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A Radar Map of Titan Seas : Tidal Dissipation and Ocean Mixing 4

through the Throat of Kraken 5

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Ralph D. Lorenz1, Randolph L. Kirk2, Alexander G. Hayes3, Yanhua Z. Anderson4, Jonathan I. Lunine3, 7

Tetsuya Tokano5, Elizabeth P. Turtle1, Michael J. Malaska4, Jason M. Soderblom6, Antoine Lucas7, Ozgur 8

Karatekin8, Stephen D. Wall4. 9

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1 Space Department, Johns Hopkins University Applied Physics Lab, Laurel, Maryland 20723, USA 11 2 U.S. Geological Survey, Flagstaff, AZ 86001, USA 12 3 Center for Radiophysics and Space Research, Cornell University, Ithaca NY 14853 USA 13 4 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA 14 5 Institut für Geophysik und Meteorologie, Universität zu Köln, Albertus-Magnus-Platz, 50923 Köln, 15 Germany 16 6 Department of Earth, Atmospheric and Planetary Science, Massachussetts Institute of Technology, 17 Cambridge, MA 02139, USA 18 7 Paris-Diderot Space Campus, Laboratoire Anneaux, Disques et Planetes, 75013 Paris, France 19 8 Royal Observatory of Belgium, B-1108 Brussels, Belgium 20 21 22 To be submitted to Icarus, February 8, 2014 23

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Abstract 28

We present a radar map of the Titan’s seas, with bathymetry estimated as proportional to distance from 29

the nearest shore. A naïve analytic bathymetry suggests a total liquid volume of ~30,000km3, smaller 30

than estimates made in 2008 when mapping coverage was incomplete, and intermediate between other 31

models. We note that Kraken Mare has two principal basins, separated by a narrow (~17km wide, 32

~40km long) strait we refer to as the ‘throat’. Tidal currents in this strait may be dramatic (~0.5m/s), 33

generating observable effects such as dynamic topography, whirlpools, and acoustic noise, much like 34

tidal races on Earth such as the Corryvreckan off Scotland. If tidal flow through this strait is the dominant 35

mixing process, the two basins take 5-70 Earth years to exchange their liquid inventory. Thus 36

compositional differences over seasonal timescales may exist, but the composition of solutes (and thus 37

evaporites) over Croll-Milankovich timescales should be homogenized. 38

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Keywords: Titan, hydrology ; Tides, solid body ; Satellites, dynamics ; Radio observations 40

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1. Introduction 44

Extraterrestrial Oceanography is now an observational, and not merely theoretical, science. After years 45

of expectation (e.g. Lorenz and Mitton, 2010) and various speculative interpretations of features in 46

groundbased and Cassini near-IR observations since 1994 that were morphologically suggestive of 47

liquids, Radar mapping by the NASA/ESA/ASI Cassini spacecraft in 2006 (Stofan et al., 2007) observed 48

dozens of lake-shaped features around Titan’s north pole with unique radiometric properties, consistent 49

with the low dielectric constant of liquid hydrocarbons. At the time, these regions were in winter 50

darkness. Later, three bodies of liquid large enough to merit designation as ‘seas’ were identified. Only 51

one major south polar lake is known, and a few small features at low latitudes are at best transient. 52

Thus the northern seas are the dominant surface liquid reservoir and thus are prime targets for future 53

exploration, not only as organic material of astrobiological interest, but also as laboratories for air:sea 54

exchange and other oceanographic processes. 55

The discovery of these features has stimulated some theoretical work on their temperature, 56

composition and sound speed structure (e.g. Tokano, 2009; Arvelo and Lorenz, 2013), and on the 57

formation of wind-driven waves (e.g. Lorenz and Hayes, 2012; Hayes et al., 2013). Tokano (2010) made 58

an initial numerical study of tides in Kraken Mare, using a low-resolution map based on partial radar and 59

near-infrared (940nm) data (the latter not being unambiguously liquid). Ligeia Mare was subsequently 60

mapped completely by radar with a higher resolution of 0.3-1km and allowed a more thorough study of 61

tides (Lorenz et al., 2012). Titan’s lakes and seas have been the subject of several mission studies (e.g. 62

