nico, schmedemann department of earth sciences, institute of geological sciences the age and...

Nico, SchmedemannDepartment of Earth Sciences, Institute of Geological Sciences

The Age and Cratering History of Phobos

Comparison of two Endmember Chronologies

2The Age and Cratering History of Phobos, Sept 21 2015

OutlineBackground:

• 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 21 2015


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.

Iapetus 951 Gaspra, Deimos, Phobos 4 Vesta

Dawn Cassini Galileo, Mars-Express

5

Background

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



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)



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).

+a2(log(D))2+…+a11(log(D))11




1 Ga

4 GaWith 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 abouta factor of 100 above the 1 Ga isochrone.



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.

𝑁𝑒𝑞𝑢=10𝑘D−2 (e.g. Neukum & Ivanov, 1994)

Nequ : equilibrium crater frequency k : =1.1 on lunar highlands, but similar on other bodies too D : crater diameter



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.



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.



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




young areas = few craters

Relative Ages:

old areas = many craters



A17A15

A14A12

L24

A16

L20

L16

rock/soil ages at sample sites

collecting lunar rock/soil samples

radiometric age dating

A11

17The Age and Cratering History of Phobos, 21 SEP 2015


• 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.



• 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

?



• 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:http://www.psrd.hawaii.edu/Aug06/cataclysmDynamics.html




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.



Lunar Chronology after Neukum and Ivanov (1994)

t – surface age in Ga

The chronology function convert crater frequencies into absolute model ages

𝑁 (1 )=5.44∗10−14¿

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.


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



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.


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


𝐷𝑡

𝐷𝑃( 𝛿𝜌 )0.43

(𝑣𝑠𝑖𝑛𝛼)0.55

= 1.21[ (𝐷𝑠𝑔+𝐷𝑡 )𝑔 ]0.28

Ivanov (2001; corrected exponents by Ivanov (2008))

= D

If D < Dsimple to complex transition then Dt ~ D

If D > Dsimple to complex transition then

D – observed crater diameterDt – transient crater diameterDP – impactor diameterG – gravity acceleration of target bodyδ – projectile density ρ – target densityv – impact velocityα – impact angleDsg – strength to gravity transition crater diameter

(Dt>>Dsg -> gravity regime; Dt<<Dsg -> stregth regime)


27


Moon Phobos (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 2.5 2.5

Impact Velocity (km/s) 17.5 8.5 5.3

Impact Angle (most probable case after Gilbert, 1893)

45 4545

Surface Gravity (m/s²) 1.626x10-3

(Willner et al., 2010)

6x10-3

(Willner et al., 2010)

Diameter Strength to Gravity Transition (km)

0.3 81 81

Diameter Simple to Complex (km) 15 4053 4053


28



Resulting production and chronology functions for cases A and B

29

“Nico-Question” from last seminar


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


31

Phobos Measurements

HRSC Basemap: Wählisch et al. (2010)

Shown data is publisched in Schmedemann et al, 2014 (doi:10.1016/j.pss.2014.04.009)


http://dx.doi.org/10.1016/j.pss.2014.04.009

32

Phobos Measurements

Average Surface to the West of Stickney: N-S grooves stratigraphically above E-W grooves


33

Phobos Measurements

Cumulative crater plots of average area west of StickneyAge of Phobos equals last global resurfacing event (break-up of parent body)

Min. Age of Phobos


34

Phobos Measurements

Area S1: Interior of Stickney


35

35

Phobos Measurements

Cumulative crater plots of S1 area inside Stickney

Age of Stickney


36

Phobos Measurements

Area S2: SRC image of Interior of Stickney; N-S grooves stratigraphically below solitary E-W groove


37

Phobos Measurements

Cumulative crater plots of S2 area inside Stickney


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.


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. Phobosformation

Age of groove formation

Age of Stickney/Limtoc


40

Deimos Quick Look


41

Deimos Quick Look


Mosaic:http://sbn.psi.edu/pds/asteroid/MULTI_SA_MULTI_6_STOOKEMAPS_V2_0/document/m2deimos/deimos_cyl_viking_mro.jpgTopographic Data: http://sbn.psi.edu/pds/asteroid/EAR_A_5_DDR_SHAPE_MODELS_V2_1/data/m2deimos.tab

42

Deimos Quick Look


Cumulative crater plot for areas 1 and 2. Differential crater plot for areas 1 and 2.

Minimum Age forDeimos

ProbableResurfacing

Possible Resurfacing/Image Issues

43

Conclusions


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: 4 - 4.2 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


48

Crater Production Function• Lunar production function is used as base line, because the main

impactor source is the same on the Moon, Phobos and Main Belt asteroids

• Case A

- vimpM = 9.4 km/s (Ivanov, 2008)- vescM = 5 km/s- vescP = 3 km/s- vimpP = 8.5 km/s

• Case B- Average impact velocities among

Main Belt asteroids are calculated following (Bottke et al., 1994)

- vimpP ~=5.3 km/s

Velocity distribution of 682 Main Belt asteroidsD>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


50

Chronology Function


• 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 GaIsochrones


51

Chronology Function


• Case B- Average impact probabilities among Main Belt Asteroids are calculated

following (Bottke et al., 1994) Pi ~ 2.9*10-18 km-2/a 2.9*10-9 km-2/Ga - Conversion from intrinsic impact probability to chronology:

f=Pinir2mean (O’Brien and Greenberg, 2005)

f: impact frequency forming craters ≥ 1 km/GaPi: intrinsic impact probabilityni: number of projectiles forming craters ≥ 1 km

o observed number of Main Belt asteroids ≥ 10 km (obs. limit): 9554o crater size on Phobos as average Main Belt asteroid from 10 km projectiles: 104.5 kmo correction factor for frequency of 104.5 km craters to 1 km craters based on Phobos

production function as MBA: 4*103

o ni: 3.8*107

r: mean radius of target body scaled to unit area = (11 km)²/4π*(11 km)²- f ~ 9*10-3

- (Neukum, 1983)The Age and Cratering History of Phobos, 21 SEP 2015

52

Topographic Correction


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



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



Correction between reference and true body surfaces: Inlays: True body cross‐sections along thetopographically 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 withrespect to the radii of the reference spheres along the x‐axis. The y‐axis gives the correction factor for cratersizes (blue) and areas (red) with respect to the ratios indicated along the x‐axis. Vesta as largest body showsthe smallest diversions (<20%) from the spherical reference body. Diversions for Lutetia, the second largestbody in this selection are up to ~40%. Gaspra’s reference sphere diverts up to ~80% from the true bodysurface. Ida’s highly irregular shape diverts up to a factor of about ~2 from its reference sphere. This extremedifference results in a factor of two incorrect crater sizes and a factor of ~4 incorrect areas.

nico, schmedemann department of earth sciences, institute of geological sciences the age and...

Documents

crater frequency

crater sizes

crater chronology function

crater frequencies

respective crater diameters

phobos phobos measurements

age estimations

lunar chronology function