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to 0.060 gave a reasonable number of streams and provided confirmation of the known streams in the Flora family. Similar results were obtained in test runs in the PLS data. For the study in the total asteroid population, we rather conservatively have chosen D, = 0.044. The search at this rejection level produced 81 streams with two members, 12 streams with three members, and 36 streams with four or more members. The number of asteroids in streams was 647 out of a total of 2929 orbits. Thus at the rejection level D, = 0.044, approximately 22 percent of the asteroid population was placed in streams. Table IV lists those streams detected in our search that had seven or more members. In nearly all cases, these streams were detected independently in searches both in the numbered asteroid population and in the PLS data. The possibility that these streams are caused mainly by selection effects peculiar to the PLS therefore appears unlikely. Alfvén's jetstreams A and C are detected. Alfvén's stream B was discernible, but was split into two groups, one with five and one with four members. At the adopted acceptance level of table IV, these groupings were rejected. The tendency of asteroids to aline their lines of apsides with Jupiter's is well known. An interesting situation occurs in Alfvén's jetstream A, where the search at D, = 0.044 split stream A into two groups of orbits having their lines of apsides oriented roughly symmetrically with respect to Jupiter's perihelion. A similar geometry exists in the Coronis and Denone streams, which also form two sets of orbits symmetrical with respect to the apsidal line of Jupiter's orbit. The streams listed by Arnold (1969) were compared with our streams (table IV). Only three orbits were common to both searches. The reason for this poor agreement is not known. As can be seen from the definition of D(M, N), the D criterion favors orbits that have their major axes alined. For low-inclination streams, this condition can be met even if there exist rather large differences in a and Q. It is possible that the stream search program of Arnold did not emphasize the alinement of the orbital major axis. The statistical significance of the streams listed in table IV was investigated by making stream searches in random samples. In one search in the combined population, we found, besides numerous two- and three-member streams, four streams with four members, one stream with five members, and one with seven members. It follows that the majority of four-, five-, and six-member streams found in the real sample are significant groupings, and thus could have been included in an extended version of table IV. The asteroidal streams represent concentrations within the recognized families of Themis, Coronis, Flora, and Nysa. The streams consist of family members that have a similar orientation of the orbital major axis. It is interesting to note that there are preferred directions of alinement. Figure 2 depicts the distribution of the longitude of perihelion is in the 647 stream orbits. Maxima in the distribution are evident at about m = 50° and 320°. The TABLE IV.-Asteroidal Streams (Jetstreams)

Preliminary Number of | Mean”
Stream members D(M, N) Family no. Members Remarks
name

Rosa 11 0.055 1 223,461, 621, 946, 1003, 1674, 4776, 6582,6634,6725, -
6745

Janina 8 .035 1 383,515, 1074, 1576, 1615, 1687, 2523,4602

Coronis 7 .033 3 158,243,993, 1079, 1570, 2549, 4122

Denone 10 .034 3 215, 761, 1100, 1128, 1289, 1363, 1497, 1635, 2560, -
4521

Elvira 8 .036 3 263, 277,832, 962, 1350, 1442, 4036,4593

Lacrimosa 17 .071 3 208, 321,452, 658, 720,975, 1029, 1223,4545, 4626, Loose assoc.;
4661,4893, 6044, 6546,6555, 6632, 66.36 doubtful stream

Anahita 19 .058 6, 32 270, 315, 939, 960, 1682, 1699, 2084, 2716,4065,4171, -
4227,4663, 6061, 6063, 6074, 6097, 6098, 6189, 7595

Nephele 14 .049 1 431,468,492, 767, 938, 1073, 1082, 1383, 1445, 2547, -
2757, 4590,4896, 6587

Hertha 9 .037 32 135, 1493, 2035, 2164,4009, 4015, 4078, 6080,9093

Gisela 10 .040 6, 7 244, 296, 352, 703, 1120, 1335, 1422, 1494,4637,6199 || Alfvén A

- 7 .035 6 810, 1150, 2526, 2659,2679, 4578,6619 Alfvén A

Eriphyla 15 .053 3 462, 811, 1010, 1245, 1336, 1423, 1725, 2522, 2567, -
2581,6534, 6542, 6565, 7631, 7633

Lucretia 8 .035 7, 8 281, 915,935, 1016, 2168,4014,4537, 6110 Alfvén C

*Computed from orbital elements a, e, i, w, and Q.

