Advances in Space Research 34 (2004) 172–178 www.elsevier.com/locate/asr
Small bodies and dust in the outer solar system T. Mukai
a,*
, A. Higuchi a, P.S. Lykawka a, H. Kimura b, I. Mann b, S. Yamamoto
c
a
Graduate School of Science and Technology, Kobe University, Kobe 657-8501, Japan b Institut f€ ur Planetologie, Westf€ alische Wilhelms-Universit€at, M€unster, Germany c Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-0033, Japan
Received 4 December 2002; received in revised form 18 March 2003; accepted 18 March 2003
Abstract We present our current understandings of small bodies and dust grains located in the outer Solar System. Small icy bodies – Edgeworth-Kuiper Belt objects (EKBOs) and Oort Cloud objects orbit the Sun at distances from Neptune’s orbit outward to 104 –105 AU. Both EKBOs and Oort Cloud objects are believed to be remnants of planetesimals formed in the proto-planetary disk. They provide a possible source for icy bodies that enter the inner Solar System and are observed as comets. A possible scenario for the formation and dynamical evolution of icy objects under the influence of gas drag forces and gravitational scattering by protoplanets is briefly discussed. The outer Solar System plays the role of a corridor for interstellar matter entering into the Solar System. Further dust grains existing beyond Neptune’s orbit are produced as ejecta of icy dust particles from the EKBOs due to the impact of interstellar dust grains. Their expected amount and lifetimes are examined. Compared to the extension of the region of planetesimals around the Sun, the region of influence of the solar wind extends to relatively small distances of the order of several hundred AU. But both complexes are coupled through the presence of interstellar dust that depends on the extension and the physical parameters of the heliosphere. The existence of a stronger solar wind in the early stages of the Solar System indicates that the heliosphere in a distant past might have been 10–100 times larger than the current one which possibly influenced the evolution of the planetary system. Ó 2004 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Outer solar system; Small bodies; Dust grains; Cometary nuclei
1. Introduction The space at distances from Neptune’s orbit outward to 104 –105 AU is not empty of solid bodies. It is widely believed that approximately 1012 comets (that is cometary nuclei), forming the Oort cloud, are present in the edge region of the Sun’s gravitational sphere of influence (see, e.g. Weissman, 1990). The total mass of the objects in the Oort Cloud amounts to 50 MEarth , where MEarth is the Earth’s mass. After the discovery of the first icy object 1992 QB1 beyond Neptune’s orbit by Jewitt and Luu (1993), during the past decade a large number of objects have been discovered in the region beyond 30 AU from the Sun. These icy objects are referred to as Edgeworth-Kuiper Belt objects (EKBOs) after the *
Corresponding author. Fax: +81-78-803-5757. E-mail address:
[email protected] (T. Mukai).
scientists who early suggested a belt of objects to exist beyond the region of the giant planets in order to explain the appearance of short-period comets. It is currently estimated that 3.5 104 EKBOs larger than 100 km exist inside an annulus space from 30 to 50 AU from the Sun and their total mass is 0.08 MEarth (Luu and Jewitt, 2002). In spite of their small total mass, these objects bear valuable information about the formation and the evolution of our planetary system and also for the comparison to the formation of planetary systems around other stars. Also during the past decade, several nearby stars were observed to have dust shells, which most likely are produced by the existence of planetesimals in these systems (Backman and Paresce, 1993; Beckwith and Sargent, 1996). The location of these dust shells is comparable to the Edgeworth-Kuiper Belt region of our solar system. Moreover, an early detection of interstellar
0273-1177/$30 Ó 2004 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2003.03.052
T. Mukai et al. / Advances in Space Research 34 (2004) 172–178
dust particles entering the solar system (Bertaux and Blamont, 1976) was confirmed with extended measurements aboard Ulysses (Gruen et al., 1994). The flux of the interstellar dust is considered as a source of dust production by impact erosion in the Edgeworth-Kuiper Belt region (Yamamoto and Mukai, 1998). The flux of interstellar dust particles into the solar system depends on their surface charge and namely small grains (see Mann and Kimura, 2000) are deflected from entering the heliosphere, which is the region around the Sun that is filled with the solar wind plasma. The extension of the heliosphere, on the other hand, as well as the mass distribution and velocity of the in-falling dust particles depend on the conditions of the local interstellar medium. This demonstrates the fact that our planetary system is not isolated, but that its evolution is connected to its cosmic environment. As a result of all these new findings, studies of the Oort Cloud, the EdgeworthKuiper belt and the dynamics of their icy planetesimals have become active fields of the solar system science, not only in the observational, but also in the theoretical respect. So the ‘‘edge of the solar system’’ moved into the center of interest for many researchers. Interestingly enough, it depends on the particular field of research where this ‘edge’ is located: while the observations of small bodies at the edge of the solar system are currently limited to the region of about 50 AU, the extension of the heliosphere is expected to be a little more than hundred AU and the Oort Cloud reaches 105 AU. In this short review about the small solid bodies beyond Neptune’s orbit, we will address the following questions: (i) how and where were the Oort Cloud objects formed? (ii) why can we find no icy objects beyond 50 AU from the Sun? (iii) how many dust grains exist beyond 30 AU? and (iv) how large was the heliosphere in the early Solar System? Although these topics seem to be scattered in sense of science, they make up a piece of a jigsaw puzzle of a whole scenario to form the current structure of the outer Solar System about 4.0 Gyr-ago in the proto-planetary disk.
