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

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A Radar Map of Titan Seas : Tidal Dissipation and Ocean Mixing
through the Throat of Kraken
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Ralph D. Lorenz1, Randolph L. Kirk2, Alexander G. Hayes3, Yanhua Z. Anderson4, Jonathan I. Lunine3,
Tetsuya Tokano5, Elizabeth P. Turtle1, Michael J. Malaska4, Jason M. Soderblom6, Antoine Lucas7, Ozgur
Karatekin8, Stephen D. Wall4.
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Space Department, Johns Hopkins University Applied Physics Lab, Laurel, Maryland 20723, USA
U.S. Geological Survey, Flagstaff, AZ 86001, USA
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Center for Radiophysics and Space Research, Cornell University, Ithaca NY 14853 USA
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Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
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Institut für Geophysik und Meteorologie, Universität zu Köln, Albertus-Magnus-Platz, 50923 Köln,
Germany
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Department of Earth, Atmospheric and Planetary Science, Massachussetts Institute of Technology,
Cambridge, MA 02139, USA
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Paris-Diderot Space Campus, Laboratoire Anneaux, Disques et Planetes, 75013 Paris, France
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Royal Observatory of Belgium, B-1108 Brussels, Belgium
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To be submitted to Icarus, February 8, 2014
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Abstract
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We present a radar map of the Titan’s seas, with bathymetry estimated as proportional to distance from
the nearest shore. A naïve analytic bathymetry suggests a total liquid volume of ~30,000km3, smaller
than estimates made in 2008 when mapping coverage was incomplete, and intermediate between other
models. We note that Kraken Mare has two principal basins, separated by a narrow (~17km wide,
~40km long) strait we refer to as the ‘throat’. Tidal currents in this strait may be dramatic (~0.5m/s),
generating observable effects such as dynamic topography, whirlpools, and acoustic noise, much like
tidal races on Earth such as the Corryvreckan off Scotland. If tidal flow through this strait is the dominant
mixing process, the two basins take 5-70 Earth years to exchange their liquid inventory. Thus
compositional differences over seasonal timescales may exist, but the composition of solutes (and thus
evaporites) over Croll-Milankovich timescales should be homogenized.
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Keywords: Titan, hydrology ; Tides, solid body ; Satellites, dynamics ; Radio observations
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1. Introduction
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Extraterrestrial Oceanography is now an observational, and not merely theoretical, science. After years
of expectation (e.g. Lorenz and Mitton, 2010) and various speculative interpretations of features in
groundbased and Cassini near-IR observations since 1994 that were morphologically suggestive of
liquids, Radar mapping by the NASA/ESA/ASI Cassini spacecraft in 2006 (Stofan et al., 2007) observed
dozens of lake-shaped features around Titan’s north pole with unique radiometric properties, consistent
with the low dielectric constant of liquid hydrocarbons. At the time, these regions were in winter
darkness. Later, three bodies of liquid large enough to merit designation as ‘seas’ were identified. Only
one major south polar lake is known, and a few small features at low latitudes are at best transient.
Thus the northern seas are the dominant surface liquid reservoir and thus are prime targets for future
exploration, not only as organic material of astrobiological interest, but also as laboratories for air:sea
exchange and other oceanographic processes.
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The discovery of these features has stimulated some theoretical work on their temperature,
composition and sound speed structure (e.g. Tokano, 2009; Arvelo and Lorenz, 2013), and on the
formation of wind-driven waves (e.g. Lorenz and Hayes, 2012; Hayes et al., 2013). Tokano (2010) made
an initial numerical study of tides in Kraken Mare, using a low-resolution map based on partial radar and
near-infrared (940nm) data (the latter not being unambiguously liquid). Ligeia Mare was subsequently
mapped completely by radar with a higher resolution of 0.3-1km and allowed a more thorough study of
tides (Lorenz et al., 2012). Titan’s lakes and seas have been the subject of several mission studies (e.g.
ESA, 2009; JPL, 2010) and Ligeia Mare was the target for the proposed Titan Mare Explorer (TiME)
Discovery mission (Stofan et al., 2013).
