1. Climate Instability on Planets with Large Day-Night Surface Temperature Contrasts
Edwin Kite (postdoc, Caltech)
Eric Gaidos (Hawaii), Michael Manga (Berkeley), Itay Halevy (Weizmann)
“Climate Instability on Tidally Locked Exoplanets”
Kite, Gaidos & Manga, ApJ 743:41 (2011)
Magma planets
Edwin Kite
Discussions: Michael Manga, Eugene Chiang, Ray Pierrehumbert.

2. Climate instability: Outline
Earth:
inference of a climate-stabilizing feedback between greenhouse-gas control of surface temperature, and temperature-dependent weathering drawdown of greenhouse gases
Exoplanets:
when can the weathering feedback be destabilizing?
Enhanced substellar weathering instability
(& substellar dissolution feedback)
Mars:
a nearby example of enhanced substellar weathering instability?
Conclusions and tests

3. Long-term climate stability: Earth
Without a stabilizing mechanism, Earth’s observed long-term climate stability is improbable.
A good candidate stabilizing mechanism is
temperature-dependent greenhouse gas
drawdown.
– Walker et al., JGR, 1981
There is suggestive, but circumstantial, evidence that
the carbonate-silicate feedback does in fact
moderate Earth’s climate (hyperthermals; ice cores)
– Cohen et al., Geology, 2004; Zeebe & Caldeira, Nat. Geo., 2008; Grotzinger and Kasting, J. Geol., 1993.
If Earth’s climate-stabilizing feedback is unique, then habitable biospheres will be rare, young, or unobservable (buried/blanketed)
The search for observable habitable environments beyond Earth depends on the generality of climate-moderating processes.
– Kasting et al., Icarus, 1993 Wt
Ts, ln([CO2])
Jet Rock,
Britain
Two levels of anthropic difficulty: first might make us falsely infer

4. Tidally locked exoplanet with a noncondensible, one-gas atmosphere:
“M-dwarf opportunity”  planets in the M-dwarf HZ will be tidally locked.
Tidally locked exoplanet with a noncondensible, one-gas atmosphere:
Pierrehumbert cookbook
WTG approximation
What happens when
atmospheric pressure
is increased?

5. Substellar region is key for planet-integrated weathering
Weathering rate varies strongly
with distance from substellar point.
Diamonds: Atmospheric temperatures
Substellar
region
is key for
planet-integrated
weathering
Pressure in bars
Also see work by Dorian Abbot’s group and
Robin Wordsworth
Kite, Gaidos & Manga, ApJ 743:41 (2011)

6. Enhanced substellar weathering instability:
Berner & Kothavala,
Am. J. Sci., 2001
Planet-integrated weathering rate:
Stable equilibrium (examples)
Unstable equilibrium (examples)
on rate of volcanism
speed depends
weathering kinetics
and resurfacing rate
speed depends on
Δtjump << Δtstar age
Δtjump >> Observational
baseline
M= Mars insolation
E = Earth insolation
V = Venus insolation

7. Climate instability phase diagram An abundance of triggers exists:
Kite, Gaidos & Manga, ApJ 743:41 (2011)

8. Substellar dissolution feedback:
Consider slow increase in insolation of a planet with deep surface water ice.
CO2 in seawater
faster than the weathering instability
complements ice-albedo feedback
Kite, Gaidos & Manga, ApJ 743:41 (2011)

9. A local test? The last 3 Ga on Mars
3±2 wt % carbonate in soil+dust, ~1 mbar CO2 per meter depth
Assume large-scale carbonate formation requires liquid water:
TODAY
(Kahn, 1985)
+2 Ga
NOW
-2 Ga
Draws on
Richardson & Mischna, JGR 2005
Resurfacing by wind and impacts is the limiting step for supply of weatherable material
Uncertainty: Kinetics of carbonate formation under Marslike conditions?
See also poster by Hollingsworth, Kahre et al.

