Does Mimas wear an ocean on its sleeve? Testing for a young ocean with crater topography and ice shell porosity

At first glance, Saturn’s moon Mimas might seem like an unlikely candidate ocean world. Its small size, low bulk density, heavily cratered surface, and fairly eccentric orbit all suggest a solid interior primarily composed of H₂O ice. This view was first challenged by measurements of Mimas’ physical librations from Cassini ISS data [1], whose amplitude exceeded what is expected from a completely frozen, hydrostatic interior—instead hinting at the presence of either an elongated core or a subsurface ocean. Recent work has further suggested that Mimas’ periapsis drift and current high eccentricity can be explained by a young, non-steady state ocean. This paints a picture in which Mimas’ ice shell has a thickness of 20–30 km and is currently thinning, resulting in an ocean that is only 10–25 Myrs old [2][3]. While this scenario is mathematically viable, more work is needed to reconcile it with surface observations, particularly the absence of compressional features [4] and the apparent lack of relaxation of large crater topography, both of which would typically be expected if an ocean were present.

Topographic relaxation, the process by which surface relief is lost as topographic stresses decay, has been widely used to probe the thermal history of icy moons [e.g., 5]. The rate of relaxation depends on the composition and thermal structure of the moon’s interior, as well as the size of the topographic feature in question. The existence of a subsurface ocean implies a warm, weak interior that would promote relaxation, seemingly contradicting the minimally relaxed state (< 10% [6]) of Mimas’ largest crater, Herschel. Given that bigger topography generates larger stresses and thus relaxes more rapidly, Herschel crater’s preserved relief offers a unique opportunity to test for the existence and longevity of the hypothesized ocean. Determining the conditions under which Herschel’s relief could be maintained can constrain whether its present-day topography is compatible with a young subsurface ocean, and if so, how long this ocean may have existed for.

In this work, we use the finite element software COMSOL Multiphysics to forward model the relaxation of Herschel crater over 25 Myr, the maximum proposed lifespan for the young ocean. We test 3 different ice shell temperature structures, varying our model’s effective surface temperature from 80 K (Mimas’ nominal surface temperature) to 100 and 120 K, corresponding to 35–50% porosity in the uppermost ~1 km of the ice shell. Our domain consists of a 2D axisymmetric shell of radius 198.2 km, with Herschel’s crater topography at the top (Figure 1A) and gravitational acceleration decreasing radially inwards from 0.064 ms^-2 at the surface. Our initial crater has a diameter of 140 km, depth of 11 km, and a 6 km tall central peak, based on measurements by [7]. We test ice shell thicknesses ranging from 15–35 km, corresponding to surface heat fluxes between ~18–50 mWm^-2. We assume a pure water ice, viscoelastic shell with no impurities, where viscous behavior is driven by dislocation creep and grain boundary sliding [8]. In terms of the temperature profile, our models assume the shell to be purely conductive, with a surface temperature between 80–120 K and a base temperature of 273 K, at which point the remainder of the domain becomes isothermal (Figure 1B). We use a temperature-dependent thermal conductivity for ice of 651/T.

We find that in models with a surface temperature of 80 K, Herschel retains most of its original relief after 25 Myr across all the ice shell thicknesses tested (15–35 km). During this time, the rim-to-floor depth decreases only by 210-947 m, corresponding to relaxation fractions between ~2–9% (Figure 2). These results suggest that in the absence of porosity, minimal relaxation of Herschel crater is consistent with the existence of a subsurface ocean. However, the addition of a near-surface porous layer— whose insulating effect is simulated by increasing the effective surface temperature of our models— significantly speeds up the relaxation process. For an effective surface temperature of 100 K (corresponding to a moderately porous, 1-km thick insulating layer) Herschel relaxes by >15% for the thinnest ice shells tested (Figure 2), far exceeding the currently observed relaxation fraction. Under these conditions, maintaining Herschel’s present-day relief over 25 Myr requires an ice shell thicker than 25 km. With an even higher near-surface porosity ( = 120 K), Herschel shallows by over 10% in merely 1.2 Myr to 2.4 kyr, strongly constraining the longevity of the proposed ocean.

Our results suggest that the relaxation state of Herschel could be consistent with the existence of a young ocean on Mimas only if its ice shell has negligible to no porosity. Our models highlight the significance of near-surface temperature variations and suggest that moderate-to-high porosity would be difficult to reconcile with Herschel’s observed morphology if the proposed ocean does indeed exist. However, we note that our results alone cannot confirm or reject the existence of an ocean, but rather place possible constraints on its longevity. Ongoing work aims to incorporate dynamic processes in the ice shell, particularly the thinning proposed by [3]. Ultimately, this will refine the range of ice shell thicknesses and structures that could be consistent with Herschel’s minimally relaxed state.

Figure 1. Model set up for an example 30 km thick ice shell.  A) Close-up of the geometry defined for Herschel, B) Ice sheet temperature gradient.

Figure 2. Modeled relaxation fraction of Herschel after 25 Myr as a function of ice shell thickness for a surface temperature of 80 and 100 K.

References:

[1] Tajeddine et al., Science, 346, 6207, 322–324 (2014). [2] Lainey et al., Nature, 626(7998), 280–282 (2024). [3] Rhoden et al., Earth and Planetary Science Letters, 635, 118689 (2024). [4] McKinnon et al., 56^th Lunar Planet. Sci. Conf., Abstract #2897 (2025) [5] Bland et al., Geophysical Research Letters, 39(17) (2012) [6] Schenk et al., 56^th Lunar Planet. Sci. Conf., Abstract #2435 (2025) [7] Moore et al., Icarus, 171, 2, 421–443 (2004) [8] Goldsby and Kohlstedt, JGR: Solid Earth, 106, 11017–11030 (2001).