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As the subsolar point has moved northwards (crossing the equator at spring equinox in 2009), the
northern seas have become progressively better-illuminated, and the Cassini orbital tour has been
designed to provide numerous observing opportunities of the seas. Sotin et al. (2012) presented
mapping at 5 microns (where the blurring due to atmospheric haze is less severe than at 940nm),
although at modest resolution (3 to 7km). Several observations of the northern polar regions have been
made to observe the near-infrared specular reflection of the sun (e.g. Stephan et al., 2010; Barnes et al.,
2012; Soderblom et al., 2012)
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In summer of 2013 several new radar observations of the seas have been made. In addition to nadirpointed altimetry and radiometry near closest approach, some high-altitude Synthetic Aperture Radar
(HiSAR, e.g. West et al., 2009) observations with a resolution of 1-2km have now covered the full extent
of Kraken Mare. These now allow a somewhat definitive map of the liquid boundaries to be generated,
which we present here. To provide a common reference for future oceanographic studies such as tidal
modeling, as well as for mission planning for a TiME-like mission, we offer in this paper numerical files as
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Supplemental Online material to this paper, and at http://www.lpl.arizona.edu/~rlorenz/titanseas.html,
for the convenience of other workers.
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2. Observations and Map Generation
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Given pre-Cassini expectations of surface liquids, secure identifications of lakes and seas were slow to
emerge. Ontario Lacus in the south was seen at Cassini’s arrival in 2004, although its nature as liquid was
not confirmed until several years later (e.g. Brown et al., 2009). In fact Ontario was found to be rather a
flat (Wye et al., 2009) and possibly muddy place (Clark et al., 2010), similar perhaps to ephemeral playa
lakes on Earth such as Etosha (Cornet et al., 2012). Northern lakes were first observed in 2006 in the
‘regular’ (5-beam) Synthetic Aperture Radar (SAR) near closest approach on flyby T16 (Stofan et al.,
2007) and on several subsequent flybys. Ligeia Mare was first observed on T25 in 2007, on T28, T29;
later on T65; and most recently on T86, T91 and T92 (Hayes et al., 2013) . Nonimaging altimetry and
radiometry was also performed on T91 - Mastrogiuseppe et al., 2014; Zebker et al., 2014). Part of the
main basin of Kraken Mare was observed in SAR on T30, although the northern margins around Mayda
Insula were seen on T25 and T28.
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Kraken Mare sprawls to mid-latitudes (~55oN) and was therefore visible in ISS images as early as 2008
(e.g. Turtle et al., 2009), although its albedo could not be distinguished from that of the sand seas nearer
the equator. Remarkably, it could be detected beyond the geometric terminator, because of solar
scattering in the haze. As the seasons have marched on through Titan’s 29.5 Earth year annual cycle,
the northern polar regions are now well-illuminated and are being observed intensively by Cassini in the
near-IR.
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In addition to the side-looking SAR at closest approach with resolutions between ~0.3 and 2km, Cassini
has developed the capability to acquire lower-resolution (typically 1-4km) single-beam SAR from higher
altitudes, e.g. West et al. (2009). These so-called HiSAR observations have lower single-look power due
to the longer range, and therefore have higher noise backgrounds (making them less sensitive to faint
targets like bottom reflection or waves on the dark seas), but are typically adequate for discriminating
the strong land-sea contrasts. Further, the HiSAR images, which use many looks to recover signal to
noise, are often cosmetically less noisy, due to the decrease in speckle noise that is typical of the 1-3
look-per-pixel normal SAR. This HiSAR mode was used on T91 and T92 to observe the areas of Kraken
Mare that had not been imaged with RADAR to date. The resultant mosaic is shown in Figure 1. A
coverage gap exists at the north pole, and image quality is somewhat poor at the southern margins of
Kraken and in the region between Kraken and Ligeia Maria.
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Comparisons of these RADAR data with near-infrared observations is likely to be fruitful. Similarly, a full
discussion of the geological interpretation of the shorelines and the origin and evolution of the sea
basins will be interesting, but is beyond the scope of the present work.
