Numerical simulations of heat exchange and vapor flow in ice fractures on Enceladus

Abstract

Cassini spacecraft observed plume of water vapor and ice particles above the south polar terrain (SPT) of Saturn's moon Enceladus in 2005. The area of the SPT is marked by four prominent linear depressions in the ice dubbed “tigers stripes” (TS) that appear to be the source of the plume. The area around TS is also the source of anomalously high heat flux. The current consensus based on analysis of Cassini observations and modeling suggests that TS are fractures in the ice that penetrate to warm sub-ice ocean. Escaping vapor laden with ice particles forms the visible plume and latent heat of condensing vapor serves as the source of the surface thermal anomaly. In the present work previously developed numerical model of vapor flow and heat exchange inside TS fractures is refined and used to explain Cassini observations. Model improvements include consideration of a possible snow layer on the surface and inclusion of surface ice sublimation into energy balance model. Results of the simulations with improved model suggest that Cassini observations of vapor mass flow and endogenic heat flux can be explained if the width of the ice fractures is in the range 0.05–0.1 m, similar to previously published results. Wider fractures are possible if only a small portion of TS total length produces vapor plume, but the whole ~500 km length of TS fractures still contributes to the surface thermal anomaly. Alternatively, wider fractures are also possible in fractures with high effective friction due to wall roughness or channel tortuosity. Simulated heat output of fractures with different widths and depths in the range of 1.5–3 km is ~2.5–3.0 GW and is only weakly dependent on fracture width. A 2-m-thick surface snow layer covering the fracture can significantly lower outgoing heat flux to 0.9–1.9 GW and reduce surface temperatures by 20–40 K. The total heat flow from different fractures (including conduction from the water-filled portion) is remarkably similar - it is ~3.3 GW and 2.3 GW for fractures without and with a surface snow layer, respectively. The simulated heat flow is lower than the observed heat flow, suggesting that each TS depression may host 2 to 6 narrow ice fractures. The long-standing puzzle of the large difference between the observed heat flow from near TS (~4.2 GW) and from the whole SPT (~15.8 GW) is explained by conduction of ~11 GW of heat from the ocean through the ~5 km-thick ice shell underlying the SPT. Predicted high surface temperatures near fracture exit result in high rates of ice sublimation, which may produce a secondary source of water vapor feeding the observed plume. Fracture outlet likely evolves into a cone-like cross-section widening towards the surface on timescales from 1 to 100 years.