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Lunar and Planetary Science XXX 1504.Pdf Lunar and Planetary Science XXX 1504.pdf DELIVERY OF METEOROIDS FROM 6 HEBE VIA YARKOVSKY THERMAL DRAG. W. F. Bottke, Jr., CRSR, Cornell University, Ithaca NY 14853-6801, USA, [email protected],D.P.Rubincam,NASA Goddard Space Flight Center, Greenbelt MD 20771, USA,J.A.Burns,CRSR, Cornell University, Ithaca NY 14853-6801, USA. Introduction after 9 Myr of integration (i.e., just before some particles hai =2:401 0:03 Yarkovsky thermal drag is a radiation effect which can begin to fall into the 6 resonance), AU, 3 1 da=dti 2:7 10 modify the semimajor axes of objects between 0.1 m to 10 a h drift rate of AU Myr . km in the main belt [1, 2]. It occurs when solar radiation is absorbed by a body orbiting the Sun. The absorbed light Single Case heats the body, but a delay takes place before the energy is An representative example of our results is provided by re-radiated. When this energy departs, it provides a small Fig. 1, which shows a meteoroid evolving under the combined ``kick'' to the body which can modify its orbit. The diurnal influence of the seasonal and diurnal Yarkovsky effects, col- component of this force is dependent on the body's spin lisions, distant perturbations, and planetary close encounters. rate and longitudinal temperature distribution. It causes the The open circles show the 9 spin axis reorientation events pro- body to spiral outward for prograde rotations and inward for duced over 42.32 Myr. The starting z -component for the spin b retrograde rotations. The ``seasonal'' component of this force axis ( z ) is -.790, which causes the object to evolve inward is dependent on the body's mean motion around the Sun and under the predominant influence of the diurnal Yarkovsky b ;b y its latitudinal temperature distribution. It causes the body to effect. The first spin axis change modifies x , but leaves b spiral inward, It is important to note that these forces have been the z strongly negative, such that evolution continues inward, empirically verified, and have already been used to explain though at a slightly faster rate. All this time, secular pertur- the orbital motion of the LAGEOS artificial satellite. bations continue to grow stronger, increasing the amplitude of e Yarkovsky thermal drag can be used to understand the the forced component as the object draws closer to the 6 res- delivery of meteoroids from the main belt to the Earth. Moti- onance. Then, at 12.20 Myr, the meteoroid, whose perihelion vation for this project comes from the fact that most meteorite is low enough to cross Mars's orbit, undergoes an encounter cosmic ray exposure (CRE) ages are 10-100 times longer than with Mars. This gravitational ``kick'' causes the meteoroid's the most probable dynamical paths carrying these bodies from a to increase, which pushing the object slightly outward. Since ^ resonant main belt orbits to the Earth [3]. Thus, meteoroids b hasn't changed, however, the inward drift continues at the have to reside in the main belt for millions of years before same rate for another 0.33 Myr. Then, at 12.53 Myr, another b spin axis re-orientation event occurs, giving z a strongly pos- reaching the 3:1 or 6 resonances. Since Yarkovsky thermal drag works over just the right timescales to explain both stony itive value (0.868). This causes the meteoroid to slow spiral and iron meteorite CRE ages, we believe it is the leading outward under the diurnal Yarkovsky effect. Enduring a few candidate to solve this problem. more Mars encounters (and a kicks), the body evolves away e from the 6 resonance, reducing the forced amplitude all the Meteoroids from 6 Hebe way back to its starting value. Finally, at 25.74 Myr, another Our formulation of the diurnal and seasonal Yarkovsky collision gets the meteoroid moving inward again. Several drag accelerations, and their inclusion into the symplectic b more spin axis flips occur, but they result in z values which integration routine ``swift-rmvs3'', was discussed last year are either strongly negative (diurnal drag dominates) or near 40 [4]. We now apply the code to study the evolution of 50 zero (seasonal drag dominates). Eventually, after Myr, R =1m e meteoroids evolving from asteroid 6 Hebe, a 200 km the object drifts deeply into the 6 resonance, causing its =2:425 S-type asteroid with osculating orbital elements a values to get pumped up to an Earth-crossing value. At this =0:169 i =15:05 AU, e ,and . Note that this places Hebe point, the code records the data and ends the run. a 0:084 close enough to the 6 resonance ( ) that its We can use Fig. 1 to make a