I

I # 7L3- 32723 NASA CONTRACTOR NhSA CR-2316 REPORT

\D r- c3

PHYSICAL AND DYNAMICAL

L(STUDIES OF METEORS

by Richurd B. South worth md Zdenek Sekmimt

Preparea’ by SMITHSONIAN INSTITUTION ASTROPHYSICAL OBSERVATORY Cambridge, Mass. 02 138 for Langley Research Center.

I4ATIONA,L AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. (:. OCTOBER 1973 I. Report No. 2. Government Accession No. 3. Recipient's Catalog No. NASA CR-2316 4. Title and Subtitle 5. Report Date October 1973 PHYSICAL AND DYNAMICAL STUDIES OF METEORS 6. Performing Organization Code

7. Author(s) 8. Performing Organization Report No, Richard B. Southworth and Zdenek Sekanina 10. Work Unit No. 9. Performing Organization Name and Address 188-45-52-03 Smithsonian Institution Astrophysical Observatory 11. Contract or Grant No. Cambridge, Massachusetts 02138 I NAS1-11204 13. Type of Report and Period Covered 2. Sponsoring Agency Name and Address Contractor Report National Aeronautics and Space Administration 14. Sponsoring Agency Code Washington, DC 20546

I 5. Supplementary Notes This is a topical report.

6. Abstract

Interplanetary distributions from a sample of 20,000 radar meteor observations are presented.

These distributions are freed from all known selection effects with the exception of a possible bias

against fragmenting meteors which has not yet been adequately assessed. These data thus represent

the largest and most accurate collection of radar meteor distributions. Both general average dis-

tribution and the distribution of meteor streams with their comet and asteroid associations are

presented. Sporadic space density and space density of meteor streams are presented.

~ ~ ~~ 17. Key Words (Suggested by Author(s)) meteor; radar obser- 18. Distribution Statement vation; distributions; selection effects; space density; fragmentation; meteor streams; luminosi. Unclassified - Unlimited ty; recombination; diffusion; meteor masses; orbital parameters; simultaneous observation; image orthicon

19. Security aasif. (of this report) 20. Security Classif. (of this page) 21. NO. of pages 22. Rice' Domestic, $4.21 Unclassified Unclassified I 108 t Foreign, $6.71

*For sale by the National Technical Information Service, Springfield, Virginia 22151 TABLE OF CONTENTS

Section Page

1 SUMMARY ...... 1 1.1 Aims ...... 1 1.2 Data ...... 1 1.3 Orbital Distribution ...... 1 1.4 Space Density ...... 2 1.5 Collisions...... 2 1.6 Streams ...... 2 1.7 Associations with Comets and Asteroids ...... 2 1.8 Height-Velocity Diagram ...... 3 1.9 Space Density in Streams ...... 3 2 INTRODUCTION ...... 5 3 OBSERVATIONS ...... 7 3.1 Radar Meteors ...... 7 3.2 Synoptic Year ...... 7 3.3 Simultaneous Radar-Television Observations ...... 8 4 SELECTIONEFFECTS ...... 9 4.1 Radar Biases ...... 9 4.2 Observational Geometry ...... 9 4.3 Ionizing Probability ...... 10 4.4 Diffusion ...... 10 4.5 Initial Radius ...... 10 4.6 Recombination ...... 12 4.7 Fragmentation ...... 13 4.8 Mass Distribution ...... 13 5 ORBITAL DISTNBUTIONS...... 15 5.1 Synoptic-Year Sample ...... 15 5.2 Velocity ...... 16 5.3 Radiants ...... 16 5.4 Orbital Elements ...... 20 6 SPACE DENSITY ...... 29 6.1 Observed Orbits ...... 29 6.2 Unobservable Orbits ...... 29 6.3 Densities ...... 31 6.4 Comparisons with Other Data ...... 33

iii TABLE OF CONTENTS (Cont.) Section Page 7 COLLISIONSINSPACE ...... 37 7.1 Significance of Collisions ...... 37 7.2 Theoretical Collision Model ...... 37 7.3 Comparison with Observation ...... 42 7.4 Sources of Meteors ...... 43 7.5 Further Research ...... 43

