Titania's Heat Fluxes Revealed by Messina Chasmata

Messina Chasmata is a relatively young tectonic structure on Titania based on cross-cutting relationships, although an absolute age has not been estimated. We investigated lithospheric flexure bounding Messina and found that the terrain along both rims reflects Titania’s thermal properties. We estimate Titania’s heat fluxes to have been 5–12 mW m−2 in this region, assuming that the lithosphere is composed of pure H2O ice without porosity. These estimates are lower if lithospheric porosity and/or NH3–H2O are also present. If Messina is ancient, forming as a result of freeze expansion, then the reflected heat fluxes are consistent with radiogenic heating. However, if Messina is instead young, then an additional heat source is required. In this scenario, perhaps tidal heating associated with the past three-body resonance shared between Titania, Ariel, and Umbriel generated this heat. However, this scenario is unlikely because the amount of tidal heating produced on Titania would have been minimal. Titania’s heat fluxes are notably lower than estimates for Miranda or Ariel, and future work is needed to investigate Umbriel and Oberon to gain a fuller understanding of Uranian moon thermal and orbital histories. Additionally, further constraints on Titania’s more ancient heat fluxes could be obtained by investigating relatively older features, such as some viscously relaxed impact craters.


Introduction
The largest Uranian satellite, Titania, exhibits evidence of an eventful geologic history.The Imaging Science Subsystem (ISS) instrument on board the Voyager 2 spacecraft imaged Titania's southern hemisphere, revealing impact craters and massive sets of tectonic features that cover a large portion of this region (Figure 1).Titania is thought to plausibly be an ocean world (Hussmann et al. 2006;Ćuk et al. 2020;Bierson & Nimmo 2022;Castillo-Rogez et al. 2023), with tectonic features on its surface that can be investigated to better understand the geology and evolution of this moon and the Uranian satellite system.Additionally, spacecraft exploration of Uranus and its large moons is the highest-priority outer solar system mission recommendation of the 2023-2032 Planetary Science and Astrobiology Decadal Survey (National Academies of Sciences et al. 2022).A better understanding of the geologic histories of the Uranian satellites would allow for refinement of the science objectives for any future mission to Uranus.
Of Uranus's five classical satellites, prior work only includes heat flux estimates from geologic features on the smallest and closest innermost moon Miranda (up to 140 mW m −2 ; Beddingfield et al. 2015aBeddingfield et al. , 2022c) ) and its neighbor Ariel (up to 92 mW m −2 ; Peterson et al. 2015;Beddingfield et al. 2022b;Bland et al. 2023).These unexpectedly high heat flux estimates have been used to constrain past tidal heating on these moons (Peterson et al. 2015) and past resonances (Ćuk et al. 2020) and to investigate whether these moons had (or still have) subsurface oceans (e.g., Castillo-Rogez et al. 2023).
Along with Miranda and Ariel, heat flux estimates are also needed for Umbriel, Titania, and Oberon to provide insight into the thermal-orbital evolution of the Uranian satellite system.In this work, we investigated Messina Chasmata and the bounding terrain on Titania to determine whether raised rims indicative of lithospheric flexure are present, allowing for heat fluxes to be estimated.

