Europlanet Science Congress 2020
Virtual meeting
21 September – 9 October 2020
Europlanet Science Congress 2020
Virtual meeting
21 September – 9 October 2020
EPSC Abstracts
Vol.14, EPSC2020-82, 2020, updated on 08 Oct 2020
Europlanet Science Congress 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Dynamics of Titan's high-pressure ice layer

Klara Kalousova1 and Christophe Sotin2
Klara Kalousova and Christophe Sotin
  • 1Charles University, Faculty of Mathematics and Physics, Department of Geophysics, Prague, Czech Republic (
  • 2Jet Propulsion Laboratory-California Institute of Technology, Pasadena, USA (

The abundance of methane and 40Ar in Titan's atmosphere points to the exchange processes between the surface and the deep interior. Here, we study heat and water transport through Titan's high-pressure (HP) ice layer using a two-phase model of solid ice-liquid water mixture. Our results show that melting may occur at the interface with silicates and that the generated liquids then ascend through the layer before reaching the ocean. This process may facilitate the transport of volatiles from the core to the ocean. We also derive scaling laws to determine the occurrence of bottom melting. Using Cassini data and reasonable values of viscosity and heat flux, we predict that exchange processes through Titan's HP ice layer might be ongoing.

Titan is likely differentiated into a hydrated silicates core [4] and a hydrosphere composed of a high-pressure (HP) ice layer, an ocean, and an ice I crust. The presence of an ocean was suggested based on the interpretation of (i) measurements of Schumann-like resonance [3], (ii) Cassini-inferred large value of k2 [5], and (iii) the large measured value of obliquity [2].

Several observations and their interpretations also point to exchange processes between the deep interior and the atmosphere, such as the large amount of 40Ar [9] and methane [1] and the observed 15N/14N isotope ratio [8]. Here, we study the dynamics of Titan's HP ice layer to investigate its permeability for volatiles transport between the silicate core and the ocean.

Numerical model
We solve the two-phase mixture equations [10] for the mixture of two coexisting phases - solid ice and liquid water. In this approach, the amount of water is described by porosity φ that is defined as a volume fraction of water in the mixture. We use the open source Finite Element Method library FEniCS [7]. For more details, see [6].

Figure 1 shows the difference of temperature T from the melting temperature Tm (top) and the corresponding porosity φ (bottom) for the reference simulation. We observe that: (i) a layer of temperate ice (T=Tm, dark red) is established at the ocean interface, (ii) melt appears in the upwelling plumes and the top temperate layer from where it is extracted into the ocean, (iii) some melt may also be generated at the silicates interface, (iv) the amount of liquid water (porosity) is small (≤ few percent). Being less dense than the HP ice, the generated water provides additional buoyancy that promotes the ascent of hot temperate plumes and the extraction of most of the water produced at the silicates interface. The main model parameters (HP ice layer thickness H, HP ice viscosity μ, incoming silicates heat flux qs) determine the convection and melt generation pattern.

The occurrence of melt at the silicates interface is determined by the efficiency of HP ice convection which is characterized by the Rayleigh number. To describe the thermal state of this interface when there is no melt (T<Tm), we perform thermal boundary layer (TBL) analysis that relates the hot TBL thickness with the Rayleigh number. We then derive an expression for the critical silicates heat flux for bottom melting which is shown in Figure 2. If, for given H and μ, the silicates heat flux qs is smaller than the critical value qsc, temperature at the silicates interface is below the melting temperature and no melt is produced. On the other hand, if the silicates heat flux is larger than the critical value, melting occurs at the interface. Note that the smaller the viscosity (leading to more efficient heat transfer by solid state convection), the larger the heat flux that is necessary for bottom melting for a given HP ice layer thickness and vice versa.

The light yellow rectangle in Figure 2 shows the estimated present day value of the heat flux coming out of the silicate core [6]. Following [2] who predict the ice I crust thickness smaller than 100 km and assuming pure H2O hydrosphere, the present day HP ice layer thickness is less than 140 km (determined by the ocean adiabat). For this value, melt is predicted at the silicates interface if the ice viscosity is 1015 Pa s or larger (Figure 2).

We investigated the dynamics of Titan's HP ice layer by solving the problem of two-phase thermal convection of solid ice and liquid water mixture. We showed that melting at the silicates interface depends on the ice viscosity, the HP ice layer thickness and the incoming heat flux and we found a corresponding scaling law for the critical silicates heat flux for bottom melting. If melting occurs at the silicates interface, argon, nitrogen and other volatiles coming out of the silicates could be dissolved in water, advected through the HP ice layer, and extracted into the ocean. Based on Cassini observations and reasonable values of HP ice viscosity, we predict that exchange processes through Titan's deep HP ice layer might be ongoing.

KK received funding from the Czech Science Foundation through project No. 19-10809S and from the Charles University Research program No. UNCE/SCI/023. CS acknowledges support by the NASA Astrobiology Institute through project `Habitability of Hydrocarbon Worlds: Titan and Beyond' (17-NAI8_2-0017). Part of this work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

[1] Atreya et al. (2006), PSS, 54, 1177-1187.
[2] Baland et al. (2014), Icarus, 237, 29-41.
[3] Beghin et al. (2012), Icarus, 218, 1028-1042.
[4] Castillo-Rogez & Lunine (2010), GRL, 37, L20205.
[5] Iess et al. (2012), Science, 337, 457-459.
[6] Kalousova & Sotin (2020), EPSL, accepted.
[7] Logg et al. (2012), The FEniCS Book.
[8] Miller et al. (2019), Astrophys. J., 871.
[9] Niemann et al. (2010), JGR, 115, E12006.
[10] Soucek et al. (2014), GAFD, 108, 639-666.

How to cite: Kalousova, K. and Sotin, C.: Dynamics of Titan's high-pressure ice layer, Europlanet Science Congress 2020, online, 21 September–9 Oct 2020, EPSC2020-82,, 2020