8 COMPUTERIZED SEARCH FOR RADIO METEOR STREAMS ...... 47 8.1 Two-Phase Computerized Stream Search in the Synoptic-Year Sample ...... 47 8.2 Phase I: Major Source of Initial Orbits ...... 48 8.3 Phase I: Other Sources of Initial Orbits ...... 50 8.4 Phase TI: The Weighting System ...... 51

9 RESULTS OF THE STREAM SEARCH ...... 57 9.1 List of the Detected Radio Streams ...... 57 9.2 Identification of Streams Detected in the 1961- 1965 Sample .... 58 9.3 New Streams: Toroidal Group, Short- and Long-Period Streams. Twin Showers. and the "Cyclid" System ...... 76 9.4 Distribution of Radiants ...... 77 9.5 Comparison with CookTsWorking List of Meteor Streams ...... 79

10 COMET-METEOR AND ASTEROID-METEOR ASSOCIATIONS ...... 85 10.1 Associations with Periodic Comets ...... 85 10.2 Adonis Meteor Streams ...... 85 10.3 Possible Associations with Other Minor Planets of the Apollo and Amor Types and with Meteorites and Bright Fireballs ..... 87 11 HEIGHT-VELOCITY DIAGRAM ...... 89 11.1 Introduction ...... 89 11.2 Height-Velocity Plots for Individual Radio Meteors ...... 89 11.3 A Height-Velocity Plot for Radio Streams ...... 97 12 SPACE DENSITY IN RADIO METEOR STREAMS ...... 99 12.1 Mean Space Density in a Stream in Terms of the Sporadic Den- sity ...... 99 12.2 Space-Density Gradient in a Stream ...... 100 12.3 Numerical Results ...... 101 12.4 Space Density from Cometary Production Rates of Solid Material; Comparison of the Two Methods ...... 103 13 REFERENCES ...... 105

iv PHYSICAL AND DYNAMICAL STUDIES OF METEORS

Special Progress Report

1. SUMMARY

1.1 Aims

This research focused on the interplanetary distribution of radar meteors, freed from observational bias. We sought both the general average distribution and the distribution of meteor streams with their comet and asteroid associations.

1.2 Data

The Havana, Illinois, 77synoptic-year*7radar observations and the Havana-Side11 simultaneous radar-television observations constituted the data. In addition to being the largest and most accurate collection, these data have two unique and crucial advan- tages:

A. There is an adequate sample of very slow meteors, which recombination has eliminated from all other surveys.

B. There is a reliable calibration of the meteor masses. The only known selection effect not yet adequately assessed is a possible bias against fragmenting mete or s .

1.3 Orbital Distribution

Low-velocity meteors predominate; the velocity mode in the atmosphere is under 15 km sec-l, and the mode in space at 1 a.u. from the sun is under 20 km sec-l. Radiants cluster to the sunward and antisun directions. Moderate eccentricities and low inclinations predominate; retrograde orbits are very rare.

1 1.4 Space Density

We extrapolated the orbital distribution observed at the earth to include unobserv- able orbits and used the resultant value to correct the space density of observed orbits. The result is meaningful between about 0.4 and 2.0 a. u., and uncertain but swggestive farther away. Meteors are concentrated to a relatively thin layer centered on the ecliptic plane. In that plane, there is a minimum of density at about 0.7 a. u., and a maximum beyond 2 a. u.

1. 5 Collisions

If this space-density distribution is in equilibrium, then most meteors must end their lives in collisions with each other. Moreover, a simplified theoretical model incorporating collisions and the Poynting-Robertson effect agrees with observation. Nonetheless, collisions need further study.

I 1.6 Streams

With the use of the most powerful stream-search technique in existence, we found 200 new streams in the synoptic-year data and confirmed the existence of two-thirds of the 83 streams detected previously in the 1961- 1965 sample of radio meteors. Some of the new streams have most uncommon orbits. A new, rich stream with a revolution period of more than 30 years has been discovered. Streams of low inclination are often detected at both nodes.

1.7 Associations with Comets and Asteroids

A number of known comet- meteor associations are confirmed, and a few new possible associations detected. The previously detected associations with the minor planet Adonis are strongly reinforced (including a major, broad stream), and several possible associations with other asteroids, meteorite Psfbram, and a Prairie Network fireball are suggested.

2

2 1.8 Height-Velocity Diagram

Plots of both the individual radio meteors and the radio streams fail to exhibit the discrete-level structure known to exist for photographic meteors. Some features of the height-velocity diagram are, however, detected.