Titania's Geology
Interior Properties: Titania and the other Uranian satellites are exposed to little tidal heating today, but they likely experienced a chaotic past that involved multiple previous resonances (Tittemore & Wisdom 1990;Ćuk et al. 2020).As summarized in Ćuk et al. (2020), Titania may have been part of a recent three-body resonance with Ariel and Umbriel that would have increased the orbital eccentricities and inclinations of those two smaller moons.However, because of its larger size and mass and its greater distance from Uranus, Titania (diameter = 1578 km, semimajor axis = 436,282 km) likely experienced less excitation than Ariel (diameter = 1158 km, semimajor axis = 190,930 km) or Umbriel (diameter = 1169 km, semimajor axis = 265,982 km).Additionally, Titania's past resonance would not have generated a sufficient amount of tidal heating based on the predicted eccentricity and viscosity (Ćuk et al. 2020).
Surface Units: In the most recent geologic map of Titania (Croft & Soderblom 1991), the surface units are divided into two groups, the Plains Materials and the Crater Materials (Figure 2).The Plains Materials include regions that are overprinted by tectonic features and craters.The Crater Materials include ejecta deposits, rims, and floors.The most ancient of these units is the heavily cratered plains (Unit Ph), which extend across most of Titania's imaged southern hemisphere.These cratered plains are estimated to be 4.5 (-0.9/+0.0)Ga (Kirchoff et al. 2022), assuming that the crater size-frequency distribution is similar to that inferred for Triton (Zahnle et al. 2003;Schenk & Zahnle 2007).
While Titania's plains are heavily cratered, they exhibit a notably lower density of craters with diameters >100 km compared to the cratered terrains of the neighboring satellites, Oberon and Umbriel (e.g., Smith et al. 1986;Croft & Soderblom 1991;Zahnle et al. 2003).Therefore, large craters must have previously formed on Titania but were subsequently erased by an unknown resurfacing event.Because the heavily cratered plains exhibit a uniform crater density, this resurfacing may have been widespread and occurred over a short timescale compared to the cratering rate (Croft & Soderblom 1991).Although resurfacing is thought to have occurred, it must be ancient, based on the age of Titania's cratered terrain, 4.5 Ga (+0.0/-0.9Ga; Kirchoff et al. 2022).
Additional geologic units have been classified where cratering is present at lower densities (Croft & Soderblom 1991).As summarized in Croft & Soderblom (1991), these units include the moderately cratered plains (Unit Pm) and the smooth plains (Unit Ps).The moderately cratered plains are associated with the Gertrude impact structure and likely represent ejecta that has covered some preexisting craters, resulting in a lower crater density than the surrounding heavily cratered plains.The smooth plains are associated with regions bounding and interior to large canyon systems.However, the origin of this material is unknown.
Messina Chasmata: The most massive known set of structures on Titania is Messina Chasmata, which is at least 1500 km in length, is up to 100 km in width, and extends beyond the terminator into the unimaged northern hemisphere (Figure 1).This chasmata and other nearby large normal fault scarps are thought to have formed as a result of expansion during interior freezing (Smith et al. 1986;Croft & Soderblom 1991).Based on cross-cutting relationships, Messina Chasmata and the surrounding large tectonic structures are interpreted to be the youngest geologic features on Titania's surface, with the exception of a few overprinting craters (Croft & Soderblom 1991;Leonard et al. 2023a).While Messina Chasmata is relatively young, absolute ages have not been estimated, and so this set of structures may have formed early in Titania's history.
As mapped and discussed in Croft & Soderblom (1991), Messina's main section consists of multiple troughs (Figure 2).The large canyons consist of subparallel and inward-facing normal fault scarps bounding down-dropped cratered plains.Messina Chasmata exhibits depths of up to 6 km in some locations, as indicated by shadow measurements along the central trough (Smith et al. 1986), limb profiles (Thomas 1988; points A, D, and E in Figure 2), and digital elevation models (DEMs; Schenk & Moore 2020).
Other Tectonic Features: Some tectonic structures consist of solitary graben-like forms, such as Belmont Chasma and the M. Jessica and M. Bona Chasmata (Figure 2).Cross-cutting relationships indicate that these chasmata formed in phases.Apparent bright slope materials were noted along fault scarps making up many chasmata (Unit Pb), which were interpreted as illuminated Sun-facing scarps (Croft & Soderblom 1991).Additionally, ridges have been identified between Messina Chasmata and Gertrude crater (region between ∼300°and 330°l ongitude in Figure 2; Croft & Soderblom 1991).The ridges are curvilinear structures up to around 1000 km in length, several tens of kilometers in width, and on the order of 1-2 km in height.
A set of NW-SE trending trough-like lineaments have also been identified (region between ∼290°and 50°longitude in Figure 2; Croft & Soderblom 1991).Examples include the features that cut across Valeria crater.The depressions cut most craters but are locally discontinuous and are cut by the younger Messina Chasmata.Other similar lineaments cut across Gertrude and the ridge system.Recent work has also identified quasi-concentric lineaments across much of Titania's imaged hemisphere, which may be remnants of a multiring impact basin, which, if present, could help explain the lack of large craters within Titania's cratered plains (Nathan et al. 2022).

