# Eos family halo - a critical assessment

We use the same two colours as Parker et al. (2008) - they serve as two "principal components":

a* = 0.85 (g-r) + 0.45 (r-i) + 0.57 and  (i-z)

At first, we plot all Sloan data with small photometric uncertainties in a*, i, z (sigma < 0.03 mag) in the plane (a*, i-z). The corresponding figure from Parker et al. (2008) is very similar. I tried to use even similar "false" colours, which will be used in the following (a,e,I) plots.

Note there is an insignificant numerical artifact arising from the fact the Sloan catalogue contains magnitudes to two decimal places only (0.01 mag), so many bodies might have the same colour index. Consequently, the "red" bodies on the right-hand side of the diagram are not that numerous as it seems at a first sight. Parkers figure is free from this artifact.

Secondly, we select the Eos family by the HCM (with vcutoff = 50 m/s) and plot the corresponding (a*, i-z) colour diagram, in order to answer an important question: "What colour the Eos members are?".

We plot the Themis and Vesta families too, for comparison. The left figure includes large uncertainties, the right one is for sigmas < 0.03 mag only. Note that the blending of Eos and Themis is significantly reduced in the latter case. Note the blending might be even caused by the photometric noise! We probably should not use data with much larger uncertainties (sigma > 0.03 mag), because such uncertainties would comparable to the typical sizes of families on the colour diagram.

Finally, let's check the false colours for the families. The Eos family members are mostly violet-to-red. The colour criterion we are going to use is quite "conservative":

0.0 mag < a* < 0.1 mag, and  -0.03 mag < (i-z) < 0.08 mag.

There is a thin-line green rectangle in the following figure, which corresponds to this criterion and covers the "core" of the family, where most of the members are located:

OK, so we know the Eos-members colours now and we thus can select the same-coloured (Eos-like) bodies from the whole Sloan catalogue. Just to be sure, we plot the colour diagram of the selected bodies once again:

We are ready to answer the crucial question: "Where the Eos-like bodies are located?" Simply let's check the following (a, e) and (a, sin I) plots. They are actually prepared in two variants - with small and "medium" photometric uncertainties. The tiny green dots denote the Eos family as identified by the HCM to ease comparison.

Of course, the Eos family is clearly visible. We can note also Eunomia and Koronis, which have quite similar colours. (The mean colour is different from Eos, but there is a significant spread of colours among family members.) We are however mostly interested in the "halo" around the Eos. Well, there are not many bodies in the surroundings of the family "core", if we look at the small-uncertainty data! Another important feature is, that the "halo" bodies seem to be concentrated on the right-hand side of the well-known J9/4 resonance, which may indicate some relation. The Eos halo is more pronounced in the medium-uncertainty data. However, we have to be still aware of photometric noise! It can easily artificially "change" colour index of a Eos-unlike asteroid a an Eos-like value.

 small photometric uncertainties (sigma < 0.03 mag) medium uncertainties (sigma < 0.06 mag)

Let me also briefly comment on the clear visibility of the "pink" Eos family at Parker et al. (2008) figures (see them below). The Eos is not that different from "orange" Eunomia as one might think. The point is that Parker defined a strong gradient in his false colours (see above) just around a* = 0.05 mag which is - coincidentally - the mean a* value for the Eos family. The mean for the Eunomia is a* = 0.15, but the spread is large, from 0.05 upto 0.25. There are definitely a lot of "pink" bodies hidden inside the huge "orange" cloud.

Regarding the size-frequency distribution of the Eos halo, we select bodies in a broad (a,e,I) "box" surrounding the Eos family and drop bodies in a smaller box containing the Eos family. We use medium error data here, in order to increase the number of bodies as much as possible. See the following (e, sin I) plot:

 larger box smaller box (similar to Morby's)

We use albedo value A= 0.12 for both the family and halo. Unfortunately, the SFD of the halo is not similar to the Eos family at all! It is rather shallow and there is no bend-off at D = 20 km.

 larger box smaller box (similar to Morby's)

Conclusions, we can draw from it:

1. If we use small-uncertainty data, the very existence of the "halo" might be questioned!
2. The size-frequency distribution of the halo is inconclusive.
3. We must not forget two dynamical routes, which can create some sort of a "halo": the J7/3 and J9/4 resonances. (Refer to Zappalla et al. (2000) too.) We have not checked yet, what are the final stages of the resonant bodies. They might be chaotically released at higher eccentricities/inclinations.

Miroslav Broz, miroslav.broz@email.cz, Oct 29th 2010