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Figure 1. A part of the north polar radar mosaic (available at
http://photojournal.jpl.nasa.gov/catalog/PIA17655) with the major seas labeled. Note that Kraken is
divided into two major basins, separated by a narrow barrier which is penetrated by a channel labeled
the Throat of Kraken.
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3. Bathymetry Model and Ocean Volume
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While there are a number of approaches to remotely measure the depth of a surface deposit (notably
nadir-pointed radar sounding that directly detects a subsurface echo, or methods exploiting the
attenuation of an assumed bottom reflector by the liquid column) none of these approaches is likely to
yield a complete survey given the coverage in the planned Cassini mission. To serve as a ‘working
hypothesis’ for modeling studies, and as a benchmark expectation against which future observations
and analysis may be compared, we first consider a hypothetical bathymetry map with a simple assumed
bottom shape, noting the empirical observation (e.g. Lorenz et al., 2008) that terrestrial lakes and seas
tend to have an aspect ratio (depth/diameter) of ~0.001.
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In this model, we simply assume a constant slope away from the shore. This is typical for basins
currently fed by a uniform sediment flux, and has been applied to Ontario Lacus in the south (Hayes et
al, 2010), around which a near-uniform slope was observed. We note that the density contrast
between likely Titan surface solids and liquid is rather modest and thus sedimentation speeds in Titan
seas are rather low (Lunine, 1992; Burr et al., 2006) : thus material introduced at the margins of Titan’s
seas could be transported rather easily. Like a growing sandpile, a uniform slope will tend to form.
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If, following Lorenz et al. (2012) we choose the slope to yield a 300m central depth for Ligeia Mare,
roughly consistent with the empirical rule of thumb (depth/width~0.001) of Lorenz et al. (2008), we find
a maximum depth of ~350m for Kraken, and summing up all the resultant depth values (Figure 2) and
multiplying by the area of a pixel yields a total estimated volume of liquid in the northern hemisphere of
33,000 km3. This is in fact just within, but at the extreme low end, of the liquid volume range estimated
by Lorenz et al. (2008).
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Figure 2. Linear depth Map of Titan’s Seas, using an assumed linear depth vs distance. The deepest
points are in the middle of the Kraken-1 basin, and the middle of Ligeia.
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Clearly, the total volume computed this way is directly proportional to the assumed slope. In fact a neardiametric depth profile of Ligeia Mare has been recently determined from Cassini RADAR altimetry data
by Mastrogiuseppe et al. (2014). We can adjust our simple bathymetry model, and the total ocean
volume, by a simple scaling factor A (i.e. depth/width=0.001*A). Empirically, from the scatter in
terrestrial lakes (Lorenz et al., 2008) with different basin origins, such a factor lies in the range 0.1<A<10,
depending on the geological nature of the seas, with A~0.1 corresponding to shallow sedimentary basins
and A~10 corresponding to tectonic extremes such as Lake Baikal. The maximum depth for Ligeia
measured by Mastrogiuseppe et al. (2014) is 170m, giving A~0.5 for Ligeia specifically. If this applies
everywhere, it follows that the total ocean volume at present is roughly half that indicated above, or
about ~15,000km3. The depth model with A=0.5 is made available as an ASCII array, together with
ancillary latitude/longitude arrays, for the convenience of modelers (see Appendix 1 and supplemental
online information.) The model is straightforward to scale to other values of A, or to transform to other
analytic functions of depth from shore.
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On the other hand, Hayes et al. (2014) have recently made an ocean volume estimate using SAR image
data, with an empirical bottom reflection function and an attenuation of the radar echo with depth (e.g.
Thompson and Squyres, 1990) that is assumed uniform. By implication, this assumes a uniform liquid
composition - an assumption challenged as a function of location later in the present paper; see also
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Tokano, 2009, for discussion of depth structure. Hayes et al. (2014) report a volume of ~70,000km3, a
little over double that that we obtain with our simple linear model A=1.
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Clearly, not all these models can be correct. Most likely the uniform slope is not a correct assumption.
However, the correctness of a uniform attenuation assumption yielding a larger volume is difficult to
assess. In any case, the model presented here serves as a benchmark against which other models can be
tested (e.g. the Hayes et al. result might imply that Kraken is generally deeper than Ligeia for a given
distance from shore, which may be a result of stronger tidal and/or wind-driven currents, or a longer
time for Ligeia to accumulate sediment.)