ESA, 2009; JPL, 2010) and Ligeia Mare was the target for the proposed Titan Mare Explorer (TiME) 63

Discovery mission (Stofan et al., 2013). 64

As the subsolar point has moved northwards (crossing the equator at spring equinox in 2009), the 65

northern seas have become progressively better-illuminated, and the Cassini orbital tour has been 66

designed to provide numerous observing opportunities of the seas. Sotin et al. (2012) presented 67

mapping at 5 microns (where the blurring due to atmospheric haze is less severe than at 940nm), 68

although at modest resolution (3 to 7km). Several observations of the northern polar regions have been 69

made to observe the near-infrared specular reflection of the sun (e.g. Stephan et al., 2010; Barnes et al., 70

2012; Soderblom et al., 2012) 71

In summer of 2013 several new radar observations of the seas have been made. In addition to nadir-72

pointed altimetry and radiometry near closest approach, some high-altitude Synthetic Aperture Radar 73

(HiSAR, e.g. West et al., 2009) observations with a resolution of 1-2km have now covered the full extent 74

of Kraken Mare. These now allow a somewhat definitive map of the liquid boundaries to be generated, 75

which we present here. To provide a common reference for future oceanographic studies such as tidal 76

modeling, as well as for mission planning for a TiME-like mission, we offer in this paper numerical files as 77

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Supplemental Online material to this paper, and at http://www.lpl.arizona.edu/~rlorenz/titanseas.html, 78

for the convenience of other workers. 79

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2. Observations and Map Generation 81

Given pre-Cassini expectations of surface liquids, secure identifications of lakes and seas were slow to 82

emerge. Ontario Lacus in the south was seen at Cassini’s arrival in 2004, although its nature as liquid was 83

not confirmed until several years later (e.g. Brown et al., 2009). In fact Ontario was found to be rather a 84

flat (Wye et al., 2009) and possibly muddy place (Clark et al., 2010), similar perhaps to ephemeral playa 85

lakes on Earth such as Etosha (Cornet et al., 2012). Northern lakes were first observed in 2006 in the 86

‘regular’ (5-beam) Synthetic Aperture Radar (SAR) near closest approach on flyby T16 (Stofan et al., 87

2007) and on several subsequent flybys. Ligeia Mare was first observed on T25 in 2007, on T28, T29; 88

later on T65; and most recently on T86, T91 and T92 (Hayes et al., 2013) . Nonimaging altimetry and 89

radiometry was also performed on T91 - Mastrogiuseppe et al., 2014; Zebker et al., 2014). Part of the 90

main basin of Kraken Mare was observed in SAR on T30, although the northern margins around Mayda 91

Insula were seen on T25 and T28. 92

Kraken Mare sprawls to mid-latitudes (~55oN) and was therefore visible in ISS images as early as 2008 93

(e.g. Turtle et al., 2009), although its albedo could not be distinguished from that of the sand seas nearer 94

the equator. Remarkably, it could be detected beyond the geometric terminator, because of solar 95

scattering in the haze. As the seasons have marched on through Titan’s 29.5 Earth year annual cycle, 96

the northern polar regions are now well-illuminated and are being observed intensively by Cassini in the 97

near-IR. 98

In addition to the side-looking SAR at closest approach with resolutions between ~0.3 and 2km, Cassini 99

has developed the capability to acquire lower-resolution (typically 1-4km) single-beam SAR from higher 100

altitudes, e.g. West et al. (2009). These so-called HiSAR observations have lower single-look power due 101

to the longer range, and therefore have higher noise backgrounds (making them less sensitive to faint 102

targets like bottom reflection or waves on the dark seas), but are typically adequate for discriminating 103

the strong land-sea contrasts. Further, the HiSAR images, which use many looks to recover signal to 104

noise, are often cosmetically less noisy, due to the decrease in speckle noise that is typical of the 1-3 105

look-per-pixel normal SAR. This HiSAR mode was used on T91 and T92 to observe the areas of Kraken 106

