Earth Moon Planet (2008) 102:179–182 DOI 10.1007/s11038-007-9217-8
On the Substantial Spatial Spread of the Quadrantid Meteoroid Stream K. Ohtsuka Æ M. Yoshikawa Æ J. Watanabe Æ E. Hidaka Æ H. Murayama Æ T. Kasuga
Received: 19 November 2007 / Accepted: 13 December 2007 / Published online: 29 December 2007 Ó Springer Science+Business Media B.V. 2007
Abstract We explored the substantial spatial spread of the Quadrantid stream, based on the backward integration of orbital motions of the Quadrantids, impulsively perturbed by Jupiter. We found that the Jovian impulses can widely spread out them in the early twentieth century, especially their perihelia extended by a factor of *90 than those at the observed epoch. We regarded the spread as the intrinsic one of the Quadrantid stream itself. Keywords
Meteors Individual (Quadrantids) Orbital evolution
1 Introduction The giant planets, such as Jupiter and Saturn, strongly perturb a motion of closely approaching small solar system body. For example, Jupiter generates the gravitational impulses in the meteoroid streams having highly-inclined orbit, like the Quadrantids (McIntosh 1991; Ohtsuka et al. 1995; Jenniskens 2006) that here we investigate and the Perseids (Trigo-Rodriguez et al. 2005). The Jovian impulses, acting on the Quadrantids in around their aphelia, are important mechanics for the orbital motions of the Quadrantids as well as the secular and resonant perturbations, since the Jovian impulses drive the orbital evolution very rapid. The orbits of K. Ohtsuka (&) E. Hidaka H. Murayama Tokyo Meteor Network, 1–27–5 Daisawa, Setagaya-ku, Tokyo 155–0032, Japan e-mail:
[email protected] M. Yoshikawa ISAS/JAXA, 3–1–1 Yoshinodai, Sagamihara, Kanagawa 229–8510, Japan J. Watanabe National Astronomical Observatory, Osawa, Mitaka, Tokyo 181–8588, Japan T. Kasuga Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, Hawaii 96822–1897, USA
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such Quadrantids should be further scattered subsequently. Ohtsuka et al. (1995) concluded that the 1987 Quadrantid swarm, photographically observed by the Tokyo Meteor Network (TMN), was indeed impulsively perturbed by Jupiter in 1984, half an orbital period before the observations (hereafter, we call such an ‘‘Impulsively Perturbed Quadrantid’’ as ‘‘IPQ’’). Two other IPQ swarms were also photographically observed in 1963 by the Tokyo Astronomical Observatory (TAO, the present National Astronomical Observatory) team (Ohtsuka et al. 1995) and in 1999 by the TMN team again. Therefore, now we have three sets of the IPQ orbit data recorded at every 12-year intervals (i.e., = heliocentric orbital period of Jupiter), except for no record in 1975. Integrating their orbital motions backward, we investigated their evolutional behavior characteristics analytically and numerically. As a result, we achieved some interesting findings, among which here we deal with the spatial spread of the IPQ orbits caused mainly by the Jovian impulses, obviously wider in the early twentieth century than those at the observed epoch. It is very important for studying the formation process of the Quadrantid stream complex to evaluate the spatial spread of the Quadrantids.
2 Data and Numerical Analysis First we selected out 13 IPQs as a data sample from among our IPQ orbit database. Since all of them were long-trail meteors, we could determine their no-atmospheric velocities (V?) well on the basis of the exponential curve fitting for the atmospheric deceleration. For that reason, their orbital parameters were precisely reduced by running our original software ‘‘METEOR J2000’’, Ver. 2.0. These IPQ orbital data are listed in Table 1, where the column heads from left to right are: meteor code number; Ep = osculation (observed) epoch in JDT (add 2400000 to this); M = mean anomaly in degree; a = semimajor axis in AU; e = eccentricity; x = argument of the perihelion in degree; X = ascending node in degree; i = inclination in degree. The 1963 and 1987 IPQ orbital data have already been reduced by Ohtsuka et al. (1995), however, they were re-reduced for this study. All of these IPQ meteoroids are in the mass of gram-order or more. Next we integrated their orbital motions backward for *2 centuries, using the ‘‘SOLEX’’, Ver. 9.1 package, developed by Vitagliano (1997), which based on a 16th-order polynomial extrapolation method, the Bulirsh-Stoer integrator. The initial data of the IPQs were taken from Table 1. The integrator can process very close encounters by a routine of the time step of automatic adjustments precisely, in which its truncation and round off errors are entirely negligible for our very short-term integration. Therefore, the SOLEX integrator should be sufficiently reliable to perform our study.
