Frictional Strength, Stability, and Potential Shear Heating on Icy Satellite Faults

We determined the frictional strength and stability of polycrystalline ice and ice‐ammonia to constrain fault behavior on icy satellites such as Enceladus and Europa. Friction experiments including velocity steps and slide‐hold‐slide tests were conducted to measure the steady‐state coefficient of friction, velocity dependence and healing between temperatures of 98 and 248 K at a normal stress of 100 kPa. Rate‐state friction parameters determined from velocity steps provide stability values. The friction results are used to infer fault strength and frictional heating of an icy crust with depth for both a pure ice crust and one containing ammonia. We find a reduced coefficient of friction for an ammonia‐bearing crust and stronger velocity dependence in the presence of partial melt. The temperature dependence of fault stability maps a seismogenic zone with depth analogous to the synoptic model for terrestrial fault stability, where we find instability between 0.7 and 3.9 km with a return to stability from 4.6 km if we assume a 6 km ice shell. We consider the role of sliding velocity and fault thickness on localized frictional heating in both systems and estimate the depth of melt generation in an ammonia‐bearing crust. Our results imply that faults at conditions similar to icy satellites can be seismogenic.


Introduction
Strike-slip fault motion has been inferred on Jupiter's moon Europa (Hoppa et al., 2000;Prockter et al., 2000;Spaun et al., 2003) and Saturn's moon Enceladus (Martin, 2016;Nimmo et al., 2007;Rossi et al., 2020;Yin et al., 2016), which is posited to produce tidally driven frictional shear heating on these bodies.The paucity of impact craters, particularly on the south polar region of Enceladus, is associated with active tectonics.The Cassini spacecraft has revealed four large faults ("tiger stripes") on the south polar region of Enceladus associated with anomalously high temperature gradients and active jets (Porco et al., 2006).By flying as close as 100 m to the surface of Enceladus, Cassini captured a plume eruption (Waite et al., 2009), whose activity has since been suggested to be linked to tidally induced stresses on the faults (Hedman et al., 2013).Although plume activity has been linked to various mechanisms, including dilation (Hurford et al., 2007) and clathrate decomposition (Kieffer et al., 2006), we explore the assumption of previous works that strike-slip sliding in response to resolved shear (fault-parallel) and normal (fault-perpendicular) stress variations during the diurnal tidal cycle (period = 1.37 days) are their source (Nimmo et al., 2007;Olgin et al., 2011;Smith-Konter & Pappalardo, 2008).Early models of faulting on this and other icy bodies such as Jupiter's moon Europa controlled failure by opening and closing faults with normal stress variations (e.g., Hoppa et al., 1999Hoppa et al., , 2000;;Tufts et al., 1999).Later models additionally considered the Coulomb criterion to assess a fault's failure potential (Smith-Konter & Pappalardo, 2008), where Coulomb friction is determined by fault friction and orientation in the stress field (Beeman et al., 1988).The use of the Coulomb criterion was an improvement because it allowed for sliding even during periods of compression on the fault.Currently published models that estimate frictional heat generation from icy faults employ a constant coefficient of friction (Nimmo et al., 2007;Nimmo & Gaidos, 2002).However, laboratory studies have shown that the coefficient of friction of ice is a dynamic variable that may depend on temperature, sliding velocity (Barnes et al., 1971;Blackford et al., 2007;Kennedy et al., 2000;Kietzig et al., 2010;Maeno & Arakawa, 2003;Marmo et al., 2005;McCarthy et al., 2022;Oksanen & Keinonen, 1982), healing rate (Zoet & Iverson, 2018), composition, and partial melt fraction (Lishman et al., 2011;Sukhorukov & Løset, 2013).Together, these dependencies can lead to a variety of potentially important feedback mechanisms on tidally driven faults throughout the thermo-orbital evolution of icy satellites.
The tiger stripes are inferred to be initially formed in tension and then reactivated as shear cracks due to the timevarying orientation of tidal stresses (Hurford et al., 2007;Nimmo et al., 2007).The maximum-resolved shear and normal stresses due to diurnal stresses as a function of fault orientation are estimated to be 45 and 70 kPa, respectively (Smith-Konter & Pappalardo, 2008).First-order determination of failure on a fault depends on Coulomb friction.However, determining whether faults will fail slowly or in dynamic instabilities as observed in laboratory and nature (stick-slips and earthquakes, respectively) depends on frictional parameters provided in the empirical rate-and state-dependent friction laws (Scholz, 2019).
In addition to the unknowns of potential fault behavior, questions remain on the thermo-mechanical processes driving the plume activity in the south polar region of Enceladus-in particular, the anomalously high heat flux in this region and the apparent asymmetry in the global ice shell geometry as a result (Kang et al., 2020).Current models are unable to reproduce the heating rates required for the predicted thinner ice shell in the southern polar region (Beuthe, 2018(Beuthe, , 2019;;Souček et al., 2019;Čadek et al., 2019); therefore, estimates on localized tidally driven frictional heating on the tiger stripe faults may help explain the excess heat.The experimentally determined values for the coefficient of friction can be used in frictional heating models to more accurately constrain the thermal gradient along active faults and the depth of partial melt.
Localized frictional heating may contribute to a possible transport mechanism if shallow partial melt can be generated as a result of the heat that migrates through the ice shell.Incorporating frictional dependencies into a more complex shear heating model will allow for better constraints on the conditions in which shallow melt may be generated in the ice shell under strike-slip features.As tidal stresses, temperature, and sliding velocity evolve over time, the coefficient of friction and heat generation will also evolve.A closer analysis of the potential feedback mechanisms of the parameters involved will better inform the sustainability of melt within an ice shell.The dynamics of melt in an ice shell may be relevant to both the exploration and habitability of icy satellites.Given the variable thickness of ice shells (Billings & Kattenhorn, 2005;Giese et al., 2008;Olgin et al., 2011) and the challenges associated with it in exploring the subsurface ocean, the existence of a stable body of liquid water in an ice shell may make for a more realistic environment for future exploration.In searching for life, melt ponds (Chivers et al., 2023) may be their own potentially habitable niches, separate from the ocean on icy satellites.Closer to the surface, melt ponds would be more likely to contain radiolytically produced oxidants and exogenic material from the surrounding environment.The existence of stable melt ponds at geodynamic settings such as double ridges or chaos terrains (Hesse et al., 2022) would aid the selection of landing sites for future missions.If the melt instead drains through the ice, melt migration may then be a transport mechanism for material from the surface to the ocean.In particular, if radiolytically produced oxidants can make their way into the ocean, they may oxygenate the ocean in the absence of photosynthesis or direct ocean-atmospheric interaction, as is present on Earth (Chyba, 2000).Therefore, melt migration could be a potential mechanism for oxidant supply to the ocean and we can better constrain this oxidant flux which would allow us to estimate the redox flux of a moon's ocean and energy availability for life throughout its history.However, this is dependent on the oxidants reaching shallow subsurface melt.Oxidants may reach subsurface melt if they are penetrated further into the ice through impact gardening and/or plume deposition (Hand et al., 2006).
Here we describe a suite of laboratory ice friction experiments using polycrystalline ice and ice + ammonia mixtures (∼3wt% NH 3 ) at icy satellite temperatures to constrain frictional fault behavior on ice-covered worlds.We expand upon the results of Schulson and Fortt (2012), using a similar double-direct shear configuration on both pure polycrystalline ice as well as ice doped with ammonia at a temperature range of 90-248 K and velocity range of 1 × 10 6 m/s to 3 × 10 5 m/s, a parameter space analogous to icy satellite conditions.Under these conditions, we establish a better understanding of the temperature and velocity dependence on the coefficient of friction of ice.We quantify the frictional stability with rate-state parameters using the temperature dependence of frictional fault stability to map a depth-dependent seismogenic zone for an icy crust.We assess the role of healing in both frictional dependencies and stability, as well as how these results may be applied to shear heating models of icy satellite faults.By measuring the frictional behavior of ice with ammonia observed on the surfaces of icy satellites (e.g., Waite et al., 2006;Waite et al., 2009), we can study the effect of a second solid phase as well as a partial melt phase on ice friction and use the effect of melt on frictional stability to infer its effect on the fault stability of icy satellites.Ammonia is used specifically because of its deep eutectic with ice.The melting point of a water ice + ammonia mixture (176 K) is significantly lower than that of just pure water ice (273 K) and thus, it has the highest likelihood of producing melt relative to other impurities present on icy satellites.We use the frictional formulation that has been established in terrestrial earthquake mechanics to apply our experimental results to explore frictional strength, stability, and healing in ice and ice mixtures under icy satellite conditions.Additionally, we describe a simple 1-D frictional heating model and discuss the implications of our results on fault behavior on icy satellites.

