1) The 1982 paper by Paolo Farinella established the initial paradigm that collisions were the dominant evolutionary process shaping asteroids, but understanding of asteroid impacts was still limited. 2) New observations and modeling have led to an updated paradigm, showing asteroids are more easily shattered but often reaccumulate, and that non-collisional processes like Yarkovsky and YORP effects are also important. 3) While the new paradigm better explains current data, some questions remain around reaccumulation and the transition between collisionally evolved and primordial asteroids.

1. Collisional evolution of
asteroids: evolving paradigms
Paolo Paolicchi,
University of Pisa, Italy
Pisa, June 2010,
Paolo Farinella Workshop

2. In the year 1982 Paolo Farinella (with me and Enzo
Zappala), published a paper:

3. We were aware of the overwhelming
difficulties of the task....however

4. We tried to define a”general scenario”

5. The AstI/II scenario
The 1982 paper was representative of the ideas, about
the collisional evolution of asteroids, which were
dominant in the 15+y period starting from Asteroids I
(1979), including Asteroids II (first difficulties...)
The collisions were considered as the fundamental
evolutionary process. It became of critical importance to
understand the physics of hypervelocity impacts, which
was partially known from a few experimental papers.

6. Later on....
As happens usually in science, the
scenario is now partially obsolete.
What have been the major changes in
data and underlying physics?

7. New data
­ The completeness limit for Main Belt was
estimated to be at 40km; the size distribution was
showing the “bump” around 100km, but no
significant structure at small sizes. Presently the
size distribution can be ­ maybe­ reliably
reconstructed for D> 1km. A new bump at 3­4 km
can be identified.

8. New data
­ The rotational properties of several very small
asteroids are known. The “V shape” of  vs. D,
showing a minimum around 100km, and
increasing values for larger and smaller objects,
was already known. Now we have discovered
that the mean rotation period does not change
much for small sizes, due also to the “2hr barrier”.
Shorter periods, with a 1/D (?) asymptotic trend
are present only for D < 100m.

9. New data
­ The data on the spin vectors remain rather
sparse, but the new observations have been
enough significant to detect anomalies in a few
family asteroids (“Slivan asteroids”), the
retrograde dominance in NEAs. These effects
support the relevance of Yarkovsky and YORP
effects, both theoretically suggested, but now
also confirmed observationally.

10. Note
Paolo has been one of the most relevant scientists involved in the
creation of the “old” scenario. Later, he has been one the
discoverers of the importance of Yarkovsky effect for asteroidal
evolution. It has been a decisive breakthrough to pass to the “new”
scenario.

11. New data
­ The spectroscopic data are much better and
much more numerous. They allowed a new
taxonomical classification, a better connection
taxonomy­chemical composition, a more
significant comparison asteroids­meteorites. The
“space weathering” of asteroids has been
introduced, experimentally tested, its effects
identified in the observations, especially for S­
complex asteroids.

12. New data
­ New observational techniques have been
implemented, such as radar, and, finally, several
asteroids have been observed from the space,
furnishing first­hand information on cratering,
surface properties (regolith), densities, shapes,
satellites.

13. New tools and ideas
The analysis of asteroid families has been thoroughly
refined, both improving the classification and the proper
elements (another relevant contribution by Paolo).
The physics of collisional fragmentation is more
profoundly understood, both through experiments (now
extended to various target sizes, impact properties,
structures of the target..) and through hydrodynamical
simulations, capable to reproduce most of the
experimental results, and usable also to analyze events
involving planetary bodies.

14. New tools and ideas
The naïve “energy scaling” has been progressively
corrected, introducing various theoretical concepts
(from the self­gravitational compression to the strain­
rate) and comparing to the outcomes of hydrocodes.
A QD* function of the size is defined, showing a
minimum around 200m: smaller bodies are stronger,
larger ones are more difficult to destroy due to self
gravity. In terms of the old jargon, S is low, FKE is
very small. Asteroids are easily shattered by a
collision, but often reaccumulate.

15. New tools and ideas
The size distribution of families is dominated ­at all
the observable sizes­ by reaccumulation; maybe
the presence of preexistent fractures is relevant.
All the observable fragments should be rubble
piles or gravitational aggregates. The same holds
for almost all asteroids, except the very small ones
and ­maybe­ the largest ones.