1.9 Space Density in Streams

The mean space density in streams is much below the sporadic density, but the central density may significantly exceed the sporadic density. The absolute stream- density values based on the statistical model of meteor streams and on the sporadic density estimated in this report are in an order-of-magnitude agreement with densities estimated from the cometary production rates of solid material.

3

2. INTRODUCTION

The Radio Meteor Project, initiated at Harvard College Observatory under the direction of Professor Fred L. Whipple, and transferred to the Smithsonian Astrophysical Observatory (SAO) in 1966, constitutes part of a broad program of meteor and meteorite research at the two observatories. Under NASA support via contract NSR 09-015-033, the project included research activities in Cambridge, Massachusetts, and data collection by an eight-station radar system near Havana, Illinois, and by an image-orthicon system at Sidell, Illinois.

Research under the current contract NAS 1-11204 is directed toward distributions of radar meteor orbits in interplanetary space. The specific tasks are the following:

A. Use of the radar/image-orthicon data to improve assessment of radar obser- vational biases.

B. Determination of meteor orbital distributions from the synoptic-year sample, including corrections for observational biase s. C. Determination of orbital parameters of meteor streams and the density dis- tribution of meteors in the streams.

D. Investigation of associations of meteor streams with comets and with asteroids.

This report contains results for each task and also unanticipated results on the space density of meteors and on collisions between meteors.

5

3. OBSERVATIONS

3.1 Radar Meteors

Multistation radar observations of meteors contain the bulk of the orbital data on meteors, nearly equaling photographic observations in accuracy while far out- numbering them. (Reliable visual or satellite orbits are still rare.) The Havana system, with more receivers and greater sensitivity than any other, acquired the largest and most reliable collection of radar meteor data. We are here directly con- cerned with the orbital data but must make extensive use of the data on the meteor's interaction with the atmosphere to evaluate selection effects.

3.2 Synoptic Year

The primary data used for this report are the radar meteor observations collected in Havana, Illinois, during the period known as the synoptic year. The equipment and observations are described in the Final Report of contract NSR 09-015-033.

The Havana facility was extensively refurbished in 1967 and 1968: Measurements were made of the antenna radiation patterns, and equipment was installed to calibrate transmitted and received signals. The synoptic year comprises nearly uniform cover- age of all hours and alternate weeks from December 1968 to December 1969, with the Havana system in its best condition.

A satisfactory observation made with the Havana system yields the meteor's radiant, velocity, and deceleration; the location of its trajectory in the atmosphere and the distribution of electrons along the trajectory; electron-diffusion rates in the atmosphere; atmospheric-wind components; and, possibly, electron recombination rates or indications of meteor fragmentation. The meteor's orbit around the sun is deduced from the radiant and the velocity, and its mass, from the velocity and the electron distribution. The computer facilities at Langley Research Center reduced the observations.

7 3.3 Simultaneous Radar-Television Observations

Beginning in 1969, an image-orthicon system on loan from U. S. Naval Research Laboratory was sited at Sidell, Illinois, to observe optically some of the same meteors observed by radar from Havana. These observations are described in the Final Report of contract NSR 09-015-033, and also by Cook et al. (1972). Because we were able to use the much better known masses of optical meteors, these simultaneous observations are the best data for calibration of the masses of the radar meteors.

8 4. SELECTION EFFECTS

4.1 Radar Biases

The meteors we observe on radar are not, we know, a random sample of the influx to the earth; corrections for the many biases have occupied meteor astronomers for years. We have lately made several advances, large and small, in measuring these biases. All the corrections used are described in the present section.

4.2 Observational Geometrv

Elford (1964) determined the probability that the Havana radar would observe a meteor as a function of radiant altitude and azimuth. His table of the response func- tion of the six stations transmitting on the double trough and receiving on a single trough at site 3 and a double trough at other sites was not included in his 1964 report but is very similar to the tables that were. We have corrected it for the subsequent antenna calibration, as follows. The important differences between the measured antenna pattern and the design pattern that Elford used are a 6" decrease in elevation of the main beam and an increase in sidelobe sensitivity, in the measured pattern. Since sidelobe meteors are routinely rejected from the reductions, they are not con- sidered here. We first revised Elford's radiant-sensitivity contours to delete his assumption that the electron line density is proportional to cos ZR, where ZR is the radiant zenith distance. Next, we rotated the contours by 6" so as to center them on the measured main beam. Then we restored a proportionality between electron line 0. density and (cos ZR) ' 5, which is more nearly correct for fragmenting meteors.

