Talk of the "International Workshop on Paolo Farinella (1953-2000): the Scientists, the man", Pisa, 14-16 June 2010

1. International Workshop on Paolo Farinella
Pisa, 14-16 June 2010
D. Turrini1, G. Magni2, A. Coradini1
1 Institute for Physics of Interplanetary Space, INAF
2 Institute for Space Astrophysics and Cosmic Physics, INAF

2. Scientific Background: Jupiter
From observations of circumstellar disks we know that their median
lifetime is about 3 Ma, with the range spanning between 1-10 Ma (Haisch,
Lada & Lada 2001, Meyer 2008).
Since the gaseous component of the Solar Nebula should still be present
when the giant planets accrete their envelopes, we know that they formed
somewhere during the first 10 Ma of the life of the Solar System.
Probing this ancient time is difficult, since most features of this early
epoch have been erased by the later evolution of the Solar System.

3. Scientific Background: Main Belt
Meteoritic studies showed that accretion and differentiation of
planetesimals in the Main Asteroid Belt took place on the same timescale
of the formation of the giant planets (Scott 2006) due to the presence of
short-lived radionuclides like 26Al and 60Fe (see e.g. Bizzarro et al. 2005).
Yang, Goldstein &
Scott (2007)
suggest that
hundreds-of-km
wide differentiated
planetesimals
formed during the
first 1.5 Ma since
CAIs.
Chronology of the early Solar
System inferred from the
radiometric ages of meteorites
(from Scott, 2007)

4. Scientific Background: Vesta
Vesta is considered to be the parent body of the HED meteorites
(Howardites, Eucrites, Diogenites): the study of the oldest Eucrites
showed that Vesta should have formed and differentiated in less than 4
Ma (see e.g. Keil 2002 and reference therein).
At present, Vesta is
the only intact
primordially
differentiated
planetesimal we
know of in the Main
Asteroid Belt
Chronology of the early Solar
System inferred from the
radiometric ages of meteorites
(from Scott, 2007)

5. The Project
Vesta is a body that underwent a complex differentiation process early in
the history of the Solar System, predating the differentiation of Mars and
the Earth and possibly the formation of Jupiter
We explored the hypothesis that either Vesta, Ceres or both asteroids
formed at the time of Jupiter's formation and investigated how they could
have been affected by the latter.

6. The Model
We simulated the evolution of a template of the early Solar System
composed by:
• Vesta
• Ceres
• the forming Jupiter
• a disk of planetesimals
The disk of planetesimals extends between 2-10 AU and is composed by
8x104 massless particles.
To evaluate the delivery of volatiles, impactors are divided into two
categories depending if they formed inside or beyond the Snow Line,
which we assumed being placed at 4 AU (Encrenaz, 2008)

7. Jupiter's formation
We considered Jupiter's formation as composed by three different stages
(e.g. Coradini, Magni & Turrini, 2010):
 a core accretion phase;
 a fast, exponential gas accretion phase;
 a slow, asymptotic gas accretion phase.
The core formation, going from a Mars-sized embryo of 0.1 Earth masses
to a critical core of 15 Earth masses, lasted 106 years.
Gas accretion was followed for 106 years and was characterized by a
timescale of 5x103 years, basing on Magni & Coradini (2004), Coradini,
Magni & Turrini (2010) and consistently with Lissauer et al. (2009).

8. Jupiter's migration
Theoretical models indicate that the interaction between the Solar Nebula
and the forming giant planets during the accretion of the gaseous
envelope cause them to migrate radially (see e.g. Papaloizou et al. 2007)
We explored four different migration scenarios:
 Jupiter formed at its present position (no migration)
 Jupiter formed at 5.45 AU (0.25 AU migration)
 Jupiter formed at 5.70 AU (0.50 AU migration)
 Jupiter formed at 6.20 AU (1.00 AU migration)
Please note that this migration is not the one described by the Nice Model
(Gomes et al. 2005, Tsiganis et al. 2005, Morbidelli et al. 2005), which is
hypothesized to take place a several 108 years later.

9. Collisional evolution
Collisions with the two target asteroids are evaluated statistically:
 at each timestep, the instantaneous orbits of Vesta and Ceres are
spread over a torus;
 the mean radius and section of each torus are respectively equal to the
semimajor axis and the gravitational cross-section of the relevant
asteroid;
 the path of each planetesimal nearing a torus is evaluated through
linear approximation;
 the crossing time is evaluated by solving the quartic equation for ray-
torus intersection
 the effective collisional time is the minimum between the crossing time
and the time spent by the asteroid in the crossed region of the torus
 the impact probability is then the ratio between the effective collisional
time and the orbital period of the asteroid

10. Impact features
Collisions with the two target asteroids are evaluated statistically.
For each impact, the code records:
 impact velocity and direction;
 mass of the impactor;
In addiction, the code evaluates:
 mass and numeric flux of impactors
 impact energy as a function of the self-gravitation energy of the
asteroid;
 crater diameter through an empirical scaling law (De Pater & Lissauer,
2001).

11. Impact flux on Vesta
Impacts on
Vesta double
during Jupiter’s
gas accretion.
Mass flux from
outer (BSL)
bodies is
significant only
if Jupiter does
not migrate
while forming.

12. Mass flux on Vesta
The total mass
impacting Vesta
is about 10% of
its present mass.

13. Impact velocities on Vesta

14. Crater distribution on Vesta
The contribution of
outer (BSL) bodies,
set aside for few
major craters, is
obliterated by that of
inner (ISL) impactors.

15. Impact flux on Ceres
Impacts on Ceres
by inner (ISL)
impactors are a
factor 2-3 more
numerous than on
Vesta.
Impacts due to
outer (BSL)
impactors are an
order of magnitude
more numerous.

16. Mass flux on Ceres
The total mass
impacting Ceres
is about 10% of
its present mass.

17. Impact velocities on Ceres

18. Crater distribution on Ceres
The contribution of
outer (BSL) bodies, is
almost completely
obliterated by that of
inner (ISL) impactors.

19. What’s next?
We plan to expand the model to account for:
 the effect of gas drag on planetesimals (Weidenschilling, 1977)
 the perturbations of embedded planetary embryos (Wetherill, 1992)
Our goal is to use our model and our results to investigate the possible
signatures of Jupiter’s formation on an early-formed and early-
differentiated Vesta and verify if they were obliterated by the later evolution
of the Solar System.
As part of an international effort lead by the University of Padova and
involving researchers from INAF, DLR and the Observatoire de la Cote
d’Azur, we aim to use our results to create a Vesta-based chronology of
the early Solar System.

20. THANKS!

21. For further details...
Detailed descriptions of the model and its
equations are available at ArXiv as e-print
0902.3579 (http://arxiv.org/abs/0902.3579)