Summary.

1. Martian impact crater lakes: geophysical modeling and connections to the hunt for life on Mars. Andrew N. Hock1, William B. Moore1, Nathalie A. Cabrol2, and Edmond A. Grin2 1Department of Earth and Space Sciences, IGPP Center for Astrobiology, University of California, Los Angeles, Los Angeles, CA 90024 Email: ahock@ucla.edu 2 Space Science Division, SETI Institute/NASA Ames Research Center, MS 245-3, Moffett Field, CA 94035-1000 Results. Summary. Life as we understand it is dependent on a source of liquid water, energy, and nutrients. In cases where sunlight is not available, or the surface environment proves inhospitable—such as the situation for present-day Mars—thermal activity and hydrothermal systems can supply energy to subsurface environments (Newsom 1980). Sources of hydrothermal energy can originate from both recent volcanic activity (Hartmann et al. 2000) and large impact craters (Newsom 1980, Newsom et al. 1996, Cabrol and Grin 1999, 2001). Impact crater lakes, though they represent a discontinuous source of heat, may have been one of the few environments on Mars where liquid water, energy, and a source of nutrients existed concurrently. Therefore, characterizing the lifetime of crater lakes (and associated hydrothermal circulation) is vital to understanding the constraints placed on any biological system that may have existed there. Here, we present a model that builds on previous work studying the contribution and lifetime of different heat sources (e.g. Onorato et al. 1978, Newsom et al. 1996, Daubar and Kring 2001) that includes the effects of hydrothermal circulation and latent heat from impact melt solidification. Using two basic models that differ only by a constant flux boundary condition, we show melt sheet cooling lifetimes on the order of 103 - 106 years for craters ranging in size from 50-200 km. As it is modeled here, the flux boundary condition impeded cooling in some cases, and in the future will require numerical treatment. Though we have not yet included geothermal heating terms (primarily from the crater central peak), their inclusion would likely have increased the cooling timescale by a factor of two (Thorsos et al. 2001). • Some Highlighted Results. • Total cooling times are not significantly different between models; additionally the determination of melt volume is a significant discrepancy between similar models. • The treatment of the flux boundary condition here is not sufficient: in many cases, the power series solution to the flux dependent model had to be reduced to linear terms in order to avoid singularities • an alternative [numerical] solution should be devised. This led to errors of order t2 in the position of the solidification boundary, and y2 in temperature. • In both models, results show that the impact melt from large craters may take 105-106 years to cool. • If, as Thorsos et al. 2001 posit, the heat provided by the central uplift in large craters is of the same order of magnitude as that of the impact melt, the times presented here may literally be only half of the story. • Combining the lines of logic that a) remnant heat from the impacts such as Gusev crater may have powered extensive hydrothermal systems and took on the order of 1 My to cool, b) the suggested water shed for Ma’adim Vallis and Gusev was likely subject to long periods of hydrologic activity concurrent with impact cratering (Irwin 2002), and c) new bathymetric and morphologic evidence strengthen the case that Gusev once contained a lake (Grin et al. 2002) leads one to the conclusion that great biologic potential once existed in environments like these, and that we must target current missions to investigate lacustrine environments on Mars, or develop the necessary technology to enable future missions to do so. • More accurate models of crater lake cooling and continued characterization of analagous terrestrial environments (including endemic biology) will result in refined hypotheses and a better understanding of the environmental constraints placed on any Table 1. Composite cooling times determined by the two models presented here. Each model was used to calculate the total cooling time as the sum of the solidification time from stage 1 (column 2, above) and the stage 2 cooling time to 20% of the initial temperature, or roughly 420 K. In the first column, the s) and f) indicate which model was used to calculate the results. f) indicates the model with the “Flux” boundary condition. Figure 4. Melt thickness as a function of crater diameter.Here, the melt is assumed to remain within the remnant crater, and the depth is calculated assuming a cylindrical volume. All values are estimated for a chondritic impactor on Mars with 10km/s incident velocity. For example, Gusev crater would (at D~150 km) have had a melt sheet ~3km thick. …Background. Hydrothermal systems associated with volcanism on Earth and Mars (Farmer 1996) are particularly interesting because they are likely sites for the early evolution of life (Shock 1996). Much of the terrestrial work on hydrothermal systems has concentrated on those heated by active volcanism (see Figure 1); however, large impacts can also generate hydrothermal systems. It is well accepted that if impact crater lakes formed on Mars, they would have represented a niche of very high biological potential, providing liquid water, energy, and shelter from harmful radiation. However, the cooling timescale (here considered as the putative timescale of habitability) for the crater lake environment remains uncertain. Previous work by Daubar and Kring (2001) has shown that melt sheet cooling plus the cooling of the