2. Origin of the Oort Cloud and the Edgeworth-Kuiper belt While the Edgeworth-Kuiper Belt and the Oort Cloud are considered as two distinct sources of comets, their respective histories of formation and evolution are intimately related. Both populations were formed during the formation of the planetary systems in the protoplanetary cloud and their orbits were and still are today influenced by the presence of large proto-planets and of the planets that exist at present. Our current understanding is that the long period comets formed in the region of the orbits of giant planets before they were gravitationally scattered into the Oort Cloud. The short
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period comets were formed beyond the orbit of Neptune in the region of the present location of the Kuiper Belt (‘in situ formation’). These different regions of formation result in different thermal histories that should be reflected in the composition of the comets. The composition of comets is not directly measured so that our knowledge is based on the observation of for instance their gas production and the differences in their dust composition. There is no clear established connection between the composition of comets inferred from observations and their region of formation as it is derived from the orbital history yet. Here we discuss some results about the nature of and the history of comets. Mumma et al. (2001) have suggested that the organic composition of comet C/1999 S4 (LINEAR) with a semi-major axis a of the orbit of 1383 AU was formed in the inner part of the proto-solar disk with a temperature about 200 K near Jupiter (5 AU), although Kawakita et al. (2001) have reported, based on their detection of an ortho-para ratio of NH3 that the ammonia ice in this new comet was formed at 28 2 K near Neptune (40 AU). It is reported in Mumma et al. (2001) that the measured compositions of four Oort Cloud comets (Halley, Hyakutake, Hale-Bopp and Lee) are consistent with formation from interstellar ices in a region of the proto-solar disk beyond Uranus. This observed evidence supports the scenario of origin of the EKBOs and the Oort Cloud (see, e.g. Weissman, 1990). That is, as Monte Carlo simulations have shown (Duncan et al., 1988), icy planetesimals formed in the zone of giant proto-planets were gravitationally scattered by protoJupiter, and consequently they reached the region of EKBOs and the further Oort Cloud region. This rough sketch, however, needs further quantitative research on the physical processes, i.e.: (i) a fall of icy planetesimals formed in the Uranus-Neptune zone due to gas drag forces to the proto-Jupiter region, (ii) a gravitational scattering of planetesimals by the giant proto-planet, and (iii) formation of the EdgeworthKuiper Belt beyond Neptune’s orbit, and the Oort Cloud in the region of a heliocentric distance of 104 –105 AU. We present our simulation results for the dynamical evolution of icy planetesimals formed in the region of 10 AU from the Sun, related to the processes (i) and (ii). We assume, as an initial condition, the presence of icy planetesimals with radii from 10 m to 1 km at 10 AU from the Sun, where enough gas components are still remained in the proto-solar disk. The model parameters for the proto-solar disk are taken from Wood and Morfill (1988). The gas drag forces move the planetesimals toward the Sun. As shown in Fig. 1, our simulation results suggest that the smaller planetesimal changes its semi-major axis faster than larger ones due to gas drag forces, i.e. within a time scale of about 104 yr for a 10 msized planetesimal. However, the planetesimals starting
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with time. Furthermore, a part of scattered planetesimals would take a large elongated orbit with eccentricity, e > 0:9 after 105 yr. To reply to the question of how and where the Oort Cloud objects were formed, we need a study of the process (iii) noted above,in addition to more detailed simulations of the dynamical evolution of planetesimals formed in the giant proto-planets’s region. Although the resonance trap prevents the planetesimals formed far from the proto-planet from approaching its protoplanet, the efficiency of the trapping might be lower for planetesimals on non-circular orbits. Fig. 1. Dynamical evolution of planetesimals with radii of 10 m to 1 km initially placed on circular orbits with a semi-major axis a of 10 AU, under the gas drag forces. The horizontal part of the evolution track indicates the evidence where the planetesimals were trapped by the gravitational resonance of proto-Jupiter placed at 5 AU with the mass of 100 MEarth .
