Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/preprints/2007/505.pdf Äàòà èçìåíåíèÿ: Mon Sep 24 12:53:06 2007 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 02:50:44 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: ï ï ï ï ï ï ï ï ï

Ap ollo asteroids (1566) Icarus and 2007 MK6 : Icarus family memb ers?
K. Ohtsuka1 , H. Arakida2 , T. Ito3 , T. Kasuga4,3 , J. Watanabe3 , D. Kinoshita5 , T. Sekiguchi3 , D. J. Asher6 , and S. Nakano7

ABSTRACT Although it is more complicated to search for near-Earth ob ject (NEO) families than main belt asteroid (MBA) families, since differential orbital evolution within a NEO family can cause current orbital elements to drastically differ from each other, we have found that Apollo asteroids (1566) Icarus and the newly discovered 2007 MK6 are almost certainly related. Specifically, their orbital evolutions show a similar profile, time shifted by only 1000 yr, based on our time-lag theory. The dynamical relationship between Icarus and 2007 MK6 along with a possible dust band, the Taurid-Perseid meteor swarm, implies the first detection of an asteroidal NEO family, namely the "Icarus asteroid family". Subject headings: minor planets, asteroids -- comets: general -- meteors, meteoroids
Tokyo Meteor Network, 1­27­5 Daisawa, Setagaya-ku, Tokyo 155­0032, JAPAN; ohtsuka@jb3.sonet.ne.jp. Waseda University, da@aoni.waseda.jp.
3 2 1

1­6­1

Nishi-Waseda,

Shinjuku-ku,

Tokyo

169­8050,

JAPAN;

araki-

National Astronomical Observatory of Japan, 2­21­1 Osawa, Mitaka, Tokyo 181-8588, JAPAN; tito@cfca.nao.ac.jp, jun.watanabe@nao.ac.jp, t.sekiguchi@nao.ac.jp. Institute for Astronomy, University of Hawaii, 2680 Wo o dlawn Drive, Honolulu, Hawaii 96822­1897; kasugats@IfA.Hawaii.Edu. Institute for Astronomy, National Central University, 300 Jhongda Rd., Jhongli, Taoyuan 32001, TAIWAN; kinoshita@astro.ncu.edu.tw.
6 7 5 4

Armagh Observatory, College Hill, Armagh, BT61 9DG, UK; dja@arm.ac.uk. OAA computing section, 1­3­19 Takenokuchi, Sumoto, Hyogo 656­0011, JAPAN; nakano@oaa.gr.jp.


­2­ 1. Introduction

Near-Earth Apollo asteroid (1566) Icarus = 1949 MA was discovered by Baade (1949) as a 16th magnitude fast-moving ob ject, on a plate taken using the 48-inch Palomar Schmidt on 1949 June 10, when Icarus approached the Earth to within 0.10 AU, near its descending no de. Its orbital parameters were highly unusual: it had smaller semima jor axis (a = 1.08 AU), smaller perihelion distance (q = 0.19 AU), larger eccentricity (e = 0.83) than any other asteroid known at that time and relatively high inclination (i = 23 ). Icarus remained the record holder in having the smallest q among all asteroids until the discovery of (3200) Phaethon in 1983. Indeed, on account of its small q , Icarus was historically of particular interest as to whether the relativistic effects on its orbital motion are detectable (e.g., Shapiro et al. 1971). In Icarus' subsequent approaches to the Earth in 1968, 1987, and 1996, the following physical data were derived: absolute magnitude (H ) = 15.95 and G-parameter = -0.04 (Tedesco 1989); rather high albedo 0.33 and diameter 1 km (e.g., Harris 1998); fast rotation perio d 2.273 hr (e.g., Gehrels et al. 1970; De Angelis 1995) and others 1 . Especially notable is that Icarus is spectrally classified as a Q-type in Tholen's taxonomy. Q-type asteroids, which generally are spectroscopic analogues of ordinary chondrites (cf. McFadden et al. 1984; Hicks et al. 1998; Fevig & Fink 2007), are regarded as being less space-weathered S-complex asteroids, with a surface age 10 Myr owing to resurfacing effects (Marchi et al. 2006). Hence Icarus may represent the rather fresh internal structure of a precursor ob ject broken up in recent history. Moreover, with q 0.19 AU, the subsolar point on Icarus should reach a temperature of 800 K by solar heating, in which case the solar thermal stress may be a trigger to destroy the asteroid's surface and subsurface. Resurfacing may alternatively be due to the tidal effects of the terrestrial planets (Nesvorny et al. 2005). ´ For the above reasons, we have expected some "Icarus Family Members" (hereafter "IFM(s)") to exist in near-Earth space. We have therefore been searching for IFMs based on time-lag measurements (see below) between the orbital evolution of Icarus and any candidate IFM. This pro cedure was successful in finding the dynamical relationship between (3200) Phaethon and (155140) 2005 UD (Ohtsuka et al. 2006, hereafter Paper I). No certain IFMs had been found in the Apollo asteroid database 2 until very recently. However, we finally identified an extremely likely candidate from the latest MPECs (Minor Planet Electronic Circulars): a recently discovered Apollo asteroid 2007 MK6 .
1 2