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Figure 2. —Distribution of the longitude of the perihelion in 647 stream orbits. (a) Number. (b) Percentage.

overall distribution (fig. 2(a)) is symmetric with respect to a weighted mean longitude of perihelion m = 12°5, which agrees closely with the longitude of perihelion in the Jupiter orbit. It is evident that Jupiter plays a predominant role in the orbital history of most of these asteroidal streams.

ACKNOWLEDGMENTS

The authors are indebted to Dr. J. R. Arnold and Drs. van Houten for kindly placing at our disposal card decks of the present and proper elements of the numbered asteroids and PLS asteroids. One of us (Lindblad) is indebted to Professor H. Alfvén for many helpful and stimulating discussions. This work has been partly supported by grants 204-43 and 204-44 from the Swedish Natural Science Research Council and by NASA contract NSR 09-015-033.

REFERENCES

Alfvén, H. 1969, Asteroidal Jet Streams. Astrophys. Space Sci. 4, 84-102.
Alfvén, H. 1970, Jet Streams in Space. Astrophys. Space Sci. 6, 161-174.
Arnold, J. 1969, Asteroid Families and Jet Streams. Astron. J. 74, 1235-1242.

[graphic]

Brouwer, D. 1951, Secular Variations of the Orbital Elements of Minor Planets. Astron. J.
56, 9-32.
Danielsson, L. 1969, Statistical Arguments for Asteroidal Jet Streams. Astrophys. Space
Sci. 5, 53-58.
Hirayama, K. 1918, Groups of Asteroids Probably of Common Origin. Astron. J. 31,
185-188.
Hirayama, K. 1928, Families of Asteroids. Jap. J. Astron. Geophys. 5, 137-162.
Houten, C. van, Houten-Groeneveld, I. van, Herget, P., and Gehrels, T. 1970, Palomar-
Leiden Survey of Faint Minor Planets. Astron. Astrophys. Suppl. Ser. 2, 339–448.
Lindblad, B. 1971, Two Computerized Stream Searches Among Meteor Orbits. Smithson.
Contrib. Astrophys. 12, in press.
Southworth, R., and Hawkins, G. 1963, Statistics of Meteor Streams. Smithson. Contrib.
Astrophys. 7, 261-285.

THE PROFILE OF A JETSTREAM

LARS DAW/ELSSON,"
University of California, San Diego

The jetstream concept was introduced by Alfvén in 1969. Since then, the subject has been studied from various aspects by Danielsson (1969), Arnold (1969), Alfvén and Arrhenius (1970), Lindblad and Southworth," and Trulsen.” In an attempt to define a jetstream, we may say that it is a group of objects moving in space with almost identical orbits. The largest objects in the jetstream may have any size, but the group must include a vast number of very small objects and their density must be large enough for the objects to interact. This means that collisions between the particles give rise to viscosity in the stream. Other interactions (e.g., by electromagnetic forces) are not excluded a priori. The meteor streams, or at least some of them, seem to have a constitution that is not in conflict with this definition. As far as asteroid streams are concerned, we know nothing. However, one might assume that the observed size spectrum of asteroids can be extrapolated to smaller objects. (We, of course, do introduce a great uncertainty if we extrapolate all the way to the size of micrometeoroids.) The best assumption we can make about the distribution of the orbital elements for the subvisual objects is that it is similar to that of the visual bodies. With these ideas as a background, Alfvén (1969) studied the classical Hirayama families among the asteroids to see whether there existed any clustering in the two orbital parameters that were not included in the analysis by Hirayama. Alfvén thus claimed to have found three streams in the Flora family, which were called Flora A, B, and C. By essentially the same principle, Arnold (1969) searched all of the main asteroidal belt for streams. An important difference was that Arnold considered all five orbital parameters at the same time; his technique was to enclose each asteroid in turn in a five-dimensional “rectangular” box with predetermined sides and to count the number of asteroids in each box. If the number was “large,” a stream was considered located.

*On leave from Royal Institute of Technology, Stockholm, Sweden.
*See p. 337.
*See p. 327.

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