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Chaotic Diffusion of the Vesta Family Induced by Close Encounters With Astronomy & Astrophysics manuscript no. article September 6, 2018 (DOI: will be inserted by hand later) Chaotic diffusion of the Vesta family induced by close encounters with massive asteroids J.-B. Delisle and J. Laskar ASD, IMCCE-CNRS UMR8028, Observatoire de Paris, UPMC, 77 Av. Denfert-Rochereau, 75014 Paris, France September 6, 2018 Abstract. We numerically estimate the semi-major axis chaotic diffusion of the Vesta family asteroids induced by close encounters with 11 massive main belt asteroids : (1) Ceres, (2) Pallas, (3) Juno, (4) Vesta, (7) Iris, (10) Hygiea, (15) Eunomia, (19) Fortuna, (324) Bamberga, (532) Herculina, (704) Interamnia. We find that most of the diffusion is due to Ceres and Vesta. By extrapolating our results, we are able to constrain the global effect of close encounters with all the main belt asteroids. A comparison of this drift estimate with the one expected for the Yarkovsky effect shows that for asteroids whose diameter is larger than about 40 km, close encounters dominate the Yarkovsky effect. Overall, our findings confirm the standard scenario for the history of the Vesta family. 1. Introduction showed that close encounters among massive asteroids in- duce strong chaos which appears to be the main limit- It is now admitted that most of V-type near-Earth aster- ing factor for planetary ephemeris on tens of Myr. In the oids (NEAs) and howardite, eucrite and diogenite (HED) continuation of this work we concentrated our study on meteorites are fragments of a collision between Vesta and the diffusion induced by close encounters of Vesta family another object which also produced the Vesta family (see members with massive asteroids. Sears 1997). V-type NEAs and HED meteorites are former members of the Vesta family that have been carried from This effect has already been studied for different as- the main asteroid belt to Earth-crossing orbits by the two teroid families (e.g. the Flora and Lixiaohua families Nesvorn´yet al. 2002; Novakovi´cet al. 2010). The most main resonances in the neighborhood of Vesta : the ν6 and 3 : 1 resonances with Jupiter. The major issue in this sce- exhaustive study (in terms of number of asteroids taken nario is the fact that the average life time of fragments into account) concerned the Gefion and Adeona families in these two resonances is too short to explain the mean (Carruba et al. 2003). The authors considered all 682 as- age of HED meteorites and V-type NEAs (Migliorini et al. teroids of radius larger than 50 km for encounters with 1997). members of the families. They concluded that the four The commonly accepted explanation for this is that largest asteroids ((1) Ceres, (2) Pallas, (4) Vesta and (10) NEAs spent most of their life time in the main asteroid Hygiea) had a much larger influence than all the 678 re- belt before entering in resonance and being carried to their maining asteroids so the latters can be considered as negli- current orbits. This supposes that a mechanism can induce gible. The Vesta family has also been the object of such an a diffusion process that brings fragments to one (or both) analysis (Carruba et al. 2007) but only close encounters of the two main resonances. The Yarkovsky effect is now with (4) Vesta were taken into account. These different admitted to be the main mechanism explaining the diffu- studies show that the effect of close encounters with mas- sion of Vesta family members (e.g. Carruba et al. 2003). sive asteroids depends a lot on the considered family and its position in phase space with respect to those of massive However other processes also contribute to the diffu- arXiv:1110.5820v1 [astro-ph.EP] 26 Oct 2011 asteroids. sion. It is in particular the case for the chaos induced by overlaps of mean motion resonances or close encounters The purpose of this work is to explore further the between asteroids in the main belt. In the case of the res- effect of close encounters for the Vesta family by con- onances, Morbidelli & Gladman (1998) showed that the sidering the effect of 11 large asteroids : (1) Ceres, (2) chaotic zone around the 3 : 1 resonance is too narrow to Pallas, (3) Juno, (4) Vesta, (7) Iris, (10) Hygiea, (15) explain the needed diffusion. Recently, Laskar et al. (2011) Eunomia, (19) Fortuna, (324) Bamberga, (532) Herculina, (704) Interamnia. Moreover, we use the results from these Send offprint requests to: J.