Nico, Schmedemann Department of Earth Sciences, Institute of Geological Sciences The Age and Cratering History of Phobos Comparison of two Endmember Chronologies

2 The Age and Cratering History of Phobos, Sept Outline Background: dating of planetary surfaces from measurements of crater size-frequency distributions the crater production function calibration of the lunar chronology function scaling the lunar crater production/chronology functions to Phobos Phobos measurements: Deimos Quick Look Conclusions

3 Background Dating of Planetary Surfaces from Measurements of Crater Size-Frequency Distributions (CSFD) The Age and Cratering History of Phobos, Sept

4 Dating of Planetary Surfaces from Measurements of Crater Size- Frequency Distributions (CSFD) Crater size-frequency measurements are a powerful tool of remote- sensing for age estimations on planetary surfaces. It provides the time frame of geological processes on planetary bodies, where radiometric age determination of rock samples is impossible. It also allows for dating vast areas for little cost, while expensive radiometric samples give ages, just from the actual sample site. Iapetus951 Gaspra, Deimos, Phobos4 Vesta DawnCassini Galileo, Mars-Express

5 Background Crater Production Function The Age and Cratering History of Phobos, Sept

6 Crater Production Function Measuring the crater sizes inside geologic units reveals a functional relationship between the crater sizes and the frequency of the crater sizes.  “Crater Size-Frequency Distribution” Apollo 12 landing site, image: LRO

7 The Age and Cratering History of Phobos, Sept Crater Production Function Measuring the crater sizes inside geologic units reveals a functional relationship between the crater sizes and the frequency of the crater sizes.  “Crater Size-Frequency Distribution” The measured crater size- frequency distribution can be approximated by the crater production function (solid line figure left) Neukum and Ivanov (1994)

8 The Age and Cratering History of Phobos, Sept Crater Production Function The production function can be approximated by a polynomial of 11th degree:  gives the relationship between crater frequencies and the respective crater diameters on a planetary surface It is stable since at least 3.5 Ga. (Is matter of discussion for earlier times.) The wavy characteristics is due to the collisional evolution of the main projectile source (Main Belt Asteroids). Neukum and Ivanov (1994)

9 The Age and Cratering History of Phobos, Sept Crater Production Function 1 Ga 4 Ga With increasing exposure age of the surface the crater frequency is rising.  vertical up-shift of representative crater production function (isochrone)  amount of up-shift is defined by the crater chronology function On the Moon the 4 Ga isochrone plots about a factor of 100 above the 1 Ga isochrone.

10 The Age and Cratering History of Phobos, Sept Crater Production Function Pitfall “Equilibrium” For continued exposure of already densely cratered surfaces the production function turns into an equilibrium distribution. Where the slope of the production function is steeper than -3 it will turn into a shallower slope of about -2. =10D −2 (e.g. Neukum & Ivanov, 1994) N equ : equilibrium crater frequency k : =1.1 on lunar highlands, but similar on other bodies too D : crater diameter

11 The Age and Cratering History of Phobos, Sept Crater Production Function Pitfall “Resurfacing-Kink” Measured crater distributions show kinks if geologic processes erased smaller craters that formed before the process stopped. Larger unaffected craters show higher exposure ages than smaller craters which formed after the resurfacing event. A step-like structure is usually an indicator for resurfacing. Small craters formed after the erosion event.

12 The Age and Cratering History of Phobos, Sept Crater Production Function Pitfall “Secondary Craters” Measured crater distributions can also show distributions steeper than the production function if the measured area is contaminated with secondary craters. In many cases secondary craters can be identified by their clustering. Excess of small craters possibly from secondaries or image artefacts.

