Collisional Evolution of the Small Bodies of the Solar System

Transcription

1 Collisional Evolution of the Small Bodies of the Solar System Originally composed by: Jean Marc Petit CNRS/Observatoire de Besançon

2 Motitvation Interested in understanding the formation and destruction for planet accretion and evolution. Need to know how they evolved since formation > link to origin and processes. Dynamical evolution covered elsewhere. 2 main issues to understand: physics of high velocity collisions effect of lots of sequential collisions on the observables

3 Motivations Observed small body populations, size distribution show plots (Main belt, TNOs). Explain cumulative distribution Families in (a,e) and/or (a,i) space: Hiryama asteroid dynamical families Typical velocity and frequency of collisions show table FreqVelCol

4 Motivations

5 Motivations

6 Motivations

7 Motivations

8 Physics of high velocity collisions (1) Different types of outcomes: Cratering: largest fragment more than ½ initial mass Fragmenting/Shattering: largest fragment less than ½ initial mass Depend on the energy of collision (so mostly velocity of the impactor) Specific energy Q < Q* > cratering Q > Q* > shattering Typically, very abrupt transition from a cratering event to a shattering one Cratering seems to be fairely well understood, and can be modelled and/or experimented with. Occurs for gentle impacts on large bodies

9 Physics of high velocity collisions (2) Fragmenting/Shattering is more complex to model and do experiments with it. Different kind of physics for the «small» and the «large» bodies. Small bodies held together by material strength Large bodies held together by gravity in this last regime, the actual composition of the bodiy plays no rôle For somewhat small bodies, need to account for the status of the material prior to collision: cracks and faults, how do they propagate,... Experiments on small targets, either with a gun or with explosives Show the different Q*(R) relations from various authors Also, difference between fragmenting and shattering.

10 Physics of high velocity collisions (3) Ductil media, such as metal can have plastic deformation Rocks «break» beyond the elestic deformation, hence releasing the stress. due to «activation» of pre-existing flaws N(E) = k Em number density of flaws that activate at or below strain E. Existence of incipient flaws due to cooling history and previous collisions Once activated, a crack propagate. No returning.

11 Physics of high velocity collisions (3)

12 Physics of high velocity collisions (4) Once a crack is formed, cohesion is lost, and cannot be re-instated. Releases stress permanently. Since it takes time for a crack to propagate, effect will depend on strain rate, hence on impact velocity, and size of target. Different effect for monolithic and pre-factured material. CONCLUSION: Most asteroids are already shattered! They are 'rubble piles' in most cases.

13 Physics of high velocity collisions (4)

14 NEAs < Itokowa Eros (below) 500 m length 10 km length

15 Itokowa 500 m length

16 Itokowa 500 m length

17 Hayabusa touchdown on Itokowa 500 m length

18 NEAR/Shoemaker explored Eros 10 km

19 NEAR/Shoemaker explored Eros 54 m across

20 Physics of high velocity collisions (5) Fragmentation is not the only story. There is reaccumulation due to gravity for large bodies

21 Physics of high velocity collisions (5)

22 Physics of high velocity collisions (6) Critical parameter called Q*, threshold specific energy which separate crattering from fragmentation/shattering Given by models and numerical simulation Very few experiments, at small sizes show experiments movie of explosion (9205_1a.mpg, 9603_1x.mpg -) movie of reaccumulation (Flora2.fli)

23 Physics of high velocity collisions (6)

24 Physics of high velocity collisions (7) Often parameterized as Q* ~ D-a (1 + c D-b ) 1/5 <= a <= 2/3; 1.8 <= b <= 3.5

25 Physics of high velocity collisions (8) From Q*, model the size distribution of fragments Erel = ½ (m1 m2/(m1 + m2)) Vrel 2 fl = ½ (Q* M/(Erel /2))1.24 dn = b2 B2 m-b2-1 b1 B1 m-b1-1 O(mmax -m) + d(mmax -m) -> mmax = M fl m<=ml m>ml

26 Physics of high velocity collisions (9) Cratering: parameterize total mass of crater, and powerlaw.

27 Size distributions (1) Cumulative Distributions N(>M) = BM M-r Differential or incremental distributions N(>R) = AR R-s dn(r) = CR R-q dr dn(m) = Em m-p dm s = 3r; s = q 1; r = p 1; q = 3p 2 q < 4: Most of the mass in the large bodies q = 4: equal mass at each size q > 4: Most mass in the small bodies

28 From Mag to Size distribution (1) We measure the magnitude of objects.

29 From Mag to Size distribution (2) object radius r in km nu is albedo in the same passband as solar colour

30 Collisional evolution of size distribution (1) Presentation of the observables measured luminosity function, change to H distribution, and finally to size distribution. Explain H Derivation/presentation (?) of Dohnanyi self similar solution, with assumptions index of size and mass distributions, cumulative and diffferential, how to go from one to the other Numerical integrations show wavy patterns. How comes? Presentation of O'Brien and Greenberg improved version non self similarity in response to collision > multifractality, power law varying with size.

31 Collisional evolution of size distribution (2) Derivation/presentation (?) of Dohnanyi self similar solution, with assumptions Asteroids are spheres of equal density All the collisional response parameters are size independant The population has an upper cut off in mass, but no lower cut off d F(m,t)/d t = rate of change of particles in range m and m+dm due to erosion + rate of loss because of catastrophic collisions + rate of creation of particles due to erosion and catastrophic shattering of larger objects

32 Collisional evolution of size distribution (3) Since problem is size independant, look for a solution that is size independant > look for a power law like distribution Search for final equilibrium (if exist at all), or solution at assymptotically long times In the end, after some tedious computations, find: d N(m) ~ m 11/6 dm (original derivation) So d N(r) ~ r 7/2 dr

33 Collisional evolution of size distribution (4) Presentation of O'Brien and Greenberg improved version non self similarity in response to collision > multifractality, power law varying with size. Q* ~ Q*0 Ds q = (7 + s/3)/(2 + s/3) If change in slope «s», then change in slope «q». Due to break in slope, a wave is generated.

34 Collisional evolution of size distribution (5)

35 Collisional evolution of size distribution (6)

36 Collisional evolution of size distribution (7) The Main Asteroid Belt has a wavy size distribution, at least down to km-size bodies Most multi-km asteroids (< km) are likely gravitational aggregates Yarkovsky has no visible effect on the main belt size distribution, but certainly plays a rôle in the size distribution of bodies sent out to NEA region

37 Collisional evolution of size distribution (8) TNO region seems not to be collisionally relaxed above km sizes (and will remain like this) Similar behaviour seems to apply to Hildas, and may be to Trojans We need un-biased data to extrapolate current distributions in a reliable way and compare models to