Introduction
Asteroid families are groupings of minor planets identified
on the basis of their proper orbital elements (Zappala' et al. 1994,
1995). They are probably remnants of larger parent bodies that were
collisionally disrupted hundreds of Myr to a few Gyr ago, with the smallest
fragments traveling the furthest from the cluster's center (Cellino et
al. 1999). One problem with this scenario is that the ejection
velocities inferred for those fragments from their observed dispersions
in their current proper orbital elements seem to be consistently higher
than those predicted by collisions in laboratory experiments (Fujiwara
et
al. 1989) and hydrocode models (Benz and Asphaug 1999).
Here we show results of long-term simulations on the Adeona,
Gefion (old Ceres), and Dora families. The purpose of these simulations
is to gain understanding on how asteroid families can dynamically evolve
over long time scales. There are essentially three effects
that can change proper elements:
-
Yarkovsky effect.
-
Resonances.
-
Gravitational scattering by large asteroids like 1 Ceres,
2
Pallas,
4
Vesta,
and 10 Hygiea
While resonances can account for motion in proper e, and
I,
only
Yarkovsky effect and encounters with large asteroids can account for mobility
in proper a. The Yarkovsky effect is size dependent,
and is dominating the dispersion in a of smaller asteroids (a 20
km regolith-covered body would experience a drift of da/dt~6*10-6
AU My-1). For D< 20 km, it is the dominant factor
in semimajor axis mobility of family members. At larger sizes,
a
mobility is mainly provided by close encounters with larger asteroids.
This mechanism, which is the main topic of this research,
has been for long considered ineffective, and very few studies have been
carried out on the long-term effects of close encounters (see Flora's
article by Nesvorny et al.). In this work we investigate the
effect of close encounters with 1 Ceres, 2 Pallas, 4 Vesta,
and 10 Hygiea for members of the Adeona and Gefion family (we used
the files from Cellino and took only well identified members [classes QC=2,3])
We also generated synthetic families which were assumed to be initially
more tightly clustered in the orbital elements space than the observed
families. This was done in order to test the hypothesis that
asteroid family start with a more compact initial distribution in orbital
elements (i.e. lower ejection velocities) and are then scattered by the
three mechanism of above. We typically assumed an initial dispersion
of a family consistent with an isotropic ejection velocity field not exceeding
100 m/s at infinity (for a description of the algorithm to generate synthetic
families see David
Nesvorny site). We generated synthetic families with centers
in the current center of Adeona, Gefion and Dora, and we submitted their
members to the action of close encounters and Yarkovsky (SWIFT-SKEEL and
SWIFT-RMVSY codes, see next section). We used the same values
of thermal parameters for C-types families (Adeona and Dora) and
S-type family (Gefion) used by Mira Broz and David Vokrouhlicky (see
yarko
site). Our goal was to estimate the long term effect of close encounters
on semimajor axis mobility, to compare its effectiveness with the mobility
from Yarkovsky effect, and to try to obtain an estimate of the ages of
the Adeona and Gefion family. In the following table we report
a list of our simulations, with their integration length and step size.
Except for the first simulation, with current
members of Adeona, for which we consider all the planets
from Venus to Neptune, all simulations used the OSS planets (plus the four
largest asteroids for the simulations with SWIFT-SKEEL).
| Simulation: |
Integration length t [Myr] |
Step size dt [day] |
propagator |
|
|
|
|
| -Adeona: Real Members |
500 |
7 |
SWIFT-SKEEL |
| -Adeona: Original distribution |
630 |
18 |
SWIFT-SKEEL |
| -Adeona: Original distribution |
880 |
20 |
SWIFT-RMVSY |
| -Gefion: Real Members |
580 |
18 |
SWIFT-SKEEL |
| -Gefion: Original distribution |
500 |
18 |
SWIFT-SKEEL |
| -Gefion: Original distribution |
770 |
20 |
SWIFT-RMVSY |
| -Dora: Original
distribution |
220 |
18 |
SWIFT-SKEEL |
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Integrators
We used two integrators for our
simulations. Close encounters are notoriously "tough" to account
for: for our simulations with large asteroids we used SWIFT-SKEEL,
from H. Levison and M. Duncan, that is able to symplectically integrate
close encounters between a massless particle and a massive body.
This algorithm combines a variant of the standard mixed-variable symplectic
method (MVS, Wisdom and Holman 1991) with an improved version of the multiple
time-step method originally developed by Skeel and Biesiadecki (1994),
(see also Biesiadecki and Skeel 1993). Further details can be found
in Duncan et al. (1998). For the integrations
with the Yarkovsky effect we used SWIFT-RMVSY of Mira Broz, which is based
on SWIFT-RMVS3 of Levison and Duncan and include the Yarkovsky effect (both
diurnal and seasonal) as a gravitational perturbation of the velocities
(for further detail, see the yarko-site).
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