- Email: [email protected]
Timescale for oceans in the past of Titan
Planetary and Space Science 78 (2013) 22–24
Contents lists available at SciVerse ScienceDirect
Planetary and Space Science journal homepage: www.elsevier.com/locate/pss
Timescale for oceans in the past of Titan Richard Larsson a,n, Christopher P. McKay b a b
Department of Computer Science, Electrical and Space Engineering, Lule˚ a University of Technology, Space Campus 1, SE-98128 Kiruna, Sweden NASA Ames Research Center, Division of Space Sciences and Astrobiology, Mail Stop 245-3, Moffett Field, CA 94035, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 February 2012 Received in revised form 7 December 2012 Accepted 7 December 2012 Available online 22 December 2012
We estimate the past extent of liquid on the surface of Titan as a function of time assuming the current rate of destruction of methane and no sources or subsurface sinks. As methane increases for increasing past time the polar lakes expand equatorward. We use a spherical harmonics model for the surface topography to compute the fraction of the surface covered as the methane inventory increases. We find that substantial parts of the equator would have been flooded by a polar ocean 300 million years ago and that the equator would have been connected to a global ocean 600 million years ago. This provides one possible explanation for the fluvial features seen at the equator on Titan. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Titan Surface Methane ocean Planetary evolution
1. Introduction Methane is the second most abundant constituent in Titan’s atmosphere with a concentration of 1.5% in the upper atmosphere to 4.5% at the surface near the equator (Niemann et al., 2005, 2010). There are also lakes of methane on the surface, but more is in the atmosphere than on the surface. The lakes have 200–2000 kg/m2 of column mass of organics and the atmosphere contains 4000 kg/m2 column mass of methane relative to the surface (Lorenz et al., 2008). Methane is destroyed by photochemistry, and due to the loss of H to space there is an irreversible conversion of methane to organic molecules with a higher C/H ratio, such as ethane and organic tholin. The rate is best estimated from the loss of H2 to space (with a loss flux rate of about 1010 cm2 s1 , Cui et al., 2008), giving a timescale for the loss of the entire estimated atmospheric and surface reservoir on Titan of 100 million years. To date there is no clear evidence of a source of methane, such as cryovolcanism. Without a source, Titan will lose its atmospheric methane in a time short compared to a geologic timescale. In addition, in the geological past Titan would have had many times more methane than the present inventory. Presumably this additional methane would have accumulated in surface reservoirs. Today, lakes are present in the polar regions (Stofan et al., 2007; Hayes et al., 2011) and there might be lakes in the equatorial region (Griffith et al., 2012), although these are not confirmed. A curious feature of Titan is the evidence of shorelines and fluvial features in the equatorial region (e.g., Moore and n
Corresponding author. Tel.: þ4672 222 55 16. E-mail address: [email protected] (R. Larsson).
0032-0633/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.pss.2012.12.001
Howard, 2010). Presently, storms seem unable to bring enough liquid from the polar lakes to the equator to explain this, as models of storm formation (Barth and Rafkin, 2007) requires a relative humidity of methane of 65% whereas the measured RH is 45% (Niemann et al., 2005). The extensive cloud events seen at the equator such as those reported by Schaller et al. (2009) are not necessarily associated with rain at the surface. Turtle et al. (2011) reported on direct observations of surface darkening over large areas of the equatorial region after the passage of clouds. They concluded that ‘‘the darkening is caused merely by surface wetting’’. This is perhaps consistent with the drizzle postulated for the Huygens landing site (Tokano et al., 2006). If so, these events seem to only be able to create occasional moist surfaces (Niemann et al., 2005; Lorenz et al., 2006; Williams et al., 2012). If present equatorial rain events are not adequate to form channels, this suggests that there was once sufficiently standing liquid on the equator to raise the RH to at least 65%, allowing stormy weather. Recently, Schneider et al. (2012) have developed a global circulation model that predicts strong precipitation at the equator even with present climate. This is in contrast with previous work but does in principle provide a way to create the equatorial channels without extensive liquid at low latitudes. However, this model makes many simplifying assumptions. For example the treatment of solar radiation is monochromatic. This is particularly problematic for predicting precipitation because, as the authors note, precipitation depends on the moist static energy which ‘‘only net radiation at the top of the atmosphere drives the vertically integrated MSE balance’’. We feel that while the Schneider et al. (2012) results open up an important alternative it is premature to dismiss previous work which indicates that heavy rain storms at the equator at present are not possible.
