1. PTYS 411 Geology and Geophysics of the Solar System Dating Planetary Surfaces

2. PYTS 411 – Dating Planetary Surfaces 2 l Older surfaces have more craters l Small craters are more frequent than large craters l Relate crater counts to a surface age, if: n Impact rate is constant n Landscape is far from equilibrium i.e. new craters don’t erase old craters n No other resurfacing processes n Target area all has one age n You have enough craters wNeed fairly old or large areas l Techniques developed for lunar maria n Telescopic work established relative ages n Apollo sample provided absolute calibration Mercury – Young and Old

3. PYTS 411 – Dating Planetary Surfaces 3 l Crater population is counted n Need some sensible criteria e.g. geologic unit, lava flow etc… n Tabulate craters in diameter bins n Bin size limits are some ratio e.g. 2 ½ l Size-frequency plot generated n In log-log space n Frequency is normalized to some area l Piecewise linear relationship: n Slope (64km<D, b ~ 2.2 n Slope (2km<D<64km), b ~ 1.8 n Slope (250m<D<2km), b ~ 3.8 n Primary vs. Secondary Branch l Vertical position related to age l These lines are isochrones l Actual data = production function - removal An ideal case…

4. PYTS 411 – Dating Planetary Surfaces 4 Incremental Cumulative Differential Relative l There are at least 4 ways to represent crater count data l Bin spacing should be geometric, √2 is most common n Plots from craterstats (Michael & Neukum, EPSL, 2010) n Definitions from the “CRATER ANALYSIS TECHNIQUES WORKING GROUP” (Icarus, 37, 1979)

5. PYTS 411 – Dating Planetary Surfaces 5 l Cumulative plots n Tends to mask deviations from the ideal n Not binned l Incremental plots n The ‘standard’ plot… Incremental Cumulative

6. PYTS 411 – Dating Planetary Surfaces 6 l Incremental plots with √2 diameter bin spacing is favored by Hartmann n Isochrons have become relatively standardized for Mars Hartmann, 2005

7. PYTS 411 – Dating Planetary Surfaces 7 l Cumulative plots l Differential plots Cumulative Differential

8. PYTS 411 – Dating Planetary Surfaces 8 l R-plots n Size-frequency plot with slope removed - Highlights differences from the ideal l Area of craters: n Rarely used Relative (R-Plot) Cumulative

9. PYTS 411 – Dating Planetary Surfaces 9 l R-plots reveal different populations of cratering bodies n Young surfaces are flat wclose to a -2 slope in log(N) vs. log(D) n Older surfaces show a different impacting population wMore on this later Strom et al., 2005

10. PYTS 411 – Dating Planetary Surfaces 10 l When a surface is saturated no more age information is added n Number of craters stops increasing n The whole premise of crater dating is that c (or k) increases linearly with time

11. PYTS 411 – Dating Planetary Surfaces 11 l Geometric saturation n Hexagonal packing allows craters to fill 90.5% of available area (P f ) n A mix of crater diameters allows N s = 1.54 D -2 wCrater arrays separated by a factor of two in diameter For equal sized craters Log (D) Log (N)

12. PYTS 411 – Dating Planetary Surfaces 12 l Equilibrium saturation: n No surface ever reaches the geometrically saturated limit. n Saturation sets in long beforehand (typically a few % of the geometric value) n Mimas reaches 13% of geometric saturation – an extreme case l Craters below a certain diameter exhibit saturation n This diameter is higher for older terrain – 250m for lunar Maria n This saturation diameter increases with time

13. PYTS 411 – Dating Planetary Surfaces 13 l Summary of a classic crater size-frequency distribution l Typical size-frequency curve n Steep-branch for sizes <1-2 km n Saturation equilibrium for sizes <250m Sample of Mare Orientale Multiple slope breaks

14. PYTS 411 – Dating Planetary Surfaces 14 l In general, it’s hardly ever as neat and tidy as the lunar mare. l Craters can get removed as fast as they arrive – an equilibrium population l production x lifetime = population n production & population known l Can find the crater lifetime… n Usually crater lifetime is a power-law of diameter: a D x n If x=0, then the crater lifetime is the surface age i.e. all craters are preserved n If x=1, then crater lifetime is proportional to depth… e.g. constant infill rate

