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Research Proposal Edwin Kite With the discovery of numerous magma planets, there is now a pressing need for selfconsistent theory relating magma planet geophysics and dynamics to measurements such as
the phase curve of Kepler 10b (Batalha et al. 2011, confirmed by subsequent analysis) and
gas/dust escape from KIC 12557548b (Rappaport et al. 2012). I propose to use my experience
as a planetary geoscientist to fill this gap, by: (1) modeling the coupling of the solid planet,
magma pool, and atmosphere, with its effects on gas/dust release; (2) carrying out threedimensional simulations of magma currents and their effects on phase curves; and (3) testing the
hypothesis that the spin state and surface magma extent of modern magma planets are a probe of
the planet-formation epoch. As I carry out these projects, I would benefit greatly from the
geologist-astrophysicist interactions and broader intellectual environment at Princeton; for
example Prof. Adam Burrows is expert in exoplanet atmospheric modelling, Prof. Gáspár Bakos is
a leader in transit-lightcurve analysis, and Prof. Christopher Chyba is expert in a broad range of
planetary-habitability questions.
Magma planets: promise and key knowledge gaps. Because magma planets are at close orbital
distance, they are – and will remain – intrinsically easier to detect and to characterize than true
Earth analogs. Already, 297 Kepler candidates have radii < 1.75 Earth radii and a substellar
temperature potentially above the peridotite solidus. The photosphere of a magma planet – its
surface – is a probe of a liquid layer that can be as deep as the planet’s radius. As a result, the
cooling time for a magma planet photosphere can be five orders of magnitude longer than for a 1bar atmosphere, and phase curves are correspondingly more sensitive to small amounts of
nonsynchronous rotation as well as energy transport by magma flows. The current extent of
magma may be a fossil of events during the formation era: an energetically viable global magma
pool cannot be shut down once established (for example, by a giant impact). The magma pool’s
boundary is set (Fig. 1) by balance between overspill driven by solid-mantle rebound and
melting/refreezing, and because pool-atmosphere equilibration is rapid, a flux of volatile-laden
rock through this gateway is required to sustain any evaporating atmosphere. These key processes
cannot be understood by modifying the shallow-water equations or a mantle convection model –
they require a fresh approach. Two immediate measurements that require improved models are the
thermal contribution to Kepler-10b’s phase curve – could a large day-night temperature contrast
indicate a poorly stirred global magma ocean, or a pond confined to the dayside? – and the
unknown source and/or launch mechanisms for the dust streaming from KIC 12557548b, which
must be ultimately magmatic.
(1) How big is the magma pool? Planets like Kepler-10b, CoRoT-7b, HD 10180b and KIC
12557548b could conserve energy with either relatively cool, global magma layers, or
alternatively hot, substellar magma pools. Atmospheric thickness varies by many orders of
magnitude between these cases. I propose to model the coupling of the solid planet, magma
pond, peripheral lava flows, and atmosphere that sets magma pond size. Consider a magma
pool that is initially in local radiative-convective equilibrium, without lateral flow – it will be lensshaped in cross-section, tens to many hundreds of km deep, with an elevated center because liquid
rock is less dense than solid rock. When flow is allowed, the pond will overspill and form a levee.
Further pond growth will depend on the detailed balance between liquid supply at the pond edge
by levee breakouts and overspill, and liquid withdrawal by freezing and mantle subsidence. Field
and lab data for lava lakes and flows on Earth and Io provide rheological data that will allow me to
set this detailed balance (e.g. Manga & Ventura, 2005). I will find steady states for the pool
boundary by combining the pond-perimeter model with viscoelastic rebound and a Stefan
condition at the base of the pond. I will then develop improved models of H, O, & Na escape from
magma planets (e.g., Murray-Clay et al. 2009). Such models are essential if observed masses and
1 Research Proposal Edwin Kite 2
1.8
Global or local magma?
Day−night T?
CoRoT−7b Kepler−10b
1.4
1.2
Alpha Spin state?
Cen Bb Magma belt or lens?
1
0.6
0.4
0.2
0
1000
Global Magma
Possible
0.8
Magma Pools
Expected
Radius (Earths)
1.6
1500
2000
KIC 12557548b:
Volcanic dust launch?
Evaporation rate?
Confirmed Magma Planets
Pose Questions
Requiring New Models
2500
3000
Substellar Temperature (K)
Figure 1. Left panel: Sketch cross-section through a magma planet’s equatorial plane (not to scale), showing fluxes and
reservoirs to be constrained in the proposed work. Center panel: Visualization of processes near the terminator of Kepler10b (Ron Miller). Right panel: Confirmed (large circles) and candidate (small circles) high-temperature small-radius
planets – density measurements indicate that hot planets below the horizontal dashed line are rock/metal planets. Magma
threshholds are shown for an easily-melted rock type (granite, gray vertical lines) and a refractory rock type (peridotite,
black vertical lines). Labelled planets (black rings) exemplify questions that will be addressed by the proposed modeling
effort. Green symbols correspond to planets with an external perturber, showing the importance of forced eccentricity,
tidal heating, and nonsynchronous rotation.
radii are to be used to constrain the origin and extent of migration of these planets. I will use
escape fluxes to drive pond fractionation (using the MAGMA code; Schaefer & Fegley, 2009). If
escape depletes the pool of dense constituents, light material will enshroud the planet and shut
down atmospheric resupply (Guenther et al., 2011). Conversely, dense ponds may drain
catastrophically, a “delayed differentiation” that would alter the entire planet’s energy balance. I
also propose to use experience gained modeling atmosphere-solid planet interactions (Kite et al.,
2009, Kite et al., 2011) and KIC 12557548b (Rappaport et al., 2012) to model secondary volatile
loss pathways such as explosive volcanism. I will also model the effect of a relict atmosphere
(e.g., S) on mantle overturn. I will explore a range of ocean temperature gradients in this task, and
identify a preferred value in Task 2.