R. Larsson, C.P. McKay / Planetary and Space Science 78 (2013) 22–24
Sotin et al., (2012) recently suggested that a model for Titan’s history involving an outburst of methane a few hundred million years ago followed by the loss methane. They pointed out that this would be consistent with both the present observations of lakes and haze accumulations on the surface and recent measurements of isotopic ratios in atmospheric methane. Several authors have considered hypothetical hydrocarbon oceans before this work (e.g., Sagan and Dermott, 1982; Lunine et al., 1983; Dubouloz et al., 1989; Sears, 1995), partly to stabilize the atmosphere against loss of methane by photolysis. This work does not consider the methane reservoir on Titan as long term stable. Instead in this paper we will calculate how long ago, given the current loss fluxes and no sources, there was enough methane such that substantial parts of the equator of Titan could be connected to a polar ocean and global ocean. We assume that at least one of the polar regions must be connected to the equator since an isolated equatorial sea would have a rate of evaporation that is larger than its rate of condensation. Essentially, the polar region condensation and the subsequent flow back of liquid to the equator is necessary to maintain an equatorial sea.
23
where the results will be presented for column mass slake ¼ 200 and 2000 kg/m2. The atmospheric partial pressure of methane is assumed constant over time. This may introduce a slight error as when the atmospheric humidity increases the amount of methane in the atmosphere will also increase. If the equatorial humidity increases from 45% to 65% the atmosphere would be able to hold 1.4 times its present level or roughly 50 Myrs of production. By using spherical harmonics it is also possible to estimate what global coverage means for good equatorial coverage. The model used to estimate the coverage at the equator assumes that the polar oceans must be connected to the equator. As such, two cases are of interest. The first is when the lowest amount of liquid at one polar ocean exceeds a level such that one of the basins of the equator is flooded. The second case is when there is such an extent of methane that the liquid can flow freely between the poles. In all cases, we have neglected any loss of methane to subsurface reservoirs. The nature of the subsurface on Titan is unknown and may be impermeable or it may be that the present lakes are indicative of subsurface reservoirs that are already full. If the subsurface can absorb liquid methane then the timescales computed here are lower limits.
2. Method 3. Results and discussion There is a continuous destruction of CH4 in the atmosphere of Titan due to UV radiation (see, e.g., Yung et al., 1984; Wilson and Atreya, 2009). The rate at which the total atmosphere and surface inventory of liquid is depleted depends on the loss rate of H2 and the relative production of other liquids, principally C2H6. Assuming pure CH4 lakes then the timescale to deplete the present inventory (or double it going backward in time) is between 100 and 143 million years covering the range of estimate for the total inventory mentioned above. In the other extreme, with CH4 converted to C2H6, the doubling time is about 95 million years. The rate of loss relative to a 2575 km sphere is vCH4 ¼
F H2 C m þ 4Hm , 2 rCH4
ð1Þ
where F H2 is the loss flux of H2 (Cui et al., 2008), Cm þ 4Hm represents the average weight of a single methane molecule (as derived from Niemann et al., 2005 12C/13C and D/H ratios) and rCH4 is the density of methane (see Tokano, 2005). Given this we see that vCH4 0:1 m3 =m2 per million year (i.e., 10 cm of column volume loss per million year related to the surface).