Fault Stability: Rate-State Friction Formulation
Frictional sliding on ice and rock is characterized by a continuum of slip from stable sliding to stick-slip motion (such as earthquakes).To achieve dynamic failure, the frictional strength must decrease with either strain or velocity.The rate and state friction formulation, which is an empirical relationship describing the dependence of the coefficient of friction (referred to as just "friction" from here on) on sliding velocity V and an internal state variable θ, is used to describe fault stability (Dieterich, 1979;Marone, 1998;Rice, 1983;Rice & Ruina, 1983).The constitutive equation for rate-state friction is where τ is the shear stress, σ n is the normal stress, μ 0 is a reference value such that μ(V 0 ,θ 0 ) = μ 0 , and D C is the critical slip distance required for the steady-state friction to evolve (Rabinowicz, 1951).Parameters a and b describe variations in frictional strength due to changes in the slip rate (the "direct effect"), and how friction evolves to a new steady state (the "evolution effect").The internal state variable θ is often described with experimental data using either the aging law (Dieterich, 1972): or the slip law (Ruina, 1983): A third equation is necessary to solve for the friction coefficient, sliding velocity, and state variable.Hooke's law is applied to a spring-slider system with a rigid slider block to approximate the elastic response: where k is the spring stiffness, v l is the load point velocity, the normal stress σ n is assumed constant, and inertia is ignored.The spring constant, k, accounts for the elastic deformation of the apparatus as well as the sample.The stiffness is normalized by the normal stress, having units of 1/length.The a and b parameters in the rate-state formulation for friction can be used to determine the velocity dependence of friction, and therefore, its stability, where Equation 1 can be rearranged to obtain: where Δμ ss is the change in steady-state friction upon a change in velocity from V 0 to V (Dieterich, 1979;Marone, 1998).The sign of a-b indicates fault stability: where a positive a-b is termed velocity strengthening (friction increases with increasing velocity) and stable; and where a negative a-b is velocity weakening (friction decreases with increasing velocity) and is associated with unstable, stick-slip sliding (akin to an earthquake), depending on whether the stiffness of the loading system is above (stable) or below (unstable) a critical stiffness K cr (Gu et al., 1984;Rice & Ruina, 1983), determined by the normal stress and rate and state parameters: Values of the rate parameter a-b have been measured via friction experiments on rock, and used to map out an idealized unstable zone with depth on Earth that can explain the distribution of earthquake nucleation with depth (e.g., Scholz, 1998).A transition occurs from velocity-strengthening behavior at shallow depths to velocity weakening at intermediate depths and back to stable sliding at the brittle-ductile transition zone.The upper stability transition is attributed to the stabilizing effect of fault gouge dilation at lower normal stresses (Blanpied et al., 1987;Byerlee & Summers, 1976;Marone et al., 1991) and the lower stability transition due to temperature effects on the brittle-ductile transition (Scholz, 1988;Tse & Rice, 1986).The velocity-weakening region can be considered an idealized seismogenic zone as slower transient slip events have also been documented in the region.
This framework has been applied to explain slip behavior of faults on Earth (Marone et al., 1991(Marone et al., , 1995;;Noda & Lapusta, 2013) and Mars (Schultz, 2003).Although the range of temperatures experienced by fault rocks on these rocky planets appears higher than those of icy bodies, in terms of homologous temperature (T/T m ), conditions in the brittle crust of both types of bodies are nearly identical (0.3 < T/T m < 0.6) and thus the mechanics may be comparable.A benefit to studying polycrystalline ice friction in the laboratory is that the full range of temperatures found in an icy shell, from coldest surface temperature to the warm ductile interior, can be achieved in a single apparatus allowing us to document frictional dependencies such as temperature, time, and sliding rates that may inform both systems.

Fault Failure: Coulomb Friction
While dynamic instabilities observed in both the laboratory and in nature (stick-slip and earthquakes, respectively) are best described by the empirical rate and state friction law, a less comprehensive determination of fault failure can be described by the Coulomb criterion (Byerlee, 1978).According to the Coulomb criterion, fault slip occurs if the magnitude of the resolved shear stress exceeds the frictional resistance determined from the normal stress.This normal stress is typically the overburden pressure (Brace & Kohlstedt, 1980;Byerlee, 1978); however, in the presence of significant tidal stresses, an additional resolved tidal normal stress term may be included.Smith-Konter and Pappalardo (2008) computed the Coulomb failure conditions on the tiger stripes of Enceladus to assess failure location, timing, and direction throughout an orbital cycle using this adapted Coulomb criterion: where ⃒ ⃒ τ s ⃒ ⃒ is the absolute value (magnitude) of the resolved tidal shear stress, σ n is the resolved tidal normal stress, and μ f is the coefficient of friction.The sum of the resolved normal stresses is ρgz + σ n ) where ρ is the density of the ice shell (which will vary based on temperature), g is the gravity on Enceladus, z is depth and ρgz is the overburden pressure.The tidal shear τ s and normal σ n stresses that are resolved on discrete fault segments are calculated using the diurnal tidal principal stresses (King et al., 1994;Turcotte & Schubert, 2002): where θ and ϕ are the colatitude and longitude respectively of the given point on the fault segment.Β is the fault orientation-radially defined with respect to the longitudinal direction, and σ θθ , σ ϕϕ , and σ θϕ are the diurnal radial, tangential, and shear 2D stress tensor components, respectively (see Supplementary information of Nimmo et al., 2007 for details of the geometry).

Previous Experimental Work on Friction of Ice
Previous experimental studies on the friction of ice using a triaxial setup of ice cylinders with a 45°inclined sawcut under high confining pressures (≤250 MPa) found that friction appeared to be independent of both temperature and sliding velocity for the conditions measured (77-115 K for temperature and 3 × 10 7 m/s to 3 × 10 5 m/s for sliding velocity) (Beeman et al., 1988).Experiments by Schulson and Fortt (2012) studying a wider range of temperatures (98-263 K) and sliding velocities (5 × 10 8 m/s to 1 × 10 3 m/s) under normal stresses less than 98 kPa showed velocity dependence of friction that varied with temperature.However, they were unable to draw a conclusion on the direct temperature dependence of the coefficient of friction of ice.They also observed a healing effect where the coefficient of static friction increases logarithmically with holding time, as seen in friction experiments on rock (Mitchell et al., 2013;Nakatani, 2001).