http://earn.dlr.de/nea/001566.htm e.g., http://cfa-www.harvard.edu/iau/lists/Apollosq.html


­3­ 2. Orbital integration of (1566) Icarus

As preliminary work for the IFM survey and for measuring the time-lags (detailed in the next section) between Icarus and unknown potential IFMs, we calculated the orbital evolution of Icarus. We performed a backward and forward numerical integration of the KS (Kustaanheimo­Stiefel) regularized equation of motion (cf. Arakida & Fukushima 2000, 2001), applying the 12th-order Adams metho d in double precision with a step size of 0.5 day. The integration covered 10000 BC to 10000 AD (JDT -1931503.5 to 5373520.5), and included terms of first order in the post-Newtonian approximation for the Sun's gravitational field since relativistic effects advance the line of apsides of Icarus at a rate of 10 /century. We also confirmed that the results of our numerical integration did not significantly change even when we adopted smaller step sizes or when we used other integration metho ds such as the extrapolation metho d. The initial orbital data of Icarus at osculation epo ch 2007 Apr 10.0 TT = JDT 2454200.5 were taken from NASA JPL's HORIZONS System 3 and are listed in Table 1. All the ma jor planets from Mercury through Neptune and the quasi-planet, Pluto, were included as perturbing bo dies (the Earth­Mo on barycenter being one bo dy, with the Mo on's mass added to the Earth's). The co ordinates of the ma jor planets were taken from the JPL Planetary and Lunar Ephemeris DE408. Over 20000 yr we found the orbital motion of Icarus to show a high degree of stability, with long-perio d secular changes according to the cycle in argument of perihelion , also known as the Kozai cycle (Kozai 1962). The corresponding large-amplitude oscillations in q and i, in antiphase with e, have perio d 25000 yr, half that of the cycle. The period of 50000 yr is somewhat larger than the 40000 yr for Phaethon and 2005 UD (Paper I).

3.

Time lag t of the orbital evolutions

In the first stage of the formation of an asteroid family, the orbital energies ( 1/a) of bo dies or fragments are slightly different from that of the precursor, since the motions of the released ob jects are slightly accelerated or decelerated relative to the precursor. This results in differences in their evolutionary rates under gravitational perturbations (there may additionally be differential nongravitational perturbations): then a time-lag (which hereafter we call t) in the orbital evolutions arises. At the starting epo ch, t 0 yr, and it tends to increase with time. We note that t is not the time since separation, but rather quantifies how separated in phase two orbits have become in their respective (similar) secular
3

http://ssd.jpl.nasa.gov/horizons.html


­4­ perturbation cycles. For measuring a difference in the evolutionary phase of two orbits, t is much more suitable than for example the difference in , since (for highly eccentric orbits particularly) d /dt is strongly dependent on the phase within the Kozai cycle (cf. Fig. 1 later). Any IFM should show a very close orbital similarity with Icarus when shifted by the appropriate t that brings both orbits to the same evolutionary phase. The following successful studies applying this time-lag theory have been made so far: i) anticipation of the Marsden and Kracht comet groups' perio dicity and their return: Ohtsuka et al. (2003) anticipated these comet groups, which initially had parabolic orbit solutions, as being fragments of Perio dic Comet 96P/Machholz. Their prediction was shown to be correct when Sekanina & Cho das (2005) linked orbits and found these comet groups to have orbital perio ds of 5­6 yr, corresponding to 96P's 5.2 yr. The Marsden and Kracht comet groups thus turned out to be decameter-size members of the 96P­Quadrantid stream complex. ii) genetic relationship of Phaethon and 2005 UD: Paper I revealed 2005 UD as being the most likely large fragment of Phaethon. This dynamical relationship was confirmed by the physical studies of Jewitt & Hsieh (2006) and Kinoshita et al. (2007), who classified both ob jects as F- or B-type. These taxonomic types are very rare, comprising only 5% of NEOs that have been classified; combined with the dynamical evidence, the genetic relationship of Phaethon and 2005 UD is beyond doubt. This time-lag theory is straightforward and is now well established as a technique to demonstrate the existence of cometary stream complexes or likely NEO families; so it should be a useful to ol to survey for IFMs.