The weight given each meteor as a function of radiant azimuth and altitude is the reciprocal of the revised radiant sensitivity, except that radiants with sensitivities less than 10%of the maximum are omitted altogether. A further weight was then applied as a function of radiant declination; this is inversely proportional to the range of right ascension within the 10% contour. Since observations were uniformly dis- tributed over the day, all radiants observable from Havana are now equitably represented.

9 4.3 Ionizing Probability

Cook -et al. 's (1972) ionizing probability, derived from the simultaneous radar- television observations at Havana and Sidell, is adopted here.

Future analysis of more of the simultaneous observations may revise the ionizing probability for fast meteors, which has perforce been extrapolated from lower velocities. Such an analysis could not, however, remove the predominance of low-velocity meteors.

4.4 Diffusion

The upper bound to meteor heights observed at Havana is set by ambipolar diffusion of the ionized column (Southworth, 1973). Thus, some of the faster meteors escape observation because they are too high. Figure 4-1 shows the distribution in height for various velocity groups among 11,061 meteors from the synoptic year; it is evident that the distributions are truncated at the right for velocities above roughly 40 km sec-l. Fitting a mean height distribution to the left sides of these truncated distributions, we found the fraction of meteors missed; we then derived the following empirical correc- tion formula. Meteors with velocities v over 34 km sec-l have their weights multi- plied by the additional factor

WD = exp [6.56 (loglov - 1.53)2 1 . (4-1)

This correction reaches its maximum WD = 2.1 at v = 72.

4.5 Initial Radius

Although the initial radius of the electron column (actually the radius reached in a few milliseconds) has appeared significant to several observers of relatively bright radar meteors, it does not seem important to the synoptic-year observations (Southworth, 1973). We propose that the radii measured with two-frequency or three- frequency radars (Baggaley, 1970; Moisya -et al., 1970; Kolomiets, 1971) should be understood as resulting from a combination of three processes: (1) diffusion of individual ions and electrons into the undisturbed atmosphere, as treated theoretically

10 N 8

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11 by Manning (1958) and bik (1955); (2) cxpansion of a hot cloud of neutral gas; and (3) lateral spread of fragments of the original meteoroid. Only the first of these has usually been considered, but the Havana-Side11 observations appear to show that (3) is quite significant for soine meteors. Baggaley's conclusion that initial radius is proportional to the 0.5 power oi atmospheric mean free path is inexplicable by use of (1) alone, but easily understood as (2) or as a combination of (1) and (3) or of (l), (2), and (3). For an order-of-magnitude estimate of (2), we compute the radius r of the C cylinder in the atmosphere that contains the same amount of heat energy as the energy deposited in the atmosphere by the meteors. We find

2 r;=GXlO -14 -mv (4-2) Pt ' where m and v are the meteor's mass and velocity, respectively; p and t are atmos- pheric density and temperature, respectively; and all units are cgs. At 100-km height and 60 kni sec-l, the brightest synoptic-year meteors (-10" elec cm-l, mass - 10-5 g at 60 km sec-l) have rc = 14 cm, which is negligible at the Havana wavelength (733 cm). 12 However, at the transition between underdense and overdense trials (line density - 10 elec cm-'), a meteor of the same height and velocity would have rc = 140 cm and an echo attenuation

A= exp [-&31?(Ef]=0.06 , (4-3) which is a severe observational bias. It is probable that process (2) has been neglected heretofore because ionizing efficiencies were believed to be higher, and masses corre- spondingly lower.

In view of the foregoing, we do not believe that the initial radius biases the synoptic-year data, except perhaps as the effect of fragmentation, which is separately discussed. No correction was applied.

4.6 Recombination

Southworth (1973) showed that recombination is an important limitation to surveys using less-sensitive equipment. For the synoptic year, however, recombination can

12 be expected to affect only the lowest bright meteors observed, and then not to attenuate them beyond observability. An empirical check comparing the height distributions for differcnt ranges of radar magnitude showed no apparent effects of recombination. No correction was applied.