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It is of note that all the models have a volume at the low end of the predictions in Lorenz et al. (2008)
which allowed for the (at the time poorly-mapped) southern hemisphere to have a liquid inventory
equivalent to that in the north. We now know on the basis of much more complete mapping coverage
(and supported by the paradigm of Titan’s present climate that favors accumulation of liquid in the
northern hemisphere at the expense of the south - e.g. Aharonson et al., 2009; Schneider et al. 2012)
that in fact there is only one (barely) significant body of liquid in the southern hemisphere, Ontario
Lacus, which appears to have a depth of only around 10m, and thus a volume of around ~200km3, or
<1% of the total liquid on Titan.
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4. Basin Architecture : The Throat of Kraken and Terrestrial Analogs
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Of special interest is the connection between the main basins. The river network at the southwestern
corner of Ligeia Mare appears, perhaps, to form a labyrinth of narrow channels that reaches towards
Kraken Mare, as had been suggested by near-infrared observations (Sotin et al., 2012).
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Of particular note in the new data is the narrow strait, which we nickname the ‘throat’, between the
two major basins of Kraken. This strait (at 67oN, 42oE) is 17km wide, and ~40km long. It is broadly
comparable in size with the Straits of Gibraltar on Earth (see later). It is interesting to compare
geomorphology of the strait (Figure 3) with the Aland strait between the Gulf of Bothnia and the Baltic
Sea (Figure 4). Like the Kraken throat, there is a labyrinth of small islands and channels in parallel with
the main strait. These likely have a minimal hydraulic impact, since they are likely shallow, but may be
of interest in understanding the origin and subsequent modification history of the basins.
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Figure 3. Zoomed section of the map showing the throat of Kraken between the two basins (scale bar in
km). The blue speckled areas are where signal to noise is poorer. Note the ~17x40 km clear channel,
and the labyrinth of narrower channels and islands to the west. The inclined stripe towards the right of
the map is an artifact of low signal-to-noise.
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Figure 4. NASA Earth Observatory image of Aland, between Sweden and Finland. Topographically, this
region may be a good analog of the Kraken throat (albeit mirrored east-west). The island of Aland
divides the hydraulic link between the Baltic to the south and the Gulf of Bothnia to the north into two
sections : a clear 40km-wide channel ‘Sea of Aland’ to the west, and a labyrinth of shallow channels
punctuated with islands to the east.
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5. Tidal Currents and Observable Effects
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The Kraken Throat constriction may be significant in modifying the response of Kraken’s liquid to tidal
forces. Tokano (2010) speculated that the constriction (at the time, of unknown width, and indeed
speculative altogether) might lead to the highest tidal currents anywhere in Titan’s seas. The accurate
measurement of the width of this channel in the new radar map now allows these currents to be
investigated in more detail.
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The tidal range of a sea on a deformable planet is diminished by a factor 2 relative to the change in
potential height (i.e. the equilibrium tide) that would be seen on a rigid spherical world. This factor is
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
numbers determining the potential and surface height response of the planet and R() denotes the real
part of a complex quantity. Sohl et al. (1995) suggested 2~0.16 for a model with an internal water-
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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
h2~1.2 (it is comparatively insensitive to ice shell thickness - see Sohl et al., 2003) we might allow 2 as
high as 0.4. We would in any case suggest 2 should be considered a somewhat free parameter
(0.1<2<0.4) in further studies of Titan’s ocean tides.
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Tokano (2010) modeled the tidal response of an idealized Kraken map and found a tidal amplitude Do of
2m (i.e. a tidal range, low tide to high tide, of 4m). This result was obtained assuming a rigid Titan, i.e.
without considering the deformation of Titan’s lithosphere. Given the internal deformation implied by
the Iess et al. (2012) result and thus (0.1<2<0.4), it seems the tidal range D~22Do should be around
~1.6-0.6m.