The fraction of the surface of Titan that is covered by liquid is shown in Fig. 1 as a function of time assuming that the only change is a constant rate of increase in the surface inventory of methane going backwards in time. Clearly for extrapolations beyond approaching a billion years this restrictive assumption will not apply due to changes in the solar constant, changes in the rate of methane destruction, and changes in the landscape on Titan. Hence, the fraction covered by liquid should be considered just a rough estimate for these longer times. At the present epoch the model matches the observed areal coverage of lakes on Titan at about 3%. The fraction of the surface covered by liquid increases rapidly with times past and at about 1 Gyrs ago 50% of the surface is covered. With increasing time (total methane content) the fraction of the surface covered continues to increase but the rate of increase slows. We find that about 25% global coverage is necessary for the southern polar ocean to flood the equator, as can be seen in Fig. 2a. This coverage corresponds to a time period of 300 million 1 0.9
2.1. Ocean coverage
0.8
Using the hypsometry found by Lorenz et al. (2011) and the seventh order spherical harmonics fit by Zebker et al. (2009) combined with the geoid of Fig. 1 of Iess et al. (2012), it is possible to calculate the global column volume necessary to cover a given percentage of the surface by P P HI Ii ¼ 1 ðAi Þ Ii ¼ 1 ðHi Ai Þ P1 VI ¼ , ð2Þ i ¼ 1 Ai where the height vector H contains the height elements, the vector A contains the area represented by each element of the height vector and the produced column volume vector V is in units of m3 per m2. Note that the surface coverage in this case is PI P1 i ¼ 1 ðAi Þ= i ¼ 1 Ai . Taking the present reservoir of methane and the speed of loss into account it is possible to convert column volume into past time as t¼
V rCH4 slake , rCH4 vCH4
ð3Þ
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
4000
3500
3000
2500
2000
1500
1000
500
0
Fig. 1. Time versus liquid coverage of Titan. The hypsometry was adopted from Lorenz et al. (2011). Values of slake represents the limits of present amount of liquids in column mass as per Lorenz et al. (2008). This plot is representing Eq. (3). The time at which the equator is connected to the polar caps, 25% coverage, and the time at which a global ocean is formed, 35% coverage, are indicated.
24
R. Larsson, C.P. McKay / Planetary and Space Science 78 (2013) 22–24
Fig. 2. Distribution of liquid coverage of Titan for 25% and 35% areal coverage. Coverage, shown in black, of 25% overflows the south pole and connects the polar ocean to the equator. As we increase coverage to 35%, the polar oceans are connected to form a global ocean. The spherical harmonics was adopted using the results from Zebker et al. (2009) with values altered by the geoid of Iess et al. (2012).
years ago. We also find that a global coverage of about 35% results in the polar oceans being fully connected to a global ocean, as can be seen in Fig. 2b. This coverage, in turn, corresponds to a time period of 600 million years ago. These timescales are upper limits in the sense that channels and other small scale features are not included in the spherical harmonics nor detailed in the topographical data of Titan, due to limited detailed measurements. It might also be of interest to note that approximately 20% coverage (or 200 Myrs) is necessary for the polar ocean to reach both Hotei Regio and Tui Regio. The landing site of Huygens is not reached by a global ocean within a timescale of 1 Gyrs. In this paper we have not presented direct evidence for a past global ocean on Titan. Instead we suggest that this is a logical consequence of the apparent lack of sources of methane and a persistent loss mechanism. Thus, going backward in time the amount of methane on Titan must increase in time and the surface reservoirs (and subsurface reservoirs if any) must become larger. Extrapolate far enough back in time and the equatorial regions of Titan would be flooded on timescales of a few hundred million years. These results are not inconsistent with models for past climate on Titan (e.g., Lorenz et al., 1999; Lunine and Rizk, 1989; McKay et al., 1993).
4. Conclusions Given no sources of methane and assuming the present loss rate of methane from the atmosphere, we conclude that the equator of Titan may have been flooded by liquid in the past on a timescale of a few hundred million years. We find that substantial parts of the equator would have been flooded by a polar ocean on a timescale of 300 million years and that the equator would have been connected to a global ocean on a timescale of 600 million years. The increased relative humidity of methane at the equator would allow storms to shape the surface more readily. Thus, an equatorial sea provides one possible explanation for the fluvial features and shoreline seen near the equator on Titan. Even further back in time, even larger parts of the equatorial region would have been covered by methane. By accepting this model, we speculate that the features observed by Moore and Howard (2010) as fluvial features was formed some 200–300 million years ago when the low latitude RH was higher. Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version of http://dx.doi.org/10.1016/j.pss.2012.12.001.