at 10 AU from the Sun cannot reach the region near proto-Jupiter, 5 AU from the Sun, since they are trapped by the gravitational resonance of proto-Jupiter, where the mass of proto-Jupiter is assumed to be 100 MEarth (the current mass of Jupiter is 318 MEarth ). This result suggests that the icy planetesimals scattered by proto-Jupiter might be formed in a region close to proto-Jupiter. We next perform the simulation for the gravitational scattering of icy planetesimals by the proto-Jupiter (see Fig. 2). The 4th-order Hermite integrator (Makino and Aarseth, 1992) is used for orbital integration. The 1600 planetesimals on the circular orbit with semi-major axis, a, a ¼ 5:41 AU are scattered by proto-Jupiter at 5 AU, and those avoiding capture by proto-Jupiter show a distribution of eccentricities e, where the gas drag forces are neglected. A time variation of such e-distribution, as shown in Fig. 2, predicts that the scattered remnants show a distribution of e with its peak value increasing
Fig. 2. Time variation of the eccentricity distribution of the 1600 planetesimals scattered by proto-Jupiter with the mass of 100 MEarth , where the planetesimals were formed on the circular orbits in the region near the orbit of proto-Jupiter.
3. Are there EKBOs beyond 50 AU from the sun? Looking at the observations of EKBOs, it is noted that there were no icy bodies detected on near-circular orbits with a > 50 AU (see Fig. 3). For the hypothesis of the in situ formation of planetesimals, the deficiency of original matter to form planetesimals is the reason of no icy objects beyond 50 AU from the Sun. On the other hand, for the migration hypothesis of icy objects, the computer simulations by Ida et al. (2000) suggest that a stellar encounter with the planetesimals initially distributed uniformly even beyond 50 AU leads to the absence of the planetesimals on circular orbits beyond 50 AU. Brunini and Melita (2002) proposed the existence of a Mars-like planetoid at about 60 AU, which produces a gap in the a-distribution of icy objects with an edge at about 50 AU. The information of icy objects increases vastly after the first discovery in 1992 (see the recent review by Luu and Jewitt, 2002) (the total number of EKBOs is 625 in the 23rd Nov. 2002, where we define the EKBOs as the
Fig. 3. The eccentricity e and semi-major axis a of icy objects in the region from 30 to 250 AU. Shown are 625 objects classified as EKBOs and 65 scattered objects with the perihelion distances q > 30 AU. The dotted curve indicates a relation between e and a at q ¼ 30 AU (a ¼ 30 AU for Neptune). The open circles denote objects detected only at one opposition, whereas closed circles denote objects that were detected at more than one opposition.