Sample Fabrication
A total of 32 samples were tested: 15 were pure ice and 17 were two-phase mixtures of ice + ammonia (Figure 1; Tables 1 and 2).In all cases, polycrystalline samples were fabricated using an adapted version of the "standard ice" protocol (Cole, 1979) in order to control grain size and porosity.Bulk seed ice made from deionized water was ground and sieved to the desired grain size range (∼250-500 μm).Grain size ranges were not varied as previous studies of ice-on-ice friction found no grain-size dependence on friction (Kennedy et al., 2000;Saltiel et al., 2021).The sieved seed ice was then packed into a rectangular aluminum mold, which was placed in an ice bath (T = 273 K) for ∼30 min under vacuum.After temperature equilibration, the mold was flooded with either degassed deionized water (for pure ice samples) or an ammonia solution of 10 w/v% (percent solute mass per volume of solution) ammonia (for ice + ammonia samples) so that the liquid flushed through the pore spaces around ice grains.The resulting bulk compositions of the fabricated ice + ammonia samples varied based on the packing density of seed ice from 2.4 to 9.8 wt% NH 3 as measured by the refractive index after experiments (McCarthy et al., 2019).This is roughly consistent with the ammonia content in Cassini measurements of plume composition at the tiger stripes on Enceladus (Waite et al., 2009), assuming that the plume composition is similar to that of the ice shell.We note that spectroscopic detection of ammonia on the surface may be difficult due to damage from solar radiation, which could erase spectroscopic signatures after 10 4 years (Moore et al., 2007).After flooding, the mold was then placed overnight on a cold copper plate within a chest freezer at ∼223 K and insulated on all sides so that the sample solidified from the bottom up to ensure the sample is nearly pore-free (Table 3).
After removing the sample from the mold, it was cut down to the necessary size in a cold room (T = 256 K), first with a saw (if necessary) and then refined to exact dimensions with a microtome.The size of the sliding sample was 50 × 100 × 50 mm and the two stationary side ice blocks were 50 × 50 × 30 mm.The side blocks were always pure ice for simplicity, whereas the sliding sample was either pure ice or ice + ammonia (Table 1).Once cut to size, the sliding surfaces were roughened with 100 grit sandpaper to an Ra of ∼7 μm (McCarthy et al., 2017) just before loading into the apparatus.

Experimental Setup
The friction experiments were conducted in a double-direct shear configuration using an ambient pressure, servohydraulic biaxial deformation apparatus, as described by McCarthy et al. (2016).Here, we incorporate a new lowtemperature cryostat to specifically achieve planetary temperatures.Figure 2 depicts the experimental setup with denote the temperature and composition (blue for pure ice and green for iceammonia) combinations used in this study.All samples as fabricated were either pure ice or had a bulk composition of ∼3-10 wt% NH 3, which is found in solution form above the solidus and in the form of the dihydrate (D) below the solidus.The fraction of melt during testing, which depends on temperature, was determined using the lever rule and this phase diagram (Table 2).The schematic diagrams on the left depict idealized microstructures of pure ice and ice-ammonia mixtures.Melt permeates the grain boundaries at temperatures above the eutectic for ice-ammonia mixtures (McCarthy et al., 2019).For a detailed discussion of eutectic (E) and peritectic reactions as well as the data upon which the figure depends, see Kargel (1992).
the biaxial apparatus, cryostat, and sample configuration.Horizontal ceramic pistons applied a normal force maintained with load cell-provided force feedback servo control.The vertical piston pushed down the central sliding block at velocities determined by a computer-controlled driving program, with feedback provided by direct current differential transformers (DCDTs), resulting in a shear force on the two 50 × 50 mm sliding interfaces.The shear force measured by the load cell was divided by the area and a factor of two when converting the voltage readings to the shear stress to account for the two sliding interfaces.The coefficient of friction was then calculated by dividing the shear stress by normal stress.To span a range of ice shell temperatures consistent with the ice-ocean interface to the near surface (248-98 K), a circulating-fluid chiller was connected to a new cryostat.The chiller was cooled using solenoid-controlled circulating liquid nitrogen (LN).Vacuum provided the insulation within the cryostat.Temperature was monitored to an accuracy of ±0.1 K by Resistance Temperature Detectors (RTDs) placed adjacent to the sliding interfaces.Samples were allowed to sit for approximately 30 min before testing to ensure no temperature gradient existed within the sample.The equilibration time was determined previously using sample embedded thermocouples.For the experiments at the coldest temperatures (<198 K), LN was connected directly to the cryostat.

Load Point Velocity Program
The normal stress was kept constant at 0.1 MPa, while the shear stress varied throughout the experiment in response to a computer-controlled load point velocity driving program (Figure 3).We do not vary normal stress as previous ice-on-ice friction studies have shown no significant difference in the frictional response in the 20-1,000 kPa range (Kennedy et al., 2000).We also assume little to no significant cohesion as previous ice-on-ice friction studies have found near zero cohesions at low pressures below 20 MPa (Beeman et al., 1988).After ramping up to a steady-state friction at a constant velocity of 10 μm/s, we employed a program of both velocity steps and slidehold-slide tests to determine the rate and state friction parameters described in Equations 1-5.A series of velocity steps were run, which imposed sudden increases in velocity to measure the system's response.The two velocity steps in this program were from 1 to 10 μm/s and from 10 to 30 μm/s.The frictional stability was estimated using the rate dependence of friction with the dimensionless parameter a-b calculated in Equation 5.For experiments exhibiting stick-slip behavior where the change in steady-state friction to calculate a-b is more ambiguous, we measured the friction drop and recurrence intervals for the stick slips.We use the following relation to constrain the rate and state parameters for experiments with stick-slips (Beeler et al., 2001;Ben-David et al., 2010;Karner & Marone, 2000): The friction drop ∆μ s , recurrence time t r (Figure 3e), and the empirical recurrence time t 0 at a projected zero friction drop (∆μ s (t 0 ) = 0) can be used to compare the a-b values of stick-slip experiments with a dynamic overshoot factor of (1 + ξ) .During the "dynamic overshoot" in a spring-slider block model, the spring force drops below the kinetic fault strength as the slip ends at a stress below the fault strength.The overshoot factor is a measure of how much the slip differs from the amount required for this stress drop (Beeler et al., 2001).For this study, the overshoot factor is unconstrained and assumed to be the same for all experiments exhibiting stick-slip.
The driving program also employed a series of slide-hold-slides in which a constant sliding velocity was interrupted by zero-velocity holds.The duration of the hold was increased incrementally to constrain the frictional healing rate described as (Beeler et al., 1994;Dieterich, 1972;Marone et al., 1991):  1), ( 10), or (30) preceding them refer to the average temperatures at the slide-hold-slides, 1, 10, and 30 μm/s velocity steps of the experiments, respectively.Temperatures with an asterisk refer to the planned temperatures used for that experiment where exact temperature data at particular times throughout the experiment from the Resistance Temperature Detectors (RTDs) is unavailable.
where Δμ is the difference between the friction peak resulting from the healing and the steady-state friction from before the hold took place and t hold is the hold time, which includes 3, 10, 30, 100, and 300 s for our experiments.We applied the driving program using LabView and collected the raw load and displacement data at a sampling rate of 1 kHz per channel.A simple moving average filter was applied to the raw displacement data (and by extension the sliding velocity) to better discern the velocity patterns throughout the experiments.The shear stress data (and by extension the coefficient of friction) were kept unfiltered to avoid smoothing out significant anomalies.Figure 3 depicts the raw friction and the filtered velocity as a function of time throughout the experiment along with the parameters involved in calculating frictional healing and stability.

