Simulations of Enceladus’ plumes with a Smoothed Particle Hydrodynamics model

Introduction: 
Volatile material, released from planetary surfaces, provides fundamental information to understand the past and ongoing processes related to the formation and evolution of planetary bodies. The emission of volatiles opens a window on the composition of planetary interiors and allows the search for biologically relevant molecules. 
An important role in the study of volatile release is played by the evidence of plume emissions from icy satellites, as those observed on Enceladus [1-9] and possibly Europa [10,11]. These plumes outgas from surface fractures [1,2] and are primarily composed of water vapor and icy grains, organics, salts and other gases [9]. The origin of such cryovolcanic activity is strongly thought to be the salty subsurface ocean beneath the icy crust of such moons [12]. 
In this work, we simulate the plume emission through a Smoothed Particle Hydrodynamics (SPH) numerical model considering the Enceladus case, a well-studied phenomenon thanks to models and the Cassini-Huygens mission measurements.

Methods:
We simulate a plume on Enceladus outgassing from a surface fracture through a SPH [13-15] model. It is a Lagrangian (mesh-free) method, where volume elements and a statistical approach are used to follow spatial and temporal variations of physical quantities. The model integrates the hydrodynamics equations for the evolution of density, velocity, and thermo-kinetic energy. We also model phase transitions from water vapor to single-sized icy grains and their possible sublimation, considering the dynamical viscous coupling between the two components. We include interactions with boundaries (fracture walls and Enceladus surface), the heating effect of the solar radiation on released particles, Enceladus’ gravity, and Saturn’s tidal field. The mentioned processes are important since they can alter the thermal and dynamical behavior of the volatile material [16, 17].
We start by considering an amount of saturated water vapor at the triple point that can outgas from a single rectangular fracture with a section of 200 m² [3] and 5 km deep, located at Enceladus' South Pole. We explore the role of icy-grain size (1 μm and 100 μm) in shaping the properties of the plume.

Results:
Within the fracture, the initial reservoir of vapor can efficiently form icy grains that rapidly dominate the plume content. After emission, the solar radiation favors the sublimation of part of the icy grains to vapor that can rapidly expand in all directions, while the remaining icy grains are less widespread. Simulations assuming a large grain size (100 μm) show a more collimated ice component, due to the weaker viscous coupling with the vapor as compared to the small grain size (1 μm) case, where the coupling is more important. The obtained average velocity of the plume is of the same order of magnitude as the observed one, namely hundreds of m/s [5], with the vapor faster than icy grains. The mass loss from the surface fracture increases in a few seconds and reaches values compatible with the expected ones [8]. 
The assumptions of a fixed amount of material causes an overall decrease in the mass loss with time, and the density perturbations inside the fracture associated with the phase transition treatment produce a superimposed short-term temporal variability (Figure 1).

Figure 1: Mass loss from the surface fracture for the simulation with 1-micron-sized icy grains

The thermal conduction with the cold Enceladus’ surface is efficient and favors the deposition of surface ice, with a symmetrical distribution around the fracture. This allows the evaluation of the deposition rate as a function of the distance from the emitting region (Figure 2). The obtained values are consistent with those reported in the literature [4].

Figure 2: Ice deposition rate at different times as a function of the projected radial distance from the emitting region, for the simulation with 1-micron-sized icy grains.

Conclusions and perspectives:
Our simulations produce results consistent with literature knowledge regarding Enceladus plumes, validating our implementation of physical processes in the SPH method. This opens the possibility to explore the release of volatiles from different planetary objects through our approach. In such a view, we are further refining the model, mainly for phase transitions and boundary interactions for which we can take advantage of Eulerian models for surface and subsurface thermophysical characterization [18, 19]. Moreover, the presence of a dusty component with a size distribution is important for several targets. In particular, for application to cometary activity as well as to characterize the evolution of a small object post-impact plume over the Moon’s surface. Similarly, this model is applicable to the sublimation of surface ice and the release of gas-ice-dust mixtures due to drilling-induced activities, planned for missions to the Moon and Mars. 
Finally, the presented model is suitable for Europa's case. It can provide a tool to interpret and plan the future possible plume observations by JUICE and Europa Clipper missions.

References:
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Acknowledgments: This work was partially supported by ISSI within the project “Thermophysical Characterization of Ice-Rich Areas on the Surface of Specific Planetary Bodies: Conditions for the Formation of a Transient Exosphere”.