Future studies that treat individual masses will need recombination corrections to electron line densities and therefore to masses on at least some meteors. However, as explained in Sections 4.8 and 5.1, the electron line densities do not enter the weights in this report.

4.7 Fragmentation

The Havana-Side11 simultaneous observations (Cook et al., 1972) appear to show that fragmentation is sometimes associated with severe attenuations of radar echo strength. This can be easily understood as the effect of lateral spread of the particles from the mean trajectory. Simple theory leads to the expectation that the effect is most important for slow meteors, and photographic meteor studies lead to the expecta- tion that it is important for some showers. However, there is as yet no radar analysis evaluating its importance, and no corrections have been applied.

The possible underrepresentation of fragmenting meteors is the only significant bias that we suspect to remain in the results reported here.

4.8 Mass Distribution

3 Although we have observed meteors covering a range of more than 10 in electron line density, the steep dependence of ionizing probability on velocity ensures a strong negative correlation between mass and velocity in the synoptic-year meteors. As it is not possible to select an unbiased sample from among these, we have assigned to each meteor a weight representing the number of meteors of some standard mass. This procedure implicitly assumes that the mass distribution is independent of orbital parameters over the range of masses observed at any one velocity, and we have not noticed any counterexamples in our data. Our data are not sufficient to show whether the orbital distribution is independent of mass over the whole range of masses observed.

13 Howcver, we expect that there is some dependence of orbital distribution on mass, and our results necessarily refer to the orbital characteristics of masses that are larger at low velocity than they are :it high.

On the assumption that orbital elements are independent of mass, a small mass is as good a sample of orbital elements as is a large one. Since, as just explained, we make this assumption for all meteors of the same velocity, we are also taking advan- tage of it to equalize, for all meteors of the same velocity, that part of the statistical weight that depends on mass. This amounts to omitting the observed total number of electrons from the weights. It has appreciably smoothed the final distributions.

We have adopted Whipple's (1967) mass distribution, specifically that the number of particles with mass 2 m is

-1.36 n= constant (m) (4-4)

The corresponding factor in the statistical weights to reduce counts to observations at equal masses is

-1.36 f=p 7 (4 - 5) where p is the ionizing probability. There is certainly a suggestion in Whipple's collection of data that the slope is lower for our smaller masses. Adopting an -5 exponent of -1.0 for masses below 10 g would increase the relative abundance of high-

velocity orbits in our distributions by a factor + 3, but would still leave them numer- ically unimportant. Since the ionizing efficiency for high velocities also remains uncertain, we have not made this adjustment.

14 5. ORBITAL DISTRIBUTIONS

5. 1 Synoptic-Year Sample

This section presents tables and graphs of the velocities, radiants, and orbits of meteors observed in the synoptic year. All graphs and tables are in three forms: (1) unweighted, (2) reduced to equal masses in the atmosphere, and (3) reduced to equal masses in space at the earth's distance from the sun. We use three forms to facilitate comparison with the great variety of other published forms. Observations from earth satellites should be compared with the second form; and observations not restricted to the ecliptic (e. g., comets), with the third form.

The tape of reduced observations contains 19, 698 meteors. We omit 505 with slant ranges over 400 lun because such observations are much more likely than others to be confused by wind shears or plasma resonance. Accordingly, the unweighted sample is 19, 193. For the sample reduced to equal masses in the atmosphere, we omit a further 4973, which were observed outside the main lobe of the antenna pattern and which would therefore introduce large statistical noise in the results if they were given the very large and uncertain weights nominally belonging to them. Thus the atmospheric sample is 14,220. For the sample reduced to equal masses in space at 1 a. u., we omit 1622 more meteors with radiant latitudes south of the ecliptic, since we cannot get a complete sample of all southern radiants. This leaves 12, 598 in the space sample.

Because we assume that in our observational dynamic range the orbital parameters are relatively independent of electron line density, the weights do not include the integrated number of electrons observed, although they do include all other mass factors; this procedure has appreciably reduced statistical noise in the results. Since the equipment parameters were nearly constant over the synoptic year, there are no corrections dependent on date of observation. All other corrections described in Section 4 are included. The spacc sample includes corrections for the collision probability with the earth.