3 Results and Concluding Remarks In our knowledge, a spatial spread of the meteoroid stream has traditionally been considered as a flat ring of Earth-focusing at near its perihelion, as against enlarging around its aphelion. Its shape has long been accepted as that of a typical meteor stream by many investigators. However, they investigated the stream structure in the Earth-crossing part only, which satisfies the following condition of the relation among a, e, and x, of meteor: R¼r¼
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að1 e2 Þ 1; 1 e cos x
ð1Þ
On the Substantial Spatial Spread of the Quadrantid Meteoroid Stream
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Table 1 Heliocentric orbital data of the IPQs at each initial (observed) epoch Ep 2400000+
M
a
e
x
X 2000.0
i
M6301
38033.27860
1.49
3.025
0.677
169.54
283.2046
72.08
M6302
38033.29980
1.20
3.226
0.697
170.67
283.2266
69.76
M6303
38033.34233
0.83
2.846
0.655
174.72
283.2700
71.19
TN20
46799.26362
0.59
3.144
0.688
175.62
283.0284
73.22
TN21
46799.26609
0.88
2.962
0.669
174.06
283.0309
73.50
TN22
46799.29343
0.47
2.987
0.671
176.81
283.0591
71.46
TN24
46799.32814
0.82
3.096
0.683
174.05
283.0946
72.38
TN25
46799.34030
0.57
2.838
0.654
176.40
283.1070
72.60
T9901-01
51182.25141
0.53
3.368
0.708
175.60
282.9325
70.76
T9901-02
51182.25769
0.44
2.986
0.671
177.02
282.9389
72.69
T9901-03
51182.29133
1.26
2.983
0.672
171.37
282.9734
72.12
T9901-05
51182.32375
0.29
3.229
0.696
177.71
283.0066
73.08
T9901-06
51182.35801
1.64
2.971
0.672
168.79
283.0417
72.09
Code no.
1963 TAO
1987 TMN
1999 TMN
where R and r are respectively Earth’s and meteor’s heliocentric (nodal) distance *1 AU. Therefore, the selection effect, defined by Eq. 1, does not provide us any substantial spatial spread information for every meteoroid stream (Babadzhanov and Obrubov 1987). Meanwhile, some investigators have ever attempted to find clues about the substantial spatial spread of meteoroid streams, modelling the stream structure. As for the Quadrantids: e.g., the long-term perturbation cycle model by Babadzhanov and Obrubov (1987), structured by the evolutional passageway of a parent candidate, Comet 96P/Machholz; the dust trail model by Vaubaillon et al. (2006), from another stronger parent candidate, Amor asteroid 2003 EH1 (for the association with the Quadrantids, see also Jenniskens 2004; Williams et al. 2004). These modeled structures seem very likely. Here we explored the substantial spatial spread of the Quadrantids, based on the backward integration of orbital motions of these actually observed IPQs. The IPQs had sometimes encountered Jupiter in the integration time-span. Consequently, the Jovian impulses can rapidly spread out the IPQs with mass [ 1 g. In the early twentieth century, the perihelia extended their width up to at least *0.6 AU in the range between 0.8 and 1.4 AU. Thus, they were widely distributed by a factor of *90 than those of *0.007 AU (range between 0.976 and 0.983 AU) at the observed epoch. Such a spreading tendency is recognized in not only near the perihelia but also around the whole orbit area, except for near the aphelia where both spreads are comparable with each other, ranging over *1 AU across the Jovian orbit. It should be also noted that since the scatter of X is very small then, 283°.4 \ X \ 284°.2, thus the spread is predominant horizontally rather than vertically in the orbital plane. The IPQs’ spread at epoch JDT 2420000.5 (1913 August 13.0 TT) and the traditional spread at the initial epoch, where all the IPQs multiply plotted, are respectively illustrated at the left and the right in Fig. 1. Hence, the stream shape seems a thin-layered ‘‘donut (or torus)’’ in the evolutional passageway structure of the Quadrantid stream complex, which is quite similar to the theoretical one of Vaubaillon et al. (2006).
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Fig. 1 Distant view of the IPQs’ orbital spread at JDT 2420000.5 (left) and at the initial (observed) epoch (right). The orbits E and J mean those of Earth and Jupiter, respectively
Although the secular perturbation also advances the orbital evolution of the Quadrantids, the IPQs in the early twentieth century would still remain in near-Quadrantid evolutional phase in the orbital evolution of the Quadrantid stream complex. Therefore, if the Quadrantid complex meteoroids are evenly distributed over the whole space of their evolutional passageway, we may regard the IPQs’ spread in those days as the intrinsic spatial spread of the Quadrantid meteor stream itself. If so, we’d better re-examine the total flux, mass, and volumes of the Quadrantid stream, considering the substantial orbital spread. References P.B. Babadzhanov, Yu.V. Obrubov, Publ. Astron. Inst. Czechosl. 67, 141–150 (1987) P. Jenniskens, AJ 130, 3018–3022 (2004) P. Jenniskens, Meteor Showers and Their Parent Comets, Chap 20 (2006) B.A. McIntosh, in Comets in the Post-Halley Era, vol. 1, eds. by R.L. Newburn, Jr. et al. (Kluwer, Dordrecht, 1991), pp. 557–591 K. Ohtsuka, M. Yoshikawa, J. Watanabe, PASJ, 47, 477–486 (1995) J.M. Trigo-Rodriguez, et al. Earth Moon Planets, 97, 269–278 (2005) J. Vaubaillon, P. Lamy, L. Jorda, MNRAS 370, 1841–1848 (2006) A. Vitagliano, Cel. Mech. Dyn. Astron. 66, 293–308 (1997) I.P. Williams, et al. MNRAS 356, 1171–1181 (2004)
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