N.21 campo bagatin-the-legacy-of-paolofarinella-in-the-devel

The legacy of Paolo Farinella in the development of

collisional evolution models

Adriano Campo Bagatin

Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal.

Instituto Universitario de Física Aplicada a las Ciencias y las Tecnologías.

Universidad de Alicante (Spain)

INTERNATIONAL WORKSHOP ON PAOLO FARINELLA (1953-2000): THE SCIENTIST AND THE MAN

Pisa, 14th to 16th of June, 2010

The legacy of Paolo Farinella in the development of collisional evolution models



Scaling laws in the strength regime

A fragmentation and cratering model

Collisional evolution of small solar systembodies.



Strain-rate scaling + Self-compression

*SQ : specific energy necessary to produce fragmentation

−α β∝ +*SQ aD bD

Scaling laws:



Shattering experiments in various materials

(Hartmann, 1969; Fujiwara et al., 1977; Fujiwara and Tsukamoto, 1980,1981; Lange and Ahrens, 1981; Matsui et al., 1982, 1984; Kawakami et al., 1983; Fujiwara and Asada, 1983; Takagi et al., 1984; Cintala and Hörz, 1984; Cintala et al, 1985; Smrekar et al., 1985; Hartmann, 1985; …)


Fujiwara (1980).

Moore et al. (1965) and Gault et al. (1972): Fragmentationgoverned by the growth and coalescence of cracks.Griffith: Cracks of lenght L begin to grow when the stress exceeds a threshold value ~ L-1/2

Then: Largest cracks control failure of target: Fracture stress ~ R-1/2 and also does Q*S.

Q*S ~ Tensile strenght (assumed ~ R-1/2)

Farinella et al. (1982), Paolicchi et al. (1983):Energy required to fragment a body depends on the areaof new created surfaces, not on target’s volume! They showd that:

Q*S~ R-1/2.




Holsapple and Housen (1986). The era of dimensional analysis begins.

They adopt a rate-dependent material model: fracture strength ~ (strain rate)1/4.

Q*S~ R-0.25

Housen and Holsapple (1990).Assumption: fracture strength is strain-rate and target-sizedependence + energy and velotciy of impactor (V).

Q*S~ V0.35R-0.24.

Holsapple (1994). The duration of the loading is important. In a large scale event, large flaws have time to coalesce and can be activated at low stresses.

Q*S~ R-0.33

Housen and Holsapple (1999).Fragmentation is accomplished through the growth andcoalescence of pre-existing flaws.

Q*S~ V0.35R-0.55 (Q*

S~ R-0.667)




Benz and Asphaug (1999). The era of Smooth Particle Hydrocodes.

Lagrangian approach.Based on solving conservation equations (mass, momentum, energy) + Hooke’s law + material e.o.s. (Tillotson).



Leinhardt and Stewart (2009).CTH + N-body approach to study collisions in the asteroid sizerange. Same power-law dependendence in the strength regime, but Q*S 20 times smaller than in B&A.

Scaling laws of porous bodies (Jutzi et al., 2010)


Scaling laws:



−α β∝ +

≤ α ≤≤ β ≤

*SQ aD bD

0.24 0.6671.8 3.5

1993: Jean-Marc Petit, Paolo Farinella.(Celestial mechanics and dynamical astronomy)

The most complete algorithm –to date- for:

fragmentation, gravitational re-accumulation,cratering

taking into account laboratory results of hiper-velocityimpacts and scaling-laws.



A fragmentation and cratering model



Collisional Systems

The Main Asteroid Belt

The Trojan Asteroids

The Trans-Neptunian Objects

310 M−⊕∼

410 M−⊕∼

110 M−⊕∼

Collisional evolution of small solar system bodies.What do we mean?



• Pietrowski (1953):

• Hellyer (1970), Dohnanyi (1969):

−∝ 5 / 3dN(m) m dm

( , )

f m tt

∂=

∂

rate of change of the number of particlesper unit volume and unit time in massrange m to m+dm due to erosion of theseparticles by collisions with smaller ones

number of particles in the mass range mto m+dm, created per unit time and unitvolume by erosive and catastrophic colli-sional crushing of larger objects

+

rate of loss, because of ‘catastrophiccollisions, in the number of particles perunit volume and unit time in the massrange m to dm

− −∝ 11 / 6dN(m) m dm



Collisional evolution of small solar system bodies.Theoretical studies

Dohnanyi’s assumptions:

i) Asteroids are spheres of equal density.

ii) All the collisional response parametersare size independent.

iii) The population has an upper cutoff in mass, but no lower cutoff.




