completed her Ph. D. thesis with me in 2006. Kaveh Pahlevan is a planetary science graduate student who is currently working with me on lunar formation and related Earth and planet formation & evolution issues. Ann Marie Cody (grad student in astronomy) is working with me on the gravity field and density distribution within giant planets. Tais Dahl (graduate student at University of Copenhagen) has worked with me on Hf-W and core formation. Victor Tsai, grad student at Harvard, worked with me on True Polar Wander while an undergrad at Caltech. Undergraduates often work with me, usually through Ph 11 but also sometimes through the SURF program. High school students have also worked with me. Ari Berlin (freshman at Yale, beginning 2006) has worked with me on Jupiter's magnetic field and Sean Wahl (senior at Troy High School, Fullerton) has worked with me on the number and nature of plates required for a sustainable plate tectonic world.

Past students have included Jonathan Lunine (professor at University of Arizona), Huw Davies (Lecturer at Cardiff University of Liverpool) and Paul Tackley (professor at ETH in Zurich). There are always plenty of opportunities for students with a strong physics background.

9. Fun Stuff

Here is a Physics Today article I wrote about earthquakes and tsunamis.

10. Crazy Stuff

One of my speculations is about the possibility of interstellar planets Stevenson (1999). During planet formation, rock and ice embryos of order Earth's mass may be formed and some of these may be ejected from the solar system. They can retain molecular hydrogen-rich atmospheres that, upon cooling, have basal pressures of 102 -104 bars. Pressure-induced far IR opacity of H2 prevents such a body from eliminating its internal radioactive heat except by developing an extensive adiabatic-convective atmosphere, so that although the effective temperature of the body is of order 30K, its surface temperature can exceed the melting point of water. These bodies will be difficult to detect.

Here is the long version of the paper on interstellar planets (short version was published as Stevenson, 1999) It contains many details not in the Nature piece.

I have also published a “modest proposal” for a mission to earth’s core. There are many practical difficulties with such a mission, and the paper was to a large extent not a practical suggestion but a provocation to get people thinking about going down rather than just going up (i.e., space missions). However, the basic physics of gravity driven fluid-filled cracks is sound. The short and less detailed version of which was published as Stevenson (2003a).

11. References

Additional publications may be found in my publications page.

Busse, F. H. 1983. A model of mean zonal flows in the major planets. Geophys. Astrophys. Fluid. Dyn. 23(2), 153-174.
Chambers, J. E. 2001. Making more terrestrial planets. Icarus 152 205-224.
Giampieri, G., M. K. Dougherty, E. J. Smith and C. T. Russell. 2006. A regular period for Saturn's magnetic field that may track its internal rotation Nature 441, p62-64 (May 4)
Guillot, T., Stevenson, D. J. Hubbard, W. B. and Saumon, D. 2004. The Interior of Jupiter. Chapter 3 in Jupiter (ed. F. Bagenal et al), Cambridge University Press.
Kanda, R. V. S., and D. J. Stevenson (2006), Suction mechanism for iron entrainment into the lower mantle, Geophys. Res. Lett., 33, L02310, doi:10.1029/2005GL025009.
Lissauer, J. J. , Stevenson, D. J. 2006 Formation of the Giant Planets. Protostars and Planets V, in press.
Machida, R. Y. Abe, The Evolution of an impact-generated partially vaporized circumplanetary disk, Astrophys. J. 617 (2004) 633-644.
Stevenson, D.J. Fluid dynamics of core formation. In Origin of the Earth, ed. H.E. Newsom, J.H. Jones, Oxford Un. Press, pp. 231-249, 1990.
Stevenson, D.J. Interior of Titan, Proceedings Symposium on Titan, publ. European Space Agency (Noordwijk, Netherlands) pp. 29-33, 1992.
Stevenson, D. J. Possibility of Life-sustaining Interstellar Planets. Nature, 400, p32, 1999.
Stevenson, David J. Mission to Earth’s Core - A Modest Proposal. Nature, 423, 239-240, 2003a.
Stevenson, David J. Planetary magnetic fields. 2003b. Earth and Planetary Science Letters, 208, 1-11.
Stevenson, D. J. A new spin on Saturn. 2006. Nature 441, 34-35 (May 4).
Thompson, C. , Stevenson, D.J. 1988. Gravitational Instability in Two-Phase Disks and the Origin of the Moon, Astrophys. J. 333 (1988) 452-481.
Ward, W. R. and Canup, R.M. 2006. The obliquity of Jupiter. Astrophysical Journal, 640:L91–L94

Last updated: October 04, 2007 07:31