Chaotic diffusion caused by close encounters with several massive asteroids

Abstract

Context. Close encounters with massive asteroids are known to be a mechanism of dynamical mobility that can significantly alter proper elements of minor bodies, and they are the main source of dynamical mobility for medium-sized and large asteroids (D > 20 km, approximately). Aims. Orbital mobility caused by close encounters with (4) Vesta has been studied in the past and could be a viable mechanism to produce the current orbital location of some of the V-type asteroids currently outside the Vesta family. It is well known, however, that the proper frequencies of precession of pericenter g and longitude of the node s of terrestrial planets change when one or more of the other planets is not considered in the integration scheme. For instance, the g 4 and s 4 frequencies are different when the full solar system is considered or when only Mars and the Jovian planets are accounted for. In this work we consider the effect that including one or more (up to 51) massive asteroids in the integration scheme has on the Vesta orbit, and, indirectly on the statistics of changes in semi-major axis caused by close encounters with this massive asteroid. Methods. By using chaos indicators such as the maximum Lyapunov exponent, and integrations with symplectic integrators able to account for the interaction between a massive asteroid and a mass-less particle, we studied the problem of scattering caused by close encounters with (4) Vesta, when only (4) Vesta (and the eight planets) are considered, and when (4) Vesta and other massive main belt asteroids are also accounted for. Results. We find that (4) Vesta proper frequencies are dependent on the number of other massive asteroids considered in the integration scheme and that, as a result, the whole statistics of encounters with (4) Vesta is also affected. Variances of the change in proper a caused by the four most massive asteroids varied up to 36.3% in the five integration schemes that we used, and the number of encounters that caused the strongest changes in semi-major axis varied up to a factor 2. The indirect effect caused by the presence of other massive asteroids therefore introduces an additional source of uncertainty in estimating the long-term effect of close encounters with massive asteroids that was not accounted for in previous works on the subject, and that strongly affects estimates of its Hurst exponent.

Chaotic diffusion caused by close encounters with several massive asteroids

“…4 display the number of close encounters among massive asteroids as a function of the number of massive asteroids included in the model. For the case of (10) Hygiea, the number of close encounters experienced by this asteroid during the simulation was somewhat limited when compared with results observed for (4) Vesta (Carruba et al 2012). The models for which this number was the highest correspond to values of g frequencies beyond a 3σ level, but not to the highest (or lowest) peaks (models with 12 and 14 asteroids, for instance).…”

“…We also show in the figure the orbital position of all real asteroids with absolute magnitudes H < 13.5 in the same a − i range of our test particles as blue asterisks 1 . As in Carruba et al (2012), we choose only the largest bodies because asteroids with diameters larger than 20 km are the ones for which close encounters are the dominant mechanism of dynamical mobility on 1 The dynamical map was computed using the orbital elements of (10) Hygiea at J2000. The location of secular resonances may vary when computed for the orbits of other asteroids.…”

“…Following the approach of Carruba et al (2012), we integrated our asteroids as massive bodies over 30 Myr with SWIFT-SKEEL, the symplectic integrator using the Wisdom and Holman mapping (Wisdom & Holman 1991;Levison & Duncan 2000). Results for the g frequency (for simplicity we do not show the s data) are shown in Fig.…”

“…For instance, the g 4 and s 4 frequencies of Mars are different when the full solar system is considered or when only Mars and the Jovian planets are accounted for. Carruba et al (2012) showed that (4) Vesta proper frequencies are dependent on the number of other massive asteroids included in the integration scheme and that, as a result, the whole statistics of encounters with (4) Vesta is also affected. Delisle & Laskar (2012) showed that dynamical mobility caused by close encounters with massive asteroids is dominated by encounters with (4) Vesta and (1) Ceres, with the other massive asteroid playing a lesser role.…”

“…Can the third, fourth, or other most massive bodies have also played a role in the dynamical mobility of minor bodies, at least in their orbital proximities? And if that is possible, how much is the drift rate in semimajor axis affected by the choice of the model used to simulate the long-term effect of close encounters with massive asteroids, as observed in the region of (4) Vesta (Carruba et al 2012)?…”