A frequency approach to identifying asteroid families

II. Families interacting with nonlinear secular resonances and low-order mean-motion resonances

¹ IPD, UNIVAP, São José dos Campos, SP, 12244-000, Brazil e-mail: valerio@univap.br
² IAG, Universidade de São Paulo, São Paulo, 05508-900, Brazil e-mail: tatiana@astro.iag.usp.br

Received: 26 March 2008
Accepted: 18 September 2008

Abstract

Aims. In an earlier paper we introduced a new method for determining asteroid families where families were identified in the proper frequency domain  (where n is the mean-motion, and g and s are the secular frequencies of the longitude of pericenter and nodes, respectively), rather than in the proper element domain (a, e, sin(i)) (semi-major axis, eccentricity, and inclination). Here we improve our techniques for reliably identifying members of families that interact with nonlinear secular resonances of argument other than g or and for asteroids near or in mean-motion resonant configurations.

Methods. We introduce several new distance metrics in the frequency space optimal for determining the diffusion in secular resonances of argument , , , s, and . We also regularize the dependence of the g frequency as a function of the n frequency (Vesta family) or of the eccentricity e (Hansa family).

Results. Our new approaches allow us to recognize as family members objects that were lost with previous methods, while keeping the advantages of the Carruba & Michtchenko (2007, A&A, 475, 1145) approach. More important, an analysis in the frequency domain permits a deeper understanding of the dynamical evolution of asteroid families not always obtainable with an analysis in the proper element domain.