Yarkovsky Origin of the Unstable Asteroids in the 2/1 Mean Motion Resonance with Jupiter
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Mon. Not. R. Astron. Soc. 000, 1–23 (2004) Printed 15 December 2004 (MN LATEX style file v2.2) Yarkovsky origin of the unstable asteroids in the 2/1 mean motion resonance with Jupiter 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 asteroid 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 magnitude 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 comets 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 enough to allow us to quantitatively analyse their origin. Recently, Roig et al. (2002) published a catalogue of 53 asteroids residing in the ⋆ E-mail: [email protected]ff.cuni.cz (MB); [email protected] J2/1 and placed them into 3 groups according to their dy- (FR); [email protected] (DV); [email protected] (DN); namical lifetime in the resonance (tJ2/1). Half of the orbits [email protected] (AM); [email protected] (WFB) were found to be stable (t 1 Gy), much like that of J2/1 ≈ c 2004 RAS ° 2 M. Broˇzet al. (3789) Zhongguo, the first stable asteroid discovered in the Alternatively, the current view of asteroid family evolu- J2/1 resonance. The remaining bodies are either marginally tion, namely that the initial break-up event was followed by stable (t 100 My) or unstable (t 10 My), with a subsequent dynamical spreading due to the effect of the J2/1 ≈ J2/1 ≈ the leading asteroids in each group being (1362) Griqua and Yarkovsky forces and chaos in weak resonances (e.g. Bottke (1922) Zulu. Importantly, the largest asteroids of all three et al. 2001; Nesvorn´yet al. 2002a; Bottke et al. 2003), offers a groups are between D = 20 30 km in diameter. natural continuous-flow model of type (ii) mentioned above. − Asteroidal sizes and dynamical lifetimes are very basic As asteroids slowly diffuse in semimajor axis over time, they indicators of their origin. We know that unstable resonant can reach the border of a resonance and fall into it. This sce- asteroids are not primordial because they cannot reside on nario provides a continuous resupply of resonant asteroids their current orbits for 4.6 Gy.1 Moreover, small asteroids (dominated by the Yarkovsky effect), and is supported by are unlikely to survive 4.6 Gy of collisional evolution. Bottke observations of asteroids on highly unstable orbits adjacent et al. (2004) estimate the collisional lifetimes of D < 10 km to the resonances (e.g. Milani & Farinella 1995; Vokrouh- asteroids are less than the age of the Solar system. lick´yet al. 2001; Guillens et al. 2003) and by a quantitative The situation is different for asteroidal populations in- model of the transport of near-Earth asteroids (NEAs) from side the J3/2 (the so called Hilda group) and in the J4/3 the main belt (Morbidelli & Vokrouhlick´y2003). (the Thule group). The dynamical lifetimes of their mem- In this paper, we show the continuous-flow of asteroids bers tend to be long (e.g. Nesvorn´y& Ferraz-Mello 1997), driven by the Yarkovsky effect may explain the presence of while the largest observed asteroids are substantially larger unstable asteroids in the J2/1 (as already suggested by Roig (D = 170 km and 125 km respectively) that those in the et al. 2002). We note that Tsiganis et al. (2003) developed a J2/1 (D = 20 30 km). Given that these objects are big and similar model for the small unstable population in the J7/3, − their eccentric orbits cross only a portion of the main belt where the asteroids are resupplied from the Koronis and Eos (e.g. Dahlgren 1998), their collisional lifetimes are definitely families, and Vokrouhlick´yet al. (2004; in preparation) did larger than the age of the Solar system. As a consequence, comparable work for the J9/4 being visited by members of the Hilda and Thule groups are likely to be primordial. the Eos family. Because the population of bodies in the J2/1 There are two end-member cases to explain the origin is substantially larger than in the weaker J7/3 and J9/4, of the J2/1 population: the model for the J2/1 can be tested in a more quantitative way. In fact, our work combines techniques that have been (i) The population is far from steady state, such that the used to explain properties of the NEA population, namely (i) observed objects were produced by a recent disruption event Tracking test bodies from their source region into a target (instantaneous-injection model), or region using numerical integration techniques (e.g. Bottke (ii) The population is in steady state and we need to find et al. 2000; Bottke et al. 2002), and (ii) A semi-analytical the process that sustains it (continuous-flow model). technique for investigating the steady-state size distribution It is also possible that both cases are partially correct, and of bodies in the target region, including the absolute number that different resonant groups have different origins. of objects (e.g. Morbidelli & Vokrouhlick´y2003). In the 1990’s, the preferred hypothesis was type (i). In Section 2, we update the observed population in Here the resonant asteroids were fragments injected into the J2/1. In Secs. 3.1 and 3.2, we describe our numerical the J2/1 during the Themis family formation event (e.g. and semi-analytical models of Yarkovsky-driven transport Morbidelli et al. 1995; Moons et al. 1998). Recent aster- from the main belt on to resonant orbits, as well as results oid family results, however, suggest this possibility is un- from those models. In the Sec. 3.3, we discuss other possible likely. Numerical simulations of large break-up events in the sources of very unstable resonant asteroids in the J2/1. Fi- asteroid belt predict escape velocities significantly smaller nally, in Appendix A, we discuss whether the direct injection than would be needed to directly inject asteroids into the of fragments into the J2/1 by sporadic collisional disruption J2/1 (Michel et al. 2001; in fact, characteristic velocities are events is plausible. too small to populate the currently observed family outside the resonance). In addition, there are several lines of evi- dence to suggest that prominent asteroid families like Koro- nis (Vokrouhlick´yet al. 2003) or Themis are several Gy old (Morbidelli et al. 2003; Bottke et al. 2004). Such ages are in- compatible with the relatively short dynamical lifetimes of 2 UPDATE OF THE RESONANT the Griquas and unstable resonant asteroids.