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icy objects with the semi-major axis a between 30 and 50 AU, and the scattered objects as the icy objects with a > 50 AU and q > 30 AU). The data can be accessed easily via the Internet (see, e.g. IAU Minor Planet Center at http://cfa-www.harvard.edu/cfa/ps/mpc.html). We present the following figures compiled from the data collected through web sites. Fig. 3 demonstrates the absence of icy objects on circular orbits with a > 50 AU. The detected objects with a > 50 AU are classified in general as the scattered EKBOs, and the appearance of such group is closely related to the curve of a perihelion distance q ¼ 30 AU. Fig. 4 shows the histograms of the number (upper panel) and the mass (lower panel) distributions of EKBOs as a function of a with a bin interval of 0.1 AU, where Pluto and Charon are omitted in the mass distribution. The mass of an EKBO was derived under the assumption that an EKBO is a sphere with a mass density of 1000 kg m3 . The existence of the ‘‘resonance’’ EKBOs, including Pluto, at about a ¼ 39:5 AU is clear. In addition, the second enhancement of the number
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Table 1 Large Edgeworth-Kuiper belt objects with semi-major axis a of about 43 AU Object
Diameter (km)
a (AU)
2002TX300 2002UX25 20000Varuna 50000Quaoar 19308(1996TO66)
990a 950a 1060b 1260c 652d
43.25 42.78 43.27 43.19 43.25
a
Recalculated based on more recent data than (Johnston, 2002). Lellouch et al. (2002). c Brown and Trujillo (2002). d Hainaut et al. (2000). b
distribution near a ¼ 44 AU appears, in contrast with a peak of the mass distribution at about a ¼ 43 AU. The peak of the mass distribution is strongly influenced by new findings of large EKBOs (see, Table 1). It seems interesting that the double peaks in the number/mass distributions of EKBOs as a function of a, also the concentration of large EKBOs appear near a ¼ 43 AU. The second peak at a ¼ 43 AU might reflect the a-distribution of the remnants scattered by the proto-planet, as simulated in Fig. 2. It might as well be a relic of the resonance concentration that was caused by missing/migrated proto-planet. The large EKBOs found at about a ¼ 43 AU might be a collision fragment of a large parent proto-planet, which was disrupted in the early time of the Solar System. However, it is too early to rule out observational effects to bias the evidence.
4. Dust beyond neptune
Fig. 4. The number distribution and mass distribution of EKBOs as a function of semi-major axis in the upper panel and the lower pane, respectively, where only EKBOs detected in more thanb one opposition are used (300 objects except Pluto and Charon). The mass is estimated under the assumption that the object is a sphere with a mass density of 1000 kg m3 , and is shown in unit of Pluto’s mass.
The outer Solar System plays the role of a corridor for interstellar matter entering into the Solar System as well as for interplanetary matter escaping from the Solar System (see, e.g. Mann and Kimura, 2000). The Ulysses dust detector reported the number density nd (in unit of m3 ) of interstellar dust grains as nd ¼ 5:64 1021 m1:67 , where m denotes a mass of dust grain in unit of kg (Kimura et al., 2003). An expected mass ratio of gas to dust in interstellar space sets the upper limit of interstellar dust grain’s mass to m < 1011 kg, which corresponds to 10 lm for a spherical grab. Larger interstellar dust particles may exist, but would not be coupled to the interstellar medium gas, which is in accord with the result that large particles were not measured in the direction of the interstellar wind that streams through the solar system. While the existence of these interstellar dust particles allows for a study of interstellar medium conditions, and moreover is closely connected to the structure of the heliosphere (see, Mann et al., 2004) it further has some influence on the Edgeworth-Kuiper belt region.
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Stern (1996) estimated the dust production rate of ð0:0095 3:2Þ 108 kg s1 , due to mutual collisions of EKBOs, whereas Yamamoto and Mukai (1998) suggested 3.1 104 kg s1 for smaller grains less than 10 lm, which were yielded by the collisions of the interstellar dust grains on EKBOs. The lifetime of ejected grains is controlled by the time scale of collision with the interstellar dust tc and the Poynting–Robertson effect tPR (Liou et al., 1996). That is, 2
tc ¼ 504=ðd þ di Þ 106 yr
and
tPR ¼ 400r2 =b yr;
where d and di denote the diameters, in unit of lm, of dust of interest in the EKBO region and the interstellar dust, respectively, r is a heliocentric distance in unit of AU and b is a ratio of the radiation pressure force to the gravity on the dust grain of interest. As shown in Fig. 5, dust grains with diameters, d, less than 6 lm would fall toward the Sun from 40 AU within 10 Myr due to the Poynting–Robertson effect. On the other hand, grains larger than 6 lm would be destroyed by collision with interstellar dust grains. Larger grains with d > 50 lm could survive against the interstellar dust collisions. Their lifetimes are limited by the Poynting–Robertson effect. The Poynting–Robertson lifetime, tPR for a 50 lm grain would be about 2 Gyr at 100 AU from the Sun, where (b ¼ 0:16 s1:2 s denotes a radius of the grain in unit of lm) is used (see Mukai, 1989). Consequently, we suppose that in the EKBOs region the larger grains (d > 50 lm) could survive, those at intermediate with d ¼ 6–50 lm would be destroyed by the interstellar dust collisions within 107 yr, and the debris after collisions become the small dust grains. The resulting small dust grains (<6 lm) would be transmitted into the inner solar system due to the Poynting– Robertson effect. The dust production rate from the collisions of interstellar dust grains on the Oort Cloud objects should be larger due to lack of heliospheric modulation. However, the time scale for falling into the EKBOs’ region (40 AU) from the Oort Cloud region
Fig. 5. Lifetime of dust grains with different diameters at 40 AU distance from the Sun, due to collision with the interstellar dust grains (solid curve) and due to the Poynting–Robertson effect (dashed curve).
