Steve Desch

Jason Cook [now at SwRI],

Wendy Hawley, Thomas Doggett

School of Earth and Space Exploration

Arizona State University

Cryovolcanism on Charon and other Kuiper Belt Objects

Can KBOs experience cryovolcanism?

•A few words about cryovolcanism.

•A description of our model to calculate the thermal evolution of KBOs

•Results for Charon, including analysis of the physics

•Likelihood of subsurface liquid on other KBOs.

•Outline of a process for bringing liquid to the surface.

KBOs the size of Charon or larger can retain subsurface liquid to the present day, and may even be experiencing cryovolcanism, provided they formed with moderate amounts of ammonia.

Crystalline Water Ice = Cryovolcanism?

Crystalline water ice observed on many large KBOs

Crystalline water ice is expected to be amorphized by cosmic rays doses of 2-3 eV/molecule (Strazzulla et al. 1992; Mastrapa & Brown 2006), which takes < 3 Myr in Kuiper Belt (Cooper et al. 2003).

Once amorphized, KBO surfaces stay amorphous because of low temperatures.

Cook et al. (2007) reviewed annealing mechanisms. Most favorable was micrometeorite impacts, but all of them were found unable to compete with cosmic-ray amorphization.

Crystalline Water Ice = Cryovolcanism?

Cook et al. (2007) intepreted crystalline water ice as diagnostic of cryovolcanism on KBOs. This would be incorrect IF

•Dust fluxes were > an order of magnitude larger than interplanetary dust flux, as is possible in planetary environments. (2003 EL61 collisional family, too?)

•Real ices don’t conform to experiments of amorphization

Cryovolcanism?Still, cryovolcanism does exist. Ariel’s surface < 100 Myr old (Plescia 1989), Triton’s even younger (Schenk & Moore 2007)

Are these objects tidally heated, or are young surfaces common on KBOs, too??

X = NH3 / (H2O+NH3). Maximum cosmochemical value is X ≈15% (Lodders 2003).

Models of molecular cloud chemistry predict N2 is efficiently dissociated, converted into NH3 (Charnley & Rodgers 2002). [Depletion of N2 recently confirmed observationally (Maret et al. 2007).] Models predict ~ 25% of all N in NH3 ices, for X ≈ 5%

Observations of 9.3 micron band of ammonia ice suggest X = 5 - 10% (Gibb et al. 2001, Gurtler et al. 2002), but are disputed (Taban et al. 2003).

Comets show X < 1.5%, but may be devolatilized.

Ammonia content of KBOs is unknown, but X = 5% is not unreasonable

Cryovolcanism needs ammonia

Description of Model

Model updates internal energy in zone i:

Qi(t) = rate of heating by long-lived radionuclides

Fluxes into zone i (Fi-1) and out of zone i (Fi) found assuming thermal conduction:

“Equation of state” is used to convert E back into temperature

Ammonia

We use simplified phase diagram to include following phases:

1. Solid water ice

2. Solid ammonia dihydrate (ADH)

3. Liquid water

4. Liquid ammonia

5. Rock (analogs being ordinary chondrites)

Ammonia

Ammonia

Energy added to each zone goes into heating components via heat capacity, or into latent heats due to phase transitions. Each shell with mass M has energy E at the end of each timestep.

We then find temperature T and fraction of mass in each (non-rock) phase that is consistent with this E:

k refers to regime in phase diagram

Ammonia

For example, in regime 1 (T< 176-dT K),

Similar (but much more complicated) expressions apply to other regimes

Ammonia

For example, in regime 3 (176+dT < T < Tliq),

Ammonia

Just a few % ammonia drastically lowers the viscosity, especially once ADH melts.

Arakawa & Maeno (1994)

Hunten et al (1984)

Limit for meter-sized rocks to slip ~ 10 km/Myr

Differentiation

If the ice contains a few % ammonia, differentiation can occur wherever T > 176 K

Maximum radius at which T=176 K ever = “Rdiff”

Within Rdiff, we separate into rocky core, then ADH +ammonia+water = “slush” layer, then water ice on top. Undifferentiated rock-ice crust lies outside Rdiff.

ADH denser than its melt, so slush layer well mixed; we mix compositions and internal energies after each timestep (this mimics convection).

Radiogenic Heating

We consider heating by long-lived radionuclides 235U, 238U, 232Th and 40K only.

Avg heating during first 1 Gyr = 5 x Avg heating during last 1 Gyr!

Thermal conductivitiesRock

We use values measured for ordinary chondrites at low temperatures (100 - 500 K) by Yomogida & Matsui (1983):

k ≈ 1.0 W/m/K, independent of temperature

Water Ice

k = 567 / T W/m/K (Klinger 1980)

Ammonia Dihydrate (ADH)k = 1.2 W/m/K (based on Lorenz & Shandera 2001)

Water / Ammonia

Liquids assumed to be convecting; k set to high value

k =40 W/m/K

ConvectionWe check for convection in water ice layer, but Ra << 1000 in all models we ran: no convection.