13 The Age and Cratering History of Phobos, Sept Crater Production Function Relative stratigraphic relationships of different surface units of the same planetary body can be identified by measuring the crater size-frequency distribution and fitting the crater production function.  Crater frequencies can be compared at very different crater diameters. older younger

14 Background Calibration of the Lunar Chronology Function The Age and Cratering History of Phobos, Sept

15 The Age and Cratering History of Phobos, Sept Calibration of the Lunar Chronology Function young areas = few craters Relative Ages: old areas = many craters

16 The Age and Cratering History of Phobos, Sept Calibration of the Lunar Chronology Function A17 A15 A14 A12 L24 A16 L20 L16 rock/soil ages at sample sites collecting lunar rock/soil samples radiometric age dating A11

17 The Age and Cratering History of Phobos, 21 SEP 2015 Calibration of the Lunar Chronology Function The distribution of radiometric ages derived from lunar rock samples and the measured crater frequencies inside the sampled geologic units give anchor points for the lunar chronology function.

18 The Age and Cratering History of Phobos, 21 SEP 2015 Calibration of the Lunar Chronology Function Prominent peaks around 3.9 Ga of lunar highland samples led to the conclusion of a terminal lunar cataclysm in which most of the lunar basins were formed. LHB ?

19 The Age and Cratering History of Phobos, 21 SEP 2015 Calibration of the Lunar Chronology Function But: Rock samples were collected exclusively from the top lunar surface. If a late basin (Imbrium) covered all sample sites with thick ejecta blankets, the samples predominantly date the Imbrium impact event. older less prominent peaks may point to pre- Imbrium impact events such as Serenitatis (Apollo 17)  40 years of discussion LHB ? Image from:

20 The Age and Cratering History of Phobos, 21 SEP 2015 Calibration of the Lunar Chronology Function Neukum and Ivanov (1994) The non-cataclysm lunar crater chronology by Neukum: One of several possible fits through given data points. Exponential decay is in agreement with dynamical models based on the cataclysm/LHB view for ages ≤4.1 Ga.

21 The Age and Cratering History of Phobos, 21 SEP 2015 Calibration of the Lunar Chronology Function Lunar Chronology after Neukum and Ivanov (1994) t – surface age in Ga The chronology function convert crater frequencies into absolute model ages

22 Relationship between production function and chronology function: Vertical axes of both plots are identical Measured cumulative crater frequency at 1 km diameter is converted into an absolute age by the chronology function. Calibration of the Lunar Chronology Function 1 Ga 4 Ga Lunar Crater Production Function The Age and Cratering History of Phobos, 21 SEP 2015

23 Background Scaling the Lunar Crater Production/Chronology Functions to Phobos The Age and Cratering History of Phobos, Sept

24 The Age and Cratering History of Phobos, 21 SEP 2015 Scaling the Lunar Crater Production/Chronology Functions to Phobos Problems: Impact conditions on Phobos are a lot different from the Moon Is Phobos a captured asteroid?  Chronology of a Main Belt asteroid? Phobos’ current orbit is not stable. What was the dynamical situation of Phobos when most of its visible craters were formed. Solution Part 1: Ivanov (2001) scaled the lunar crater production function and lunar chronology to the impact conditions of Mars. The same projectile population was assumed. Solution Part 2: Use of the framework by Ivanov (2001) to derive the crater production function for Phobos for two Endmember cases of its dynamical evolution.

25 The Age and Cratering History of Phobos, 21 SEP 2015 Scaling the Lunar Crater Production Function to Phobos Endmember Cases: A.Phobos has ever been a satellite of Mars in its current orbit o Average projectile impact velocities are converted form Mars to Phobos’ orbit o Average impact rate equals Martian impact rate – corrected for different crater scaling B.Phobos is a recently captured asteroid and nearly all of its craters formed inside the asteroid Main Belt. o Average projectile impact velocities equals average Main Belt impact velocities o Average impact rate equals average Main Belt impact rates

26 Scaling the Lunar Crater Production Function to Phobos Ivanov (2001; corrected exponents by Ivanov (2008)) If D < D simple to complex transition then D t ~ D If D > D simple to complex transition then D– observed crater diameter D t – transient crater diameter D P – impactor diameter G– gravity acceleration of target body δ – projectile density ρ – target density v – impact velocity α – impact angle D sg – strength to gravity transition crater diameter (Dt>>D sg -> gravity regime; Dt stregth regime) The Age and Cratering History of Phobos, 21 SEP 2015