Dohnanyi’s result confirmed by other researchers:

• Paolicchi (1994)

• Williams and Wetherill (1994)The -11/6 exponent changes less than when

the relative importance of cratering and catastrophic breakup

events, the mass distribution of fragments from a single impact, etc.

are varied in a substantial way.

• Tanaka (1996) The resulting power--law distribution is

independent on the details of collisional outcomes

as long as the fragmentation model is self--similar,

and the value of the exponent itself is determined

only by the mass-dependence of the collisional rate

• Martins (1999)Non steady-state: dN(m,t+dt) can be described

as a power series of

410−

( )5/3 nqm −




Waves in theMain Asteroid Belt?

Where is theDohnanyi’s slope?


Collisional evolution of small solar system bodies.Observables: size distribution

SKADS

Dohnany

Collisional evolution of asteroids.

Fragmentation algorithm (Petit and Farinella, 1993)

+ Evolution algorithm



Collisional evolution of small solar system bodies.



Campo Bagatin et al. (1994)

Release of Dohnani’siii) assumption:

Introducing a sharplower cutoff in thesize distribution



Collisional evolution of small solar system bodies.Models results.

Release of Dohnani’sii) assumption:

NON self-similarity in fragmentation physics

Durda et al. (1998)


Discontinuities (Campo Bagatinet al., 1994, Durda et al., 1997) and size dependence of Q* (Durda et al., 1997) triggerwavy behaviour in distributions.


Collisional evolution of small solar system bodies.Models results.



Collisional evolution of small solar system bodies.Our model upgraded

First estimations of the abundances ofgravitational aggregates in the M.A.B.

Depending on scaling-law, most 10<D<100 kmbodies should be G.A.

From asteroids to TNOs (Davis & Farinella, 1997):

First simulations of the EKB collisional evolution.

Prediction of a roll over in size distribution around50-100 km.

Larger bodies keep their primordial size distribution> Dohnanyi’s slope.

Small (<50 km) bodies are fragments rather than primordial.

Estimation of fragment production as a source of JFC.



Collisional evolution of small solar system bodies.



ObservablesThousands of TNOs observed.4 dwarf planets.Roll-over of size distribution confirmed around50-150 km.High slopes in size distributions of large TNOs(dN~D-adD, a~4.5-4.8).Number of cold classical objects constrained by CFEPS (45000-55000).

A dynamical framework: the Nice model.



Collisional evolution of small solar system bodies. The EKB, 15 years after.

Asteroid LIke Collisional ANd Dynamical Evolution Package(ALICANDEP) (Campo Bagatin & Benavidez):

Mutually interacting 3-zone collisional evolution.Maxwellinan distributions for relative velocities.Zones evolve in time according to the NM (positions, orbital elements, volumes)Dynamical depletion statistically implemented in different phases (pre-LHB, LHB, post-LHB)Migration of bodies according to NM.Algorithm for keeping track of

- Gravitational aggregates- Dynamically “cold” bodies- Primordial populations.




Observables met.4 dwarf planets.Roll-over of size distribution confirmed around 50-150 km.High slope in s.d. (dN~D-adD, a~4.5-4.8) of large TNOsconfirmed. Number of cold classical objects (45000-55000) and ratio ofPlutinos/Classical objects (CFEPS)

Model’s implication on initial conditions.M0~60 ME if size distribution for small objects was shallowerthan dN~D-bdD, b~3.0.Scaling law not much “weaker” than B&A 1999 for ice.Initial distributions compatible with surf. density ~ r-3/2.

Other model predictions.Present mass: 0.15-0.18 ME

~50% prob. of existence of more bodies > 2000 km5-10% Plutinos, 25-30 % Classical objects are primordialA few Mars-size objects survived the LHB. Lately scattered by Neptune’s perturbations.




Paolo’s intuition and work had a key role in thedevelopment of fragmentation models.

His pioneering work in collisional evolution has widely improved our understanding of theevolution of small bodies populations.

His legacy is still inspiring current research in thisarea.



Summary

We definitely miss Paolo, both the amazing great personand the outstanding scientist.



Conclusion

Thank you, once again, for yourhuman and scientific legacy!

The legacy of Paolo Farinella in the development of

collisional evolution models


Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal.

Instituto Universitario de Física Aplicada a las Ciencias y las Tecnologías.

Universidad de Alicante (Spain)

INTERNATIONAL WORKSHOP ON PAOLO FARINELLA (1953-2000): THE SCIENTIST AND THE MAN

Pisa, 14th to 16th of June, 2010

Education

N.21 campo bagatin-the-legacy-of-paolofarinella-in-the-devel