uplifted geothermal gradient from a crater’s central peak can power hydrothermal systems for 104-105 years in a 100-km crater, and up to 106 years in a 180 km crater. Additionally, Thorsos et al. (2001) determined that the central uplift in complex craters may provide just as much energy to drive hydrothermal systems as the heat from impact melting. However, the relative effect of latent heat of solidification and hydrothermal flux on a cooling impact has not been directly investigated. The goal of this study is to discern the effect such boundary conditions have on the timescale of impact melt cooling in order to better understand the biological potential of heated paleolakes on Mars. Future Work. The crucial next step in this work is the development of a numerical model that takes in to account heating by the uplifted geothermal gradient at the central peak, and includes time- and temperature-dependent surface flux terms. Though the analytical solutions presented above are fairly good at describing the effects of melt crystallization and prescribed surface heat flux, the “real-world” problem (Figure 10)is much too complex, and lends itself to numerical modeling. I also hope to determine more realistic conditions for the model by conducting field study of selected terrestrial analogs. The basis of the proposed fieldwork is that characterization of the physical processes that govern cooling and hydrothermal circulation at terrestrial heated lakes will lead to a better conception of what the paleolake environment may have once been on Mars. Factors such as sealing time, circulation depth, sediment porosity, etc. that affect hydrothermal flux, for example, are not well-constrained, and should be included in a complete model. Results of the fully three-dimensional version of the preliminary model will be applied to better direct future astrobiological exploration of Mars. Two of the high priority landing sites identified by the most recent 2003 Mars Exploration Rover (MER) landing site selection process are associated with impact crater basins (Gusev Crater and Isidis Planitia). Additionally, as landing ellipses continue to shrink (hopefully to ~10 km for 2007 or 2009), future landed missions will be better equipped to target areas such as impact crater lakes (Figure 11), where hydrologic and thermal activity may have been contemporary. Figure 1. This is a view of the caldera lake atop El Chichon volcano, Mexico; formed in 1982, it is a few hundred meters deep and about a kilometer wide. Lake waters are acidic and hypersaline—environments such as this may serve as terrestrial analogues for heated lakes on Mars. Figure 5. [Stage 1 Cooling] Comparison of the solidification boundary location ym(t) for the two scenarios presented in Figs 1 and 2. The blue line indicates the motion of the solidification boundary from the similarity solution of Turcotte and Schubert (1982), while the red traces are derived from the power series solution. The dotted red line is the solution if the surface flux, F=1 W/m^2. Note the drastic increase in solidification speed in the dashed line as F is set to 20 W/m^2. The Models. Analytic solutions to the one-dimensional, time-dependent heat equation were developed and applied to the case of impact melt sheet cooling. Two scenarios, differing by the boundary conditions alone, were investigated. The first case (Figure 2) is a form of the well-known Stefan problem, wherein latent heat of solidification is included as a heating term at the moving boundary between a liquid and solid phase; it is likened to the physical situation of lava lake solidification. The second case (Figure 3) also includes the latent heat of solidification, but adds an additional boundary condition of constant flux from the solid surface. Physically, the constant flux term in the second model can be thought of as hydrothermal flux. Figure 6. [Stage 1 Cooling] Comparison of the solidification timescales for the Stefan problem and the prescribed flux problem. Again, the blue trace is for the former, and the red traces represents the latter. Axis units are log years and kilometers. Here, the effects of changing flux are clear. If the prescribed flux is too low, it can actually slow cooling times; additionally, we can see that the functional dependence of the power series solution causes inflated solidification times for small crater diameter. Figure 10. Schematic drawing—modified from Newsom et al. 1996—of the heat sources to be employed in future versions of the cooling model. Most notably, it will be important to describe the hydrothermal flux as a function of time (drawing analogy to terrestrial mid-ocean spreading ridges) and to include the heat from the uplifted geothermal gradient at the central peak. Figure 2. Schematic representation of the first case, known as the Stefan problem. In the left panel, coordinates and heating terms are shown, and the right hand panel shows the heat equation and the appropriate boundary conditions. Figure 7. [Stage 2 Cooling] The cooling timescale for the second stage, or the amount of time it takes the bottom of the finite slab to reach 20% of the initial (melt) temperature, was determined numerically. The solution is shown visually, here: The solid black trace represents T=0.2*(Initial Temp) The red traces represent the cooling at depth y=l, as a function of time, for a 70 and 100 km crater. As T(y=l)=Initial Temp., the slab is considered “cool.” The second stage cooling ceases about 20 000 years later for the 100 km crater. References. Cabrol N.A. and E.A. Grin, Distribution, classification, and ages of martian impact crater lakes, Icarus, 142, 160-172, 1999. Cabrol, N.A. and E.A. Grin, Evolution of lacustrine environments on Mars (Is Mars only hydrologically dormant?), Icarus, 149, 291-328, 2001. Carslaw, H.S. and J.C. Jaeger, Conduction of Heat in Solids, Clarendon Press: Oxford, 1986. Daubar, I.J. and D.A. Kring, Impact-induced hydrothermal systems: heat sources and lifetimes, Lunar and Planet. Sci. Conf. XXXII, abstract 1727, 2001. Farmer, J.D., Hydrothermal systems on Mars: an assessment of present evidence, in Evolution of hydrothermal systems on Earth (and Mars?) (G. Bock and J. Goode, eds.), Wiley: New York, 1996.  