WHY DO WE WANT TO MODEL THE COLLISIONAL EVOLUTION OF MBPs?

SOLAR SYSTEM FORMATION : what was the primordial distribution of the minor body population before the collisional evolution begins? Constraints on the planetesimal accretion process.

COLLISIONAL PHYSICS: to understand the formation of families and family erosion. Statistical testing of scaling laws on many events.

INTRA-POPULATION FLUXES: interrelation among different populations in the solar system (MBAs – NEOs, Trojans – SPC, TNOs – Centaurus….)

LIFETIME OF BINARIES, LIMITS ON FAMILY YARKO-EXPANSION.

Initial population of Minor Bodies. GUESSGUESS

Fragmentation models (Q*

D, Q*S, .)

Dynamics (Vimp, <Pi>, Yarkowsky, PR drag…)

OUTPUTOUTPUT (Final size distriution, N. of families…)

Observational constraints

The MODEL

MBAs, Trojans, Hildas, KBOs

Size and velocity distribution of escaping fragments, cf, sf

Dp ρp,

cp, sp

Dt ρt, ct, st

Vimp

c = structure: porosity, rubble pile, monoliths..

s = spin rate

Simple analytic equations

FRAGMENTATION MODEL -1 THE DREAM

Benz-Aspahug, 1999: Q*D (D), fl

(Q*D , E) . Nf (Df, Q*

D , E) ??

FRAGMENTATION MODEL -2: THE SINERGY

Impact experiments

Scaling laws

HydrocodesAsteroid families

Size distribution of minor bodiesCraters on planets and asteroidsBinary asteroids

Meteorites

DYNAMICAL EFFECTS:

2) Resonances cause outflow from the belt

3) Dissipative forces (Yarkowsky, PR drag) (O’Brien & Greenberg, 2001): the small body tail problem.

Penco, Dell’Oro, La Spina, Paolicchi, Cellino, Campo Bagatin., in press.

1) Vi , <Pi> (Farinella, Davis, Dahlgren, Bottke, Marzari, Dell’Oro, Paolicchi, Greenberg, Vedder, Gil-Hutton…….)

Initial population guess

Time (yr)

Planetesimal accretion ( about 1 Myr)

Giant impacts – Mass depletion, stirring of orbital elements ( about 100-200 Myr)

Collisional evolution models (about 4.5 Gyr)

MBAs

Troj

ans

Resonance sweeping,

Endogenic dynamical

excitation

THE ‘CLASSICAL’ NUMERICAL MODEL:

1) Bodies distributed in size-bins

2) <pi> vimp input from the dynamics of the population

3) Montecarlo method: computation of representative collisions and distribution of new generated fragments in the bins (the fragmentation model is used here).4) Time evolution controlled by relative changes in each bin.

6) Tail control with interpolation (???)

5) Families are treated as sub-populations

PREDICTIONS OF THE MODEL THAT CAN BE COMPARED TO OBSERVATIONS (The Main Belt case)

1) Size distribution of Main Belt Asteroids

2) Number of families and their slope (Marzari and Davis, 1999)

3) Basaltic crust of Vesta (Davis et al. 1984)

4) Rotation rates (difficult to implement, physics not yet clear)

5) CRE ages of stony meteorites (O’Brien and Grenberg, 2001)

6) Fraction of rubble-piles among asteroids (Bagatin et al. 2001)

N(>D) = K D-b

0.4

1.5

Gaspra

20

200

Ida

-3.40

5

SDSS

-1.30

20

3Durda

-2.34

SDSS

-3.0040

PLS

-1.95

SIZE DISTRIBUTION

-2.70

Bumps, waves…. what is the origin?

1) Transition regimes in scaling laws or dishomogeneity

3) Different populations

S = 2.7 g cm-3 por: 30%C = 1.4 g cm-3 por: 40%

(from Britt et al. 2002: Ast III)

2) Small size cutoff (non-gravitational forces) ?? Maybe . too gradual to produce waves.

Dl (km) Model Observed N. asteroids

50 29 21 4.1 103

40 79 64 1.3 104

20 325 ? 8.2 104

10 503 ? 5.4 105

5 544 ? 3.2 106

Number of families vs. completeness limit.

Marzari et al. 1999

Nu m

b er o

f bod

ies

Diameter

1) COLLISIONAL EROSION

2) NO DYNAMICAL EROSION

VESTA: basaltic crust almost intact. The body was not disrupted over the solar system age.

Different populations and families

Yar

kovs

ky e

ffec

t, PR

dra

g

CPU time

MODEL

FUTURE DIRECTIONS:

Include all dynamical effects and handle the problem of the small body tail

Derive strong constraints on the primordial populations of minor bodies, study the history of families

Testing different fragmentation models and scaling laws while waiting for the dream to come true (The perfect fragmentation model)

– High shot repetition rate (1 shot / 25 min) – Velocity 2-5.5 km/s (200 m/s step) – Projectiles 0.4 - 3 mm– Target temperature control 150-370 K– 4 shadowgraphs up to 1 MHz– Shock accelerometers up to 200000g.

Resonant freq. 1.2 MHz

1) Guns:

FRAGMENTATION MODEL -3: LABORATORY EXPERIMENTS

2) Explosives Review: Holsapple et al. 2002 (Ast. III)