Possible explosion crater origin of small lake basins with raised rims on Titan

The Cassini mission discovered lakes and seas comprising mostly methane in the polar regions of Titan. Lakes of liquid nitrogen may have existed during the epochs of Titan’s past in which methane was photochemically depleted, leaving a nearly pure molecular nitrogen atmosphere and, thus, far colder temperatures. The modern-day small lake basins with sharp edges have been suggested to originate from dissolution processes, due to their morphological similarity to terrestrial karstic lakes. Here we analyse the morphology of the small lake basins that feature raised rims to elucidate their origin, using delay-Doppler processed altimetric and bathymetric data acquired during the last close flyby of Titan by the Cassini spacecraft. We find that the morphology of the raised-rim basins is analogous to that of explosion craters from magma–water interaction on Earth and therefore propose that these basins are from near-surface vapour explosions, rather than karstic. We calculate that the phase transition of liquid nitrogen in the near subsurface during a warming event can generate explosions sufficient to form the basins. Hence, we suggest that raised-rim basins are evidence for one or more warming events terminating a nitrogen-dominated cold episode on Titan. Some lake basins in the polar regions of Titan may be craters from nitrogen vapour explosions due to past warming, according to analysis of their morphology in comparison to terrestrial explosion craters from magma–water interaction.

T itan is the lone extraterrestrial body in our Solar System with persistent lakes and seas on its surface 1 . Approximately 650 lacustrine features are found throughout the polar regions, with most lakes and seas found in the northern hemisphere [1][2][3] . The south polar regions possess few filled lakes and a larger percentage of dry lakes and palaeolakes 4,5 . Titan's lakes and seas are filled with liquid hydrocarbons, mostly methane with dissolved nitrogen 6,7 and participate in an alkanological cycle similar to the terrestrial hydrological cycle 3 . This alkanological cycle is possible as the conditions on Titan (surface temperature of ~93 K) allow methane to be close to its triple point and to be present in liquid, gas and solid phases 8 . The formation of liquids within the lakes is probably the result of a complex hydrology including precipitation, surface runoff and subsurface aquifers in the icy crust 3 . The surfaces of the lakes on Titan's north pole are on the same equipotential surface 9 , demonstrating intercrustal flows of liquids and the presence of liquid hydrocarbon aquifers 3,9 .

Sharp-edge depressions with raised rims
We used delay-Doppler processed altimetric and bathymetric data acquired during the last close flyby (T126; 22 April 2017) of Titan by the Cassini spacecraft 7,10 in conjunction with a morphological analysis to elucidate the origin of small lake basins featuring raised rims. Figure 1 shows the altimetry (solid line) and the bathymetry (dotted line) of the lake named Winnipeg Lacus (78° N, 155° W) and the altimetric track overlying the Cassini synthetic aperture radar (SAR) images. The altimetric data (solid line) of Winnipeg Lacus depicts a rim (~300 m high) adjacent to a rampart-like structure surrounding the lake. The bathymetric profile shows a maximum lacustrine depression depth of ~100 m (ref. 7 ). The morphology of the seas and lakes of Titan can be described as broad and sharp-edge depressions (SEDs) 9,[11][12][13] . Broad depressions typify the hydrocarbon seas and some larger lakes with typical diameters of a few hundred kilometres. The smaller lakes (median diameter = 77 ± 20 km (±1 s.d.)) are SEDs with a circular or irregular shape that are liquid filled to varying degrees 3,9,11,12 . Recent analysis of Cassini Radar SAR data of SEDs in Titan's north pole found that 75% have observable rims where those with lake areas >750 km 2 had a higher probability of presenting an observable rim 9,13 .
The irregular shape of most SEDs is not consistent with the planform morphology of impact craters. Due to similar planform morphology with terrestrial karst lakes, a karstic dissolution origin of the lake basins has been suggested 14,15 . However, water ice is insoluble in liquid hydrocarbons 16 and theoretical modelling of the materials expected to be on Titan's crust indicates that for the present environmental conditions a limited number of materials are capable of producing dissolution 15 . Further, deposition of photochemical products via precipitation 17 to the poles is insufficient to produce an erodible organic sedimentary layer that can produce the depth of the SED basins 9 . The presence of raised rims in SED basins 9,[11][12][13] undermines the karst lake model for SEDs with raised rims. According to the karst model, the lake basins on Titan should be produced as dolines formed by collapse, dissolution or subsidence of the terrain; such processes do not produce rims. While SEDs with raised rims are not formed by a karstic process, their presence in a karstic-like environment is not excluded.