Model Set Up
We implemented a simple 1-D model for frictional heating on a single preexisting fault in the brittle layer of a conductive shell.We applied this model to the tiger stripes of Enceladus to explore how temperature-dependent frictional properties affect heat and partial melt generation due to frictional sliding.The thickness of the ice shell at the south polar terrain on Enceladus is estimated at 6 km (Nimmo, 2020).To estimate frictional heating, we use a solution for heat diffusion during sliding on a fault of finite thickness Note.Bulk composition was determined using refractive index measurements of a melted sample after testing.Partial melt fraction was calculated using the lever rule determined from the bulk composition, the temperature of testing, and the phase diagram from Figure 1.Temperatures listed with (shs), ( 1), ( 10), or (30) preceding them refer to the average temperatures at the slide-hold-slides, 1, 10, and 30 μm/s velocity steps of the experiments respectively.Temperatures with an asterisk refer to the planned temperatures used for that experiment where exact temperature data at particular times throughout the experiment from the Resistance Temperature Detectors (RTDs) is unavailable.Note.The value listed for the coefficient of friction (Beeman et al., 1988) is used to compare the results of frictional heat generation with a constant value with an experimentally determined temperature dependent one.

Journal of Geophysical Research: Planets
10.1029/2023JE008215 ZAMAN ET AL. (Lachenbruch, 1986) where deformation is assumed to be homogenous in the fault zone and heat is transferred only by conduction.We choose a relatively high sliding velocity of 1 m/s based on potentially coseismic velocities described by Sleep (2019), but we explore the model sensitivity to sliding velocity, as well as slip magnitude, slip duration, and fault half-width given that they are largely unconstrained at icy satellite conditions.Temperature, T, was calculated as a function of time, t, during/after slip, and distance, x, away from the fault center, expressed as where t* is slip duration, a 0 is the fault half-width, A 0 is the heat generation rate, ρ is the bulk density, c is the heat capacity, and α is the thermal diffusivity.H{t t * } denotes the Heaviside step function such that H{t t * } = 0 for t < t*, and H{t t * } = 1 otherwise.The model considers heat generation only from friction in the brittle layer and does not consider viscous heating in the ductile layer.We also do not consider any energy from frictional heating going into vapor production.The volumetric frictional heat generation rate A 0 used in Equation 12 is calculated by where u is the slip magnitude and τ S is the shear stress calculated using the friction coefficient, tidal normal stress, and overburden pressure from the relation in Equation 7. We calculate the tidal normal and shear stresses involved in the slip events using Equations 8 and 9 at an arbitrarily chosen point on the tiger stripes of Enceladus (315°W, 80°S on the Damascus Fault).We consider points in time in the orbit of Enceladus where there is effectively zero tidal normal stress at those coordinates, maximum fault compression (most positive tidal normal stress at those coordinates in the orbital period), and maximum fault tension (most negative tidal normal stress at those coordinates in the orbital period).For simplicity, we arbitrarily choose slip magnitude of 1 m and slip duration of 1 s for simplicity.Then, we solve for the temperature change due to a single slip event using Equation 12.In reality, the slip duration will depend on the Mohr-Coulomb criterion continuing to be satisfied as the tidal stresses vary throughout Enceladus' orbit.The time between slip events would be determined by the amount of time throughout the orbital period where the Mohr-Coulomb criterion is not satisfied.

Frictional Dependencies
Taking the mean friction from steady-state periods in our experiments, we observe a temperature dependence of the steady-state friction for the three sliding velocities tested (1, 10, and 30 μm/s) for both pure ice and iceammonia samples.The strong inverse temperature dependence of friction appears to be relatively similar at these sliding velocities at approximately 0.0025/K for both pure ice and ice-ammonia (Figure S1 in Supporting Information S1).We note that this temperature relation only applies to the narrow velocity range studied.The steady-state friction of pure ice is consistently greater than that of the ice-ammonia samples at the same temperatures, with the average steady-state friction for pure ice ranging from ∼0.6 to ∼0.9 over a temperature range of 248-98 K at 10 μm/s sliding velocity, while the average steady-state friction for ice-ammonia at the same temperature range and sliding velocity is ∼0.45-∼0.7.Similarly, at 1 μm/s, the average steady-state friction for pure ice ranges from ∼0.7 to ∼0.92 for a temperature range of 173-98 K, while the friction of the ice-ammonia mixture at the same sliding velocity and temperature range varies from ∼0.55 to ∼0.72.Although our average steady-state friction values are consistent with previously reported ice-on-ice friction experiments at similar temperatures, using cohesionless fits (Beeman et al., 1988;Schulson & Fortt, 2012) we measure higher friction values at some conditions, particularly at colder temperatures.
Figure 4 shows the average steady-state friction coefficients from the experiments (all sliding velocities and both pure ice and ice-ammonia) as a function of homologous temperature T/T m (T m = 273 K for pure ice and T m = 176 K for ice-ammonia) along with results from previous ice friction studies at similar conditions.For the ice-ammonia binary system samples, we note that below T m , the stable second phase is the dihydrate and for temperatures above T m , the ammonia is in a liquid solution whose composition changes as a function of temperature according to the liquidus (Figure 1).We report the average steady-state friction values from the different sliding velocities (squares for 10 6 m/s and circles for 10 5 m/s, reporting both 10 and 30 μm/s as circles) and find that the velocity dependence in our experiments was much smaller than the temperature dependence (see Figure S1 in Supporting Information S1 for a comparison of the temperature dependence of friction at the three measured sliding velocities).We do not include error bars in experiments exhibiting stick-slip and report only the mean friction (open points in Figure 4) given the large range in friction resulting from stick-slip behavior.We note however that Schulson and Fortt (2012) includes a 95% confidence error range from least mean squares analyses for their stick-slip experiments and we include those in Figure 4. We include ice-on-ice friction experiments from previous studies at sliding velocities around an order of magnitude of 10 5 m/s or less, normal stresses around an order of magnitude of 10 MPa or less and low to ambient confining pressures around an order of magnitude of 0.1 MPa or less.From Schulson and Fortt (2012), we include experiments at 10 5 and 10 6 m/s sliding velocity at 60 kPa normal stress.From Beeman et al. (1988) et al., 2016) as this study.We find that our results largely agree with previous studies apart from the colder (<173 K) experiments, where Schulson and Fortt ( 2012) report lower values for friction than we do.We also find that the friction of pure ice, ice-ammonia, and saline ice all show a similar temperature dependence when normalized in homologous temperature space.For samples from this study measured at subsolidus conditions, we find a single linear relationship with homologous temperature regardless of sliding velocity (1, 10, or 30 μm/s) or composition (pure ice v.s.ice-ammonia), as described by This equation is valid for a homologous temperature range of 0.36 < T/T m < 0.91 for pure ice (98-248 K) and up to 0.98 for a two-phase ice mixture-like ice-ammonia for a sliding velocity range of the order of 10 6 to 10 5 m/s.In the homologous temperature range of 0.93-0.99,there is a steeper drop-off in friction for pure single-phase ice described by the linear fit μ = 5.1-0.0182T (K) (McCarthy et al., 2017) as the sample approaches the melting temperature.This is in good agreement with our fit since between the temperature ranges explored by this study and McCarthy et al., 2017 (around 251 K for pure ice or a homologous temperature of 0.92), we get an estimated friction coefficient of 0.53 using the fit from McCarthy et al., 2017 and 0.52 using the fit from this study.The friction of two-phase ice mixtures does not have a steep drop off at high homologous temperatures since melt is only forming at the boundaries of the otherwise solid ice grains (e.g., a homologous temperature of 1.0 for iceammonia is the eutectic temperature of 176 K, where the ammonia melt is present at the solid ice grain boundaries).