27 Scaling the Lunar Crater Production Function to Phobos MoonPhobos (Case A) Phobos Asteroid Case (Case B) Target Density (g/cm³) 2.5 (est. surface regolith) 1.9 (Willner et al., 2010) 1.9 (Willner et al., 2010) Projectile Density (g/cm³)2.5 Impact Velocity (km/s) Impact Angle (most probable case after Gilbert, 1893) 45 Surface Gravity (m/s²)1.62 6x10 -3 (Willner et al., 2010) 6x10 -3 (Willner et al., 2010) Diameter Strength to Gravity Transition (km) Diameter Simple to Complex (km) The Age and Cratering History of Phobos, 21 SEP 2015

28 Scaling the Lunar Crater Production Function to Phobos The Age and Cratering History of Phobos, 21 SEP 2015 Resulting production and chronology functions for cases A and B

29 “Nico-Question” from last seminar The Age and Cratering History of Phobos, 21 SEP 2015 On Phobos (Case A) a crater of 0.5/1/10 km diameter is forming once in ~ 0.1/0.8/4.1 Ga. What is the age of the youngest crater?  Small craters form much more frequent than large craters.

30 Phobos Measurements The Age and Cratering History of Phobos, Sept

31 Phobos Measurements HRSC Basemap: Wählisch et al. (2010) Shown data is publisched in Schmedemann et al, 2014 (doi: /j.pss ) /j.pss The Age and Cratering History of Phobos, 21 SEP 2015

32 Phobos Measurements Average Surface to the West of Stickney: N-S grooves stratigraphically above E-W grooves The Age and Cratering History of Phobos, 21 SEP 2015

33 Phobos Measurements Cumulative crater plots of average area west of Stickney Age of Phobos equals last global resurfacing event (break-up of parent body) Min. Age of Phobos The Age and Cratering History of Phobos, 21 SEP 2015

34 Phobos Measurements Area S1: Interior of Stickney The Age and Cratering History of Phobos, 21 SEP 2015

35 Phobos Measurements Cumulative crater plots of S1 area inside Stickney Age of Stickney The Age and Cratering History of Phobos, 21 SEP 2015

36 Phobos Measurements Area S2: SRC image of Interior of Stickney; N-S grooves stratigraphically below solitary E-W groove The Age and Cratering History of Phobos, 21 SEP 2015

37 Phobos Measurements Cumulative crater plots of S2 area inside Stickney The Age and Cratering History of Phobos, 21 SEP 2015

38 Phobos Measurements Randomness Test Analysis according to Michael et al. (2012) The spatial distribution of craters within each measured bin is consistent with being random, if the analysis results are between -3 and 3 standard deviations. The Age and Cratering History of Phobos, 21 SEP 2015

39 Phobos Measurements Comparison of cumulative crater plots of average and S1 area. Stratigraphic relations suggest a formation age of grooves ~3.8 Ga/ Stickney ~4.1 Ga. Min. Phobos formation Age of groove formation Age of Stickney/ Limtoc The Age and Cratering History of Phobos, 21 SEP 2015

40 Deimos Quick Look The Age and Cratering History of Phobos, Sept

41 Deimos Quick Look The Age and Cratering History of Phobos, 21 SEP 2015 Mosaic: Topographic Data:

42 Deimos Quick Look The Age and Cratering History of Phobos, 21 SEP 2015 Cumulative crater plot for areas 1 and 2. Differential crater plot for areas 1 and 2. Minimum Age for Deimos Probable Resurfacing Possible Resurfacing/ Image Issues

43 Conclusions The Age and Cratering History of Phobos, Sept

44 Conclusion Phobos Production and chronology function were derived for two end-member cases of Phobos’ evolution  Case A: Phobos was always in its current orbit  Case B: Phobos is a recently captured MB asteroid Case A is more realistic because it also covers a capture of Phobos in the early Solar System, when a lot more bodies were available for capturing than today. Oldest surface age 4.3 Ga  last global resurfacing/break-up of Phobos parent Age of Stickney: Ga Surface ages show multiple resurfacing events, probably connected to the formation of Stickney and the grooves Groove formation appears to be ancient (3 – 4 Ga)