16. However
As well known, a linear velocity field (such as Hubble law, or a
zero­app. ejecta field) has no intrinsic scale: all reaccumulates, a
small subcondensation does, and viceversa. You can introduce a
multiple reaccumulation breaking the simmetry (as in SEM) but
few bodies reaccumulate more than two­three fragments. The
simulations entail clusters of fragments reaccumulating together.
Why? Pre­existing fractures? Converging motion in the initial
velocity field? What else?
And, more important, is it real? (I would like to discuss again this
points with Paolo, as we did in the past....)

17. New tools and ideas
According to the new ideas the transition strength­
gravity takes place for small objects, and the
possible transition in the size distribution is
marked by a secondary “bump” around 3km.
By the way, the old concept of a “pile of rubble”
similar to a fluid is also obsolete. The “new” rubble
piles (GA) take into account the interactions
among the solid components and may be severely
different from figures of equilibrium.

18. New tools and ideas
The bump in the size distribution around 120 km
corresponds to some changes in physical
properties (minimum of the mean rotation rate Ω;
minimum of the lightcurve amplitude,a maximum of
the relative excess of prograde asteroids,
represented in terms of the cumulative excess for
bodies larger than a given size in units of the
expected statistical deviation).

19. New tools and ideas
Is the ~100km bump connected not to the transition
strength­gravity (old paradigm), but to the transition
between a collisionally evolved population and a quasi
primordial one?. The larger bodies may retain original
properties, or consequences of the primordial evolution.
The bodies smaller than 120km might be the only real
“outcomes of collisional evolution”, due to the former
breakup of large bodies or to mutual collisional events.
The mass of MB, after the first dramatic era, has been not
much larger than the present one.

20. New tools and ideas
The “low mass belt model” entails, differently from
the previous ones, a quasi constant creation of
fragments and, through the Yarkovsky driven
delivery into resonances, a regular creation of
NEAs. The result is in agreement with the analysis
of lunar craters. Moreover, the model is consistent
with the observed properties of Vesta (its partially
intact basaltic crust, with one very big crater).

21. New tools and ideas: families
The families stand as the most relevant outcomes of big
(“catastrophic”)collisional events. Their dynamical
structure is not only due to the original properties, but
also to the post­impact evolution mainly due to
Yarkovsky­Yorp effects . The combined analysis
allows also to estimate the age. Note the recent
rediscussion of Yorp effects suggesting a possible
random­walk evolution of the spin rate.

22. New tools and ideas: the
“collisional weathering”
The solar wind (ion implantation) is the main cause of
asteroids space weathering. The timescale of the process
is around 106y. However we find a marked slope increase
with age for old asteroids. This different (and much larger)
timescale can be connected to the partial surface
refreshment due to cratering collisions and to the formation
of regolith. The slope increase with time may be a witness
of the collisional evolution and may help to constrain some
parameters of the process (work in progress).

23. New tools and ideas: general
considerations
The collisional evolution is intimately entangled
with other physical processes, such as Yarkovsky­
YORP and the space weathering. Moreover, direct
consequences of the primordial formation and
evolution are also presently observable in the
high­size tail of the asteroidal belt. The analysis is
now more difficult to do!

24. Work TBD and critical points­ I
Topics which deserve a further analysis:
­ Under what conditions the reaccumulation may create a
“democratic” size distribution, avoiding runaway into a few
very large reaccumulated bodies or formation of much
debris?
­ Does really the 100­120km bump mark the transition
between evolved and primordial asteroids?
­ The evolution of the GA concept (texture, shape, rotational
properties...) has to be finalized.

25. Work TBD and critical points­ II
­The RP problem: are all bodies larger than 100m
GA?
­ May different data and theoretical models lead to
not consistent age estimates?
Ghosts from the old paradigm? Probably points to
be clarified or first indications for the next
paradigm.

26. CONCLUSIONS
Sometimes, the evolution of scientific knowledge is slackened by
personal attitudes: we stick to our ideas (especially whenever our
contribution to their assessment has been significant), and are
skeptic about new suggestions. On the other hand, we sometimes
overestimate the predictive power of “our” new ideas. Paolo was
fundamental to define the first paradigm, to introduce new
physical ideas essential to support the second. We miss him, his
“candid” attitude towards science, to enter the scenario to come...