Fault Stability
We measured the a-b values from velocity steps to determine the velocity-strengthening or velocity-weakening behavior.Plotting a-b for the range of temperatures for both pure ice and ice + ammonia samples using the 1-10 μm/s and 10-30 μm/s velocity step results in a temperature-dependent stability map as shown in Figure 5.We find that both a, the "direct effect" and b, the "evolution effect" have the same relationship with temperature and neither dominate the behavior of the a-b values.We assume a thermal gradient down to 6 km for the ice shell in the south polar region of Enceladus with an ambient surface temperature of 70 K, a constant heat flux of 100 mW m 2 , and a constant thermal conductivity of 3 W m 1 K 1 (Barr, 2008;Bland et al., 2012;Giese et al., 2008;Nimmo et al., 2007;O'Neill & Nimmo, 2010).Using this thermal gradient, we find the potential for seismic activity to be between 0.7 and 3.9 km depth with a return to stability from 4.6 km based on experiments where stick-slips occurred.
The stable velocity steps from the experiments were analyzed with a nonlinear-least-squares fitting routine to a spring slider (RSFit3000), where the rate and state Equations 1-4 are cast as coupled ordinary differential equations (Skarbek & Savage, 2019).Using a single state variable, the rate and state parameters were calculated with fits using both the Aging and Slip laws (Equations 2 and 3, respectively).We use the parameters given by the Slip law since recent studies have shown that it better describes experimental data (Bhattacharya et al., 2015(Bhattacharya et al., , 2017) ) although the results are similar and both are listed in Table S1.
To treat the velocity steps that exhibit stick-slip, we use Equation 10 to constrain the relative positions of the a-b values along with a dynamic overshoot factor in the stick-slip experiments using the friction drops and recurrence interval times from the stick slips (Figure S2 in Supporting Information S1).We find that when setting the dynamic overshoot factor to 0.1, the a-b values resemble the estimated a-b values for stick-slip experiments using Equation 5 and assuming the "steady-state" friction to be the mean friction.These values are listed in Table S1 along with the rate and state parameters of the stable sliding experiments obtained using RSFit3000.
The a-b values for pure ice most closely resemble the curve shape of the crustal stability transition on Earth (Scholz, 1988) with a lower stability transition between 198 and 223 K (about 3.8-4.6km depth in the 6 km ice shell) at 100 kPa.The partial melt phase (temperatures higher than the eutectic in the ice + ammonia samples so that there is ammonia melt at the grain boundaries) makes the fault stability more unstable in the 190-230 K range depending on the velocity, where the velocity jump from 10 to 30 μm/s results in overall greater instability than from 1 to 10 μm/s in the ice + ammonia data.The ice-ammonia results also generally appear to exhibit less stickslip than the pure ice experiments at the same conditions.

Fault Healing
As predicted by the rate and state friction laws, frictional healing increases with the logarithm of hold time for both pure ice and ice-ammonia throughout our temperature range from 98-248 K (Figure 6).The frictional healing rate, shown in Figures 7a and 7b, increases with temperature.This relationship is consistent with ice-onice data from Schulson and Fortt (2012) over this same temperature range.Pure ice and ice-ammonia appear to have similar healing rates at the same temperatures, implying that a second phase may not affect healing significantly.We do not include experiments exhibiting stick-slip behavior as the change in friction with healing is more ambiguous and in some cases there appears to be no healing effect.We also estimate the cutoff time, t c (Figures 7c and 7d) using the following relationship with the healing rate and hold time (Nakatani & Scholz, 2004): The cutoff time is the initial hold time required before healing begins.We use a least squares curve fit to fit Equation 15 to our healing data and estimate the cutoff time and healing rate.