few interesting observations. ejecta has a relatively high probability of being perturbed First of all, the 6 resonance does not appear to have a onto chaotic orbits which quickly become Earth-crossing. sharp boundary. Particles spiraling inward see their forced e Our simulations included perturbations from planets Venus amplitudes increase to Mars-crossing values well before the through Neptune. Each meteoroid was tracked for 50 Myr cross the nominal 6 boundary. Second, encounters with Mars of integration time. Thermal and material properties were before entering deeply into the 6 resonance are common, chosen to be consistent S class asteroids with porous or dusty though it only appears to delay the inward evolution of the surfaces. Each meteoroid was started with a random spin axis meteoroid's by a few Myr at best. Third, we find that only orientation; collisions were included to ``flip'' their spin axis the particles that survive long enough to pass deeply into the e from time to time. 6 resonance undergo large jumps. By the time this occurs, The maximum seasonal and diurnal da=dt rates for our many of the bodies have already reached Earth-crossing orbits. 3 1 2 1 10 2 10 meteoroids were AU Myr and 1 AU Myr . Since the diurnal drift rate is larger than the Evolution of Distribution seasonal drift rate, particles move inward and outward in a. Snapshots from the orbital evolution of all our Hebe-like a; e Collisions and the non-negligible seasonal drift rate, however, meteoroids in space are shown in Fig. 2. Solid lines ai cause h for the distribution to drift inward. For example, show the approximate values needed to reach Mars-crossing Lunar and Planetary Science XXX 1504.pdf YARKOVSKY THERMAL DRAG: W. F. Bottke et al. orbits, Earth-crossing orbits, the 3:1 resonance, and the 6 resonance, the latter assuming the meteoroids have a mean i 2.4 14 15 between - . Frame 2a and 2b show the meteoroids after 1 Myr and 2 Myr of evolution. Note how the Yarkovsky effect is causing the bodies to spread in a, while secular 2.35 υ Approximate 6 boundary perturbations are spreading the objects in e. After 5 Myr of evolution (Frame 2c), the bodies are now spread over a large Collision / Spin axis change part of the inner main belt. After 10 Myr of evolution (Frame 2.3 0 10203040 2d), one object has entered the 6 resonance, while a different object can be seen on a Mars-crossing orbit. Actually, at this time in the integration, at least 15 bodies (30%) have achieved 0.6 Mars-crossing orbits, though none have yet been removed from their main belt orbits. After 20 Myr of evolution (Frame 0.4 2e), objects can now be seen in the 3:1 resonance, the 6 resonance, and on Mars-crossing orbits. At this point, 9 0.2 particles have reached Earth-crossing orbits and have been removed from the run. The last frame shows the meteoroid distribution at the end of the integration (50 Myr). Only 17 0 0 10203040 particles remain, with two more working their way into the 6 resonance. In terms of overall statistical results, we found that 44 Figure 1: Evolution of single meteoroid from 6 Hebe. Note of the meteoroids became Mars-crossers (88%), while 34 how spin axis changes can change the sign of da=dt, and how became Earth-crossers (68%). The shortest interval needed encounters with Mars both push the object away from the 6 for a particle to reach a crossing orbit with Mars and Earth resonance and pull it inwards. was 5.53 Myr and 10.88 Myr, respectively. The median planet-crossing times for meteoroids with Mars and Earth were 11.92 Myr and 23.33 Myr, respectively. Note that most particles become Mars-crossing before well before they cross the derived ``boundary'' for the 6 resonance, implying the boundary itself is difficult to qualify. A related trend, though not readily apparent from Fig. 2, is that the meteoroids' forced e amplitude grows as the distribution nears the 6 resonance. (a) (b) This gives the overall distribution an almost triangular shape, with the point of the triangle near the 3:1 resonance and the base of the triangle near the 6 resonance. Finally, some bodies appear to reach Mars-crossing orbits well away from the 3:1 or 6 resonances; we suspect that higher-order mean-motion resonances with Mars are the cause. Conclusions (i) Delivery times of Hebe-like meteoroids to Earth- crossing orbits are consistent with stony meteorite CRE ages (c) (d) of tens of Myrs. (ii) Mars plays a bigger role in the evolution of material into the 6 resonance than previously thought. (iii) The 6 resonance is an efficient means of delivering material to Earth-crossing orbits.
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