SEDs with raised rims as explosive craters
We propose that SEDs with raised rims are craters that are successively filled with hydrocarbon liquid and result from explosive eruptions probably due to phase transitions of liquid molecular nitrogen in the shallow subsurface during a colder period in Titan's past 18 . Examples of morphologies produced by explosive eruptions on Earth are maar craters, tuff rings and tuff cones produced during phreatic or phreatomagmatic eruptions. Maar craters are the result of shallow subsurface interactions and have floors that are below the surrounding topography; tuff rings and tuff cones are the result of interactions with liquid just below or at the surface 19 .

and Valerio Poggiali 3
The Cassini mission discovered lakes and seas comprising mostly methane in the polar regions of Titan. Lakes of liquid nitrogen may have existed during the epochs of Titan's past in which methane was photochemically depleted, leaving a nearly pure molecular nitrogen atmosphere and, thus, far colder temperatures. The modern-day small lake basins with sharp edges have been suggested to originate from dissolution processes, due to their morphological similarity to terrestrial karstic lakes. Here we analyse the morphology of the small lake basins that feature raised rims to elucidate their origin, using delay-Doppler processed altimetric and bathymetric data acquired during the last close flyby of Titan by the Cassini spacecraft. We find that the morphology of the raised-rim basins is analogous to that of explosion craters from magma-water interaction on Earth and therefore propose that these basins are from near-surface vapour explosions, rather than karstic. We calculate that the phase transition of liquid nitrogen in the near subsurface during a warming event can generate explosions sufficient to form the basins. Hence, we suggest that raised-rim basins are evidence for one or more warming events terminating a nitrogen-dominated cold episode on Titan.
Explosive crater morphology of relatively flat floors, raised rims and typically rampart-like borders is a match for the morphology of SED basins with raised rims with and without rampart-like borders.
Terrestrial maars have circular and irregular shapes and often have composite or coalesced forms 19,20 . Maar irregularity can be due to closely spaced explosive vents, which can erupt in a single complex  20,21 . The spatial relationship between explosion epicentres can result in either a circular or irregular crater 20,21 (for example, Devil Mountain maar, USA 22 and Nejapa maar, Nicaragua 23 ). For a given explosion energy and material substrate strength, the explosion depth is a controlling factor in determining whether a crater and ejecta are produced or whether the energy is contained in the subsurface, at which point the containment depth is reached 24 . Explosion energies and depths for Titan differ due to the lower material strength of water ice compared with rock and are discussed later.
Crater shape and size are influenced by other factors such as subsidence, collapse and erosion 19,25 . Analysis of maars and similar landforms in the West Eifel Volcanic Field (Germany) found that maars affected by fluvial erosion lose their original shape and often have an irregular shape 26 . Analyses of maars in the Hopi Buttes Volcanic Field (USA) demonstrate the complex morphology that can result from fluvial erosion, including 'concave-lakeward' and 'tongue-like' morphology found in the Teshim and Morale Claim Butte maars 27 . Elongated, irregular terrestrial maars influenced by multiple eruptive events and erosion may reflect processes that formed Winnipeg Lacus as well as SEDs with raised rims featuring irregularities, including elongation, protrusions and other complex morphology (Fig. 1).
While fluvial erosion may be a secondary force in transforming Titan's surface 28 , it is possible that it could have been more significant in a colder, nitrogen-dominated Titan. Since the density of liquid nitrogen is near water ice compared with liquid methane, nitrogen liquid would have a greater ability than methane liquid to erode Titan's surface 29 .
Many maars are surrounded by ejected deposits known as a tephra ring; tephra refers to ejecta material of the maar. Tephra is a heterogeneous mix of surface and subsurface material and is found in both the crater and the surrounding ring. Tephra volume is controlled by the explosion depth as a function of explosive energy and material substrate; the closer the explosion depth is to the containment depth, the smaller the volume of tephra ejected will be 24,30 . Tephra deposition is determined by the angle of the jets coming from the explosion vent; wider jets produce greater deposits whereas more vertically focused jets result in fallback of tephra into the crater 30 . Cassini spectral and radar analysis of SEDs with raised rims on Titan found that some (<10) are surrounded by rampartlike radar bright ring structures, including Winnipeg Lacus (Fig. 1) and the lakes featured in Fig. 2 that are suggestive of tephra rings 31 .
Analysis of Cassini RADAR backscatter indicated that Titan's north polar empty lake basins have a heterogeneous composition and differ compositionally from their surroundings 32 . Cassini Visible and Infrared Mapping Spectrometer (VIMS) spectral analysis of empty lake basins and ramparts found they share the same composition 30 . Eruptive jets, depending on their placement in the crater, can produce laterally focused directional jets, which can result in asymmetric ejecta deposition 20,30 . Pre-eruptive surface topography can affect ejecta deposition, for example, creating a partial tephra ring at the Barombi Mbo amalgamated maar, Cameroon 33 . Material substrate affects tephra formation; in highly permeable water-saturated substrates, a maar crater cannot form, rather a tephra ring or cone (for example, tuff ring and cone) forms at the surface (for example, Diamond Head tuff cone, USA). In this environment, the tephra may be water saturated and thus have a smaller ejecta angle 19 . Collapse and erosion can play important roles in the presence or absence of a tephra ring 19,30,33 . The apparent lack of more rampart structures around SEDs constrains the explosive origin model; however, the paucity of ramparts could be due to explosion depth, material properties, and fluvial erosion and precipitation, both probably more substantial in a cold nitrogen-dominated Titan 29 .

