Predicting the origins of C-type family halo asteroids using ANNs 

  Asteroid families are groups of asteroids that have formed from the fragments of a larger ‘parent’ body that has been disrupted. When viewed in a space with the axis of proper orbital elements: semi-major axis (a), eccentricity (e), and inclination (i), families appear as relatively compact clusters within a background of unrelated asteroids. Halos are dense shells of asteroids that surround these families and tend to have similar properties to the core family yet are not considered as members. Isolating these halo structures and predicting their family membership remains and ongoing challenge. We present the results of using artificial neural networks (ANNs) aiming to solve this.   In this work we focused on C-type families in the inner-main belt, between 2.1 and 2.5 au. C-type families are notably dark, with reflectance less than 5-10% and are distinctive from the backgrounds they are situated in. This is useful for verifying the predictions of the ANNs. The Erigone family was focused on as it has a well-documented halo (Carruba 2016), is separate from the other larger structures of the Vesta and Flora families, is comparatively young, estimated between 200-250 Myr (Spoto 2015), and is numerous, with ~2000 bodies having measured albedos. It therefore served as the ideal testbed to expand upon for more varied C-type families.   The network structure we used are multi-layer perceptrons (MLPs). The input neurons used include the three orbital elements with the metric by Zappala (1990), their standard deviations, and absolute difference in albedo from the parent, h-magnitude, and inverse diameter. The network was kept to 2 hidden-layers and to prevent overfitting. Asteroids associated with the 8 C-type families were labelled with a single neuron output layer as 1, and other background asteroid not within this volume were labelled 0. The final architecture of the network was 9:27:3:1. The models were trained using values from the MP3C database hosted by the Observatoire Côte d’Azur (https://mp3c.oca.eu/). To isolate the family and halo complex, a volume of ±5 standard deviations in the family's centre in proper orbital space was defined. Once the network was trained, the halo asteroids in the box were then introduced as ‘unseen’ data to be evaluated by the network. Additionally, family members were re-introduced as unknown control values. We verified that the network was working as intended by making sure the network was able to correctly categorise known family members.   Our network was able to recover 99.83% of the Erigone family with a predicted certainty of >0.9. 581 asteroids from the halo were predicted by the ANN to be family members, an increase of 32%. The ANNs predictions were pruned manually, where any asteroids with an albedo greater than 0.1 and further than 3 std in (a, e, i) away from the centre were discarded. The experiment was repeated with 5 other C-type families, and large portions of additional asteroids were predicted to be family members: 84 Kilo (+43%), 329 Svea (+42%), 623 Chimaera (+43%), 752 Sulamatis (+25%). These experiments reinforce the notion that asteroid family halos contain a significant number of family asteroids that have been missed for inclusion in the family. We find that ANNs are good complements to the surveying done previously with algorithms such as the Hierarchical Clustering Method (HCM). Additionally, we make the case that they will be useful tools for the expected massive influx of new asteroids that will come with the Vera Rubin Observatory’s LSST.      References:  V. Carruba, S. Aljbaae, O. C. Winter, On the Erigone family and the z2 secular resonance, Monthly Notices of the Royal Astronomical Society, Volume 455, Issue 3, 21 January 2016, Pages 2279–2288, https://doi.org/10.1093/mnras/stv2430  Spoto, F., Milani, A., Knežević, Z., 2015. Asteroid family ages. Icarus 257, 275–289. URL: http://dx.doi.org/10.1016/j.icarus.2015.04.041, doi:10.1016/j.icarus.2015.04.041  Zappala, Vincenzo & Cellino, Alberto & Farinella, Paolo & Knezevic, Zoran. (1990). Asteroid families. I. Identification by hierarchical clustering and reliability assessment. The Astronomical Journal. 100. 2030-2046. 10.1086/115658.