Mare that had not been imaged with RADAR to date. The resultant mosaic is shown in Figure 1. A 107

coverage gap exists at the north pole, and image quality is somewhat poor at the southern margins of 108

Kraken and in the region between Kraken and Ligeia Maria. 109

Comparisons of these RADAR data with near-infrared observations is likely to be fruitful. Similarly, a full 110

discussion of the geological interpretation of the shorelines and the origin and evolution of the sea 111

basins will be interesting, but is beyond the scope of the present work. 112

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Figure 1. A part of the north polar radar mosaic (available at 115

http://photojournal.jpl.nasa.gov/catalog/PIA17655) with the major seas labeled. Note that Kraken is 116

divided into two major basins, separated by a narrow barrier which is penetrated by a channel labeled 117

the Throat of Kraken. 118

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3. Bathymetry Model and Ocean Volume 122

While there are a number of approaches to remotely measure the depth of a surface deposit (notably 123

nadir-pointed radar sounding that directly detects a subsurface echo, or methods exploiting the 124

attenuation of an assumed bottom reflector by the liquid column) none of these approaches is likely to 125

yield a complete survey given the coverage in the planned Cassini mission. To serve as a ‘working 126

hypothesis’ for modeling studies, and as a benchmark expectation against which future observations 127

and analysis may be compared, we first consider a hypothetical bathymetry map with a simple assumed 128

bottom shape, noting the empirical observation (e.g. Lorenz et al., 2008) that terrestrial lakes and seas 129

tend to have an aspect ratio (depth/diameter) of ~0.001. 130

In this model, we simply assume a constant slope away from the shore. This is typical for basins 131

currently fed by a uniform sediment flux, and has been applied to Ontario Lacus in the south (Hayes et 132

al, 2010), around which a near-uniform slope was observed. We note that the density contrast 133

between likely Titan surface solids and liquid is rather modest and thus sedimentation speeds in Titan 134

seas are rather low (Lunine, 1992; Burr et al., 2006) : thus material introduced at the margins of Titan’s 135

seas could be transported rather easily. Like a growing sandpile, a uniform slope will tend to form. 136

If, following Lorenz et al. (2012) we choose the slope to yield a 300m central depth for Ligeia Mare, 137

roughly consistent with the empirical rule of thumb (depth/width~0.001) of Lorenz et al. (2008), we find 138

a maximum depth of ~350m for Kraken, and summing up all the resultant depth values (Figure 2) and 139

multiplying by the area of a pixel yields a total estimated volume of liquid in the northern hemisphere of 140

33,000 km3. This is in fact just within, but at the extreme low end, of the liquid volume range estimated 141

by Lorenz et al. (2008). 142

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Figure 2. Linear depth Map of Titan’s Seas, using an assumed linear depth vs distance. The deepest 145

points are in the middle of the Kraken-1 basin, and the middle of Ligeia. 146

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Clearly, the total volume computed this way is directly proportional to the assumed slope. In fact a near-148

diametric depth profile of Ligeia Mare has been recently determined from Cassini RADAR altimetry data 149

by Mastrogiuseppe et al. (2014). We can adjust our simple bathymetry model, and the total ocean 150

volume, by a simple scaling factor A (i.e. depth/width=0.001*A). Empirically, from the scatter in 151

terrestrial lakes (Lorenz et al., 2008) with different basin origins, such a factor lies in the range 0.1<A<10, 152

depending on the geological nature of the seas, with A~0.1 corresponding to shallow sedimentary basins 153