15 5.2 Velocity

Figure 5-1 shows the distribution of no-atmosphere velocities: dotted lines for the unweighted sample, dashed for the atmospheric sample, and solid for the space sample. By comparison with distributions observed on less-sensitive equipment (e. g. , the earlier Havana data; Hawkins, 1963), there is a considerable enhancement in the fre- quency of velocities under 30 km sec-l. Moreover, velocities down to 11 km sec-l are observed, whereas earlier surveys barely reached 15 km sec-l. Recombination caused the bias against slow meteors on less-sensitive equipment (Southworth, 1973).

Corrected for ionizing efficiency and reduced to equal masses, the velocity dis- tribution in the atmospheric sample shows the greatest concentration toward low velocities of any published distribution known to us. The mean is approximately 14.5 km sec-l. However, the space sample shows that these very low velocities are less common outside the earth's gravitational field.

5. 3 Radiants

Figures 5-2, 5-3, and 5-4 show the distribution of radiants with respect to celestial latitude p and longitude measured from the sun XR - in the form of com- R Xo puter tabulations with superposed contours. The unweighted sample exhibits familiar features: concentration of most of the radiants to a broad band about the apex con- taining the "toroidal, It "sun, and 'tantisun'' clusters, and a relatively small cluster at the apex itself.

The atmospheric sample, even though smoothed, is comparatively noisy because of the high weights given a few slow meteors. Nonetheless, one sees that the sun and antisun clusters remain significant but that the remainder are more generally spread over the sky.

In the space sample, the sun and antisun clusters have split into northern and southern divisions, of which only the northern divisions can be reliably observed at Havana. The total distribution now consists of two broad concentrations, which

16 302-081 I 1 I I l

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IO 20 30 40 50 60 72 co NO -ATMOSPHERE VELOCITY

Figure 5-1. Distribution of no-atmosphere velocities. The plotted numbers are fractions of the samples within a 2-km sec-l interval in velocity, or the fraction over 72 km sec-l. The observed, atmospheric, and space samples are explained in the text.

17 9u E5 22 2 lZiL2 22222222Llll222222LZ 23222222 4 13 3 3433s 44332233322232334433 EL 3 4\64 b 5655554133 333333334554344 5 5 -5- 75 565654 4.-*.2~-Y~l"*-r.r. ~..)..b..3.'4..t.4..3..4 71, f; 7 * 3 4455 7 65 10 9 5 5 5 5*.*- 7--3 4 3 3 2 2 2 3 '3'3-2 2 2 3 3 3 2 3 3.- *-..4.*5 5 6889 bU I1 9 c 5 5 5 .-4 3 23332222LZ2222222122 3 3 'e.4 5 7 811 I1 9 7 5 5 .-3* 4 4 3 3 3 3. 6 8 911 I1 9 7 fp.5 5 .) 5 2335-5- 7 I 11 IC 8 "5 5 5 5 4 s-'q i 9 b5543* 46 9 1.' i-2 1 I I I I I t I I I I i I I 2. 5 7- 7 IO 8W.7 35 54432i2Illlll 11111 I1 5 7', 9 3L .s 7 5 4 4 3**2 121lllll 11111 I1 23 '7 1 5 5 4 t.2 lZZZllll 11111 111 2L :s 7 l2ZZlll iii iii I5 5 12lllll 111 1 3 IU 5 5 --- 4'2 L I I 1 I I 11 111 L. 4:1 I I I I I I I -5 1 1111 -lL 3211 1111 I1 1 11 -1%-_ 54 31'11 I1 I -ii 33.211111 111 12237 -25 LZ'IIIII i11123 -j, I ! ! : : llllil -3: 1111 111111 -*,. I1 I1 1 -*: -5L -55 -tL

76 45 e1,

.rV 3: 36 25 26 I5 IC 5 U -5 -IC -1 5 -iL, -25 -3c -35 -*L -4:. -56, -55 -6 1, -65 -7U Figure 5-2. Distribution of observed radiants in latitude and longitude from the sun. The tabulated figures are the observed number within cells extending 5" in latitude and longitude, smoothed by averaging blocks of nine adjacent cells. The radiant density per square degree in a cell is equal to 0.04 sec p multiplied by the tabulated number. Contours have been drawn at 4.0 radiants per square degree (solid line), 1.2 (dashed), 0.4 (dotted), and 0.12 (crosses). Contours were not drawn in southern latitudes, where the sample is obviously incomplete. The average density of observed radiants north of the ecliptic is 0.79 per square degree.