Warming events in a past nitrogen-dominated atmosphere
The photochemical lifetime of methane in Titan's atmosphere is several tens of million years, and the value of 12 C/ 13 C in Titan's atmosphere indicates that the current atmospheric inventory of methane probably outgassed ~10 7 -10 8 yr ago 34 . Evolution models suggest that Titan's crust is composed of water ice and clathrate hydrate, with mostly methane as primary guest species, and that episodic methane outgassing could be a cause for the continued presence of methane in the atmosphere 35 . However, in the absence of continuous or frequent outgassing from the crust or deeper methane sources, Titan's atmosphere in the past may have been episodically methane depleted. Under such conditions, the greenhouse effect would have been limited to the collision-induced absorption of N 2 -N 2 , resulting in a Titan that was colder than at present, with a mean surface temperature lower than 81 K (refs. 18,29 ).
Under the hypothesis that the interval between methane outgassing events was so infrequent that the atmosphere would be depleted, Titan's surface may have been characterized by the presence of liquid nitrogen lakes and of liquid nitrogen aquifers at the poles within the crust. If the temperature was low enough-81 K on the basis of the vapour pressure of pure molecular nitrogen-liquid nitrogen might have been stable on the surface and subsurface,  participating in a cycle similar to the present methane cycle 18,29 . During this period, the molecular nitrogen liquid at and near the surface could have been close to the equilibrium vapour pressure at the high latitudes 18 such that a small temperature variation produced by an exothermic or endothermic warming event could result in an extremely rapid rise in the vapour pressure of liquid within the nitrogen-dominated aquifers. The phase transition from liquid to vapour and the subsequent pressurization of subsurface N 2 gas could have resulted in an explosive eruption. The surface on a nitrogen-dominated Titan would have been able to absorb about five times the insolation compared with the current methane-dominated Titan 29 . On Titan, increasing the molar fraction of methane in a liquid methane-nitrogen mixture results in an increase of the equilibrium vapour pressure (Fig. 3), resulting in a less volatile mixture. This potentially explosive process, depending on the amount of methane present in the liquid nitrogen solution, would have been limited to shorter-term warming events or would have only occurred at the beginning of a global warming scenario. A similar phase transition process probably occurred during at least two geyser-like eruptions captured by Voyager 2 during its flyby of Neptune's largest moon, Triton 36 . Models suggest that an exothermic warming event, probably insolation during Triton's southern spring/summer, caused sunlight to be absorbed by organic particles within the nitrogen-dominated icy crust, prompting a greenhouse effect and raising the temperature therein; this resulted in a subliming phase transition and subsequent increasing pressurization of N 2 gas in the subsurface, which produced venting of nitrogen, organic gas and particles 36,37 . Geothermal heating may also have played a role in these events 38 . Between 1989 and 1998, Triton experienced a ~2 K increase in temperature 39 and an increase in atmospheric pressure probably due to an increase of N 2 in the atmosphere 39 . Streaks seen by Voyager 2 on Triton's surface and anomalous 'reddening' events recorded between 1997 and 2000 that appeared to correspond with variation in methane absorption band strength may have been evidence of venting caused by global warming 40,41 .
We have investigated whether warming events in a past nitrogendominated atmosphere of a cold Titan could have produced explosions in the external crustal layer due to a phase transition occurring in the nitrogen-dominated aquifers. Figure 3 shows the vapour pressure of a solution composed of methane, ethane and nitrogen as measured for Winnipeg Lacus and Ligeia Mare (72% of CH 4 , 11% C 2 H 6 , 16% N 2 molar fraction 7 ) (red solid line) with Cassini RADAR altimetry data. For comparison, a model for the vapour pressure of a nitrogen-dominated solution (20% of CH 4 , 80% N 2 molar fraction) is shown (red dashed line). Figure 3 shows the vapour pressure of molecular nitrogen (red dotted line) and methane (grey dashed line). We used the Antoine equation to describe the relation between the vapour pressure and temperature for pure methane, ethane and molecular nitrogen. The vapour pressure of the methane, ethane and molecular nitrogen solution is determined using Raoult's equation. We display the methane clathrates dissociation curve (solid brown line). The dissociation pressure as a function of temperature of methane clathrates is computed 42 . The temperature profile for a cold Titan with a surface temperature of 80 K at the north pole is indicated by the blue dotted line, and the temperature profile for the present recorded surface temperature of 91 K at the north pole is indicated by the blue solid line. The temperature profile for a model with a surface temperature of 87 K is shown. The model presented in Fig. 3 is for an internal heat flux of 0.007 W m −2 , a thermal conductivity of 3.5 W m −1 K −1 (pure water ice) and an atmospheric pressure of 0.15 MPa.