and A~10 corresponding to tectonic extremes such as Lake Baikal. The maximum depth for Ligeia 154

measured by Mastrogiuseppe et al. (2014) is 170m, giving A~0.5 for Ligeia specifically. If this applies 155

everywhere, it follows that the total ocean volume at present is roughly half that indicated above, or 156

about ~15,000km3. The depth model with A=0.5 is made available as an ASCII array, together with 157

ancillary latitude/longitude arrays, for the convenience of modelers (see Appendix 1 and supplemental 158

online information.) The model is straightforward to scale to other values of A, or to transform to other 159

analytic functions of depth from shore. 160

On the other hand, Hayes et al. (2014) have recently made an ocean volume estimate using SAR image 161

data, with an empirical bottom reflection function and an attenuation of the radar echo with depth (e.g. 162

Thompson and Squyres, 1990) that is assumed uniform. By implication, this assumes a uniform liquid 163

composition - an assumption challenged as a function of location later in the present paper; see also 164

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Tokano, 2009, for discussion of depth structure. Hayes et al. (2014) report a volume of ~70,000km3, a 165

little over double that that we obtain with our simple linear model A=1. 166

Clearly, not all these models can be correct. Most likely the uniform slope is not a correct assumption. 167

However, the correctness of a uniform attenuation assumption yielding a larger volume is difficult to 168

assess. In any case, the model presented here serves as a benchmark against which other models can be 169

tested (e.g. the Hayes et al. result might imply that Kraken is generally deeper than Ligeia for a given 170

distance from shore, which may be a result of stronger tidal and/or wind-driven currents, or a longer 171

time for Ligeia to accumulate sediment.) 172

It is of note that all the models have a volume at the low end of the predictions in Lorenz et al. (2008) 173

which allowed for the (at the time poorly-mapped) southern hemisphere to have a liquid inventory 174

equivalent to that in the north. We now know on the basis of much more complete mapping coverage 175

(and supported by the paradigm of Titan’s present climate that favors accumulation of liquid in the 176

northern hemisphere at the expense of the south - e.g. Aharonson et al., 2009; Schneider et al. 2012) 177

that in fact there is only one (barely) significant body of liquid in the southern hemisphere, Ontario 178

Lacus, which appears to have a depth of only around 10m, and thus a volume of around ~200km3, or 179

<1% of the total liquid on Titan. 180

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4. Basin Architecture : The Throat of Kraken and Terrestrial Analogs 182

Of special interest is the connection between the main basins. The river network at the southwestern 183

corner of Ligeia Mare appears, perhaps, to form a labyrinth of narrow channels that reaches towards 184

Kraken Mare, as had been suggested by near-infrared observations (Sotin et al., 2012). 185

Of particular note in the new data is the narrow strait, which we nickname the ‘throat’, between the 186

two major basins of Kraken. This strait (at 67oN, 42oE) is 17km wide, and ~40km long. It is broadly 187

comparable in size with the Straits of Gibraltar on Earth (see later). It is interesting to compare 188

geomorphology of the strait (Figure 3) with the Aland strait between the Gulf of Bothnia and the Baltic 189

Sea (Figure 4). Like the Kraken throat, there is a labyrinth of small islands and channels in parallel with 190

the main strait. These likely have a minimal hydraulic impact, since they are likely shallow, but may be 191

of interest in understanding the origin and subsequent modification history of the basins. 192

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Figure 3. Zoomed section of the map showing the throat of Kraken between the two basins (scale bar in 195

km). The blue speckled areas are where signal to noise is poorer. Note the ~17x40 km clear channel, 196

and the labyrinth of narrower channels and islands to the west. The inclined stripe towards the right of 197

the map is an artifact of low signal-to-noise. 198

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Figure 4. NASA Earth Observatory image of Aland, between Sweden and Finland. Topographically, this 201

region may be a good analog of the Kraken throat (albeit mirrored east-west). The island of Aland 202

divides the hydraulic link between the Baltic to the south and the Gulf of Bothnia to the north into two 203

sections : a clear 40km-wide channel ‘Sea of Aland’ to the west, and a labyrinth of shallow channels 204

punctuated with islands to the east. 205

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5. Tidal Currents and Observable Effects 207

