Asteroid families age determination: the role of the physical effects

The availability of  large data set of asteroids  proper elements made
possible in recent years a deeper and deeper analysis of the structure
of the  asteroid dynamical families in  the Main Belt (Milani  et al.,
2014). At the same time the  Yarkovsky effect, the importance of which
has been  largely recognized,  has imposed  a new  data interpretation
paradigm.   Precisely  the  Yarkovsky  effect  is  the  basis  of  one
estimation method  of the age  of the asteroid families  analyzing the
shape of the family members  distribution in the plane diameter versus
proper semimajor axes, the so called V-shape (Spoto et al., 2015).

This very important  goal has been achieved under  the assumption that
the  post-formation  evolution of  the  semimajor  axes producing  the
V-shape  structure was  linear  in time  and  dominates their  present
dispersion.  In  particular the  impact of the  initial values  of the
fragments ejection  velocities, determining the initial  dispersion of
the semimajor  axes, is supposed  to be marginal,  assumption probably
correct for old enough families. If  this is not the case, the initial
ejection velocity  field introduces a more  or less large bias  in the
age  determination.  We  conducted a  series of  numerical experiments
simulating  the  formation and  dynamical  evolution  of the  asteroid
families in order to evaluate the extent of this bias.

Moreover in  our model we  included a series of  mechanisms concerning
the initial  break-up outcomes.  In particular  two aspects  have been
taken  into   account:  the   effect  of  the   initial  gravitational
re-accumulation  on the  structure of  the V-shape  and the  effect of
possible  correlations between  spin direction  and ejection  velocity
direction (Milani et  al., 2019). We show how the  former effect could
be responsible of  some systematic features of  the V-shape structure,
while  the second  can in  some  cases mitigate  the bias  in the  age
determination introduced by the initial ejection field.

Finally we discuss the role of  the family members spin axes evolution
due to  non destructive  collisions, affecting  the efficiency  of the
Yarkovsky-driven  semimajor axis  mobility.  We show  how this  latter
mechanism modifies the determination of the age.

 

References:

Milani A., Cellino A., Knezevic Z., Novakovic B., Spoto F., Paolicchi P.
2014.
Asteroid families classification: Exploiting very large datasets.
Icarus, 239, 46-73.

Spoto F., Milani A., Knezevic Z.
2015.
Asteroid family ages.
Icarus, 257, 275-289.

Milani A., Knezevic Z., Spoto F., Paolicchi P.
2019.
Asteroid cratering families: recognition and collisional interpretation.
Astronomy and Astrophysics, 622, A47.