Model Results
We compare shear heating models with a constant coefficient of friction (µ = 0.55) to a temperature-dependent value of friction using our experimentally determined linear relation in Equation 14and the results from McCarthy et al., 2017 for temperatures warmer than explored in this study (>248 K). Figure 8 shows a parameter sweep of the shallowest depth in the ice shell at which partial melt may be generated from a single slip event spanning orders of magnitude of slip distance and duration.We consider four cases for the ice shell: a pure ice shell with a constant friction, an ice-ammonia shell with a constant friction, a pure ice shell with temperaturedependent friction, and an ice-ammonia shell with a temperature-dependent friction.The shallowest depth at which partial melt may be generated is defined as the shallowest depth at which the temperature in the ice shell reaches the melting point for its given composition (273 K for pure ice and 176 K for ice-ammonia) after the slip event.We calculate the fault failure depth using the Mohr-Coulomb criterion at maximum fault tension (most negative tidal normal stress) at an arbitrarily chosen point on the Tiger Stripes (315°W, 80°S on the Damascus Fault) and the overburden pressure.The frictional behavior controls both the heat generation (volumetric frictional heat generation rate, A 0, from Equation 12) and fault strength (Mohr-Coulomb criterion from Equation 7) in this model.Given an initial surface temperature of 70 K (Bland et al., 2012), the behavior of the 1-D temperature evolution with depth in the fault appears to be similar regardless of whether friction was constant or temperaturedependent for both the pure ice and ice-ammonia cases.Partial melt generation is shallower with an ice-ammonia shell given the lowered melting point.Equivalent sliding velocities appear to result in different partial melt generation depths, with slip magnitude playing a larger role than slip duration.The fault failure depth (the bottom of the slipping region) varied between the ice shell scenarios: 1,398 m for the constant friction ice shell (both pure ice and ice-ammonia), 1,308 m for the temperature-dependent ice-ammonia shell, and 1,254 m for the temperature-dependent pure ice shell.The overall friction is lower for the constant friction case, resulting in the weakest (and thereby deepest) fault.In the temperature-dependent friction case, the ice-ammonia shell is weaker than that of the pure ice, given the lower friction for ice-ammonia.
Given the uncertainty in sliding velocity and fault half-width, we conducted a sensitivity analysis of these parameters to constrain their effect on the temperature rise with depth (Figure 9).The endmember cases of maximum fault tension and compression, as well as the intermediate case of effectively no tidal normal stress were considered using the Coulomb failure framework described by Equation 7, where greater fault compression leads to more heat generation.Varying sliding velocity by orders of magnitude, we find that greater velocities generate significantly more temperature rise up to 1 m/s, where the thermal diffusion length scale is greater than the fault width.Smaller fault half-widths lead to greater heat generation and greater fault compression within a tidal cycle leads to stronger fault width dependence for heat generation with a drop-off outside the 10 5 -10 2 m range at either end.It should be noted that this temperature rises assume that the Coulomb criterion is met to begin with and so whether fault slip occurs and heat is actually generated up to the surface is dependent on the tidal cycle (degree of fault tension or compression).In the case of maximum fault compression, the maximum tidal normal stress is greater than the absolute value (magnitude) of the tidal shear stress and so fault slip and heat generation will not actually occur.We find a strong linear relationship between the steady-state friction of one and two-phase ice and homologous temperature (from 0.36 to 0.91) of μ = 1.22 0.76 T T m (Figure 4), which may be useful in future numerical models involving fault friction in an ice shell.At higher homologous temperatures (0.93-0.99) there is a stronger temperature dependence and drop-off in friction for pure single-phase ice relative to two-phase ice mixtures at similar homologous temperatures.We observe both a temperature and partial melt dependence on frictional strength, with friction decreasing with increasing temperature and partial melt (inclusion of ammonia).However, the extent of the temperature dependence varies with partial melt/composition and sliding velocity.There is a degree of compositional dependence on temperature dependence since the melt should (in theory) be frozen below 176 K, but the ice-ammonia friction is still lower than that of pure ice at those colder temperatures.A partial melt dependence may exist and can be calculated using the ice-ammonia phase diagram and the ice-ammonia friction experiments above the eutectic.A sliding velocity dependence did not vary with temperature within our arguably narrow range of velocities (1-30 μm/s) but has been documented in previous ice-on-ice friction experiments at greater orders of magnitude sliding velocities (Beeman et al., 1988;Kennedy et al., 2000;Schulson & Fortt, 2012).In these studies, greater sliding velocities generally correlate with stronger temperature dependence.Beeman et al. (1988) and Kennedy et al. (2000) observe less of a temperature dependence at 10 6 m/s sliding velocity, whereas Schulson and Fortt (2012) and Kennedy et al. (2000) observe strong temperature dependence at 10 3 m/s.Our experiments include 10 5 m/s sliding velocities and expectedly have lower temperature dependence by comparison.The temperature and velocity dependence on friction may be related to the degree of premelting at the slip interface, where greater sliding velocities and warmer temperatures (even below the melting point) may result in aqueous films that can reduce friction (Persson, 2015).The presence of premelt is what gives ice at warmer temperatures its apparent slipperiness, which decreases at lower homologous temperatures (Dash et al., 2006).
We find generally good agreement between our results and previous ice-on-ice friction studies at the same velocity range apart from the colder (<173 K) temperatures from Schulson and Fortt (2012), who reported lower friction values at those temperatures at a lower normal stress (60 kPa) than explored in this study (100 kPa).We note however that most pure ice experiments across all the presented studies appear to exhibit stick-slip at 198 K and below for these velocity and stress conditions.This stick-slip behavior may account for the difference in friction between our results and those of Schulson and Fortt (2012) at these colder temperatures.A notable exception is the experiment at 98 K and 10 5 m/s sliding velocity from Schulson and Fortt (2012), where they see a return to stability.Although our analogous experiment still appears to exhibit stick-slip, this result is still generally in agreement with our analysis of frictional stability from our experiments and the synoptic model of a seismogenic zone (Scholz, 1998).We also note that roughness and differences in machine stiffness may play a role in the discrepancy in results between this study and Schulson and Fortt (2012) at colder temperatures.Our samples had a roughness Ra of ∼7 μm while Schulson and Fortt (2012) reported a roughness Ra of ∼0.43 μm in the direction of milling and ∼2.01 μm in the orthogonal direction for most of their experiments.They also studied the role of roughness in ice friction and found friction to increase in the range of roughness Ra from 0.4-12 μm.
We included the results of saline ice friction from Kennedy et al. (2000) to compare to our ice-ammonia experiments and better constrain the effect of a second phase on the friction of ice.The saline ice friction results appear to be in good agreement with our ice-ammonia friction results when normalized by their respective eutectic melting temperatures (252 K for saline ice and 176 K for ice-ammonia) at both subsolidus and suprasolidus conditions.However, the homologous temperature dependence of friction appears to be different between subsolidus and suprasolidus conditions as shown by a changing slope beyond a homologous temperature of 1.0 in Figure 4. From our experiments, we find a strong linear relationship between the steady-state friction of one and two-phase ice and homologous temperature of μ = 1.22 0.76 T T m , which may be useful in future numerical models involving fault friction in an ice shell.

Frictional Fault Stability: A Temperature Dependent Seismogenic Zone
The frictional stability of ice with temperature (and by extension depth within the ice shell) roughly resembles the synoptic model for frictional stability with depth for crustal faults on Earth (Scholz, 1998) with some notable deviations.For the 1-10 μm/s steps, the warmer stability transition (analogous to where the brittle-ductile transition zone may be) appears to be between 198 and 223 K (about 3.8-4.6km depth in the 6 km ice shell) for pure ice.A colder stability transition may depend on velocity, with faster velocity promoting stable behavior.Although we do not see a return to stability at colder temperatures, Schulson and Fortt (2012) observed stable sliding in their experiment at 98 K and 10 5 m/s sliding velocity.In rock frictional studies, the transition to stability at shallow conditions has been attributed to well-developed fault gouges (Byerlee & Summers, 1976).We did not observe the formation of fault gouges in our experiments.However, in a recent study in our lab, ice sample interfaces were initially welded shut and allowed to fracture upon shearing (Singh et al., 2023).In that study, several high velocity sliding intervals resulted in significant ice gouge at the interfaces.In many cases, the frictional response after the rapid sliding pulses became stable.That study also observed a transition from unstable to stable sliding at T = 198-220 K (at 10 μm/s).Thus, the observed stability with temperature profile in ice is robust when a gouge is generated.Our results indicate that when there is little gouge (e.g., if the gouge refreezes into solid ice between slip events), unstable slip might be able to nucleate close to the surface of the icy satellite.
The ice-ammonia data for the 10-30 μm/s velocity step includes a strong velocity-weakening regime at around 190-230 K as well as stronger velocity strengthening relative to the pure ice at temperatures warmer than 230 K, showing a potentially stronger velocity dependence on both rate strengthening and weakening when melt is included.The ice-ammonia experiments associated with the more velocity-weakening regime however mostly do not necessarily exhibit stick-slip, especially relative to the pure ice case where all of the experiments exhibit stickslip behavior at 198 K and colder.The reduced stiffness of partially molten material may be contributing to the lack of stick-slips in some of the velocity-weakening ice-ammonia experiments.There is a return to stability near the eutectic from around 150 to 170 K.This return to stability matches the transition to velocity stable for pure ice in homologous temperature space, where the transition occurs around 0.75 to 0.85 for both pure ice and iceammonia.
We also explored the effect of melt fraction on frictional stability using the ice-ammonia phase diagram with our ice-ammonia experiments above the eutectic (176 K).Our experiments close to but below the eutectic at 173 K may also exhibit melt-related behavior due to its proximity to the eutectic and the activation energy it takes for melting/freezing to occur (Flanders et al., 1997).However, based on our results, the melt fraction does not appear to play a significant role in the frictional stability of ice in the studied range of ∼0.11-∼0.43.If a larger melt fraction outside the range studied in our work appears to affect the frictional stability of ice mixtures, it may aid in interpreting future seismic data and work in conjunction with ice-penetrating radar (Blankenship et al., 2018) to detect heterogeneities in the ice shell such as melt lenses.
The analogous behavior of frictional stability with depth (temperature) for crustal rock and ice may imply the existence of a universal seismogenic zone model that is dependent on homologous temperature.Looking at our results (Figure 5), although there is a stability transition between 0.75 and 0.85 for both pure ice and ice-ammonia (The pure ice stability transition in Figure 5a The colder ice-ammonia stability transition in Figure 5b), the frictional stability as a function of temperature appears to be roughly similar for both pure ice and ice-ammonia otherwise so that they do not match up when compared by homologous temperature (the ice-ammonia stability curve is shifted "down" toward higher homologous temperature).This idea may be further complicated by the likelihood that the specific deformation mechanisms involved in crustal rock or ice may also play a role in the behavior of frictional stability with depth.Schulson and Fortt (2012) qualitatively observed stability transitions with ice by noticing that stick-slip behavior occurs at intermediate temperatures (133-223 K for 10 μm/s sliding velocity), before becoming stable at both colder and warmer temperatures.Their results are relatively consistent with ours, although we do not observe a complete return to stability at colder temperatures.Further, Schulson and Fortt (2012) observe that the stability transitions occur at different velocities.Several experiments in our study exhibited velocity-strengthening behavior for one of the velocity steps and velocity weakening for the other, for instance in an ice-ammonia experiment at 223 K (C0179) where the 1-10 μm/s velocity step is strongly velocity strengthening with an a-b of 0.062 but the 10-30 μm/s velocity step is strongly velocity weakening with an a-b of 0.137 with no stick slips observed.Both studies thus indicate that rate dependence is itself velocity-dependent, which effects can be studied more closely in future work.
Additionally, it is important to consider how frictional stability might differ with dynamically varying sliding velocities, especially sinusoidal oscillations (McCarthy et al., 2022;Skarbek et al., 2022), which are analogous to tidally driven faulting on icy satellites.This will be the topic of our continuing research.