4. 4.1.

Survey Procedure

The survey for IFMs in the Apollo asteroid database and latest MPECs uses the same pro cedure as in Paper I. We again applied the following three criteria as the retrieving engine for our IFM survey. The first is the traditional orbital similarity criterion DSH of Southworth & Hawkins (1963), who defined DSH as a distance between the orbits of two ob jects A and B in five-dimensional orbital element space (e, q , , ,i), as follows:
5 2 DSH = j =1

fj2 (P

A,j

-P

B,j

)2 ,

(1)

where PA or B,j are orbital elements and fj are functions of the elements that ensure suitable weights are given to each term in (1). Thus we searched for potential IFMs on the basis of


­5­ Icarus' orbital evolution from the integration described in Section 2. For each Near-Earth Apollo, we found the minimum DSH between it and Icarus, as Icarus' orbit evolves. A minimum DSH 0.15 means that Icarus and the given asteroid are within the probable asso ciation range. The second and third criteria are the C1 and C2 integrals derived by Moiseev (1945) and Lidov (1961) respectively, which we calculate for candidates selected by DSH : C C
1 2

=

1 - e2 cos2 i,

(2) (3)

= e2 0.4 - sin2 i sin2 .

These integrals describe the secular orbital variations well. Both C1 and C2 are almost invariant for the orbital motions of Phaethon and 2005 UD (Paper I), and should also be useful criteria to distinguish IFMs.

4.2.

Detection of the IFM candidate: Near-Earth Apollo asteroid 2007 MK

6

In this way, we finally detected a very likely IFM candidate from the latest MPECs: Near-Earth Apollo asteroid 2007 MK6 , which was recently discovered in the Catalina sky survey, on 2007 June 21.2 (Hill et al. 2007). So on after, Ohtsuka (2007) made the identification of 2007 MK6 with another Apollo, 2006 KT27 , so 2007 MK6 = 2006 KT27 ; the latter was both discovered (on 2006 May 26) and observed only (12 positions over a 1 day arc) by the Mt. Lemmon survey. This extended the arc to more than one year. Nakano successfully linked their orbits, based on 54 positions at two oppositions (covering 2006 May 26 to 2007 June 27) with an RMS residual of 0 .74. The absolute magnitude H 19.9 corresponds to an ob ject a few hundred meters in size at most, if we assume 2007 MK6 is a high-albedo ob ject such as an S-type. Using Nakano's data, listed in Table 1, we integrated 2007 MK6 using the same metho d as for Icarus. The dynamical evolutions of both asteroids are illustrated in Fig. 1. Icarus and 2007 MK6 sometimes encounter the terrestrial planets. Encounters with Venus or Earth can cause changes in a but these are small enough that the other elements display a stable secular evolution, as with Phaethon and 2005 UD (Paper I). Neither asteroid has a no dal intersection epo ch with Venus or Earth in the past 10000 yr, hence the interval of constant a in Fig. 1. Comparing the orbital elements of 2007 MK6 at the current epo ch with the changing orbit of Icarus over time, as described in Section 4.1, we found a strikingly go o d match with Icarus at around 1034 AD (Table 1); thus t 1000 yr. The corresponding minimum value


­6­ of DSH 4600 almost MK6 is is only 0.0098. Both t and DSH are fairly small compared to the respective values yr and 0.04 between Phaethon­2005 UD (Paper I). The C1 and C2 parameters are constant, within the ranges 0.26­0.28 and 0.24­0.25 respectively. Therefore 2007 a very strong candidate IFM.

