The (not so) peculiar case of the Padua family

Abstract

The Agnia asteroid family was recently studied by Vokrouhlický et al. because of its peculiar and, so far, unique relationship with the z1 secular resonance. The Agnia family is almost entirely contained within the high‐order secular resonance z1. Here, I study another family in the middle belt that is characterized by its interaction with the z1 resonance, the Padua family. More than 75 per cent of its members are currently on z1 librating orbits, and therefore several of the techniques used by Vokrouhlický et al. can also be applied to this family. As for the case of the Agnia family, numerical integration methods and Monte Carlo models can be used to set lower and upper limits on the family age, and to obtain estimates on the fraction of prograde rotators. The constraints obtained on the family age and original ejection velocity field may be used to set limits on the dynamical mobility caused by low‐energy collisions, that is dependent on the yet poorly known exponent α that best fits the size distribution of objects of less than 5 km in diameter. In this work, the Padua dynamical family was obtained in both the proper element and frequency domains. Numerical simulations of family members in the space of the z1 resonance variable (σ, dσ/dt) suggest that the family is at least 25 Myr old. The conservation of the z1K′2 conserved quantity implies that the original ejection velocity field was of VEJ= 35.0 ± 8.5 m s−1. Monte Carlo models of the diffusion of the semimajor axis caused by the Yarkovsky and Yarkovsky–O'Keefe–Radzievsky–Paddack (YORP) effects also confirm the results obtained with the alternative approaches. The Padua family is 24+28−20 Myr old, and it was probably created by an impact that ejected fragments with average ejection velocities of VEJ= 30.0+2.0−4.0 m s−1. The fact that the Padua family is at least 25 Myr old suggests that low‐energy collisions as modelled by Dell'Oro & Cellino should have played a minor role in the semimajor axis diffusion of the family members. My results are at best consistent with a value of α equal to −2.3. Families interacting with secular resonances such as the Agnia and Padua families can provide useful information not only about their age and original ejection velocity field, but also on the yet poorly known cumulative size distribution of objects of diameters of 5 km and less.

Characterizing the original ejection velocity field of the Koronis family

“…To check if all important secular resonances were identified in the dynamical maps, we also computed the orbital location of all secular resonances whose combination of proper g and s is within the values covered by the Koronis family, and checked the number of likely resonators (Carruba, 2009) for each resonance (likely resonators are defined as the objects whose combination of asteroidal proper frequencies is within ±0.3 arcsec/yr from the resonance center. For the case of the z 1 = g − g 6 + s − s 6 resonance, this would correspond to g + s = g 6 + s 6 = 1.898 arcsec/yr; the actual threshold may vary for higher order resonances, but the 0.3 arcsec/yr boundary usually provide a good first order of magnitude criteria).…”

Secular dynamics and family identification among highly inclined asteroids in the Euphrosyne region

“…So, resonances as the ν 6 = g − g 6 are g ‐type resonance, resonances like the z 1 = g − g 6 + s − s 6 are g + s resonances and so forth. As a preliminary criterion justified from past experiences with secular resonances (Carruba 2009a), we considered asteroids as more likely to be inside a secular resonance if the resonant combination of their proper frequencies is to within 0.3 arcsec yr −1 from the resonance centre. For instance, in the case of the z 1 resonance we considered resonant candidates asteroids with values of g + s to within ± 0.3 arcsec yr −1 from the planetary frequency combination g 6 + s 6 .…”

On the Emmenthal distribution of highly inclined asteroids

“…To identify regions that were originally underpopulated, we need to eliminate areas whose low number density is caused by the destabilizing effects of the local dynamics. Based on several previous studies of the dynamics of highly inclined objects (see, for instance, Carruba 2009a,b, 2010a,b; Carruba et al 2011b), we can distinguish between destabilizing resonances (resonances that cause a change in the asteroid eccentricity that is large enough to bring its pericentre to regions of terrestrial planet encounters, causing the loss of at least 50 per cent of the bodies initially inside the resonance because of a collision with the Sun or other planets during time‐scales of 10 Myr or less, in conservative simulations of the orbital evolution of an asteroid subjected to the influence of the Sun and all the planets) and diffusive resonances (resonances whose passage through causes a significant change in the asteroid proper elements, but not large enough to cause the loss of the body). We can safely assume that bodies in regions affected by or near destabilizing resonances will be lost on time‐scales of up to 10 Myr, so that local low densities do not reflect a non‐uniform primordial distribution.…”