Digital Elevation Model Generation
We generated a DEM using Voyager 2 ISS images that cover Messina Chasmata and the surrounding terrain (Figure 3) to investigate flexure-related topography bounding Messina Chasmata.Our DEM was generated using the Ames Stereo Pipeline (ASP) software (Broxton & Edwards 2008;Moratto et al. 2010;Beyer et al. 2018aBeyer et al. , 2018b)).We used a stereographic projection for the DEM with coordinates centered on Messina, and the ISS data were first processed using the Integrated Software for Imagers and Spectrometers (ISIS; Anderson et al. 2004).We followed the steps to preprocess the ISS data for input into ASP outlined in previous work (Beddingfield et al. 2015a(Beddingfield et al. , 2015b;;Beddingfield & Cartwright 2021a).To generate the DEM, we applied photoclinometry (PC) techniques (Alexandrov & Beyer 2018) utilized for DEM generation, which are also detailed in past work (Beddingfield et al. 2022b(Beddingfield et al. , 2022c(Beddingfield et al. , 2023)).These PC techniques were utilized to generate a higher resolution and more accurate DEM than stereogrammetry alone, resulting in a horizontal DEM resolution of 2.88 km pixel −2 and an estimated vertical uncertainty of 7%.The methodology to create the DEM and estimates for uncertainty are described in greater detail in Appendix A.1.
By analyzing our DEM, we found evidence that topography related to lithospheric flexure is present bounding Messina Chasmata along the north and south rims (Figure 4).However, additional topography related to impact craters and faults is also present along the rims.For example, some additional topography is due to the presence of smaller scarps that are visible in both the ISS images and our DEM (Figure 3).These structures were mapped by Croft & Soderblom (1991) and are shown in Figure 2. When analyzing Messina Chasmata, we avoided locations where these structures notably overprint the rims.In other locations, large impact craters either overprint the rims of Messina or are present in the nearby vicinity of the rim.For example, a notable large crater overprints Messina's northwest rim, where the elevation is the highest.Therefore, we did not analyze this main rim section.
While we worked to avoid investigating sections of Messina's rims that exhibited topography unrelated to flexure, some additional topography in the analyzed regions was unavoidable.Therefore, we excluded notable unrelated topography in our flexural models.In some regions of Messina's south rim, topography related to flexure was too subtle to investigate owing to the low resolution of the Voyager 2 ISS images and therefore our DEM.