-B. Delisle, e-mail: interactions to extrapolate and obtain an estimate of the [email protected] effect which would be raised by the whole main asteroid 2 Delisle and Laskar: Chaotic diffusion induced by massive asteroids belt. Finally we compare the semi-major axis diffusion in- Simulation initial distribution duced by the Yarkovsky effect and the diffusion due to catalog objects close encounters (in the case of the Vesta family). 0.14 0.13 2. Numerical simulations 0.12 0.11 We ran two sets of numerical simulations. Both of them 0.10 e comprise the 8 planets of the Solar System, Pluto, the 0.09 Moon and the 11 asteroids enumerated above. In both sim- 0.08 ulations, we generate a synthetic Vesta family produced by 0.07 an initial collision of another object with Vesta. We do not 0.06 model a realistic collision process but instead we consider 0.05 a set of test particles initially at the same position as Vesta 8.0 but with different relative velocities. This is not a problem 7.5 because we are mainly interested in this work in exploring 7.0 the phase space in the region of the Vesta family. The rel- 6.5 ative velocities of the fragments of collision are sampled both in norm and direction. For the norm, we take 8 dif- I (deg) 6.0 1 ferent values (every 50 ms− ) between the escape velocity 5.5 1 at Vesta’s surface (around 350 ms− ) and twice this value 5.0 1 (700 ms− ). The inclination is sampled between 50◦ and − 4.5 50◦ every 10◦ (11 different values). Finally, the direction 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.5 in the invariant plane is taken every 10◦ (36 values). This a (AU) way we create 3168 test particles that represent the Vesta family. We plotted the positions of these particles in the Fig. 1. Initial distribution of the synthetic Vesta family (a, e) and (a, I) planes (where a is the semi-major axis, e in the (a, e) plane (top) and the (a, I) plane (bottom). the eccentricity and I the inclination) superimposed with Real members proper elements (from Nesvorn´y2010) are the catalog published by Nesvorn´y(2010) of current Vesta superimposed for comparison. family members (Fig.1). Note that despite we did not com- pute the proper elements whereas the catalog uses them 3. Global overview of the diffusion the two sets of points superimpose quite well. Moreover we constructed an initial set of particles just after the origi- The goal of this study is to understand whether the cur- nal collision whereas the catalog exposes the remnants of rent flux of V-type asteroids coming from the main belt the family after approximately 1.2 Gyr of evolution (see and carried to near-Earth orbits through strong planetary Carruba et al. 2007). resonances can be explained by the chaos induced by close In the first simulation (the reference simulation, S), encounters in the main asteroid belt (or at least that these the 11 asteroids are considered as test particles as well encounters contribute significantly). The simplest way to and thus do not perturb the fragments of collision. In the check this assumption is to look in both S and SE simula- second simulation (SE) the 11 asteroids are considered as tions to the number of NEAs as a function of time and to the planets and thereby interact with members of the syn- see if the consideration of asteroidal interactions implies thetic Vesta family. Both solutions are integrated over 30 a greater number of NEAs. We use the usual criterion to Myr using the symplectic integrator described in (Laskar decide whether an asteroid is a NEA or not : if the perias- et al. 2011) and references therein. The effects of all plan- tron of its orbit become smaller than 1.3 AU the asteroid ets and Pluto are taken into account, as well as general is considered as a NEA (see for example Morbidelli et al. relativity. 2002). In Fig.2 we plot the evolution of the number of In order to be able to analyze the evolution of the test NEAs in both simulations as a function of time. We can particles and in particular the impact of close encounters see on this graph that the close encounters have not a with the 11 asteroids we set up different logs. We record major effect on the population of NEAs on the duration for each particle its instantaneous orbital elements every of the simulation. However, we did not ran our simula- 1 kyr. We do not compute proper elements but instead we tions on the total age of the Vesta family (around 1.2 Gyr) use the minimum and maximum values (see Laskar 1994) and we can think that just after the collision that origi- taken by a, e and I on time spans of 10 kyr. Actually, we nated the Vesta family, the population of V-type NEAs is use the average of the minimum and maximum values as dominated by fragments of the collision that were directly proper elements.
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