The comparison of the saturation vapour pressure with the expected temperature profile within the ice shell allows an evaluation of whether methane, nitrogen and their mixture are in liquid or vapour phases at the surface and within the crust. For the current conditions, CH 4 -C 2 H 6 -N 2 liquid is thermodynamically stable on the surface and within subsurface aquifers (compare red solid line with the vapour pressure of the liquid solution with the expected current temperature profile in blue solid line). In a cold Titan with a nitrogen-dominated atmosphere, liquid N 2 is stable at the surface and within aquifers. Because nitrogen exists close to its equilibrium vapour pressure during this cold period on Titan, its vapour pressure increases rapidly with increasing temperature; thus, small temperature changes can produce the transition phase from liquid to vapour both on the surface and within the crust (compare red dotted line with blue dotted line). Molecular nitrogen efficiently dissolves methane. An aquifer with pure liquid nitrogen or with a small molar fraction of dissolved methane can react to temperature changes, producing a phase transition from liquid to vapour. The presence of methane makes any solution with nitrogen more thermodynamically stable such that an increasing amount of methane would probably halt the phase transition process.
The ability of an underground explosion to form craters and subsequently ejecta is a function of the explosive energy, explosion depth and material substrate properties. We used the scaling law of explosion craters according to experimental and test results from chemical and nuclear explosions 43 to model the craterization processes, adopting the cube root scaling law 24,43 that is consistent with field results 44 . The craterization process for a given explosion energy is dominated by tensile strength of the material substrate with respect to gravity and other variables such as atmospheric pressure 43 . The scaled depth of subsurface explosions is d sc = dE −1/3 (refs. 24,44 ). Under terrestrial conditions, the scaled crater diameter reaches a maximum (0.014 m J −1/3 ) when the scaled depth is 0.004 m J −1/3 (refs. 24,44 ). Explosion depths less than the optimal scaled depth will allow the release of enough energy to produce craters and ejecta while explosion depths greater than the scaled depth will have their explosive energy progressively confined to the subsurface until the containment depth, 0.008 m J −1/3 (refs. 24,44 ), is reached and all explosive energy is maintained in the subsurface 24,45 .
The laboratory-measured tensile strength (Y) of water ice is ~10 6 Pa; however, the measured tensile strength of the ice of the We have determined the required volume of nitrogen deposits to produce explosion craters. The latent heat of vapourization of N 2 is 200 kJ kg −1 . The density of liquid nitrogen at 80 K is 793 kg m −3 . We assume that the entire energy produced by the phase transition is converted to explosive energy. Under this assumption, an explosion containment depth of 100 m requires a liquid nitrogen deposit with a volume of 80-1,700 m 3 , corresponding to tensile stresses of Y = 0.1-2.2 MPa (Supplementary Information). The phase transition of liquid nitrogen deposits is an efficient mechanism to produce explosions.
We interpret the morphological characteristics of the SEDs with raised rims as evidence of their explosive eruptive origin, suggesting that these SED basins were formed due to the phase transition of liquid nitrogen in the near subsurface during a warming event or events on a cold nitrogen-dominated Titan that may have existed at various times during Titan's past. These climatic conditions caused N 2 to exist near its equilibrium vapour pressure at high latitudes, making the vapour pressure of N 2 a steep function of increasing temperature. This resulted in pressurization of N 2 in the subsurface and a probable explosive release resulting in a crater where the rim is formed by the ejected material from the crater interior. This explosive process may or may not release methane as part of the process.
The presence of explosive eruption craters forming the SED basins therefore is evidence that Titan has experienced cold nitrogen-dominated epochs followed by rewarming to conditions more like those today. On Triton, the venting of nitrogen and possibly methane and an increase of atmospheric pressure are probably due to warming events that may mirror processes that happened in Titan's nitrogen-dominated past. The morphology of SEDs with raised rims is analogous to the morphology associated with terrestrial phreatic and phreatomagmatic explosions.

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