Role of Healing
Healing plays a role in fault stability and possibly frictional dependencies since it occurs during periods of quiescence before a fault is reactivated.This likely happens periodically on icy satellites throughout their orbital evolutions based on tidal stress patterns.Sliding interfaces strengthen during stationary contact due to healing, which is typically attributed to an increase in the real area of contact of microscopic asperities at the interface and the quality or strength of the contacts (e.g., Zoet & Iverson, 2018).The change in friction from healing is logarithmically related to hold time as shown in this study (Figure 6), which is consistent with healing in a broad swath of geologic and engineering materials (Nakatani andScholz, 2004, 2006;Richardson & Marone, 1999).We additionally observe that the healing rate parameter displays positive temperature dependence, as is predicted by micromechanical models using thermally activated viscous mechanisms at asperity contacts with model friction (e.g., Aharonov & Scholz, 2018;Scholz & Engelder, 1976).We do not expect any significant grain growth affecting healing at these low temperatures and short timescales (Gow, 1969).However, we cannot rule out sintering at the asperity scale, particularly at the warmer temperatures studied.We also do not anticipate a complete welding of the interface due to the long timescales required for crack healing (e.g., Hammond et al., 2018).
The inclusion of a second phase appears to play little to no role in healing, which may imply that the inclusion of melt may not make a meaningful difference in the growth of real contact area.This is surprising because melt certainly affects the viscous response of ice by reducing viscosity (e.g., Arakawa & Maeno, 1994;Durham et al., 1993).However, unlike the viscous response, the frictional behavior does not depend on the bulk structure and composition of the material, but rather the area of real contact at the asperities of the sliding interface.Given that, the pockets of melt at the grain boundary triple junctions (see schematic in Figure 1) are possibly not contributing to the underlying micromechanics of frictional healing if the asperities are interacting at a smaller scale than the melt pockets (Schulson & Fortt, 2013).In the case of granular ice mixtures, such as the icemagnesium chloride mixtures in Okazaki et al., 2024, it is possible that the healing behavior may differ due to the salt asperities at the interface.It is also possible that the melt simply cannot contribute at timescales of less than 300 s holds measured here or that a melt fraction greater than the range studied here (∼0.11-0.43)would be required to see a more discernible effect on healing.Alternatively, the inclusion of melt may significantly affect both the contact area and contact quality at the interface and the two effectively cancel each other out (real area of contact grows faster but the strength of the contacts weaken or vice versa) so that there is no discernible net effect on healing.

Frictional Heating on the Tiger Stripes of Enceladus
With a temperature-dependent friction coefficient, less frictional heat should be generated per unit of slip relative to a constant friction model if friction decreases as the fault gets hotter.Comparing the temperature evolution of a constant friction coefficient with that of a temperature-dependent friction coefficient in our simple 1-D shear heating model instead appears to result in similar behavior with depth at the fault center.However, because the friction of the ice changes with depth over time along with the thermal gradient, the strength of the fault may be more variable in the case of temperature -dependent friction, potentially connecting frictional heat generation with frictional fault strength.A deeper fault also correlates with a greater slip distance (Hammond, 2020).Relating fault failure depth to slip distance result in feedback, where heat generation decreases frictional strength leading to deeper fault failure depths and greater slip distances.This would counter the decrease in heat generation from reduced friction as the ice warms.Slip distances could be more self consistently solved for in a numerical model with a velocity field.Incorporating the potential velocity dependence on the temperature dependence of friction along with the relationship between fault failure depth and slip distance may reveal feedback mechanisms involving frictional dependencies not present in our simplistic model.
A numerical model with the appropriate time stepping could also use the appropriate slip duration based on when the Mohr-Coulomb criterion allows slip to occur from tidal stresses throughout the orbital period of Enceladus as explored in Smith-Konter and Pappalardo (2008) and Olgin et al., 2011.The tidal stress patterns are sinusoidal and not constant, as in the stresses applied in our friction experiments in this study.Friction may exhibit a dependence on the velocity pattern in addition to the velocity magnitude (McCarthy et al., 2022;Skarbek et al., 2022) and thus we would have to incorporate the results of ice-on-ice friction experiments specifically from oscillatory loading to accurately gauge its behavior.
Smith-Konter and Pappalardo (2008) find the diurnal slip windows for frictional sliding on Enceladus to occur when the coefficient of friction is less than 0.3 for 4 km fault failure depths.Given that we find a higher coefficient of friction in all of our experiments, it may be more difficult than previously assumed for frictional sliding to initiate on Enceladus, as Schulson and Fortt (2012) have also concluded from their friction experiments.However, shallower fault failure depths are still possible at a higher coefficient of friction (>0.3).Olgin et al. (2011) point out that fault failure depths much shallower than 1 km may be speculative given the lack of sufficient contact from lower overburden pressures relative to the diurnal tensile stresses.
Assuming we can generate and maintain frictional sliding, the potential feedback mechanisms between frictional heat generation and fault strength and stability driven by frictional dependencies (the effect of temperature, partial melt, and sliding velocity on friction) may lead to shallow melt generation in the ice shell.This process may support the idea that the plume activity at the tiger stripes is linked to strike-slip sliding in response to resolved tidal shear and normal stress variations throughout the orbit of Enceladus (Nimmo et al., 2007;Olgin et al., 2011;Smith-Konter & Pappalardo, 2008).It may also aid in explaining the anomalously high heat fluxes in the south polar region.