The Kraken Throat constriction may be significant in modifying the response of Kraken’s liquid to tidal 208

forces. Tokano (2010) speculated that the constriction (at the time, of unknown width, and indeed 209

speculative altogether) might lead to the highest tidal currents anywhere in Titan’s seas. The accurate 210

measurement of the width of this channel in the new radar map now allows these currents to be 211

investigated in more detail. 212

The tidal range of a sea on a deformable planet is diminished by a factor 2 relative to the change in 213

potential height (i.e. the equilibrium tide) that would be seen on a rigid spherical world. This factor is 214

given (e.g. Sohl et al., 1995) by the expression 2=1+R(k2)-R(h2) where k2 and h2 are the 2nd-degree Love 215

numbers determining the potential and surface height response of the planet and R() denotes the real 216

part of a complex quantity. Sohl et al. (1995) suggested 2~0.16 for a model with an internal water-217

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ammonia ocean with k2~0.3-0.4 ; given k2~0.6 as measured by Cassini (Iess et al., 2012) and an assumed 218

h2~1.2 (it is comparatively insensitive to ice shell thickness - see Sohl et al., 2003) we might allow 2 as 219

high as 0.4. We would in any case suggest 2 should be considered a somewhat free parameter 220

(0.1<2<0.4) in further studies of Titan’s ocean tides. 221

Tokano (2010) modeled the tidal response of an idealized Kraken map and found a tidal amplitude Do of 222

2m (i.e. a tidal range, low tide to high tide, of 4m). This result was obtained assuming a rigid Titan, i.e. 223

without considering the deformation of Titan’s lithosphere. Given the internal deformation implied by 224

the Iess et al. (2012) result and thus (0.1<2<0.4), it seems the tidal range D~22Do should be around 225

~1.6-0.6m. 226

Now, the two basins have a characteristic dimension L of the order of 300 km, and so the tidal cycle 227

represents a migration of a wedge-like volume of liquid of ~0.52DoL2/4 in each half period (i.e. 8 days 228

or ~6x105 s). This corresponds to ~2140 km3 or ~20-60 km3 in that period, or an average flow of up to 229

105 m3/s, the bulk of which passes through the throat. Assuming a depth d for a uniform channel width 230

W, the average speed U is then (0.3~1)x105/Wd : given W~17 km and for d~10-100 m, we then find 231

U~0.02-0.6 ms-1. 232

The propagation speed of a shallow water wave is (gd)0.5, so a 10m deep channel on Titan (g=1.35ms-2) 233

would allow speeds of up to 3.7 ms-1, or rather higher than the tidal currents require. Thus a 234

hydrodynamic shock (i.e. a standing bore) would not form, although if one contrived a channel only a 235

few meters deep, it perhaps could. 236

It is interesting to compare these speeds with tidal races on Earth, the most notable of which are the 237

Saltstraumen in Norway, the Skookumchuck narrows near Vancouver, Canada (and the nearby 238

Deception Pass in Washington, USA), and the Corryvreckan off the west coast of Scotland. The former 239

two are just a few hundred meters across and somewhat shallow, but the Corryvreckan (from the Gaelic 240

Coire Bhreacain meaning "cauldron of the speckled seas") between the islands of Jura and Scarba is a ~1 241

km wide strait which sees ~5 ms-1 currents in 30-70 m of water. The turbulent flow in the maelstrom 242