10. Climate instability: Conclusions and tests
Enhanced substellar weathering instability may destabilize climate on some habitable-zone planets. The instability requires large ΔTs, but does not require 1:1 synchronous rotation.
Substellar dissolution feedback is less likely to destabilize climate. It is only possible for restrictive conditions.
Enhanced substellar weathering instability only works when most of the greenhouse forcing is associated with a weak greenhouse gas that also forms the majority of the atmosphere
- Does not work for Earth, but may work for Mars.
- It would be incorrect to use our results to dampen the entirely justified excitement about targeting M-dwarfs for transiting rocky planet searches.
Test 1: Do GCMs reproduce the results from simple energy balance models?
Test 2: If enhanced substellar weathering instability is widespread, we would expect to see a bimodal distribution of day-night temperature contrasts and thermal emission from habitable-zone rocky planets in synchronous rotation. Emission temperatures would be either close to isothermal, or close to radiative equilibrium.

11. Magma planets: processes and observables
User “blackcat”, Planetside Forums

12. The magma planet opportunity
Detectable: Much more likely to intersect stellar disk than HZ planet; given that a planet transits, 10x-1000x more transits than HZ equivalents. Intrinsically common (Howard et al., ArXiv 2011)
Characterizable: Optical phase curve of Kepler-10b tentatively detected (Batalha et al., ApJ 2011). Much greater S/N for JWST.
Natural laboratory: Composition probed by atmosphere, and magma pond size. Distillation by partial melting, sublimation and escape. Solar system links: e.g., Tidally sustained global subsurface magma ocean in Io today (Khuruna et al., Science 2011). Io also has a surface magma sea - Loki Patera. Surprisingly close dynamical similarity to Earth’s ocean. Fundamental processes: Runaway planetary differentiation (e.g. during formation) always produces magma oceans. These primordial magma oceans set the initial conditions for subsequent planetary evolution. Initial conditions matter: e.g. Earth’s LLVSPs and ULVZs are key to mantle circulation and mass extinctions (Jackson & Carlson, Nature 2011) and appear to be relics of Earth’s primordial magma ocean.

13. : Outside the magma pond
Structure
: Inside the magma pond
: Outside the magma pond
Physics: Can magma circulation cause large changes in surface temperature (phase curve)?
Chemistry: Are magma ponds sites of planetary-scale differentiation?
Assumptions: Planet is in 1:1 spin-orbit synchronous rotation.
Volatiles are absent – atmosphere consists of vaporized surface material.

14. Progress
Recent review: Léger et al., Icarus 2011
2(+1) magma planets detected: CoRoT-7b, Kepler-10b, + disintegrating planet-sized rocky comet around KIC Validation by Spitzer (Fressin et al., arXiv 2011) and RV. Possible optical phase curve (Rouan et al., ApJL 2011). Insolation gradient forces degree-1 mantle convection in simulation (e.g., van Summeren et al., ApJ 2011). Sophisticated models of 3D thermal-tidal runaways by Běhounková (ApJ 2011). Models do not treat melting. Atmospheric composition modelled by Schaeffer + Fegley + Lodders (e.g., Schaefer & Fegley, ApJ 2009) Na-only axisymmetric atmospheric simulation (Castan and Menou, ApJL 2011) – supersonic winds, pressures near surface-temperature equilibrium
6 ppm

15. Inside the magma pond Viscosity of liquid peridotite:
Material properties
Viscosity of liquid peridotite:
10-1 Pa s near solidus
Dingwell et al., EPSL 2004
Insensitive to composition
across full Solar System
basalt range
Giordano & Dingwell, EPSL 2003
Giordano & Dingwell, EPSL 2003
Open question: Effect of melting on NIR spectral features, albedo?

16. Structure of a static magma pool
dH/dTsurf ~3.2 K/km (Earth gravity)
Sleep, Treatise Geophys., 2007
partial melt
fraction
magma sea x z
solid planet
subsolidus adiabat
U ~ 40 m/s, Ro~4 (!), Ek  0
in geostrophic limit
grossly unstable to horizontal convection
Kite et al., ApJ 2009

17. “Earth-like” Circulation
Disclaimer:
1. Lava slabs near pond margin sink (mixing source)
2. Strongly variable viscosity (most important near margin)
Neglecting Coriolis forces:
Convection must occur: no critical Ra#
Almost all T variation confined to thin surface B.L.
Strong plumelike downwelling near pond edge, passive/diffusive
upwelling elsewhere
2D Boussinesq numerical simulation,
validated by dye-tracer experiments:
TEMPERATURE: ORANGE=COLD
SUBSTELLAR POINT
EDGE OF POND
STREAMFUNCTION
STRATIFIED B.L | SMALL-SCALE CONVECTION IN B.L.
Hughes & Griffiths, Ann. Rev. Fluid Mech. 2008
Open questions: With Coriolis forces – substellar magma vortex, or gyres?
How does strongly variable viscosity affect behavior of Ekman B.L.?