Conclusions
Our laboratory ice-on-ice friction experiments run at low temperatures applicable to the outer solar system (98-248 K) with both pure polycrystalline ice and ice-ammonia mixtures to better constrain frictional fault behavior on icy satellites, particularly the temperature dependence of the friction coefficient of ice as well as its frictional stability.Using our experimental results, we find a linear relationship between the friction of ice and ice mixtures and homologous temperature for the range of temperatures explored, which can be applied to shear heating models of icy satellites to better constrain frictional heat generation.We explored the effect of a temperaturedependent friction with a simple analytical model of shear heating on the tiger stripes of Enceladus and consider what other parameters may play a role in potential feedback mechanisms with treating friction as a dynamic variable.We also established a temperature-dependent seismogenic zone within an icy shell using the rate-state friction parameters of our laboratory results and found it to be analogous to established terrestrial models of seismicity on Earth.Identifying the source of seismicity in a tidally loaded fault system could benefit the interpretation of observations in future missions to icy satellites that include a seismic package such as the Dragonfly mission (Barnes et al., 2021) to Titan and the proposed Enceladus Orbilander mission (MacKenzie et al., 2021).In addition to improving our understanding of ice shell structure, using friction to constrain the depth and lifetime of shallow subsurface partial melt may have implications for the habitability of that melt drains to a source either in the ice shell or into the subsurface ocean.

Figure 1 .
Figure1.Annotated phase diagram for system H 2 O-NH 3 at 1 atm.Symbols denote the temperature and composition (blue for pure ice and green for iceammonia) combinations used in this study.All samples as fabricated were either pure ice or had a bulk composition of ∼3-10 wt% NH 3, which is found in solution form above the solidus and in the form of the dihydrate (D) below the solidus.The fraction of melt during testing, which depends on temperature, was determined using the lever rule and this phase diagram (Table2).The schematic diagrams on the left depict idealized microstructures of pure ice and ice-ammonia mixtures.Melt permeates the grain boundaries at temperatures above the eutectic for ice-ammonia mixtures(McCarthy et al., 2019).For a detailed discussion of eutectic (E) and peritectic reactions as well as the data upon which the figure depends, seeKargel (1992).

Figure 2 .
Figure 2. (a) Schematic of the biaxial apparatus used for these experiments including the LN-controlled cooling of the circulating fluid, which travels through channels in aluminum panels surrounding the sample.An RTD inserted into the metal monitored the temperature at the interface.(b) The cryostat uses a vacuum as an insulation and low thermal conductivity materials for all components that traverse through the cryostat or hold up the sample in its double-direct shear configuration.

Figure 3 .
Figure3.Example outputs from the friction experiments depicting a velocity step (3a) and slide-hold-slide (3b) program and the frictional response for a stable sliding experiment (3c and 3d from experiment C54) and an unstable sliding experiment with stick-slips (3e and 3f from experiment C253) as a function of time throughout the experiment.Rate and state parameters are depicted in the stable frictional response to a velocity step (3c).Healing parameters are depicted in the stable frictional response to a slide-hold-slide (3d), where ∆μ c is the relaxation during the hold.Friction drop and recurrence time of stickslips are depicted in the unstable frictional response to a velocity step (3e).

Figure 4 .
Figure 4. Steady-state friction from all experiments for 1, 10, and 30 μm/s sliding velocities for both pure ice (blue) and iceammonia (green) along with results from previous ice-on-ice friction studies at similar conditions.Note that at T/T m < 1, the ammonia is in the form of the dihydrate and at T/T m > 1 as a liquid solution.Homologous temperature is defined by normalizing by the melting temperature of each system (T m = 273 K for pure ice, T m = 176 K for ice-ammonia, T m = 252 K for saline ice, and T m = 240 K for ice-magnesium chloride).For two-phase systems such as ice-ammonia, saline ice, and icemagnesium chloride, melt pockets form at the boundaries of the solid grains above the eutectic temperature.The open points indicate an experiment exhibiting stick-slip (We do not include error bars for experiments exhibiting stick-slip from this study-the error bars on the other experiments from this study span the entire range of friction values during steady-state).The square points represent data at an order of magnitude of 10 6 m/s sliding velocity and the circle points represent data at an order of magnitude of 10 5 m/s sliding velocity.The friction values from our experiments follow an inverse linear trend of 0.76 over the full range of normalized temperature.

Figure 5 .
Figure 5. 5a depicts a-b values for pure ice as a function of temperature (reflecting depth through an ice shell) using both the 1-10 μm/s and 10-30 μm/s velocity steps.Values to the right of the red dashed line (a-b = 0) are velocity strengthening and considered stably sliding and values to the left are velocity weakening and potentially seismogenic if there is stick-slip behavior.The open points are experiments exhibiting stick slip.5b depicts the calculated a-b values for ice-ammonia with the green dashed line marking the ice-ammonia eutectic temperature.The error bars denote the standard deviation.The a-b values for the stick-slip experiments were calculated using Equation 10, using the associated frictional stress drops and recurrence interval times.The dynamic overshoot factor (1 + ξ) was assumed to be 0.1 for all experiments.

Figure 6 .
Figure 6.The change in friction Δμ following a hold for both pure ice (6a) and ice-ammonia (6b) from 98 to 248 K (each curve is a separate experiment) demonstrates that in both systems the increase in friction with log hold time is temperature dependent.Each shape/color combination corresponds to an individual friction experiment.

Figure 7 .
Figure 7.The healing parameter, β (7a and 7b) and cutoff time, t c (7c and 7d) calculated for pure ice (7a and 7c) and iceammonia (7b and 7d) using Equation 15 from the change in friction with hold time from Figure 6.

Figure 8 .
Figure 8. Parameter sweep of the shallowest depth at which partial melt may be generated in the ice shell at the Tiger Stripes for a range of slip magnitudes and slip durations from a single slip event.8a and 8b (top) assume a pure ice shell while 8c and 8d (bottom) assume an ice-ammonia shell.8a and 8c (left) assume a constant coefficient of friction (μ = 0.55) while 8b and 8d (right) assume a temperature-dependent friction based on experimentally determined ice friction results.

Figure 9 .
Figure 9. Temperature rise as a function of fault depth at varying slip velocities using an estimated 0.0005 m fault half-width (9a, 9b, and 9c) and varying fault widths using an estimated 1 m/s slip velocity (9d, 9e, and 9f) with a constant friction coefficient of μ = 0.55.Each of the three plots represents heat generation during a slip event at different points in orbit where, from left to right, tidal stresses result in maximum fault tension, net zero tidal normal stress, and maximum fault compression.The results from Figure 8 use a 0.0005 m fault half-width.

Table 1
Temperature Conditions for Experiments Using Pure Ice Samples Note.Temperatures listed with (shs), (

Table 2
Conditions for Experiments Using Ice-Ammonia Samples

Table 3
Parameters Used for the 1-D Analytical Shear Heating Model Where Slip Magnitude Is Related to Sliding Velocity Through Slip Duration, t*