References Barth, E.L., Rafkin, S.C.R., 2007. TRAMS: A new dynamic cloud model for Titan’s methane clouds. Geophysical Research Letters 34, L03203. Cui, J., et al., 2008. Distribution and escape of molecular hydrogen in Titan’s thermosphere and exosphere. Journal of Geophysical Research 113, E10004. Dubouloz, N., et al., 1989. Titan’s hypothesized ocean properties: the influence of surface temperature and atmospheric composition uncertainties. Icarus 82, 81. Griffith, C.A., et al., 2012. Possible tropical lakes on Titan from observations of dark terrain. Nature 486, 237. Hayes, A.G., et al., 2011. Transient surface liquid in Titan’s polar regions from Cassini. Icarus 211, 655. Iess, L., et al., 2012. The tides of Titan. Science 337, 457. Lorenz, R.D., McKay, C.P., Lunine, J.I., 1999. Analytic investigation of climate stability on Titan: sensitivity to volatile inventory. Planetary and Space Science 47, 1503. Lorenz, R.D., et al., 2006. Titan’s damp surface: constraints on titan surface thermal properties from the temperature evolution of the Huygens GCMS inlet. Meteoritics & Planetary Science 41, 1405. Lorenz, R.D., et al., 2008. Titan’s inventory of organic surface materials. Geophysical Research Letters 35, L02206. Lorenz, R.D., et al., 2011. Hypsometry of Titan. Icarus 211, 699. Lunine, J.I., Stevenson, D.J., Yung, Y.L., 1983. Ethane ocean on Titan. Science 222, 1229. Lunine, J.I., Rizk, B., 1989. Thermal evolution of Titan’s atmosphere. Icarus 80, 370. McKay, C.P., et al., 1993. Coupled atmosphere-ocean models of Titan’s past. Icarus 102, 88. Moore, J.M., Howard, A.D., 2010. Are the basins of Titan’s Hotei Regio and Tui Regio sites of former low latitude seas? Geophysical Research Letters 37, L22205. Niemann, H.B., et al., 2005. The abundances of constituents of Titan’s atmosphere from the GCMS instrument on the Huygens probe. Nature 438, 779. Niemann, H.B., et al., 2010. Composition of Titan’s lower atmosphere and simple surface volatiles as measured by the cassini-huygens probe gas chromatograph mass spectrometer experiment. Journal of Geophysical Research 115, E12006. Sagan, C., Dermott, S.F., 1982. The tide in the seas of Titan. Nature 300, 731. Schaller, E.L., et al., 2009. Storms in the tropics of Titan. Nature 460, 873. Schneider, T., et al., 2012. Polar methane accumulation and rainstorms on Titan from simulations of the methane cycle. Nature 481, 58. Sears, W.D., 1995. Tidal dissipation in oceans on Titan. Icarus 113, 39. Sotin, C., et al., 2012. Observations of Titan’s Northern lakes at 5mm: Implications for the organic cycle and geology. Icarus 221, 768. Stofan, E.R., et al., 2007. The lakes of Titan. Nature 445, 61. Tokano, T., 2005. Meteorological assessment of the surface temperatures on Titan: constraints on the surface type. Icarus 173, 222. Tokano, T., et al., 2006. Methane drizzle on Titan. Nature 442, 432. Turtle, E.P., et al., 2011. Rapid and extensive surface changes near Titan’s equator: evidence of April showers. Science 331, 1414. Williams, K.E., McKay, C.P., Persson, F., 2012. The surface energy balance at the Huygens landing site and the moist surface conditions on Titan. Planetary and Space Science 60, 376. Wilson, E.H., Atreya, S.K., 2009. Titan’s carbon budget and the case of the missing ethane. Journal of Physical Chemistry A 113, 11221. Yung, Y.L., Allen, M., Pinto, J.P., 1984. Photochemistry of the atmosphere of Titan: comparison between model and observations. Astrophysical Journal Supplement 55, 465. Zebker, H.A., et al., 2009. Size and shape of Saturn’s Moon Titan. Science 324, 921.