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Now, the two basins have a characteristic dimension L of the order of 300 km, and so the tidal cycle
represents a migration of a wedge-like volume of liquid of ~0.52DoL2/4 in each half period (i.e. 8 days
or ~6x105 s). This corresponds to ~2140 km3 or ~20-60 km3 in that period, or an average flow of up to
105 m3/s, the bulk of which passes through the throat. Assuming a depth d for a uniform channel width
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
U~0.02-0.6 ms-1.
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The propagation speed of a shallow water wave is (gd)0.5, so a 10m deep channel on Titan (g=1.35ms-2)
would allow speeds of up to 3.7 ms-1, or rather higher than the tidal currents require. Thus a
hydrodynamic shock (i.e. a standing bore) would not form, although if one contrived a channel only a
few meters deep, it perhaps could.
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It is interesting to compare these speeds with tidal races on Earth, the most notable of which are the
Saltstraumen in Norway, the Skookumchuck narrows near Vancouver, Canada (and the nearby
Deception Pass in Washington, USA), and the Corryvreckan off the west coast of Scotland. The former
two are just a few hundred meters across and somewhat shallow, but the Corryvreckan (from the Gaelic
Coire Bhreacain meaning "cauldron of the speckled seas") between the islands of Jura and Scarba is a ~1
km wide strait which sees ~5 ms-1 currents in 30-70 m of water. The turbulent flow in the maelstrom
(generated by the interaction of the tidal flow with the irregular seafloor) generates dynamic
topography (Figure 5) such as whirlpools, and sound which can be heard some 16km away. The
potential for passive acoustic detection (through the atmosphere, or through the liquid - both media
allow transmission of sound - e.g. Leighton and White, 2004; Petculescu and Achi, 2012; Arvelo and
Lorenz, 2013) of such sites of dissipation merits consideration in future exploration of Titan’s seas.
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Figure 5. Although a perfectly calm day, the sea in the Corryvreckan is rough with breaking waves These
result from the energetic tidal flow through the channel. Photo: R. Lorenz
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The dynamically irregular sea surface generated by the tidal flow may have a similar influence to that of
wind-driven waves on remotely-sensed surface roughness. Thus radar reflectivity and sunglint
measurements, already used by Cassini to rule out waves on a number of occasions, may find roughness
near the throat regardless of wind conditions. Unfortunately the present HiSAR data in the throat
region is too insensitive to detect such roughness, but future observations may be directed to this
region. It may be noted that very large wave structures in the Strait of Gibraltar can be detected by
spaceborne radar (figure 6), and, indeed, by sunglint (figure 7).
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These waves have a large wavelength but a small surface height amplitude as they are the surface
expression of internal waves at the boundary between the fresher Atlantic water flowing into the
Mediterranean at the surface, and a deep salty outflow. It is possible to imagine an analogous situation
with methane-rich and ethane-rich liquids on Titan. The waves are generated as a diurnal tidal pulse
flows over the shallow Camarinal Sill at Gibraltar. The waves refract around coastal features and can be
traced for as much as 150 km.
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Figure 6. Synthetic Aperture Radar image of the Strait of Gibraltar acquired in 1995 by the ERS-1
satellite. The rugged land is easily distinguished from the sea, but the sea surface is far from uniform in
radar texture. A pronounced difference in backscatter in the Atlantic and the smooth sheltered
Mediterranean at right is evident, as are a number of narrow dark slicks left in the wake of ships. Also
prominent just to the east of the strait are a set of waves - these are the surface expression of internal
waves set up by tidal flow across a shallow sill in the strait. Image: European Space Agency
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Figure 7. Image (cropped and rotated from Roll: 712 Frame: 29) of the Strait of Gibraltar from the
Space Shuttle mission STS098 in February 2001. Image Science and Analysis Laboratory, NASA-Johnson
Space Center. "The Gateway to Astronaut Photography of Earth." The sea is bright due to a nearspecular reflection geometry of the sun. This geometry permits a packet of waves (arrowed), caused by
the tidal flow across a shallow sill, to be visible in the Mediterranean to the southeast of the strait.