(2) What is the surface temperature gradient across the magma pond? The low viscosity of
substellar magma underpins many dynamical similarities between Earth’s ocean and the cores of
substellar magma pools, and order-of-magnitude calculations show that magma currents can
significantly cool the substellar region. Building on experience modifiying MRAMS (Kite et al.
2011b, 2011c), I propose to modify MITgcm by adding a magma equation of state that
exploits recent shock-wave measurements of silicate liquids in the CMFAS system (Asimow
& Ahrens 2010) and appropriate atmospheric boundary conditions (e.g. Castou & Menou
2011), and compare our results to the Kepler-10b phase curve. The circulation will feed back on
magma pool geometry through melting and refreezing at the base of the magma pool. Solid planet
viscosity is many orders-of-magnitude larger than viscosity above the liquidus, allowing
separation of timescales between changes in the magma pool boundary (and pool-averaged
composition) and the circulation within the pool. Next, I will develop a crystal growth and settling
parameterization and add it to MITgcm. Sandström’s theorem sets a tight bound on the intensity of
currents driven solely by insolation gradients. Mixing generated by crystal settling will speed up
magma currents relative to a circulation driven by starlight and wind alone. Albedo will initially
2 Research Proposal Edwin Kite be specified using measurements of analog ceramic materials. To keep the problem simple, I
propose to use idealized parameterizations of the mushy rheologies that may occur at the pond
margin as well as of tidal stirring and dissipation within the liquid pond. Results from Task 2 will
update Task 1, and determine the expected advection timescale, day-night temperature contrast,
and hotspot offset for a magma planet.
Tasks 1 and 2 address basic questions: what is the thickness of the atmosphere, and what is the
day-night temperature contrast? The underlying feedbacks are intrinsically interesting, and a
global modeling framework that relates magma planet observations to geophysical parameters is
urgently needed: neither Kepler-10b’s phase curve nor volcanic loading of KIC 12557548b’s
extended atmosphere can be attacked using 1D atmospheric models or mantle convection models.
My proposed model will be continually refined with Kepler data. I expect additional Kepler phase
curves to become available. For the optimal systems, upper limits on H and Na loss are possible
with HST. SPHERE and GEMINI can directly image accretional magma oceans sufficiently far
from the star (Miller-Ricci et al. 2009), and additional facilities capable of characterizing
permanent magma seas will see first light later in the proposal period. (3) Probing the epoch of formation with magma planets. Kepler shows a marked depletion in
very hot Neptune-radius objects, which might result from evaporation, migration from different
birth radii, or some third alternative. Magma planets cannot have formed in situ, and their early
travels are coupled to the development of magma ponds. Tidal heating is unimportant for the
surface energy balance (Moore et al., 2007), but tides can still affect magma pool observables. For
example, the Moon is trapped in 1:1 spin-orbit resonance by its solidity; a magma planet in
‘quasisynchronous’ rotation may defer tidal locking indefinitely. I will carry out numerical
experiments to test the hypothesis that if a planet had global magma ocean on arrival at its modern
orbit (because of a volatile blanket, incomplete despinning, or a recent impact), it would retain a
global magma ocean even after volatiles are lost. α Cen Bb highlights the potentially key role of
eccentricity-pumping external perturbers (in this case α Cen A) in smearing out thermal emission
into a belt via slow nonsynchronous rotation. However, if for any reason Bb is despun for long
enough to grow a darkside lithosphere, the associated quadropole moment will keep it despun, and
its magma distribution will be a potentially permanent record of that despinning event. Using
experience modifying swifter as part of my work on the Fom b discovery team (Chiang et al.,
2009; Kalas et al., 2008), I propose to investigate despinning of evolving, migrating magma
planets in planetary systems. Finally, I will incorporate scaling relations fit to results of Tasks 1
and 2, and coupled to gas/dust loss models, to calculate magma planet compositional evolution as
a function of time. This research will underpin efforts to understand the density trends that are
emerging from Kepler and RV data (Wu & Lithwick, 2012, and many others).
Conclusion. To interpret magma planet data it is necessary to understand magma pools. Modeling
magma pools requires a hybrid approach incorporating geology, volcanology and dynamics. In the
past the Spitzer fellowship has not been awarded to geologists – but such overlaps will be
increasingly needed as observers home in on analogs to Earth.
Asimow & Ahrens, 2010, JGR 115, B10209 * Batalha et al., 2011, ApJ 729, 1 * Castan & Menou, 2011, ApJ 743,
L36 * Chiang, Kite, et al., 2009, ApJ 693, 734 * Guenther et al., 2011, A&A 525, A24 * Kalas, and 8 others including
Kite, 2008, Science, 322,1345 * Kite et al. 2009, ApJ 700, 1732 * Kite et al. 2011b, JGR, 116, E07002 * Kite et al.
2011, JGR, 116, E10002 * Kite et al. 2011a, ApJ 743, 41 * Manga & Ventura, Eds., 2005, Kinematics & Dynamics of
Lava Flows, GSA Sp. Paper 396 * Miller-Ricci et al. 2009, ApJ 704, 780 * Moore et al., in Lopes & Spencer, 2007, Io
After Galileo, Springer. * Murray-Clay et al., 2009, ApJ 693, 23. * Rappaport, and 10 others including Kite, 2012,
ApJ 752, 1 * Schaefer & Fegley, 2009, ApJ 703, L113. * Wu & Lithwick, arXiv:1210:7810.
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