Contents lists available at SciVerse ScienceDirect
Planetary and Space Science journal homepage: www.elsevier.com/locate/pss
Timescale for oceans in the past of Titan Richard Larsson a,n, Christopher P. McKay b a b
Department of Computer Science, Electrical and Space Engineering, Lule˚ a University of Technology, Space Campus 1, SE-98128 Kiruna, Sweden NASA Ames Research Center, Division of Space Sciences and Astrobiology, Mail Stop 245-3, Moffett Field, CA 94035, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 February 2012 Received in revised form 7 December 2012 Accepted 7 December 2012 Available online 22 December 2012
We estimate the past extent of liquid on the surface of Titan as a function of time assuming the current rate of destruction of methane and no sources or subsurface sinks. As methane increases for increasing past time the polar lakes expand equatorward. We use a spherical harmonics model for the surface topography to compute the fraction of the surface covered as the methane inventory increases. We find that substantial parts of the equator would have been flooded by a polar ocean 300 million years ago and that the equator would have been connected to a global ocean 600 million years ago. This provides one possible explanation for the fluvial features seen at the equator on Titan. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Titan Surface Methane ocean Planetary evolution
1. Introduction Methane is the second most abundant constituent in Titan’s atmosphere with a concentration of 1.5% in the upper atmosphere to 4.5% at the surface near the equator (Niemann et al., 2005, 2010). There are also lakes of methane on the surface, but more is in the atmosphere than on the surface. The lakes have 200–2000 kg/m2 of column mass of organics and the atmosphere contains 4000 kg/m2 column mass of methane relative to the surface (Lorenz et al., 2008). Methane is destroyed by photochemistry, and due to the loss of H to space there is an irreversible conversion of methane to organic molecules with a higher C/H ratio, such as ethane and organic tholin. The rate is best estimated from the loss of H2 to space (with a loss flux rate of about 1010 cm2 s1 , Cui et al., 2008), giving a timescale for the loss of the entire estimated atmospheric and surface reservoir on Titan of 100 million years. To date there is no clear evidence of a source of methane, such as cryovolcanism. Without a source, Titan will lose its atmospheric methane in a time short compared to a geologic timescale. In addition, in the geological past Titan would have had many times more methane than the present inventory. Presumably this additional methane would have accumulated in surface reservoirs. Today, lakes are present in the polar regions (Stofan et al., 2007; Hayes et al., 2011) and there might be lakes in the equatorial region (Griffith et al., 2012), although these are not confirmed. A curious feature of Titan is the evidence of shorelines and fluvial features in the equatorial region (e.g., Moore and n
Corresponding author. Tel.: þ4672 222 55 16. E-mail address: [email protected] (R. Larsson).
0032-0633/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.pss.2012.12.001
Howard, 2010). Presently, storms seem unable to bring enough liquid from the polar lakes to the equator to explain this, as models of storm formation (Barth and Rafkin, 2007) requires a relative humidity of methane of 65% whereas the measured RH is 45% (Niemann et al., 2005). The extensive cloud events seen at the equator such as those reported by Schaller et al. (2009) are not necessarily associated with rain at the surface. Turtle et al. (2011) reported on direct observations of surface darkening over large areas of the equatorial region after the passage of clouds. They concluded that ‘‘the darkening is caused merely by surface wetting’’. This is perhaps consistent with the drizzle postulated for the Huygens landing site (Tokano et al., 2006). If so, these events seem to only be able to create occasional moist surfaces (Niemann et al., 2005; Lorenz et al., 2006; Williams et al., 2012). If present equatorial rain events are not adequate to form channels, this suggests that there was once sufficiently standing liquid on the equator to raise the RH to at least 65%, allowing stormy weather. Recently, Schneider et al. (2012) have developed a global circulation model that predicts strong precipitation at the equator even with present climate. This is in contrast with previous work but does in principle provide a way to create the equatorial channels without extensive liquid at low latitudes. However, this model makes many simplifying assumptions. For example the treatment of solar radiation is monochromatic. This is particularly problematic for predicting precipitation because, as the authors note, precipitation depends on the moist static energy which ‘‘only net radiation at the top of the atmosphere drives the vertically integrated MSE balance’’. We feel that while the Schneider et al. (2012) results open up an important alternative it is premature to dismiss previous work which indicates that heavy rain storms at the equator at present are not possible.