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6. Tidal Dissipation and Orbital Evolution
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Tides have long been of interest (e.g. Sagan and Dermott, 1982) on Titan, in that the present-day orbital
eccentricity of Titan (0.029) is difficult to reconcile with tidal dissipation which would tend to circularize
the orbit. Various aspects of the problem are discussed in Lorenz, 1994; Dermott and Sagan, 1995;
Sears, 1994 and Sohl et al., 1995. It is well-known that much of the tidal dissipation in Earth’s oceans
(which play a major role in the secular increase in the length of the terrestrial day, and the slow
recession of the moon - see e.g. Brosche and Sundermann, 1978) occurs in shallow seas and straits. It is
interesting to consider whether the tidal dissipation associated with the bottom friction in the Kraken
throat specifically could be significant for Titan’s orbital evolution.
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Sohl et al. (1995) found that the dissipation associated with an e-folding timescale for the decay of
Titan’s orbital eccentricity can be expressed roughly as P~A/ , where P is in Watts, A~ 1011 W/Gyr and
is the timescale in Gyr. Dissipation in the interior was modeled as low as ~1010 W for a differentiated
but solid body, or 5-6 times higher for an undifferentiated model or one with an internal ocean. These
models pointed to the difficulty of maintaining Titan’s orbital eccentricity even in the absence of surface
liquids. Global oceans 100 m thick generated dissipation of 2x1010 - 2x1012 W, depending on the interior
structure (which affected 2) with dissipation varying as the inverse cube of depth. Hence oceans of a
few hundred meters or shallower caused dissipation that exceeded that of the interior, and led to
recircularization timescales of less than the age of the solar system.
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A question that now confronts us is whether the Titan that has been revealed to us by Cassini - with
somewhat shallow (and therefore dissipative) seas, but ones that are rather limited in geographical
extent - has significant dissipation. Ultimately, this question should be addressed (as it has been for the
effect of the oceans on the evolution of the Earth-moon system) by numerical models, but an order-ofmagnitude estimate can be made here.
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The dissipation on the seabed is written flU3, where f is a bottom friction coefficient (for a shallow
strait at the relevant Reynolds number, f~0.01 see Sohl et al., 1995 for discussion), l the density of the
liquid (we assume ~500-650 kgm-3, see Lorenz et al., 2010) and U the speed. For U~0.5 m/s, there is
dissipation of the order of 1 Wm-2, comparable with the summertime solar flux on the surface. Over the
17x40 km strait, the total dissipation is ~7x108 W. This may be compared, given tidal currents of ~1
cm/s expected in the bulk of Kraken and Ligeia Mare (Tokano, 2010; Lorenz et al., 2012) with ~6x10-6
W/m2 or about 106 W for all of Titan’s seas put together, a fraction of 1% of the dissipation in the throat.
Thus in the present epoch, while the throat is likely responsible for most of the sea dissipation, the seas
are too limited in extent and too deep to have a significant orbital effect.
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7. Basin Mixing Timescales and Evolution of the Seas
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While topography determines the local shape of the seas, the concentration of Titan’s seas at high
northern latitudes in global terms attests to a climatological ontrol of the distribution of liquids, with the
north presently favored for accumulation of methane rainfall because in the present astronomical
epoch, the rainy season is longer in the north (Schneider et al., 2012). A variation with latitude of
precipitation, as well as of evaporation, might lead to a gradient in Kraken’s composition if the seas are
not well-mixed by tides and wind-driven currents. The latter have not yet been modeled, but mixing by
tides can be estimated.
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Tidal flow through the throat likely dominates the surface exchange of liquid between the two basins
: it seems unlikely that wind-driven circulations will be larger, and subterranean hydraulic connection
will have a very low conductance (Hayes et al., 2008) . Given a tidal cycling of 20-60 km3 of liquid each
Titan day through the throat, and a volume of 6,000~30,000km3 for each basin, a first-order mixing
timescale is 100~1500 Titan days, or ~5 to 70 Earth years. These mixing timescales are short compared
with the period of astronomical variation of the seasons (the Croll-Milankovich cycles) of ~50,000 years,
so long-term geological consequences of the sea composition (notably, the composition of evaporites
left after the seas evaporate) should be somewhat uniform with latitude.
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On the other hand, this mixing timescale is comparable with or longer than a Titan season of ~7
years. Since the supply of methane-rich rainfall to the seas in summer varies with latitude (e.g.