(generated by the interaction of the tidal flow with the irregular seafloor) generates dynamic 243

topography (Figure 5) such as whirlpools, and sound which can be heard some 16km away. The 244

potential for passive acoustic detection (through the atmosphere, or through the liquid - both media 245

allow transmission of sound - e.g. Leighton and White, 2004; Petculescu and Achi, 2012; Arvelo and 246

Lorenz, 2013) of such sites of dissipation merits consideration in future exploration of Titan’s seas. 247

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Figure 5. Although a perfectly calm day, the sea in the Corryvreckan is rough with breaking waves These 251

result from the energetic tidal flow through the channel. Photo: R. Lorenz 252

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The dynamically irregular sea surface generated by the tidal flow may have a similar influence to that of 254

wind-driven waves on remotely-sensed surface roughness. Thus radar reflectivity and sunglint 255

measurements, already used by Cassini to rule out waves on a number of occasions, may find roughness 256

near the throat regardless of wind conditions. Unfortunately the present HiSAR data in the throat 257

region is too insensitive to detect such roughness, but future observations may be directed to this 258

region. It may be noted that very large wave structures in the Strait of Gibraltar can be detected by 259

spaceborne radar (figure 6), and, indeed, by sunglint (figure 7). 260

These waves have a large wavelength but a small surface height amplitude as they are the surface 261

expression of internal waves at the boundary between the fresher Atlantic water flowing into the 262

Mediterranean at the surface, and a deep salty outflow. It is possible to imagine an analogous situation 263

with methane-rich and ethane-rich liquids on Titan. The waves are generated as a diurnal tidal pulse 264

flows over the shallow Camarinal Sill at Gibraltar. The waves refract around coastal features and can be 265

traced for as much as 150 km. 266

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Figure 6. Synthetic Aperture Radar image of the Strait of Gibraltar acquired in 1995 by the ERS-1 272

satellite. The rugged land is easily distinguished from the sea, but the sea surface is far from uniform in 273

radar texture. A pronounced difference in backscatter in the Atlantic and the smooth sheltered 274

Mediterranean at right is evident, as are a number of narrow dark slicks left in the wake of ships. Also 275

prominent just to the east of the strait are a set of waves - these are the surface expression of internal 276

waves set up by tidal flow across a shallow sill in the strait. Image: European Space Agency 277

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Figure 7. Image (cropped and rotated from Roll: 712 Frame: 29) of the Strait of Gibraltar from the 282

Space Shuttle mission STS098 in February 2001. Image Science and Analysis Laboratory, NASA-Johnson 283

Space Center. "The Gateway to Astronaut Photography of Earth." The sea is bright due to a near-284

specular reflection geometry of the sun. This geometry permits a packet of waves (arrowed), caused by 285

the tidal flow across a shallow sill, to be visible in the Mediterranean to the southeast of the strait. 286

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6. Tidal Dissipation and Orbital Evolution 290

Tides have long been of interest (e.g. Sagan and Dermott, 1982) on Titan, in that the present-day orbital 291

eccentricity of Titan (0.029) is difficult to reconcile with tidal dissipation which would tend to circularize 292

the orbit. Various aspects of the problem are discussed in Lorenz, 1994; Dermott and Sagan, 1995; 293

Sears, 1994 and Sohl et al., 1995. It is well-known that much of the tidal dissipation in Earth’s oceans 294

(which play a major role in the secular increase in the length of the terrestrial day, and the slow 295

recession of the moon - see e.g. Brosche and Sundermann, 1978) occurs in shallow seas and straits. It is 296

interesting to consider whether the tidal dissipation associated with the bottom friction in the Kraken 297

throat specifically could be significant for Titan’s orbital evolution. 298

Sohl et al. (1995) found that the dissipation associated with an e-folding timescale for the decay of 299

