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| Titel |
Enceladus-Mimas paradox: a result of different early evolutions of satellites? |
| VerfasserIn |
Leszek Czechowski, Piotr Witek |
| 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 |
250110551
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| Publikation (Nr.) |
 EGU/EGU2015-10569.pdf |
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| Zusammenfassung |
| Summary: Thermal history of Mimas and Enceladus is investigated from the beginning of
accretion to 400 Myr. The following heat sources are included: short lived and long lived
radioactive isotopes, accretion, serpentinization, and phase changes. We find that temperature
of Mimas’ interior was significantly lower than of Enceladus. Comparison of thermal models
of Mimas and Enceladus indicates that conditions favorable for starting tidal heating lasted
for short time (~107yr) in Mimas and for ~108 yr in Enceladus. This could explain
Mimas-Enceladus paradox.
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:
Comparison of thermal models of Mimas and Enceladus indicates that conditions
favorable for starting tidal heating (interior hot enough) lasted for short time (~107yr)
in Mimas and for ~108 yr in Enceladus. This could explain Mimas-Enceladus
paradox.
3. Conclusions: The Mimas-Enceladus paradox is probably the result of short time when
Mimas was hot enough to allow for substantial tidal heating. The Mimas-Tethys resonance
formed later when Mimas was already cool. (see also [1, 4]) The full text of the paper will be
published in Acta Geophysica [5].
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.
[4] Czechowski, L. (2006) Parameterized model of convection driven by tidal and
radiogenic heating. Adv. Space Res. 38, 788-793.
[5] Czechowski, L., Witek, P. (2015) Comparisons of early evolutions of Mimas and
Enceladus. Submitted to Acta Geophysica. |
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