Estimating Titania's Heat Fluxes
Because Messina Chasmata exhibits raised rims with topography indicative of lithospheric flexure (Figure 4), we analyzed the associated curvature to estimate the lithospheric heat fluxes following Messina Chasmata's formation (Figure 5).We applied the techniques discussed in detail in other studies, which investigated lithospheric flexure on icy bodies (e.g., Ruiz 2005;Giese et al. 2007;Peterson et al. 2015;Beddingfield & Cartwright 2022a;Beddingfield et al. 2022bBeddingfield et al. , 2023)).Because these techniques have been described extensively in these previous studies, we only summarize the methodology here.
Heat flux is given by where k is the thermal conductivity of Titania's lithosphere, which varies as 567/T (Klinger 1980).We used a value of 5 W m −1 K −1 , which represents the cold near-surface conditions of Titania's surface (75 K).T b is the temperature at the base of the lithosphere, T s is the surface temperature, and T e is the elastic thickness.We considered thermal conductivities for a pure H 2 O ice lithosphere and a lithosphere containing NH 3 hydrates mixed with H 2 O ice, which is likely an important mixture for modeling the lithospheric heat fluxes of some icy moons (Lorenz & Shandera 2001;Beddingfield et al. 2022b).As summarized in Lorenz & Shandera (2001), the thermal conductivity of NH 3 hydrates mixed with H 2 O ice is two to three times lower than that of pure water ice.We provide a summary of the values used for each parameter with references in Table 1.
In the Uranian system, NH 3 -bearing species are likely present along with H 2 O on the surfaces of Miranda (e.g., Bauer et al. 2002;Cartwright et al. 2015Cartwright et al. , 2020b;;DeColibus et al. 2022DeColibus et al. , 2023)), Ariel (Cartwright et al. 2020a), and Umbriel (Cartwright et al. 2023).Therefore, NH 3 -bearing species may also be present on Titania.Although we cannot directly determine whether NH 3 -bearing species are present in Titaniaʼs lithosphere, near-infrared telescope observations detected a weak absorption feature near 2.2 μm in reflectance spectra of Titania (Cartwright et al. 2018), which is consistent with the presence of NH 3 hydrates on its surface.Additional telescope measurements and laboratory analyses are needed to confirm this interpretation.In particular, updated optical constants for a range of different NH-bearing species are needed.Nonetheless, the possible presence of NH 3 hydrates on Titania's surface may indicate that this constituent is present in the lithosphere, which would have important implications for heat fluxes.While it is not certain that the possible presence of NH 3 hydrates on Titania's surface would indicate that this constituent is present in the lithosphere, this constituent may have been one of the primary constituents of the satellitesimals that accreted into the Uranian moons (e.g., Lewis 1972;Prinn & Fegley 1989).
In addition to composition, we considered both compact ices, k c , and porous ices, k(f).Similar to the lack of constraints on the amount of NH 3 -bearing species in Titania's lithosphere, the degree of lithosphere porosity is not well constrained.Therefore, we considered a large range of lithospheric porosities (0-0.25) to encapsulate a range of possible scenarios on Titania.As summarized in Durham et al. (2005), ice porosities may be present in the lithospheres of icy bodies, where the pressure is less than 1 MPa.However, the porosity of ice within the lithospheres of large icy satellites decreases with depth owing to increasing pressures (e.g., Giese et al. 2007), and it therefore may have a minimal effect on the heat fluxes of Titania (D = 1578 km).However, if present, porosity would reduce heat fluxes by reducing the thermal conductivity of the ice in Titania's lithosphere.
We incorporated the porosity of ice into our calculations for thermal conductivity where and where k c is the thermal conductivity of nonporous ice, f is porosity, f p is the percolation limit, and a and b are conductivity  2 for a full list of estimated values of F for porosities of 0%-25%.In addition to topography associated with flexure, topography associated with impact craters and faults is present.This topography was excluded from our flexural models.factors (Shoshany et al. 2002).The values for f p , a, and b (Table 1) have been utilized to estimate possible lithospheric thermal conductivities on Enceladus (Besserer et al. 2013).These values assume that the lithosphere is composed of H 2 O ice and that analogous estimates for H 2 O mixed with small amounts of NH 3 hydrates are not available.Consequently, we applied these values to our heat flux estimates that assumed a lithosphere composed of pure H 2 O ice, as well as a lithosphere with H 2 O ice and small amounts of NH 3 hydrates.T s is the surface temperature of Titania, and T b is the temperature at the base of Titania's lithosphere, where Q a is the activation energy for creep, and n is the rheologic parameter for grain boundary sliding, which is the relevant deformation mechanism for the grain size range we are considering (e.g., Durham & Stern 2001;Goldsby & Kohlstedt 2001).R = 8.3145 J mol −1 K −1 is the gas constant, D e is the Deborah number, μ is the shear modulus, A is the material parameter,   is the strain rate, d is the grain size, and p is the grain size exponent (see Table 1 for values used and references).The value used for D e , 0.01, is the transitional value between elastic and viscous behavior (Mancktelow 1999).The depth at which this transition occurs is the base of Titania's elastic layer and has been used in past heat flux studies derived from flexure on icy bodies (e.g., Nimmo et al. 2002;Peterson et al. 2015;Beddingfield & Cartwright 2022a;Beddingfield et al. 2022bBeddingfield et al. , 2023)).
The effective elastic thickness is given by where ν is Poissonʼs ratio and E is Youngʼs modulus (e.g., Gammon et al. 1983).As discussed in Pappalardo et al. (1997), the value for Youngʼs modulus of cryogenic ice has been estimated through extrapolation of existing data (Hobbs 1974;Mellor 1980;Maykut & Untersteiner 1986) and is consistent with estimates made by Gammon et al. (1983).Young's modulus is almost equivalent for NH 3 hydrates and pure H 2 O at cryogenic temperatures (Lorenz & Shandera 2001).K max is the maximum curvature of the topography from flexure, T m is the mechanical thickness of Titania's lithosphere, σ(z) is the fiber stress, which is the differential stress at depth z, and z n is the depth to the neutral stress plane, where σ(z n ) = 0.
Results: We estimate the elastic thicknesses of Titania in the regions bounding Messina Chasmata to range from 13.9 to 18.3 km (Figure 6(a)).If pure H 2 O ice without porosity is assumed for Titania's lithosphere (with a thermal conductivity, k c , of 5 W m −1 K −1 ), then the resulting heat fluxes are estimated to range from 5 to 12 mW m −2 in this region (Figure 6(b)).If Titania's lithosphere is instead composed of H 2 O ice mixed with modest amounts of NH 3 hydrates (k c of 1-2 W m −1 K −1 ), then the estimated heat fluxes in this region are lower, ranging from 1 to 5 mW m −2 (Figure 6(c)).
The possible presence of porosity within Titania's lithosphere has a small effect on our results.If lithospheric porosity  2).Furthermore, our results show that elastic thicknesses and heat fluxes do not vary significantly across the nearly 400 km stretch of Messina Chasmata that we investigated in this study.Our results are also consistent between the northern and southern rims of Messina Chasmata.