Titan’s orbital eccentricity can be expressed roughly as P~A/ , where P is in Watts, A~ 1011 W/Gyr and 300

is the timescale in Gyr. Dissipation in the interior was modeled as low as ~1010 W for a differentiated 301

but solid body, or 5-6 times higher for an undifferentiated model or one with an internal ocean. These 302

models pointed to the difficulty of maintaining Titan’s orbital eccentricity even in the absence of surface 303

liquids. Global oceans 100 m thick generated dissipation of 2x1010 - 2x1012 W, depending on the interior 304

structure (which affected 2) with dissipation varying as the inverse cube of depth. Hence oceans of a 305

few hundred meters or shallower caused dissipation that exceeded that of the interior, and led to 306

recircularization timescales of less than the age of the solar system. 307

A question that now confronts us is whether the Titan that has been revealed to us by Cassini - with 308

somewhat shallow (and therefore dissipative) seas, but ones that are rather limited in geographical 309

extent - has significant dissipation. Ultimately, this question should be addressed (as it has been for the 310

effect of the oceans on the evolution of the Earth-moon system) by numerical models, but an order-of-311

magnitude estimate can be made here. 312

The dissipation on the seabed is written flU3, where f is a bottom friction coefficient (for a shallow 313

strait at the relevant Reynolds number, f~0.01 see Sohl et al., 1995 for discussion), l the density of the 314

liquid (we assume ~500-650 kgm-3, see Lorenz et al., 2010) and U the speed. For U~0.5 m/s, there is 315

dissipation of the order of 1 Wm-2, comparable with the summertime solar flux on the surface. Over the 316

17x40 km strait, the total dissipation is ~7x108 W. This may be compared, given tidal currents of ~1 317

cm/s expected in the bulk of Kraken and Ligeia Mare (Tokano, 2010; Lorenz et al., 2012) with ~6x10-6 318

W/m2 or about 106 W for all of Titan’s seas put together, a fraction of 1% of the dissipation in the throat. 319

Thus in the present epoch, while the throat is likely responsible for most of the sea dissipation, the seas 320

are too limited in extent and too deep to have a significant orbital effect. 321

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7. Basin Mixing Timescales and Evolution of the Seas 323

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While topography determines the local shape of the seas, the concentration of Titan’s seas at high 324

northern latitudes in global terms attests to a climatological ontrol of the distribution of liquids, with the 325

north presently favored for accumulation of methane rainfall because in the present astronomical 326

epoch, the rainy season is longer in the north (Schneider et al., 2012). A variation with latitude of 327

precipitation, as well as of evaporation, might lead to a gradient in Kraken’s composition if the seas are 328

not well-mixed by tides and wind-driven currents. The latter have not yet been modeled, but mixing by 329

tides can be estimated. 330

Tidal flow through the throat likely dominates the surface exchange of liquid between the two basins 331

: it seems unlikely that wind-driven circulations will be larger, and subterranean hydraulic connection 332

will have a very low conductance (Hayes et al., 2008) . Given a tidal cycling of 20-60 km3 of liquid each 333

Titan day through the throat, and a volume of 6,000~30,000km3 for each basin, a first-order mixing 334

timescale is 100~1500 Titan days, or ~5 to 70 Earth years. These mixing timescales are short compared 335

with the period of astronomical variation of the seasons (the Croll-Milankovich cycles) of ~50,000 years, 336

so long-term geological consequences of the sea composition (notably, the composition of evaporites 337

left after the seas evaporate) should be somewhat uniform with latitude. 338

On the other hand, this mixing timescale is comparable with or longer than a Titan season of ~7 339

years. Since the supply of methane-rich rainfall to the seas in summer varies with latitude (e.g. 340

Schneider et al., 2012), we might expect there to be, at some seasons at least, a compositional 341

difference between the two basins. The magnitude of such compositional differences will need to be 342

evaluated with numerical models, preferably taking possible stratification (Tokano, 2009) into account. 343

These considerations strictly pertain to the present day. There have likely been dramatic changes over 344

time (e.g. Lunine et al., 1983, 1998; Lorenz et al., 1997) of the total amount of liquid on Titan’s surface, 345

and its distribution between north and south (Aharonson et al., 2009). The drowned valleys in Ligeia 346