R. Larsson, C.P. McKay / Planetary and Space Science 78 (2013) 22–24
Sotin et al., (2012) recently suggested that a model for Titan’s history involving an outburst of methane a few hundred million years ago followed by the loss methane. They pointed out that this would be consistent with both the present observations of lakes and haze accumulations on the surface and recent measurements of isotopic ratios in atmospheric methane. Several authors have considered hypothetical hydrocarbon oceans before this work (e.g., Sagan and Dermott, 1982; Lunine et al., 1983; Dubouloz et al., 1989; Sears, 1995), partly to stabilize the atmosphere against loss of methane by photolysis. This work does not consider the methane reservoir on Titan as long term stable. Instead in this paper we will calculate how long ago, given the current loss fluxes and no sources, there was enough methane such that substantial parts of the equator of Titan could be connected to a polar ocean and global ocean. We assume that at least one of the polar regions must be connected to the equator since an isolated equatorial sea would have a rate of evaporation that is larger than its rate of condensation. Essentially, the polar region condensation and the subsequent flow back of liquid to the equator is necessary to maintain an equatorial sea.
23
where the results will be presented for column mass slake ¼ 200 and 2000 kg/m2. The atmospheric partial pressure of methane is assumed constant over time. This may introduce a slight error as when the atmospheric humidity increases the amount of methane in the atmosphere will also increase. If the equatorial humidity increases from 45% to 65% the atmosphere would be able to hold 1.4 times its present level or roughly 50 Myrs of production. By using spherical harmonics it is also possible to estimate what global coverage means for good equatorial coverage. The model used to estimate the coverage at the equator assumes that the polar oceans must be connected to the equator. As such, two cases are of interest. The first is when the lowest amount of liquid at one polar ocean exceeds a level such that one of the basins of the equator is flooded. The second case is when there is such an extent of methane that the liquid can flow freely between the poles. In all cases, we have neglected any loss of methane to subsurface reservoirs. The nature of the subsurface on Titan is unknown and may be impermeable or it may be that the present lakes are indicative of subsurface reservoirs that are already full. If the subsurface can absorb liquid methane then the timescales computed here are lower limits.
2. Method 3. Results and discussion There is a continuous destruction of CH4 in the atmosphere of Titan due to UV radiation (see, e.g., Yung et al., 1984; Wilson and Atreya, 2009). The rate at which the total atmosphere and surface inventory of liquid is depleted depends on the loss rate of H2 and the relative production of other liquids, principally C2H6. Assuming pure CH4 lakes then the timescale to deplete the present inventory (or double it going backward in time) is between 100 and 143 million years covering the range of estimate for the total inventory mentioned above. In the other extreme, with CH4 converted to C2H6, the doubling time is about 95 million years. The rate of loss relative to a 2575 km sphere is vCH4 ¼
F H2 C m þ 4Hm , 2 rCH4
ð1Þ
where F H2 is the loss flux of H2 (Cui et al., 2008), Cm þ 4Hm represents the average weight of a single methane molecule (as derived from Niemann et al., 2005 12C/13C and D/H ratios) and rCH4 is the density of methane (see Tokano, 2005). Given this we see that vCH4 0:1 m3 =m2 per million year (i.e., 10 cm of column volume loss per million year related to the surface).