Schneider et al., 2012), we might expect there to be, at some seasons at least, a compositional
difference between the two basins. The magnitude of such compositional differences will need to be
evaluated with numerical models, preferably taking possible stratification (Tokano, 2009) into account.
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These considerations strictly pertain to the present day. There have likely been dramatic changes over
time (e.g. Lunine et al., 1983, 1998; Lorenz et al., 1997) of the total amount of liquid on Titan’s surface,
and its distribution between north and south (Aharonson et al., 2009). The drowned valleys in Ligeia
(e.g. Wasiak et al., 2013) attest to rising base levels in the northern seas. If, for example, the throat is
only 50m deep, and northern sea level were 50m lower, say, 20,000 years ago, the two basins would be
isolated by an isthmus and could have very different compositions. On the other hand, in the more
distant past, if the total methane inventory were larger, a deeper Kraken-Ligeia connection may have
allowed more vigorous transport, and Punga Mare and many of the smaller lakes may also have been
directly connected with Kraken.
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354
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359
We note (as hinted at by Near-infrared observations by Sotin et al. (2012)) that a labyrinth of dark
channels may connect Kraken and Ligeia. Inspection suggests that roughly speaking this labyrinth can
be characterized by 1-2 parallel channels of length ~ 100 km and no more than 10km wide. The blue
appearance in the mosaic (figure 1) indicates a moderate radar brightness, with probable bottom echo
contribution, suggesting they may be shallow. Hence this labyrinth is unlikely to admit a significant flow,
or cause much dissipation, but numerical models should consider a range of effective widths and depths
to evaluate mixing between Kraken and Ligiea.
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8. Conclusions
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365
We have presented a radar map of the northern seas of Titan. Using a simple uniform-slope seabed
model, we estimate a total volume for the seas of ~30,000km3, within roughly a factor of two of other
estimates. The map is made available electronically to facilitate future numerical modeling efforts.
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369
A strait or throat that divides the two major basins of Kraken Mare has been measured at 17km width,
and may be the site of significant tidal currents that could have observable effects, as is the case in
comparable sites on Earth. The tidal dissipation in the present configuration of Titan’s seas, dominated
by this throat, is however too small to be significant in Titan’s orbital evolution.
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374
Tidal mixing between the two basins through the throat is fast compared with the astronomical climate
cycles, but slow compared with the seasons. Thus there may be a compositional distinction between the
two Kraken basins. The hydraulic connection between Ligeia and Kraken is more tenuous, and thus a
composition difference is likely. We note that a modest drop in past sea level could isolate the major
basins from each other completely.
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Acknowledgements
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R.L. acknowledges the support of the NASA Outer Planets Research program via grant “Physical
Processes in Titan's Seas” NNX13AK97G, as well as via Cassini project grant “Cassini Radar Science
Support” NNX13AH14G. The Cassini/Huygens mission is a joint endeavor of NASA and ESA, as well as
several European national agencies and is managed for NASA by the California Institute of Technology’s
Jet Propulsion Laboratory. We acknowledge stimulating discussions with the Cassini radar team.
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Appendix 1. Map file
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The bathymetry map (Supplemental Online File: see also
http://www.lpl.arizona.edu/~rlorenz/titansea.html) is an array of integers, 325 rows by 270 columns,
with the value corresponding to estimated depth in meters. The (x,y) coordinates (0<=x<325, 0<=y<275)
for a location at latitude (LAT) and longitude (LON) are given approximately by the transformations
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x = Xc + S*[cos(LAT)*cos(LON)]
y = Yc + S*[cos(LAT)*sin(LON)]
with parameters S=-495, Xc=232, Yc=245. Because there is some distortion in the map projection, these
data should not be used for data correlation studies - the original mosaic (figure 1) or better yet, the raw
radar images archived on the NASA Planetary Data System (PDS) should be used.
The file here is generated with the assumption of A=0.5, thus the Ligeia central depth is ~170m and the
greatest depth overall in Kraken is 197m. The array can simply be scaled (or indeed transformed to some
other function such as depth proportional to square root of distance from shore) as desired.
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