Mon. Not. R. Astron. Soc. 000, 1–23 (2004) Printed 15 December 2004 (MN LATEX style file v2.2)

Yarkovsky origin of the unstable in the 2/1 resonance with

M. Broˇz1⋆, D. Vokrouhlick´y1⋆, F. Roig2⋆, D. Nesvorn´y3⋆, W.F. Bottke3⋆, and A. Morbidelli4⋆ 1Institute of Astronomy, Charles University, Prague, V Holeˇsoviˇck´ach 2, 18000 Prague 8, Czech Republic 2Observat´orio Nacional - MCT, Rua Gal. Jos´eCristino 77, Rio de Janeiro, 20921-400 RJ, Brasil 3Department of Space Studies, Southwest Research Institute, 1050 Walnut St., Suite 400, Boulder, CO 80302, USA 4Observatoire de la Cˆote d’Azur, Dept. Cassiopee, BP 4224, 06304 Nice Cedex 4, France

Accepted ???, Received 15 December 2004

ABSTRACT The 2/1 mean motion resonance with Jupiter, intersecting the main belt at ≈ 3.27 AU, contains a small population of objects. Numerical investigations have classified three groups within this population: asteroids residing on stable orbits (i.e., Zhongguos), marginally stable orbits with dynamical lifetimes on the order 100 My (i.e., Griquas) and unstable orbits. In this paper, we reexamine the origin, evolution and survivability of objects in the 2/1 population. Using recent asteroid survey data, we have identified one hundred new members since the last search, which increases the resonant population to 153. The most interesting new asteroids are those located in the theoretically-predicted stable island A, which until now had though to be empty. Next, we investigated whether the population of objects residing on the unstable orbits could be resupplied by material from the edges of the 2/1 resonance by the thermal drag force called the Yarkovsky effect. Using N-body simulations, we showed that test particles pushed into the 2/1 resonance by the Yarkovsky effect visit the same regions occupied by the unstable asteroids. We also found that our tests bodies had dynami- cal lifetimes consistent with the integrated orbits of the unstable population. Using a semi-analytical Monte-Carlo model, we computed the steady-state size distribution of H < 14 asteroids on unstable orbits within the resonance. Our results pro- vide a good match with the available observational data. Finally, we discuss whether some 2/1 objects may be temporarily-captured Jupiter family or near-Earth asteroids. Key words: celestial mechanics – minor planets, asteroids – methods: numerical.

1 INTRODUCTION of analytical methods (e.g., perturbation theory). More re- cently, semi-analytical and numerical methods have allowed In 1869 the first asteroid, 108 Hecuba, was found to reside to make great progress in our understanding of resonant near the 2/1 mean motion resonance with Jupiter (Luther dynamics. In particular, we can now decipher some of the 1869; Tietjen 1869). (Hereafter, we denote this resonance minute details of asteroid motion inside the J2/1 (e.g. Mur- as J2/1, with other resonances denoted accordingly.) Since ray 1986; Henrard & Lemaˆıtre 1987; Lemaˆıtre & Henrard that time, asteroidal dynamics near or inside mean motion 1990; Morbidelli & Moons 1993; Ferraz-Mello 1994; Hen- resonances with Jupiter have attracted attention. For exam- rard et al. 1995; Morbidelli 1996; Nesvorn´y& Ferraz-Mello ple, Hansen, Bohlin and von Zeipel were among the first in 1997; Moons et al. 1998; Morbidelli 2002). a long list of researchers who tried to deal with the difficul- ties of insufficient convergence of the resonant trigonometric Although today we recognize that Hecuba itself is just perturbation series for Hecuba-like orbits (historical notes outside the J2/1, we know that more than hundred asteroids in Hagihara 1975). These cases demonstrated the limits reside inside the J2/1. This sample is large