(104 AU) is about tPR ¼ 400r2 =b 1010 yr. Therefore, such grains produced in the Oort Cloud region still remain there. These estimates are based on the present day knowledge of the outer solar system. From our currentunderstanding of the evolution of planetesimals we can however-infer that the number of planetesimals in the outersolar system was larger and hence also the mechanisms of dust production more effective. Keeping the time scalesfor the evolution of dust in the Edgeworth-Kuiper Belt as well as the connection to other systems in mind it seemsworthwhile to consider the evolution of the heliosphere in time.
5. The size of heliosphere in the early solar system The size of the heliosphere, Rs , is derived from the balance between the ram pressure of the solar wind PSW and the interstellar pressure Pi where PSW ¼ PSW ðr ¼ 1 AUÞð1=Rs Þ2 and PSW ðr ¼ 1 AU Þ ¼ mp N1 V12 ;
PSW (r ¼ 1 AU) denotes the solar wind pressure at 1 AU from the Sun, mp is the proton mass, N1 is the number density of protons in the solar wind at 1 AU and V1 is the solar wind velocity at 1 AU. When we use Pi ¼ 1:3 1013 N m2 , N1 ¼ 5 106 protons m3 and V1 ¼ 400 km s1 , the size of the heliosphere Rs , becomes about 100 AU. This value of Rs varies by a factor of 2–3 with changes in the allowable parameters of interest. Wood et al. (2002) have recently derived the massloss rate dM=dt of solar-like stars as a function of age t, i.e. dM=dt / t2:000:52 . As shown in Fig. 6, this relation predicts that the mass-loss, rate of the Sun in the early stage of its age was l00–l000 times stronger than the cuitent value.
Fig. 6. An estimate of the long-time variation of the mass-loss rate of the Sun derived from a relation given by Wood et al. (2002). A circle indicates the current value, and the dotted and dash-dotted lines denote, respectively, the maximum and minimum mass loss rate expected from the relation. The horizontal lines mean the 10, 100 and 1000 times stronger mass loss rate than the current value.
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When we assume that the velocity of the solar wind was constant with a time, the time variation of ram pressure of the solar wind is deduced from the time variation of mass-loss rate. If the interstellar pressure Pi took the same value as that estimated at the current location of the Solar System, the size of the heliosphere Rs would be extended to 103 –104 AU from the Sun in the early Solar System. However, it should be noted that the interstellar pressure Pi might be changed with the movement of the Solar System in our Galaxy. What we know is only the recent galactic environment of the Sun, i.e. the Sun entered the Local Interstellar Cloud (LIC) about 105 yr ago and will leave the LIC about 3000 yr later (Linsky et al., 2000). Statistically the Sun encountered over 16 dense clouds, in which Pi is expected to be stronger than the current value, and consequently the size of the heliosphere, Rs , might decrease during such a time period. It is realistic to assume that the size of heliosphere varies with the age of the Sun. Although there still remain unknown parameters, such as Pi , to estimate Rs , we can conclude that the environment in the space region from Neptune’s orbit outward to 104 –105 AU changed with the time. It is noteworthy that the assumption used here of linear proportionality between the mass flow rate and the boundary distance leads to an upper limit on Rs The actual distance could be much less due to nonlinear effects such as adiabatic cooling, charge exchange with the interstellar gas, and details of shock formation at the boundary. When the solar wind was stronger than the current one, we have to include the effect of such strong solar wind on the scenario of the formation arid evolution of the Solar System. That is, the dynamical friction by the solar wind pressure, called pseudo-Poynting–Robertson effect (Mukai and Yamamoto, 1982), as well as the surface alteration by impinging wind particles, might play an important role in that stage.