Grin, E., D. Fike, and N. Cabrol, New evidence supporting an ice-covered lake in Gusev crater, Lunar and Planet. Sci. Conf. XXXIII, abstract 1145, 2002. Hartmann, W.K., J.A. Grier, D.C. Berman, W. Bottke, B. Gladman, A. Morbidelli, J-M. Petit, and L. Dones, Martian chronology: new mars global surveyor results of absolute calibration, geologically young volcanism, and fluvial episodes, Lunar and Planet. Sci. Conf XXXI, abstract 1179, 2000. Irwin, R.P. III, T.A. Maxwell, A.D. Howard, and R.A. Craddock, Topographic controls on martian valley networks and lakes, Lunar and Planet. Sci. Conf. XXXIII, abstract 1705, 2002. Newsom, H.E., Hydrothermal alteration of impact crater melt sheets with implications for Mars, Icarus, 44, 207-216, 1980. Newsom, H.E., G.E. Britell, C.A. Hibbitts, L.J. Crossey, and A.M. Kudo, Impact crater lakes on Mars, J. Geophys. Res., 101, 14951-14955, 1996. Onorato, P.I.K, D.R Uhlmann, and C.H. Simmons, The thermal history of the Manicouagan impact melt sheet, Quebec, J. Geophys. Res., 83, 2789-2798, 1978. Ozisik, M.N., Boundary value problems of heat conduction, Dover Publications: New York, 1968. Shock, E.L., Hydrothermal systems as environments for the emergence of life, in Evolution of hydrothermal systems on Earth (and Mars?) (G. Bock and J. Goode, eds.), Wiley: New York, 1996.  Stein, C.A., S. Stein, and A.M. Pelayo, Heat flow and Hydrothermal circulation, in Seafloor Hydrothermal Systems, (S.E. Humphris et al. eds.) American Geophysical Union: Washington, D.C. 1995.  Thorsos, I.E., H.E. Newsom, and A.G. Davies, Availability of heat to drive hydrothermal systems in large martian impact craters, Lunar and Planet. Sci. Conf. XXXII, abstract 2011, 2001.   Turcotte, D.L. and G. Schubert, Geodynamics: application of continuum physics to geological problems, Wiley: New York, 1982. Figure 3. Schematic representation of the second case, with the flux boundary condition. In the left panel, coordinates and heating terms are shown, and the right hand panel shows the heat equation and the appropriate boundary conditions. Models, cont’d. In each case, it is necessary to calculate melt cooling times in two stages. The melt sheet is treated as a semi-infinite slab in the first cooling stage, and the time of solidification results. For the first case above, the heat equation with the boundary conditions shown was solved using the similarity approach, as per Turcotte and Schubert (1982). The case of solidification with constant flux from the solid at y=0, the situation is more complex and required assuming a power series solution for the position of the solidification boundary and for the temperature profile in 0<y<ym (Carslaw and Jaeger, 1986). In both cases, after the solidification boundary reaches the bottom of the melt sheet latent heat of crystallization ceases as a heating term. In stage 2, the melt sheet is treated as a slab of finite depth, l, with infinite lateral extent. Here, for ease of comparison, I have followed Daubar and Kring (2001) in defining the cooling time of the second stage as the time it takes for the bottom of the solidified melt sheet to cool to 20% of its initial temperature. Therefore, the total cooling time for each model scenario is the sum of the time it takes a semi-infinite slab to solidify down to depth l time (stage 1) and the time it takes a laterally-infinite slab to cool to 20% of its original temperature (stage 2). The treatment of the problem during the first stage as a half space is fair: edge effects can be neglected due to the sheets lateral extent, and the thermal layer—the distance beyond which the initial conditions remain unperturbed due to conditions applied to the boundaries—depth is less than the depth of the melt (Ozisik, 1968). However, melt volume depends on a variety of parameters, including impactor composition and velocity, and is determined by an empirical relationship. The depth of the melt is a critical factor in the model, yet remains one of the least constrained parameters. Here, I have modeled the melt volume, Vm=cDtcd, as a cylindrical volume with height l=Vm/(πRtc2). D and R are the diameter and radius of the transient crater, respectively, and c=0.000215, d=3.85 for a chondrite impacting Mars at 10km/s (Thorsos et al. 2001). Figures 8, 9. [Stage 2 Cooling] Dimensionless temperature versus depth in melt sheet. In effect, these two plots show the progressive cooling (going from the solid line to the dotted, where each like-patterned trace represents the same timestep in each model) of each system to approximately 20% of the initial melt temperature. In this scenario, the flux bounded melt (right hand plot) takes longer to cool overall, but cools down very quickly in the last 40 000 years of the run. Acknowledgements. Support for this work was provided by UCLA, IGPP Center for Astrobiology. Many thanks to Bill Moore for modeling guidance and time, and to Nathalie Cabrol and Edmond Grin for much shared wisdom Contact Information. Andrew N. Hock UCLA Geophysics IGPP Center for Astrobiology ahock@ucla.edu Office: 310.825.6168