18 A,- '0 0 Z0 30 40 so 60 70 80 90 100 110 120 130 140 1SO 160 170 180 90 LO 4 4 122111111433 222 16 I? 11 13 1313 122 2 4 4 85 1114 5 7 TI3 2 2 2 13- 5 1 80 I215 4 2243 3 18 17 19 IS 1413 145 S 210 9 I5 !5 1 4 1; 9 9 8:s 5 4 6 5 b &I41311._.__ __ 9 910 4 9 24 Z? 22 11 15 15 3 8 LO 9 6 Id 14 15 5 6 I9 11' b 10 is t 545i b 4 \1 20 24 24 I4 11 3 I2 12 14 11 14 12 Y 6 3\10 10 1 V 11 22 12' 6 24 22 110 1 12 14 11 5 4 1h21 23 30 21 2S 15 20 20 21 15 18 12 0 8 11 \2 13 10 11 12 65 1 43 431 8 8 12 12 9 60 8 11 10 RU23 22 20 22 20 19 15 14 16 18/14 12 10 .9 11 11 1s 14 41 41/13 9 12 12 n 8 12 14 u 7 'tpX2b 31 26 25 .fi 14 16 10 42 18 18 20 15 33 30 12 10432 9 11 13 6 1 S 6?\18 21 2 11 14 IS Ad18 23 I8 16 13 I9 201 13 988651976 4 18 21 q 11 8p 33 38 26 11 11 11 IE 2n 23 32 301 8 10 10 10 5 0-e 9 4 1 40 1 14 I1 LO 14911 11 22 34 38 29 18 20 36 31 3q 20 13 ZO(31 34 43 49 44 36 35 3 lot842) ZfYT.18 22 lb249 3S 36 39 32 39 4# 21 -9 85 80 P 9 3221 22 29 15 21/15 14 23 44 45 38 38 30 5t 51 Sal 43 26 21 25 -2) If 86 8blO4 31 7422 22 22 20 23 3 84 7270 20 22 15 ' I? 2\ 36 19 56 52 5 . 7222 10 11 25 36 19 31 21 2u Ad35 11 29131115 I6 12 5 64 16 6 112112109 0 5b 83 6 1641b420914 -5 8 K 65 63 90 60 YO 5 143115217143160164 -10 - -~ 66 8U 65 $1 55 30 63 5; 43111204123128128 2t 2; 39 48 49 45 26 19 61 61 7i 12'11 11 33 29 34 41 41 42 -15 un 8 i2 20 43 36 11 82 15 42 17 25 15 24 2U 39 31 35 12 11 72 67 6S 29 29 16 88 88 42 -20 11 21 37 20 24 13 17 15 14 15 10 13 14 15 14 If 26 23 18 29 29 70 85 0s 44 12 12 12 161620 1 8 6 6 8 -i5 7 I 1 12 9 u 18 18 18 -30 si i5 85 44 12 12 12 8 n 8 5 911 8 6 594 4 5 6 25 21 19 14 14 14 9 -35 44 44 44 12 12 12 9 9 I11 5 2 290 4 5 4 23 19 19 9 9 9 5 55 1 1290 -40 2 1 19 I9 13 13 13 -45 A LO 2 22 1121 11 13 13 13 11 -50 11 13 13 13 -55 -6@

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Figure 5-3. Distribution of radiants from the atmospheric sample, as in Figure 5-2. The weights have not been normalized, so that the contours represent only relative radiant densities. On the same scale, the average radiant density north of the ecliptic is 1.40 per square degree. A few very high-weighted radiants have made this a rough distribution in spite of the smoothing. The obvious rectangular blocks of nine adjacent figures larger than their neighbors each represent one high-weighted radiant.

19 peak in these clusters. Moreover, the clusters have shifted away from the apex, and the relative numbers in the apex and antapex hemispheres are more nearly equal than any previously reported.