The fraction of the surface of Titan that is covered by liquid is shown in Fig. 1 as a function of time assuming that the only change is a constant rate of increase in the surface inventory of methane going backwards in time. Clearly for extrapolations beyond approaching a billion years this restrictive assumption will not apply due to changes in the solar constant, changes in the rate of methane destruction, and changes in the landscape on Titan. Hence, the fraction covered by liquid should be considered just a rough estimate for these longer times. At the present epoch the model matches the observed areal coverage of lakes on Titan at about 3%. The fraction of the surface covered by liquid increases rapidly with times past and at about 1 Gyrs ago 50% of the surface is covered. With increasing time (total methane content) the fraction of the surface covered continues to increase but the rate of increase slows. We find that about 25% global coverage is necessary for the southern polar ocean to flood the equator, as can be seen in Fig. 2a. This coverage corresponds to a time period of 300 million 1 0.9
2.1. Ocean coverage
0.8
Using the hypsometry found by Lorenz et al. (2011) and the seventh order spherical harmonics fit by Zebker et al. (2009) combined with the geoid of Fig. 1 of Iess et al. (2012), it is possible to calculate the global column volume necessary to cover a given percentage of the surface by P P HI Ii ¼ 1 ðAi Þ Ii ¼ 1 ðHi Ai Þ P1 VI ¼ , ð2Þ i ¼ 1 Ai where the height vector H contains the height elements, the vector A contains the area represented by each element of the height vector and the produced column volume vector V is in units of m3 per m2. Note that the surface coverage in this case is PI P1 i ¼ 1 ðAi Þ= i ¼ 1 Ai . Taking the present reservoir of methane and the speed of loss into account it is possible to convert column volume into past time as t¼
V rCH4 slake , rCH4 vCH4
ð3Þ
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
4000
3500
3000
2500
2000
1500
1000
500
0
Fig. 1. Time versus liquid coverage of Titan. The hypsometry was adopted from Lorenz et al. (2011). Values of slake represents the limits of present amount of liquids in column mass as per Lorenz et al. (2008). This plot is representing Eq. (3). The time at which the equator is connected to the polar caps, 25% coverage, and the time at which a global ocean is formed, 35% coverage, are indicated.
24
R. Larsson, C.P. McKay / Planetary and Space Science 78 (2013) 22–24
Fig. 2. Distribution of liquid coverage of Titan for 25% and 35% areal coverage. Coverage, shown in black, of 25% overflows the south pole and connects the polar ocean to the equator. As we increase coverage to 35%, the polar oceans are connected to form a global ocean. The spherical harmonics was adopted using the results from Zebker et al. (2009) with values altered by the geoid of Iess et al. (2012).
years ago. We also find that a global coverage of about 35% results in the polar oceans being fully connected to a global ocean, as can be seen in Fig. 2b. This coverage, in turn, corresponds to a time period of 600 million years ago. These timescales are upper limits in the sense that channels and other small scale features are not included in the spherical harmonics nor detailed in the topographical data of Titan, due to limited detailed measurements. It might also be of interest to note that approximately 20% coverage (or 200 Myrs) is necessary for the polar ocean to reach both Hotei Regio and Tui Regio. The landing site of Huygens is not reached by a global ocean within a timescale of 1 Gyrs. In this paper we have not presented direct evidence for a past global ocean on Titan. Instead we suggest that this is a logical consequence of the apparent lack of sources of methane and a persistent loss mechanism. Thus, going backward in time the amount of methane on Titan must increase in time and the surface reservoirs (and subsurface reservoirs if any) must become larger. Extrapolate far enough back in time and the equatorial regions of Titan would be flooded on timescales of a few hundred million years. These results are not inconsistent with models for past climate on Titan (e.g., Lorenz et al., 1999; Lunine and Rizk, 1989; McKay et al., 1993).
4. Conclusions Given no sources of methane and assuming the present loss rate of methane from the atmosphere, we conclude that the equator of Titan may have been flooded by liquid in the past on a timescale of a few hundred million years. We find that substantial parts of the equator would have been flooded by a polar ocean on a timescale of 300 million years and that the equator would have been connected to a global ocean on a timescale of 600 million years. The increased relative humidity of methane at the equator would allow storms to shape the surface more readily. Thus, an equatorial sea provides one possible explanation for the fluvial features and shoreline seen near the equator on Titan. Even further back in time, even larger parts of the equatorial region would have been covered by methane. By accepting this model, we speculate that the features observed by Moore and Howard (2010) as fluvial features was formed some 200–300 million years ago when the low latitude RH was higher. Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version of http://dx.doi.org/10.1016/j.pss.2012.12.001.
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