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| Titel |
Early thermal history of Rhea: the role of serpentinization and liquid state convection |
| VerfasserIn |
Leszek Czechowski, Anna Losiak |
| Konferenz |
EGU General Assembly 2015
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 17 (2015) |
| Datensatznummer |
250110960
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| Publikation (Nr.) |
 EGU/EGU2015-11008.pdf |
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| Zusammenfassung |
| Intorduction:
Thermal history of Rhea from the beginning of accretion is investigated. The numerical
model of convection combined with the parameterized theory is developed. Melting of the
satellite’s matter, gravitational differentiation and serpentinization of silicates are included.
The role of the following parameters of the model is investigated: time of beginning of
accretion, duration of accretion, viscosity of ice close to the melting point, activation energy
in the formula for viscosity E, thermal conductivity of silicate component, ammonia content
X, and energy of serpentinization.
1. Numerical model: In our calculations we use numerical model developed by
Czechowski (2012) (see e.g. description in [1]). The model is based on parameterized theory
of convection combined with 1-dimensional equation of the heat transfer in spherical
coordinates:
/T(r,t)-
Ïcp /t = div(k(r,T ) gradT (r,t))+ Q(r,T),
where r is the radial distance (spherical coordinate), Ï is the density [kg m-3], cp [J kg1 K-1
] is the specific heat, Q [W kg-1] is the heating rate, and k[W m-1 K-1] is the thermal
conductivity. Q(r,t) includes sources and sinks of the heat. The equation is solved in time
dependent region [0, R(t)]. During accretion the radius R(t) increases in time according to
formula: R(t) = atfor tini tac , i.e. after the accretion
(see e.g. [2]), where tinidenotes beginning of accretion and tac denotes duration of this
process.
If the Rayleigh number in the considered layer exceeds its critical value Racr then
convection starts. It leads to effective heat transfer. The full description of convection is given
by a velocity field and temperature distribution. However, we are interested in convection as a
process of heat transport only. For solid state convection (SSC) heat transport can be
described by dimensionless Nusselt number Nu. We use the following definition of the
Nu:
Nu= (True total surface heat flow)/(Total heat flow without convection).
The heat transport by SSC is modelled simply by multiplying the coefficient of the heat
conduction in the considered layer, i.e.:
kconv =Nu k.
This approach is used successfully in parameterized theory of convection for SSC in the
Earth and other planets (e.g. [3], [4]).
Parameterization of liquid state convection (LSC) is even simpler. Ra in molten region is
very high (usually higher than 1016). The LSC could be very intensive resulting in almost
adiabatic temperature gradient given by:
dT-= gαmT–,
dr cpm
where αm and cpm are thermal expansion coefficient and specific heat in molten region, g is
the local gravity. In Enceladus and Mimas the adiabatic gradient is low and therefore LSC
region is almost isothermal.
2. Results:
1. We found that time of beginning of accretion and duration of accretion are crucial for
early evolution, especially for differentiation.
2. Viscosity of ice close to melting point, activation energy in formula for viscosity E, and
ammonia content X are very important for evolution, but not dramatic differences are found if
realistic values are considered.
3. The energy of serpentinization is important for evolution, but its role is also not
dominant.
4. LSC operating in molten part could delay the differentiation and the core formation for
a few hundreds Myr.
5. The gravity data could be interpreted that Rhea is fully differentiated only if its core
has high porosity and low density ~1300 kg m-3. In fact, there is not mechanism
that could remove the water from molten core and the core of Rhea is probably
porous.
Acknowledgements: The research is partly supported by National Science Centre (grant
2011/ 01/ B/ ST10/06653).
ReferencesÂ:
[1] Czechowski, L. (2014) Some remarks on the early evolution of Enceladus. Planet. Sp.
Sc. 104, 185-199.
[2] Merk, R., Breuer, D., Spohn, T. (2002). Numerical modeling of 26Al induced
radioactive melting of asteroids concerning accretion. Icarus 199, 183-191.
[3] Sharpe, H.N., Peltier, W.R., (1978) Parameterized mantle convection and the Earth’s
thermal history. Geophys. Res. Lett. 5, 737-740. |
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