(e.g. Wasiak et al., 2013) attest to rising base levels in the northern seas. If, for example, the throat is 347

only 50m deep, and northern sea level were 50m lower, say, 20,000 years ago, the two basins would be 348

isolated by an isthmus and could have very different compositions. On the other hand, in the more 349

distant past, if the total methane inventory were larger, a deeper Kraken-Ligeia connection may have 350

allowed more vigorous transport, and Punga Mare and many of the smaller lakes may also have been 351

directly connected with Kraken. 352

We note (as hinted at by Near-infrared observations by Sotin et al. (2012)) that a labyrinth of dark 353

channels may connect Kraken and Ligeia. Inspection suggests that roughly speaking this labyrinth can 354

be characterized by 1-2 parallel channels of length ~ 100 km and no more than 10km wide. The blue 355

appearance in the mosaic (figure 1) indicates a moderate radar brightness, with probable bottom echo 356

contribution, suggesting they may be shallow. Hence this labyrinth is unlikely to admit a significant flow, 357

or cause much dissipation, but numerical models should consider a range of effective widths and depths 358

to evaluate mixing between Kraken and Ligiea. 359

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8. Conclusions 362

We have presented a radar map of the northern seas of Titan. Using a simple uniform-slope seabed 363

model, we estimate a total volume for the seas of ~30,000km3, within roughly a factor of two of other 364

estimates. The map is made available electronically to facilitate future numerical modeling efforts. 365

A strait or throat that divides the two major basins of Kraken Mare has been measured at 17km width, 366

and may be the site of significant tidal currents that could have observable effects, as is the case in 367

comparable sites on Earth. The tidal dissipation in the present configuration of Titan’s seas, dominated 368

by this throat, is however too small to be significant in Titan’s orbital evolution. 369

Tidal mixing between the two basins through the throat is fast compared with the astronomical climate 370

cycles, but slow compared with the seasons. Thus there may be a compositional distinction between the 371

two Kraken basins. The hydraulic connection between Ligeia and Kraken is more tenuous, and thus a 372

composition difference is likely. We note that a modest drop in past sea level could isolate the major 373

basins from each other completely. 374

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376

Acknowledgements 377

R.L. acknowledges the support of the NASA Outer Planets Research program via grant “Physical 378

Processes in Titan's Seas” NNX13AK97G, as well as via Cassini project grant “Cassini Radar Science 379

Support” NNX13AH14G. The Cassini/Huygens mission is a joint endeavor of NASA and ESA, as well as 380

several European national agencies and is managed for NASA by the California Institute of Technology’s 381

Jet Propulsion Laboratory. We acknowledge stimulating discussions with the Cassini radar team. 382

383

18

Appendix 1. Map file 384

The bathymetry map (Supplemental Online File: see also 385

http://www.lpl.arizona.edu/~rlorenz/titansea.html) is an array of integers, 325 rows by 270 columns, 386

with the value corresponding to estimated depth in meters. The (x,y) coordinates (0<=x<325, 0<=y<275) 387

for a location at latitude (LAT) and longitude (LON) are given approximately by the transformations 388

x = Xc + S*[cos(LAT)*cos(LON)] 389 y = Yc + S*[cos(LAT)*sin(LON)] 390 391 with parameters S=-495, Xc=232, Yc=245. Because there is some distortion in the map projection, these 392 data should not be used for data correlation studies - the original mosaic (figure 1) or better yet, the raw 393 radar images archived on the NASA Planetary Data System (PDS) should be used. 394 395 The file here is generated with the assumption of A=0.5, thus the Ligeia central depth is ~170m and the 396 greatest depth overall in Kraken is 197m. The array can simply be scaled (or indeed transformed to some 397 other function such as depth proportional to square root of distance from shore) as desired. 398 399

400

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