Thermal conductivities

Conductivities of non-rock components combined using geometric mean, using volume fractions

Conductivities of rock and ice components combined using percolation theory formula of Sirono & Yamamoto (2001)

Conductivity of undifferentiated rock-ice mixture on Charon well described by

k(T) = 3.21 (T/100 K)-0.73 W/m/K

Thermal conductivities

Results

Canonical case, a Charon-like body

R = 600 km

= 1.7 g cm-3 (rock fraction 63%)

X = 5%

Differentiation starts at t=65 Myr, reaches fullest extent by 100 Myr

Rdiff = 474 km... half the mass differentiates

t=0 Gyr

t=4 Gyr

t=1 Gyr

t=2 Gyr

t=3 Gyr

t=4.6 Gyr

t=1.74 Gyr

slush layer

ice+rock crust

water ice layer

rocky core

water ice layer

ice+rock crust

rocky core

slush layer

rock

H2O(s)

ADH

H2O(s)rock

H2O(s) + ADH

H2O(l) + NH3(l)

Differentiation takes place within ~ 100 Myr

All ammonia within Rdiff leads to liquid. No additional liquid is created without ammonia antifreeze.

Temperatures in slush layer drop below ~ 176 K; freezing starts at t = 4.3 Gyr

Present-day steady-state radiogenic heat flux at surface would be F = 1.28 erg cm-2 s-1.

Analytical estimate of temperature at base of ice shell would be T = 100 (0.993)3.704 exp(0.287) = 129 K.

Flux is enhanced over steady-state radiogenic heat flux by amount F by release of heat from rocky core.

Temperatures in ice shell and in undifferentiated crust explained to within 1% by model with ≈0.28. Temperature at base of ice layer predicted to be T = 100 (0.993+0.172)3.704 exp(0.287+0.581) ~ 182 K.

Release of heat from core predicted to enhance flux by amount ≈0.33

Release of stored heat from core is significant!

Release of latent heat is also significant!

Freezing commences at t=4.3 Gyr

Mass of water/ammonia liquid that freezes = 4 x 1022 g

Latent heat released during freezing = 5 x 1033 erg

Release of this latent heat would enhance surface flux by a whopping 0.4 erg cm-2 s-1 if released in just 0.1 Gyr.

Release of latent heat buffers freezing, prolongs it to take > 0.6 Gyr

Doubling ammonia (X=10%) creates more liquid, and also prolongs it to take ~ 1.5 Gyr!

Our model is highly favorable to maintenance of subsurface liquid:

•Undifferentiated crust containing half the rock (as well as ADH) is thermally insulating (compared to pure water ice).

•Core containing the other half of the rock---and its radionuclides---concentrates and stores heat

•Release of stored heat and latent heat of freezing is significant, and demands a time evolution model.

•These physical effects would not be captured in a steady-state, fully differentiated model.

Bigger is better... but beware

chondrite melting point

R = 800 km

P > 200 MPa

Recipe for present-day liquid:

X > 5%

M > 1024 g, > 1.3 g cm-3

(R > 500 km, f_rock > 40%)

How does subsurface liquid surface?

Crawford & Stevenson (1988) use linear elastic fracture mechanics to show that the stress intensity at the tip of a fluid-filled crack of length l, extending from base of ice layer (top of subsrface ocean), is

If this exceeds Kc = 6 x 108 dyne cm-3/2, the crack will self-propagate.

How does subsurface liquid surface?

On Europa, ∆ = 1.00 g cm-3 - 0.92 g cm-3 > 0, and tension T is needed to initiate a crack. The crack has a maximum possible length.

In our models, ∆ = 0.88 g cm-3 - 1.71 g cm-3 < 0, and buoyancy can drive the crack all the way to the surface.

Cracks will propagate at several m/s (Crawford & Stevenson 1988), reaching the surface in ~ 1 day.

How does subsurface liquid surface?

Cracks as small as 0.8 km can become self-propagating within Charon’s ice layer.

Cracks are likely to be initiated during freezing of slush layer, when its volume must increase by 7%.

Displacement of 7% of ADH over 0.6 Gyr would coat Charon’s surface with water-ammonia ices to depth ~ 1 m / Myr = 1 mm / kyr (~ 0.6 km total).

Heat flux carried to surface only 0.004 erg cm-2 s-1, too small to affect thermal evolution.

Conclusions

Basic structure of KBOs 400-800 km in radius

thermally insulating, undifferentiated rock-ice crust

pure water ice layer, does not convect

ADH - ammonia - water layer buffered near 176 K hot rocky core

cracks form here

Conclusions

•Our models include time evolution, ammonia and differentiation. These are significant factors for thermal evolution of KBOs, and their effects are favorable for maintaining subsurface liquid.

•Rule-of-thumb for subsurface liquid today:

M > 1024 g, > 1.3 g cm-3, X > 5%

Charon and Orcus likely to have subsurface liquid.

•Liquid could be brought to surface via cracks, especially as bodies freeze (which is now for Charon)

•Obvious astrobiological implications: can bacteria live in water that’s 32% ammonia, and near -100ºC ??