6. Conclusion The study of small bodies and dust grains located in the outer Solar System provides valuable information about the evolution of the solar system as a whole and the in situ analysis of such materials would have the potential ability to solve key questions about the origin of the Solar System and its age evolution. This region is influenced by the in-fall of interstellar medium dust, the condition of which depending on the extension of the heliosphere and hence on the evolution of the Sun as well as on the parameters of the interstellar medium that the solar system passed in its history. The existence of a stronger solar wind in the early stage of the Solar System indicates that the heliosphere in a distant past might have been 10–100 times larger than the current one
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which possibly influenced the evolution of the planetary system. The composition of the solid bodies beyond Neptune’s orbit reflects the early environment in the edge of the proto-solar disk, while the orbital evolution of the objects reflects the formation history of the planetary system. We note a lack of icy objects detected on nearly circular orbits beyond 50 AU from the Sun, as well as double peaks in the number/mass distributions of EKBOs as a function of semi-major axis. In addition, we note a new mystery that recent findings of large EKBOs (20000 Varuna, 2002 TX300, 50000 Quaoar, 2002 UX25) have nearly the same semi-major axis of 43 AU as 19308 (1996 TO66). References Backman, D.E., Paresce, F. Main-sequence stars with circumstellar solid material – the VEGA phenomenon, in: Protostars and Planets. vol. III. pp. 1253–1304, 1993. Beckwith, S.V.W., Sargent, A.I. Circumstellar disks and the search for neighbouring planetary systems. Nature 383, 139–144, 1996. Bertaux, J.L., Blamont, J.E. Possible evidence for penetration of interstellar dust into the solar system. Nature 262, 263–266, 1976. Brown, M.E., Trujillo, C. Direct measurement of the size of the large Kuiper belt object (5000) Quacar. Astron. J. 127, 2413–2417, 2002. Brunini, A., Melita, M.D. The existence of a planet beyond 50 AU and the orbital distribution of the classical Edgeworth-Kuiper-belt objects. Icarus 160, 32–43, 2002. Duncan, M., Quinn, T., Tremainw, S. The origin of short-period comets. Astrophys. J. 328, 69–73, 1988. Gruen, E., Gustafson, B., Mann, I., Baguhl, M., Morfill, G.E., Staubach, P., Taylor, A., Zook, H.A. Interstellar dust in the heliosphere. Astron. Astrophys. 286, 915–924, 1994. Hainaut, O.R., Delahadde, C.E., Boehnhardt, H., Dotto, E., et al. Physical properties of TNO 1996 TO66. Lightcurves and possible cometary activity. Astron. Astrophys. 356, 1076–1088, 2000. Ida, S., Larwood, J., Burkert, A. Evidence for early stellar encounters in the orbital distribution of Edgeworth-Kuiper belt objects. Astrophys. J. 528, 351–356, 2000. Jewitt, D.C., Luu, J.X. Discovery of the candidate Kuiper belt object 1992 QB1 . Nature 362, 730–732, 1993. Johnston, W.R., data published in web site. 2002. Kawakita, H., Watanabe, J., Ando, H., Aoki, W., et al. The spin temperature of NH3 in comet C/1999 S4 (LINEAR). Science 294, 1089–1091, 2001. Kimura, H., Mann, I., Jessberger, E.K. Composition, structure and size distribution of dust in the local interstellar cloud. Astrophys. J. 583, 314–321, 2003. Lellouch, E., Moreno, R., Ortiz, J.L., Paubert, G., Doressoundiram, A., Peixinho, N. Coordinated thermal and optical observations of trans-Neptunian object (20000) varuna from sierra nevada. Astron. Astrophys. 391, 1133–1139, 2002. Linsky, J.L., Redfield, S., Wood, B.E., Piskunov, N. The threedimensional structure of the warm local interstellar medium. I. Methodology. Astrophys. J. 528, 756–766, 2000. Liou, J.-C., Zook, H.A., Dermott, S.F. Kuiper belt dust grains as a source of interplanetary dust particles. Icarus 124, 429–440, 1996. Luu, J.X., Jewitt, D.C. Kuiper belt objects: relics from the accretion disk of the Sun. Annu. Rev. Astron. Astrophys. 40, 63–101, 2002. Makino, J., Aarseth, S.J. On a Hermite integrator with Ahmad-Cohen scheme for gravitational many-body problems. PASJ 44, 141–151, 1992.
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