Comparison with Radiogenic Heat Fluxes
The expected surface heat flux is a combination of internal heat production, heat redistribution (e.g., for warming up the interior), the contribution of latent heat of melting (endothermic) and freezing (exothermic), and the thermal conductivities of the rocky mantle and overlaying hydrosphere.We computed the surface heat flux expected at the surface of Titania for the model presented in Castillo-Rogez et al. (2023) for a time of formation of 4 Myr after the formation of calcium-aluminum inclusions but assuming a maximum surface porosity of 25%.This model assumes a CI chondrite composition, no tidal heating, and no redistribution of potassium during internal differentiation.
Heat flux as a function of time is presented in Figure 7.This heat flux is much lower, by up to 40×, than the heat flux produced from radioisotope decay heat, primarily due to internal consumption.A heat flux increase in the first 200-300 Myr after formation and peaking at about 4 mW m −2 is due to the latent heat released by the freezing of the ocean.Otherwise, the predicted surface heat flux is at or lower than 1 mW m −2 for most of Titania's history.
We investigated a spectrum of thermal evolution models based on the methodology developed in Castillo-Rogez et al.
(2023) in order to identify the latest time at which freezing is expected depending on the amount of accreted 26 Al and thermal conductivities of the rocky mantle and hydrosphere.Freezing and the peak of heat flux associated with freezing may be delayed to about 350 Myr after formation if the average thermal conductivity of the shell is 4 W m −1 K −1 .However, the thermal conductivity is likely lower owing to retention of porosity in the top 50-80 km of the shell.
If Messina formed in the first few hundred million years after Titania's formation, then the heat flux inferred from our analysis may be explained by heat produced from short-lived radioisotope decay (first 10 Myr) or ocean freezing.If Messina is young, the expected radiogenic heat flux falls below our estimated heat fluxes for Messina Chasmata (5-12 mW m −2 ), and Titania does not currently experience significant tidal heating.Therefore, we make the interpretation that Titania's elevated heat fluxes reflected by Messina may be the result of radiogenic heating.Consequently, Titania's lithospheric heat fluxes at the time Messina Chasmata formed were likely higher than at present.

Comparison with Other Icy Bodies
Prior studies that have estimated heat fluxes for other icy bodies, calculated using lithospheric flexure, listric fault geometry, and impact crater relaxation, typically assume lithospheres made of pure H 2 O ice with porosities of 0% (see Figures 8 and 9 for references).Consequently, to more appropriately compare our estimates to those for other icy bodies, we rely on our estimates that assume a pure and nonporous H 2 O ice lithospheric composition for Titania.However, additional estimates that account for NH 3 -H 2 O and porosity are provided in Appendix A.2.
As shown in Figure 9, Titania's estimated range of heat fluxes (5-12 mW m −2 ) are notably lower than those estimated for Miranda in the regions bounding Arden Corona (31-112 mW m −2 ; Beddingfield et al. 2015a) and Inverness Corona (35-140 mW m −2 ; Beddingfield et al. 2022c).Similarly, Titania's heat flux range is notably lower than the majority of estimates for Ariel, including for the region  unsurprising that Titania's heat fluxes are notably lower than those estimated for Miranda or Ariel.
We also compare Titania's heat fluxes with those of other icy bodies throughout the solar system (Figure 9).Titania's heat fluxes are most similar to the lower end of the heat flux range estimated for Tethys (Giese et al. 2007;White et al. 2017;Beddingfield et al. 2023) and Triton (Ruiz 2003;Sori 2021).Future studies that investigate flexure associated with more ancient tectonic structures and viscous relaxation states of ancient impact craters would reveal additional insight into Titania's thermal and orbital evolution.Future studies that estimate heat fluxes for Umbriel and Oberon are also needed to compare with existing estimates for Titania, Miranda, and Ariel to gain a fuller understanding of the evolution of the Uranian satellite system.

