Families or not?

An important observation on the orbital distribution of irregular satellites is that satellite families at Saturn, Uranus and Neptune are not well defined. At Jupiter one finds 3-4 reasonably compact retrograde families, corresponding to each of the previously known retrograde irregulars and one prograde family. Beyond Jupiter, family associations are not clear, as satellites within suspected families are more loosely associated with each other.

This could be partly due to our inventory of small, faint jovian satellites being more complete. In other words, beyond Jupiter we only see the large (and hence bright) parent bodies rather than the small and faint collisional fragments. That, however, does not explain why the orbital element scatter is so large at Saturn where the completeness limit is close to that of Jupiter. The satellite Phoebe in particular, is one of the largest irregular satellites and should have suffered several collisional events during its lifetime as imaging from the recent Cassini spacecraft flyby indicates. However, objects at similar orbital inclinations as Phoebe are not close enough to it to qualify as family members. In fact, some of these objects do not even cross Phoebe's orbit. Similar ``loose'' or ``scattered'' groups are seen at Uranus and Neptune.

A starting point to addressing this problem is to study the jovian families where statistical confidence is best. There are two well-defined retrograde and one prograde multi-member families, named after the largest member, namely the Carme (9 members), Ananke (7), and Himalia (4). The compactness of these families may be quantified through a set of equations collectively known as the Gauss equations. These translate small differences between orbital elements of the parent and satellite to an equivalent ejection velocity of the fragment from the parent.

The maximum such ejection velocity within the Carme family is 50 m/s and 80 m/s for Ananke. These agree with ejection velocities predicted from SPH code simulations of collisional fragmentation of asteroids. Within the Himalia family, however, velocities vary from 50 to 320 m/s and these are generally too high.

So, how is this prograde family different from the retrograde ones? One obvious difference is that Himalia is a fairly large satellite (at D=170 km it is the largest jovian irregular) while for the retrograde parent bodies D<80 km. Himalia's mass ratio to its primary is of order 10^-9, larger than that of the asteroid Ceres to the Sun. Although the gravitational influence of Himalia to its group is minute, it would have operated for aeons so the cumulative effect could be significant.

The role of scattering

I have run simulations to show that, over a period of 100 Myr Himalia would scatter the orbital semimajor axis separations of its group members to 10-15%. This is significant and, if extrapolated over the age of the solar system, it implies that the group was more compact than it is now (Christou, Icarus 2005, in press). That is contrary to the current doctrine that very little has happened to these irregular satellite families following their collisional formation.

The semimajor axis evolution of "clones" of the four Himalia group members, Himalia (purple), Elara (blue), Lysithea (red) 
and Leda (green) for 100 Myr as they are scattered by Himalia. The scattering growth rate (ie the opening angle of the ``fans'') 
is similar for each satellite and can be used to estimate how far the satellites migrated to reach their current locations 
over time.

Furthermore, this process puts constraints on the lifetime of the cluster. Scattering is not a reversible process; it always spreads the cluster at a rate which is typically a simple function of a constant parameter and so it serves to mark the time since a group's formation. By measuring the scattering rate and applying it to each of the satellites in turn, we found that (a) JVII Elara must have been created at the very early stage of the solar system's existence, otherwise there would not have been enough time to reach its present position (b) JX Lysithea and JXIII Leda could have been created at a later date. In particular, Lysithea could have been created as recently as the last Gyr of the solar system's existence.

I also serendipitously discovered a mechanism altering the inclination of this satellite: a transient locking between the nodes of Himalia and Lysithea. It is presently not clear (a) what is the long term effect to Lysithea's orbit (b) whether such processes are generic to irregular satellite groups.

All these predictions depend critically on how massive Himalia actually is. There are no direct determinations of this satellite's mass so we have relied on guesses based on its estimated size and density. These cover a wide spectrum of possibilities and it is significant that for some choices the mechanism is ineffective ie the issue of mass constitutes a test of the model. Specifically, if Himalia is both (i) underdense (rho<1.3 g/cm3) which would be the case, for example, if it is the reaccumulation of collisional fragments (ii) as small as the low-resolution imaging by Cassini indicated then it is not an effective scatterer and some other mechanism must be responsible for the large ejection velocities within the Himalia group.

An episode of temporary locking of the nodes of JVI Himalia and 
JX Lysithea lasting over 10 Myr (lower panel). During the same 
period the inclination of Lysithea (upper panel) increases by 
0.1 degrees.

To summarise, work done at the Observatory so far has demonstrated the potential of gravitational scattering to explain features in the orbital distribution of the irregulars. This is not the end of the affair however since several important questions remain unanswered. These include:

  1. What is, in fact, Himalia's mass? This is the one crucial parameter knowledge of which is required to ``clinch'' the scattering hypothesis. Unlike the following, this particular question can only be answered through observations.
  2. Would the magnitude of the scattering in hypothetical families of other large irregular satellites, namely Nereid at Neptune, Caliban and Sycorax at Uranus and Phoebe at Saturn, be consistent with the existence of "loose families" of these satellites as observed today?
  3. How reliably can the scattering rate be used to infer the age of the families (and by implication, the time at which large impacts took place on, or among, irregular satellite parent bodies)? This, for example, would help to place constraints on epochs at which the influx of impactors on planetary surfaces was enhanced such as the so-called ``heavy-bombardment'' inferred from Apollo data on lunar impact basin ages.
  4. What is the role of resonances in this process? (a) are secular or mean motion resonances between known satellites operating at present or have been operating in the past? (b) what are the effects of such resonances, if any, on the satellite scattering rate?
These questions (apart from #1) can be answered by further multi-particle simulations and we plan to carry these out in the future.

Last Revised: 2005 January 10th
WWW contact: aac@arm.ac.uk