45 Conclusion Deimos Production and chronology functions were derived for the case that Deimos was always in its current orbit (similar to Case A for Phobos) Image data is highly inhomogeneous  crater distributions are highly distorted on a global scale Oldest surface age 3.7/3.8 Ga  Minimum for last global resurfacing/break-up of Deimos parent Age of region with highest image resolution: 700/800 Ma  probable large resurfacing event A possible resurfacing ~ 40 Ma could also be caused by issues with image quality. Much more work and better imaging data is required for better results. Many small craters show elongated morphology  projection distortion/secondary craters If they are secondaries/sesquinaries, an external source (Phobos/Mars?) would be required due to low escape velocity.

46 Discussion

47 Apex-/Antapex Asymmetry Form recent orbit a factor 4 is expected according to Morota et al. (2008). Large (old) craters show apex-/antapex ratio of <1  Phobos may have turned over after some larger impact. Sparse statistics for large craters  inconclusive The Age and Cratering History of Phobos, 21 SEP 2015

48 Crater Production Function Velocity distribution of 682 Main Belt asteroids D>50 km Bottke et al. (1994) The Age and Cratering History of Phobos, 21 SEP 2015

49 Chronology Function Case A  Impact probability of Mars (Ivanov, 2001)  0.45 x lunar impact rate  Correction for different crater scaling between Mars and Phobos  0.97 x lunar impact rate (same projectile is forming larger craters on Phobos than on Mars or the same crater size is achieved by smaller projectiles on Phobos) Lunar chronology is used as base line, because the main impactor source is the same on the Moon, Phobos and Main Belt asteroids The Age and Cratering History of Phobos, 21 SEP 2015

50 Chronology Function Lunar chronology is used as base line, because the main impactor source is the same on the Moon, Phobos and Main Belt asteroids Case A  Impact rate at Mars (Ivanov, 2001)  0.45 x lunar impact rate  Correction for different crater scaling between Mars and Phobos  0.97 x lunar impact rate (same projectile is forming larger craters on Phobos than on Mars or the same crater size is achieved by smaller projectiles on Phobos) 1 Ga isochrones for Phobos and Mars 1 Ga Isochrones The Age and Cratering History of Phobos, 21 SEP 2015

51 Chronology Function The Age and Cratering History of Phobos, 21 SEP 2015

52 Topographic Correction The Age and Cratering History of Phobos, 21 SEP 2015 True shape (blue) of Phobos along its most variable meridian. Topographic deviations from the reference body may lead to significant errors in spatial measurements that are always conducted on the reference body.

53 Topographic Correction The Age and Cratering History of Phobos, 21 SEP 2015 True shape (blue) of Deimos along its most variable meridian. Topographic deviations from the reference body may lead to significant errors in spatial measurements that are always conducted on the reference body.

54 Topographic Correction The Age and Cratering History of Phobos, 21 SEP 2015 Correction between reference and true body surfaces: Inlays: True body cross ‐ sections along the topographically most variable meridian for Gaspra, Ida, Lutetia and Vesta are given as blue outlines. Respective reference spheres are indicated as red outlines with the same center as the true ‐ body crosssections. Main Panel: Minimum and maximum radii for each of the four asteroids are given as ratio with respect to the radii of the reference spheres along the x ‐ axis. The y ‐ axis gives the correction factor for crater sizes (blue) and areas (red) with respect to the ratios indicated along the x ‐ axis. Vesta as largest body shows the smallest diversions (<20%) from the spherical reference body. Diversions for Lutetia, the second largest body in this selection are up to ~40%. Gaspra’s reference sphere diverts up to ~80% from the true body surface. Ida’s highly irregular shape diverts up to a factor of about ~2 from its reference sphere. This extreme difference results in a factor of two incorrect crater sizes and a factor of ~4 incorrect areas.