Messina's Relative Age
Messina Chasmata represents the youngest known geologic feature on Titania, other than a few overprinting impact craters (Croft & Soderblom 1991).However, absolute age estimates for Messina are not available, and therefore it may be ancient.Because the formation of the bounding flexure analyzed in this work formed in response to the presence of Messina Chasmata, our results are indicative of heat fluxes following the formation of this relatively young structure on Titania.To better assess the relative age of Messina in comparison with other geologic features in the vicinity of this chasmata, we further investigated the local cross-cutting relationships with other tectonic structures and impact craters.
We first processed one of the highest-resolution images of Titania (c2684313, 2.88 km pixel −1 ), following the methods described in Leonard et al. (2023b).From this image, we then created a structural map (Figure 10), identifying linear features greater than ∼9 km in width.We also identified rims of craters greater than ∼17 km in diameter and small craters between ∼9 and 17 km in diameter (∼4-6 pixels in diameter).These values were chosen because we consider them to be the minimum required to identify the presence of a structure as a linear and point feature, respectively.Some references provide additional estimates that account for lithospheric porosity and possible NH 3 -H 2 O constituents in the lithospheres, but we do not include them here for a more straightforward comparison.Other than Titania, in the Uranian system, heat flux estimates are provided for two regions on Miranda (Beddingfield et al. 2015a(Beddingfield et al. , 2022c) and many regions on Ariel (Peterson et al. 2015;Beddingfield et al. 2022b;Bland et al. 2023).In the Jovian system, heat flux estimates are provided for Europa (Hussmann et al. 2002;Nimmo & Manga 2002;Ruiz 2003Ruiz , 2005;;Tobie et al. 2003;Showman & Han 2004) and Ganymede (Nimmo et al. 2002;Nimmo & Pappalardo 2004;Bland et al. 2017;Singer et al. 2018).For moons in the Saturnian system, heat flux estimates are provided for Enceladus (Bland et al. 2007(Bland et al. , 2012(Bland et al. , 2015;;Barr 2008;Giese et al. 2008;O'Neill & Nimmo 2010;Han et al. 2012;Leonard et al. 2021a), Dione (Hammond et al. 2013;White et al. 2017), Tethys (Giese et al. 2007;White et al. 2017;Beddingfield et al. 2023), Rhea (Nimmo et al. 2010;White et al. 2013), and Iapetus (White et al. 2013).In the Neptunian system, heat fluxes are provided for Triton (Ruiz 2003;Sori 2021).In the Pluto system, heat fluxes are provided for Pluto (Conrad et al. 2019(Conrad et al. , 2021;;McKinnon et al. 2023) and Charon (Conrad et al. 2021).
In the structural map (Figure 10), we identified three types of linear features (scarps, crater rims, and lineaments) and one type of point feature (small craters).Dashed lines in the structural map indicate where the linear structure identification was uncertain.Scarps were identified by a linear to curvilinear trace at the top of a well-defined slope.Crater rims are quasicircular raised structures (diameters greater than ∼17 km) interpreted to have formed from an impact event.Lineaments are defined as features that appear quasi-linear in planform with a narrow width.
Most lineaments appear to be ridges (topographic highs), but a few lineaments are troughs (topographic lows), and others do not have well-defined topographic signatures, but they are associated with apparent brightness variations.We grouped lineaments together, due to the inconsistent identification using apparent topography from varying lighting conditions, but also due to the relatively consistent overall NW-SE orientation of the features, similarly noted by Croft & Soderblom (1991).Lastly, small craters were interpreted to be impact craters that would have been identified with a crater rim but are too small (∼9-17 km diameter) to map at this scale and resolution, and they are therefore represented by point features.We only labeled small craters that we could confidently identify.
From the structural map we identified cross-cutting relationships between the primary scarps that make up Messina Chasmata.In Figure 10, we show that Scarp A cross-cuts Scarp B, indicating that Scarp A is younger than Scarp B. Similarly, Scarp C also cross-cuts Scarp B, indicating that despite the segmentation of Scarp C, it is also younger than Scarp B. These relative ages are particularly interesting when compared to the results from the flexure analysis and calculated elastic thicknesses at these scarps (Figure 6(a)), where Scarp A and Scarp C are both associated with slightly higher elastic thicknesses (and slightly lower heat fluxes).Because Scarp A and C appear younger than Scarp B, this could indicate that the ice shell thickened slightly between the formation of these scarps, lending credence to the hypothesis that Messina Chasmata formed owing to interior freezing resulting in ice shell thickening.
A few other notable observations from the structural map include the relative age of Messina Chasmata with respect to the other structural features in the region.Three craters (crater rims) were identified within Messina Chasmata itself, but they are dashed to indicate the uncertainty of whether they are truly crater rims formed from an impact event and not a quasicircular scarp or mass-wasting feature.For example, the larger potential crater identified near Scarp B has a particularly unclear age relationship with the scarp.It seems likely that this potential crater predates the formation of Scarp B, as we would expect that the scarp face would have been affected significantly if the impact postdates the formation of the scarp.However, the northern part of the crater rim, which we would expect to see if the crater predates the scarp, is missing to the north of the scarp.With higher-resolution imaging, we would be able to resolve the uncertainty in these structures and their cross-cutting relationships with the scarps that make up Messina Chasmata.
In addition to the crater rims, the identified lineaments have an unclear age relationship with the faults making up Messina Chasmata.While we do not identify any lineaments on the floor within Messina Chasmata, which would indicate that the lineaments predate the formation of the Chasmata, it is unclear whether this interpretation is due to an imaging bias resulting from the low image resolution.The lineaments do appear to postdate most of the crater rims in this region, due to either cross-cutting the crater rims or deflecting from the crater rims.Thus, we posit that NW-SE trending lineaments predate the formation of Messina Chasmata but appear to postdate most of the impact craters (crater rims) in the region.Additional studies are needed to better constrain the absolute age of Messina Chasmata.These studies would allow us to better compare our estimated heat fluxes with those predicted from radiogenic decay and/or tidal heating.