15. PYTS 411 – Dating Planetary Surfaces 15 l Viscous relaxation of icy topography can make craters undetectable l Maxwell time n Stress causes elastic deformation and creep n Time after which creep strain equals elastic strain n t M = ε el / (Δε creep /t) = η/μ n μ is the shear modulus (rigidity), η is the viscosity l On Earth n t M for rock >10 9 years n t M for ice ~ 100s sec n Ganymede ice is intermediate Pathare and Paige, 2005

16. PYTS 411 – Dating Planetary Surfaces 16 Viscous relaxation on the icy Galilean satellites Images by Paul Schenk Lunar and Planetary Institute l Relaxed craters n Penepalimpset → Palimpset

17. PYTS 411 – Dating Planetary Surfaces 17 l Secondary craters confuse the picture n Steep-branch of lunar production function caused controversy n Are these true secondaries or collisional fragments generated in space l Asteroid Gaspra n Also has steep-branch n Definitely lacks true secondaries n Case closed? Not really…

18. PYTS 411 – Dating Planetary Surfaces 18 l Analysis of Zunil by McEwen et al. n Modeling suggests this one crater can account for all craters a few 10’s of meters in size n They suggest most small craters on Mars should be secondaries l Secondary distribution n Lumpy in space and time n Can’t use these craters for dating a surface

19. PYTS 411 – Dating Planetary Surfaces 19 l Moon is divided into two terrain types n Light-toned Terrae (highlands) – plagioclase feldspar n Dark-toned Mare – volcanic basalts n Maria have ~200 times fewer craters l Apollo and Luna missions n Sampled both terrains n Mare ages 3.1-3.8 Ga n Terrae ages all 3.8-4.0 Ga l Lunar meteorites n Confirm above ages are representative of most of the moon. Linking Crater Counts to Age

20. PYTS 411 – Dating Planetary Surfaces 20 l Crater counts had already established relative ages n Samples of the impact melt with geologic context allowed absolute dates to be connected to crater counts l Lunar cataclysm? n Highland crust solidified at ~4.45Ga n Impact melt from large basins cluster in age wImbrium 3.85Ga wNectaris 3.9-3.92 Ga

21. PYTS 411 – Dating Planetary Surfaces 21 l Before and after the late heavy bombardment l Cataclysm or tail-end of accretion? n Lunar mass favors cataclysm n Impact melt >4Ga is very scarce n Pb isotope record reset at ~3.8Ga l Cataclysm referred to as ‘Late Heavy Bombardment’ } weak

22. PYTS 411 – Dating Planetary Surfaces 22 l Origin of the late heavy bombardment projectiles n Convert crater size distribution to projectile size distribution wUsing Pi scaling laws n Display both as R-plots to highlight structure n LHB – matches main-belt asteroids n Post LHB craters – match the near-Earth asteroid population l LHB caused by surge of asteroidal material entering the inner solar system n Migration of Jupiter can move orbital-resonances through the asteroid belt Strom et al., 2005

23. PYTS 411 – Dating Planetary Surfaces 23 l Lunar impact rates can be scaled to other planets n Must assume the same projectile population i.e. this doesn‘t work for the outer solar system where a different projectile population dominates l Two-step process – e.g. Mars n R bolide is the ratio of projectile fluxes wComes from dynamical studies ~2.6 (very uncertain) n R crater is the ratio of crater sizes formed by the same projectile wImpact energy ratio come from dynamical studies ~ 0.71 wRatio of gravities = 2.3 wR crater ~ 0.75 Schmitt and Housen, 1987 Hartmann, 2005

24. PYTS 411 – Dating Planetary Surfaces 24 l The problem is that we can’t date martian materials in the lab… l But we can start to test these impact rates on Mars…. June 4 th 2008 August 10 th 2008

25. PYTS 411 – Dating Planetary Surfaces 25 l ~300 impact events recognized so far n Crater sizes from a few meters to a few decameters n Effective diameter of clusters reconstructed from l Very biased and incomplete sample

26. PYTS 411 – Dating Planetary Surfaces 26 l Crater flux close to what we expect, but we’re not seeing all impacts… n Efficiency of atmospheric screening also not well known Daubar et al., 2013

27. PYTS 411 – Dating Planetary Surfaces 27 l Outer solar system chronology relies entirely on dynamical models n E.g. Titan shows a global ‘age’ of <1 Gyr Titan Cratering Neish and Lorenz, 2011