The two orbital evolutions show a similar profile, with quasi-sinusoidal changes, simply shifted by t 1000 yr. Their smaller t than Phaethon­2005 UD suggests a younger separation age, but DSH between Icarus­2007 MK6 at the same osculation epo ch has never been below 0.03 in our integration timespan. Only in quite rare cases (such as the Karin cluster in the main belt; Nesvorny et al. 2002) can an exact separation age be found unambiguously, ´ although we may certainly expect DSH to have been smaller around the time that Icarus and 2007 MK6 separated. Some test integrations back 105 yr tentatively show t decreasing back in time but random small changes in a due to close encounters make it hard to reach a precise quantitative conclusion about the separation age. However, this age is clearly within 10 Myr, the resurfacing age of Q-type NEOs, possibly two orders of magnitude shorter. The Icarus­2007 MK6 parent may well have been injected into the near-Earth environment of the order of 10 Ma (cf. Bottke et al. 2002), but with the separation o ccurring much more recently. We also surveyed meteor data related to the IFMs. Consequently, we noticed a likely meteor swarm found by Sekanina (1973) in the Harvard (Havana) radar meteor orbit survey: the daytime Taurid-Perseid meteor swarm, recorded around June 18 in the radar's 1961­1965 term of operation. The orbital parameters are in go o d agreement with those of Icarus, as presented in Table 2. Their DSH 0.08 is in the probable asso ciation range. Although we cannot accurately measure their t, both the current orbits lo ok to be at almost the same evolutionary phase. No further orbital data were found in the radar meteor orbit database. We may therefore regard the Taurids-Perseids as a transient Earth-crossing IFM dust band rather than a cometary meteor stream.

5.

Discussion and Conclusions

There have been numerous studies on the formation of main belt asteroid (MBA) families, and also some on NEO families. Statistical studies using NEO orbit data, based on orbital similarity, often generate positive results on the existence of NEO families. However, Fu et al. (2005) concluded that it is unlikely that these results are anything more than random fluctuations in the NEO orbit population. In a past IFM study, Steel et al. (1992) noted an orbital similarity between (5786) Talos = 1991 RC and Icarus. Their orbital elements, except for and , indeed coincide well with each other. However, Talos' longitude


­7­ of perihelion remains widely separated (by 50 ) from that of Icarus over the past 11000 yr integrated by Steel et al., so that it is difficult to verify a genetic relationship. If there exist NEO families having high-eccentricity and rather highly inclined orbits, then unless their origin is extremely recent, their differential orbital evolutions, shifted by t, will lead to their current orbital elements being drastically different. For this reason it is more complicated to search for NEO families than MBA families. Nevertheless, we found Near-Earth Apollo asteroids Icarus and 2007 MK6 to be very likely candidates for IFMs, based on our time-lag theory. Their t 1000 yr and minimized DSH 0.0098 are even smaller than those, 4600 yr and 0.04, of the well-established Phaethon­2005 UD relationship. Since Phaethon and 2005 UD may have a cometary origin (Paper I), therefore, the dynamical relationship between Icarus and 2007 MK6 along with a possible IFM dust band may constitute the first detection of an asteroidal NEO family, namely the "Icarus asteroid family". In this case, Icarus should be the parent bo dy, but as it is only a 1-km size ob ject, the Icarus family is on a smaller scale than MBA families. The next Earth approaches of Icarus and 2007 MK6 will o ccur respectively on 2015 June 17 to 0.05 AU and 2016 June 15 to 0.10 AU, providing go o d opportunities to determine additional physical parameters and to further study their common origin. It is possible that further accurate astrometry and advances in the numerical analysis will eventually resolve the separation age. The authors are grateful to the anonymous referee for his careful reading of the manuscript and for his comments.

REFERENCES Arakida, H., & Fukushima, T. 2000, AJ, 120, 3333 Arakida, H., & Fukushima, T. 2001, AJ, 121, 1764 Baade, W. 1949, IAU Circ., 1226 Bottke, W. F., Morbidelli, A., Jedicke, R., et al. 2002, Icarus, 156, 399 De Angelis, G. 1995, Planet. Space Sci., 43, 649 Fevig, R. A., & Fink, U. 2007, Icarus, 133, 69 Fu, H., Jedicke, R., Durda, D. D., et al. 2005, Icarus, 178, 434


