International Workshop on Paolo Farinella

Pisa, 14-16 June 2010

D. Turrini1, G. Magni2, A. Coradini1

1 Institute for Physics of Interplanetary Space, INAF2 Institute for Space Astrophysics and Cosmic Physics, INAF

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.

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).

Chronology of the early Solar

System inferred from the

radiometric ages of meteorites

(from Scott, 2007)

Yang, Goldstein &

Scott (2007)

suggest that

hundreds-of-km

wide differentiated

planetesimals

formed during the

first 1.5 Ma since

CAIs.

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).

Chronology of the early Solar

System inferred from the

radiometric ages of meteorites

(from Scott, 2007)

At present, Vesta is

the only intact

primordially

differentiated

planetesimal we

know of in the Main

Asteroid Belt

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.

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

The Project

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)

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.

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).

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.

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)

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.

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)

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

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).

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.

Mass flux on Vesta

The total mass

impacting Vesta

is about 10% of

its present mass.

Impact velocities on Vesta

The contribution of

outer (BSL) bodies,

set aside for few

major craters, is

obliterated by that of

inner (ISL) impactors.

Crater distribution on Vesta

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.

Mass flux on Ceres

The total mass

impacting Ceres

is about 10% of

its present mass.

Impact velocities on Ceres

Crater distribution on Ceres

The contribution of

outer (BSL) bodies, is

almost completely

obliterated by that of

inner (ISL) impactors.

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.

THANKS!

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)