Among highly inclined asteroids the external region of the main belt beyond the 5J:2A mean‐motion resonance with Jupiter has long been known to host the Euphrosyne and Alauda families. The region is confined in semimajor axis between the 5J:‐2A and 2J:‐1A mean‐motion resonances with Jupiter, and is characterized by the presence of the ν6, ν5 and ν16 linear secular resonances, as well as by the z1, z2, z3 and other non‐linear secular resonances. In this work we employed the frequency modified Fourier transform method to obtain synthetic proper elements for 6841 numbered and 4034 multi‐opposition objects in the region of the Euphrosyne family, and used this data to obtain families and clumps in the domain of proper elements and frequencies. With respect to other works on family identification in the area, here we focused our investigation on the effect that the complicated local web of secular resonances has had on the dynamical evolutions of families and clumps. We detected all main linear and non‐linear secular resonances, up to order six, in the region and identified for the first time new populations of objects in ν6 anti‐aligned librating and ν5 anti‐aligned and aligned librating resonant states. We identified two new clumps among ν6 anti‐aligned librating objects, making them the second and the third groups in this resonant configuration ever found after the discovery of the Tina family. Once the local dynamics was fully understood, we then obtained dynamical groups in the domain of proper elements and in the domain of proper frequencies most apt to study the secular resonance present in each region, and computed ν6 resonant proper elements to study groups in regions affected by the ν6 secular resonance. We identified 18 families and 39 clumps in the Euphrosyne region, of which 12 families and five clumps were in frequency domains. Of particular interest was the group around (69559) (1997 UG5), found in both proper element and frequency domains, characterized by its interaction with five secular resonances. It is the first time that a group of asteroids is found in such an interesting resonant configuration. More importantly, we introduced new techniques for asteroid family identification in presence of secular resonances, which could in principle be used for other areas of the asteroid belt.
In a previous paper, the current state of knowledge on the region of the Pallas dynamical family was revised. Here the dynamical evolution and possible origin of dynamical groups in the region are investigated. First, we study the case of asteroids at high eccentricity (e > 0.31). These objects are unstable because of encounters with Mars on time-scales of up to 340 Myr. Local background asteroids are currently the major source of high-eccentricity objects, but Barcelona family members will become the dominant source in about 250 Myr.Next, attention is focused on the lack of chaotic dynamics near the ν 6 secular resonance border in the region. Contrary to the case of the Phocaea family region, very limited chaotic behaviour was observed for real and fictitious particles in the central main belt near the ν 6 resonance. Using analytical and numerical tools, we find that the limited amplitude of the inclination region near the ν 6 resonance in the Pallas family region for which close encounters with Mars are possible explains the lack of chaotic behaviour found in a previous paper by Carruba.Finally, we investigate the long-term stability of the minor families and clumps identified in the previous paper, when non-gravitational effects are considered. We find that none of the minor clumps obtained by Carruba is currently interacting with non-linear secular resonances in the region. RA111 have large detectability times and could be considered reasonable candidates for groups originating from collisional events. We confirm the presence of the (4203) Brucato family observable in the space of proper frequencies (n, g, g + s) that has the largest detectability time of all groups in the region.
Highly inclined asteroids are objects with sin (i) > 0.3. Among highly inclined asteroids, we can distinguish between objects with inclinations smaller than that of the centre of the ν6= g − g6 secular resonance and objects at higher inclinations. Using the current mechanisms of dynamical mobility, it is not easy to increase the values of an asteroid with an initial small inclination to values higher than that of the centre of the ν6 resonance. The presence of highly inclined objects might therefore be related to the early phases of the Solar system. It has been observed that several dynamically stable regions are characterized by a very low number density of objects, unlike low‐inclined bodies that tend to occupy all the dynamically viable regions. The distribution of asteroids at a high inclination in the domain of proper elements in dynamically stable regions resembles an Emmenthal cheese, with regions of low number density close to highly populated areas. While this phenomenon has been observed qualitatively in the past, no quantitative study has yet been carried out on the extent and long‐term stability of these regions. In this paper, we identify two dynamically stable regions characterized by very low values of number density and permanence times of 100 Myr or more when the Yarkovsky force is considered. We show that the low number density of objects in these areas cannot be produced as a statistical fluctuation of any simple one‐dimensional statistical distribution, such as the Poissonian, uniform and Gaussian distributions, or of a tri‐dimensional distribution, such as the tri‐variate normal distribution. The presence of unoccupied dynamically stable regions could indicate that the primordial asteroidal population might not have reached all available zones at high‐i. This sets constraints on the scenarios for the early phases of the history of our Solar system.
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