18. Can surface temperature be homogenized by oceanic heat transport alone?
Consider a planet with an entirely molten surface
and a radiatively unimportant atmosphere:
Cooling timescale for well-mixed B.L. on nightside:
( ρ cp ΔH ΔT ) / (εσT4) ~ 1 year for 10 km to cool 100K
Geostrophic velocity (true day-night mean velocity will be less – depends on eddy viscosity, Ekman B.L. properties):
usurf ~ (kageostrophic g ΔH ρα ΔT) / (fcor ρ L) ~ 1 m/s  distance: 3 x 107 m
ΔT ~ 100K may be enough to drive a magma flow that prevents further steepening of the temperature gradient (optimistic!)
Gradients in crystal fraction give much steeper density gradients / mixing (robust)
Wind-driven circulation?
PERCOLATION/
FILTER PRESSING?

19. A nearby magma sea: Loki Patera, Io
200 km diameter, mostly covered by cool lava crust. Peak Io lava temps. ~1500K
Galileo SSI
image
Matson et al., JGR 2006
Rathbun et al., GRL 2002;
Rhoden and Kite, DPS/EPSC, 2011;
- reanalysis indicates the 540-day (quasi)periodicity was real, and not
an alias of the ~1.7 day tidal period due to observation geometry, but
there is no evidence for periodicity in post-2003 data.
Davies et al., GRL 2012.
NIMS-derived model age
(blue = young, hot)
Davies et al., GRL 2003
Magma seas have “weather”:
The maximum length scale at which magma ponds can produce large-amplitude thermal-emission variability is >=200km (decorrelation scale for activity is >=10^4 km^2).
Inference from Loki: Lava crust foundering may generate large-amplitude variability near the edge of the pond. (What are sources of variability above the liquidus?)

20. Outside the magma pond
Crustal flow timescale >> circulation time
Chemical fractionation by partial melting and sublimation: energy available from delayed differentiation ~ f m g H ~ 1034J (107 yr insolation)
suppose 1% of insolation (1018 W) goes to vaporizing Fe2SiO4 (Lvap ~ 3.2 MJ/kg) and transporting Fe (~50% mass) to an Fe pool on the surface from which it sinks to the base of the mantle: gain is ~10x
 Thermal emission can exceed insolation for some planets
 A detectable component of nightside energy budget?

21. The magma planet opportunity: Processes and observables
GAS TAIL
GRAIN (SPHERULE) TAIL
ASH FROM ERUPTIONS
PHASE CURVE
EMISSION SPECTRUM
PRECESSION
ALBEDO
WIND SPEEDS
ELLIPTICITY?
ASYNCHRONOUS ROTATION?
ENSEMBLE OBS. (KEPLER)
MAGNETIC EFFECTS?
bold = already achieved

22. Bonus slides

23. How many solar system climates are vulnerable to runaway weathering instability?

24. “The closest habitable exoplanet orbits an M-dwarf”
Planets in the M-dwarf Habitable Zone: Deep, frequent transits. M-dwarfs common.
Example: GJ 1214b (Charbonneau et al., Nature, 2009).
1.5%-depth transit every 1.6 days. 40 ly distant; 6.6 Earth masses, 2.7 Earth radii
Humanity’s first spectrum of a Super-Earth!
Desert et al., ApJL, 2011; Bean et al. ApJ 2011
JWST: no earlier than 2018
TESS/ELEKTRA/PLATO + Warm Spitzer follow-up
M-dwarf habitable zone  Tidally locked, assume 1:1 spin:orbit synchronous