The Need for a Flagship Mission to the Uranian System
Several time-critical science objectives for understanding Uranus's system of moons require an ice giant mission in the coming decade, and a flagship-class mission to the Uranian system is the highest recommended priority for the outer solar system made by the 2023-2032 Planetary Science and Astrobiology Decadal Survey (National Academies of Sciences et al. 2022).Voyager 2 did not image the unilluminated northern hemispheres of the moons owing to seasonal geometries as a result of the system's near-perpendicular tilt relative to the Sun.
A new mission to the Uranian system presents an opportunity to image and study these unexplored terrains that were previously in darkness.Revealing the moon's northern hemispheres would address a suite of critical science questions that would provide insight into the origins, properties, and histories of these moons.However, to address these topics, a spacecraft would need to arrive at Uranus no later than the 2040s, while the northern polar regions of the Uranian moons are still illuminated by the Sun.The Uranian system transitions into southern spring in 2050, and the north polar regions will then be cast into darkness until the 2090s.
A flagship orbiter that performs multiple close flybys of Titania would provide substantially higher resolution images than those obtained by Voyager 2. These new images would allow us to more fully investigate Titania's surface (e.g., Beddingfield et al. 2021b;Cartwright et al. 2021).New closeup images collected by a Uranus orbiter would provide data for the generation of high-resolution DEMs and analyses of smaller features than can be investigated with the Voyager 2 data.These new studies would provide us with a better understanding of how heat fluxes vary spatially and temporally, which in turn would allow us to better constrain the Uranian moon's complex orbital histories (Beddingfield et al. 2021b;Cartwright et al. 2021;Leonard et al. 2021b;Cohen et al. 2022).
An orbiter with a visible/near-infrared mapping spectrometer is critical because it would allow us to determine whether NH 3 -bearing species are spatially associated with Titania's tectonic features and other younger terrains.Spatially resolved spectral information would provide important insight into the ages of Titania's different terrains and geologic features, the composition of its lithosphere (Cartwright et al. 2020b(Cartwright et al. , 2021)), and its predicted subsurface ocean (Hussmann et al. 2006;Ćuk et al. 2020;Bierson & Nimmo 2022;Castillo-Rogez et al. 2023).A magnetometer could investigate potential evidence of oceans in Titania and the other moons by searching for induced magnetic fields (e.g., Cochrane et al. 2021;Weiss et al. 2021;Castillo-Rogez et al. 2023).

Conclusions
We modeled flexure associated with topography from a DEM that we created of Messina Chasmata on Titania.Our results show that the elastic thicknesses were 13.9-18.3km following the formation of Messina, which is the youngest known tectonic feature on Titania.If pure H 2 O ice without porosity is assumed for Titania's lithosphere, then the estimated heat fluxes range from 5 to 12 mW m −2 .We estimate the heat fluxes to be 3-12 mW m −2 when lithospheric porosities up to 25% are accounted for.If Titania's lithosphere includes modest amounts of NH 3 hydrates, then the estimated heat fluxes in this region are lower, ranging from 1 to 5 mW m −2 , and porosity has a negligible effect on these results.
As inferred from our structural map, cross-cutting relationships between the scarps that make up Messina Chasmata indicate that the ice may have thickened between the formation of the different scarps, potentially indicating ice shell thickening as the source of extensional stresses that created Messina Chasmata.Although Titania is thought to have been part of a geologically recent three-body resonance, it likely experienced only a small orbital excitation and relatively little tidal heating compared to the smaller moons.Therefore, it is not surprising that Titania's heat fluxes are low in comparison with those estimated for Miranda and Ariel.Titania's heat fluxes may be explained by radiogenic heating in Titania's ancient past.However, future work is needed to estimate Messina's absolute age to further constrain Titania's thermal history.
A flagship-class orbiter to the Uranian system, with multiple close flybys of Titania, is needed to reveal more of the surface in order to better constrain Titania's thermal and orbital history.
To accomplish this, it is critical for the orbiter to arrive in the Uranian system no later than the 2040s, while Titania's northern high latitudes, which were not imaged by the Voyager 2 spacecraft, will still be illuminated by the Sun.
ridges.This value is given by h = F s tan( ) , where s is the observed shadow length and Φ is the solar incidence angle.
Based on slight differences in ridge heights estimated using these two different techniques, we estimate the topographic uncertainties associated with the DEM in the areas where we analyzed shadows to be 7%, which is somewhat higher than estimates for DEMs of Ariel (Beddingfield et al. 2022b) and Miranda (Beddingfield & Cartwright 2022a), due to the lower resolution of images covering Titania.The DEM horizontal resolution is equivalent to the resolution of the input Voyager ISS image with the best resolution (2.88 km pixel −2 ).Because our study area is large relative to the diameter of Titania, the DEM covers a surface that is notably affected by the curvature of this moon.Therefore, locations close to the north edge of the DEM and the shadowed region near Titania's terminator are displayed at an apparent lower elevation than the southern region in the DEM, reflecting the curvature of this moon.