­8­ Gehrels, T., Ro emer, E., Taylor, R. C., & Zellner, B. H. 1970, AJ, 75, 186 Harris, A.W. 1998, Icarus, 131, 291 Hicks, M. D., Fink, U., & Grundy, W. M. 1998, Icarus, 133, 69 Hill, R. E., Gibbs, A. R., Boattini, A., et al. 2007, MPEC-M32 Jewitt, D., & Hsieh, H. 2006, AJ, 132, 1624 Kinoshita, D., Ohtsuka, K., Sekiguchi, T., et al. 2007, A&A, 466, 1153 Kozai, Y. 1962, AJ, 67, 591 Lidov, M. L. 1961, Iskusstvennie Sputniki Zemli, 8, 5 Marchi, S., Magrin, S., Nesvorny, D., et al. 2006, MNRAS, 368, L39 ´ McFadden, L. A., Gaffey, M. J., & McCord, T. B. 1984, Icarus, 59, 25 Moiseev, N. D. 1945, Trudy Gosudarstvennogo Astron. Inst. P.K. Shternberga, 15, 75 Nesvorny, D., Bottke, W. F., Dones, L., & Levison, H. F. 2002, Nature, 417, 720 ´ Nesvorny, D., Jedicke, R., Whiteley, R. J., & Zeljko, I. 2005, Icarus, 173, 132 ´ Ohtsuka, K. 2007, MPEC-M49 Ohtsuka, K., Nakano, S., & Yoshikawa, M. 2003, PASJ, 55, 321 Ohtsuka, K., Sekiguchi, T., Kinoshita, D., et al. 2006, A&A, 450, L25 (Paper I) Sekanina, Z. 1973, Icarus, 18, 253 Sekanina, Z., & Cho das, P. W. 2005, ApJS, 161, 551 Shapiro, I. I., Smith, W. B., Ash, M. E., & Herrick, S. 1971, AJ, 76, 588 Southworth, R. B., & Hawkins, G. S. 1963, Smithon. Contr. Astrophys., 7, 261 Steel, D., McNaught, R. H., & Asher, D. 1992, Minor Planet Bull., 19, 9 Tedesco, E. F. 1989, in Asteroids II, ed. R. B. Binzel et al. (Tucson: Univ. Arizona), 1090

A This preprint was prepared with the AAS L TEX macros v5.2.


­9­

Table 1: Orbital parameters of (1566) ob ject osculation epo ch (TT) mean anomaly M perihelion distance q (AU) semima jor axis a (AU) eccentricity e argument of perihelion longitude of ascending no de inclination i # of observations arc (oppositions) RMS residual absolute mag. H reference

Icarus and 2007 MK6 (equinox J2000) (1566) Icarus 2007 MK6 2007 Apr. 10.0 1034 Jul. 03.0 2007 Apr. 10.0 285 .14414 161 .45243 336 .75725 0.1866177 0.1930133 0.1959358 1.0778849 1.0776443 1.0807494 0.8268668 0.8208933 0.8187038 25 .37252 25 .38152 31 .29236 88 .08105 93 .55925 92 .94672 25 .07805 25 .15553 22 .85385 711 54 1949­2006 (14) 2006­2007 (2) 0 .74 1 .12 15.95 19.9 JPL this work Nakano


­ 10 ­

Table 2: (1566) Icarus and the Tauridstionary phase ob ject epo ch q (TT) (AU) Icarus 1963 Jul. 3.0 0.18697 Tau-Per 1961­1965 0.163

Perseids (Sekanina 1973) at almost the same evolua e i (AU) (2000.0) 1.07791 0.82655 31 .032 88 .337 22 .940 86 .7 23 .3 1.268 0.871 36 .3


­ 11 ­
0.23 0.22 2007 MK6 0.21 0.20 Icarus 0.19 0.18 0.17
1.088 1.086 1.084 1.082 1.080 1.078 1.076 0.85 0.84 0.83 0.82 0.81 0.80 0.79 2007 MK6 20 15 10
0.254
Icarus 180 270 360

q a
Icarus

90

0



2007 MK6

360

270

180
2007 MK6

2007 MK6 90 Icarus 0
35

e
Icarus

30 2007 MK6 25 Icarus

i
Icarus 2007 MK6

0.280 0.276 0.272 0.268 0.264

C1
2007 MK6 Icarus -1 0 1 2
6

0.252 0.250 0.248 0.246 0.244

-2

3

4

5

0.242 -2

C2
-1 0 1 2
6

3

4

5

Julian Day [10 JDT]

Julian Day [10 JDT]

Fig. 1.-- perihelion perihelion and the C

Orbital evolution of (1566) Icarus and 2007 MK6 . The eight graphs show: q = distance in AU; a = semima jor axis in AU; e = eccentricity; = argument of in degrees; = longitude of ascending no de in degrees; i = inclination in degrees; 1 and C2 integrals. The abscissa of all is time (Julian Terrestrial Date, JDT).