A.2. Additional Heat Flux Results
Here we show our heat flux results for all variables used (Figure 11 and Table 2).

Figure 2 .
Figure 2. Annotated and modified version of the geologic map of Titania's imaged southern hemisphere (Croft & Soderblom 1991).Our study area location is shown by the yellow box.The Plains Materials include the following units: Pb: bright slope material; Ps: smooth plains; Pm: moderately cratered plains; and Ph: heavily cratered plains.The Crater Materials include the following: C3: rayed/bright deposit craters; C2: fresh appearing, no rays; C1: moderately degraded craters; Ce: elongate craters (possibly secondaries); Cr: crater rim massifs; and Cf: crater floor material.Points B-E indicate locations of limb profiles analyzed by Thomas (1988).

Figure 3 .
Figure 3.A map-projected portion of Voyager 2 ISS image c2684313, and the associated DEM that we created of our study area (see Appendix A.1 for additional information).South is down, and the white squares are removed reseau points.

Figure 4 .
Figure 4. 3D representation of our DEM with vertical exaggeration (Figure 3).Evidence for flexure in the topography is observable bounding both rims of Messina Chasmata (examples shown by white arrows).The ridges and grooves, mapped by Croft & Soderblom (1991; see tectonic symbols in Figure 2), trending approximately perpendicular to Messina, are observable in our DEM.For a scale bar and elevation color bar, see Figure 3.South is to the right, and white squares are removed reseau points.See Figure 2 for the location of our study area on Titania.

Figure 5 .
Figure 5. (a) Annotated version of a portion of Voyager 2 ISS image c2684313 (2.88 km pixel −1 ) showing the locations of the profile lines used for this analysis along the rims of Messina Chasmata.(b) Profile topographic data (black) with superimposed model flexural profiles (cyan) for all study locations (A-J).Gray arrows show locations where flexural curvature is evident.See Figures 6 and 11 for estimated values for T e and F. See Table2for a full list of estimated values of F for porosities of 0%-25%.In addition to topography associated with flexure, topography associated with impact craters and faults is present.This topography was excluded from our flexural models.

Figure 6 .
Figure 6.(a) Estimated elastic thicknesses on Titania.(b) Estimated heat fluxes on Titania assuming a porosity of 0%.(c) Estimated heat fluxes assuming a pure H 2 O lithospheric composition and porosities ranging from 5% to 25%.(d) Estimated heat fluxes assuming an H 2 O ice lithosphere with small amounts of NH 3 hydrates and porosities ranging from 5% to 25%.See Table 2 in Appendix A.2 for the full set of estimated values.For the location of our study area, see the yellow box in Figure 2.

Figure 7 .
Figure 7. Surface heat flux predicted at the surface of Titania (solid gray line) for the interior evolution model featured in Castillo-Rogez et al. (2023) for a time of formation of 4 Myr after the formation of calcium-aluminum inclusions, no tidal heating, and assuming a maximum porosity of 25%.For comparison, the heat flux corresponding to radioisotope decay heat assuming a perfect conductor is presented (dashed black line).See text for more details.

Figure 8 .
Figure 8. Ranges of estimated heat fluxes for Uranus's large moons, assuming pure H 2 O ice lithospheres without porosity.The relative sizes of the moons are shown, and they are ordered with increasing distance from Uranus (from left to right).Our estimates are provided for Titania (D = 1578 km).Other heat flux estimates are provided for Miranda (D = 472 km; Beddingfield et al. 2015a, 2022c) and Ariel (D = 1158 km; Peterson et al. 2015; Beddingfield et al. 2022b; Bland et al. 2023).Heat fluxes have not yet been investigated for Titania's neighboring moons, Umbriel (D = 1169 km) or Oberon (D = 1523 km).

Figure 10 .
Figure 10.Top: processed Voyager 2 ISS image (c2684313) of the Messina Chasmata region.Bottom: structural map of the Messina Chasmata region.Dashed lines indicate where identification of the structure is uncertain.Labels (A, B, and C) indicate specific scarps that are discussed in the text.White arrows indicate areas with important cross-cutting relationships between the scarps.

Figure 11 .
Figure 11.Mapped estimates of heat fluxes that take into account porosity and assuming a lithosphere with the following properties: (a) pure H 2 O ice with 5% porosity; (b) H 2 O ice with H 2 O-NH 3 and 5% porosity; (c) pure H 2 O ice with 15% porosity; (d) H 2 O ice with H 2 O-NH 3 and 15% porosity; (e) pure H 2 O ice with 25% porosity; (f) H 2 O ice with H 2 O-NH 3 and 25% porosity.

Table 1
Values Used for Each Parameter to Estimate Elastic Thicknesses and Heat Fluxes in the Regions Bounding Messina Chasmata of Titania