'R- '0 0 10 20 30 40 50 60 70 80 90 100 110 I20 130 140 150 160 170 I80 90 622 1222 85 31223122.-_ &3767456 80 43 9 12 9 17 16 15 12 14 15 75 IO is I1 16 70 23 20 65 31 28 48 45 47 41 -67 68 72 60 32 55 45 51 92105 92 PR :: 40 35 30 25 ZU 15 10 5 0

'R- '0 180 190 200 210 22C 230 240 250 260 270 280 190 300 310 320 330 340 350 360 90 2223333442 85 I 22222 111 11222112233454 80 3 4 4 4 4 2 2 2 3 318 8 7 6 6 7 44 4 5 91011 9 7 75 11 I3 14 10 8 3 3 2 2 6 (12 I4 I6 15 13 7 0 21 24 24 16 I1 9 6 5 4 8 10 I6 17 23 22 26 4* 59 bO 62 56 51 62 75 b2 44 65 28 30 32 25 18 14I 8 6 S 10A2 I4 17 23 27 30 64 R7 82103 89 85 64 7 60 27 27 30 28 21 I 56 60 6b 62 5j 71 97 7 b 38 55 99 98 96 98110 42 3b 106121120111106 9 3G 39 47 45 PR :i 123127115 78 79 0 47 20 31 61 b3 8, 158134 89 76 75 4c 51 29 29 2ki8 'L' 35 42 29 26/13 15 .a 3L 62 36 23 21 13 3 3 7 ao 13 35 36 35 (93 87 q9 45 53 7612514014b 25 t3 36 '20 17 9 2 4 I '0 16 u 35 37 21 3* bqq97 53 67 eCeiis13i 20 67 3d20 I1 :a 3 4 4 3 15 (2 43 65 bh 51, 33 p L2 54 60 83 112131 15 42 29 22 I1 :a 3 5 7 c2 15 3-8 52 54 63 53 50 57 5Q 62 64 &9 03 IO 41 do 23 13: 6 2 4 5 fAl q 19 Ii'44 51 58 52 50 55 50 52 61 8310 5 M 17 14 IL' + 1 3 S {'S..Y'W.4>b-p 49 42 51 39 43 47 67 8% 0 9 11 7 .d 1 3 5 '4 hN026 22 26 24 39 51 58

Figure 5-4. Distribution of radiants from the space sample, as in Figures 5-2 and 5-3. On the scale of weights used, the average radiant density north of the ecliptic is 2.86 per square degree. The smoothing process has arti- ficially lowered the bottom line of tabulated densities by one-third, but a real decrease also occurs at low latitudes.

5.4 Orbital Elements

Figures 5-5 to 5-10 show the distributions of the elements a, l/a, e, q, q', and i. The observed sample differs from previous observatjons primarily in the added importance of low-velocity meteors, which perforce have orbits with low to moderate eccentricity, low to moderate inclinations, and perihelia and aphelia not far from the earth's orbit.

20 302-081 r I I

I00

U W m 5 3 z W 3 5 J W U

t

L I I 0.5 I .o I .5 2 IO 00 SEMIMAJOR AXIS a

Figure 5-5. Distribution of semimajor axes a. The scale on the abscissa has been broken to permit showing details near 1 a. u. The plotted numbers are fractions of the samples per 1-a.u. interval of semimajor axis, or the fraction greater than 10 .a. u.

21 302 -081 __ I 1 I I

ATMOSPHERIC ------

\ :- -1 , \I 1 I L 0 I 2 INVERSE SEMIMAJOR AXIS I/a Figure 5-6. Distribution of inverse semimajor axes l/a. The plotted numbers are the fractions of the samples within intervals of 0.1 in l/a.

The atmospheric sample is dominated by near-circular or moderately eccentric orbits of low inclination. Other types are numerically insignificant.

The space-sample inclinations are also low, but the peak of the distribution is near

7 O rather than 0". Eccentricities, however, peak near 0.5. These are in harmony, as they must be, with the radiant distribution and with a predominance of low geocentric velocities directed approximately radially to and from the sun. The general trend of the distribution of perihelion distance is a necessary consequence of observation at the earth and of a broad spread of eccentricities. However, a rise above the trend near 0.2 and a dip below 0. 1 may be indicative, respectively, of the perihelion of some significant source of the particles, ar of particle removal by solar heating, or of both.

22 The general trend of the distribution of aphelion is also a consequence of observation at the earth, but a modest rise above the trend in the asteroid belt is very probably sig- nificant for the origin of many of these meteors (Section 7 has other evidence on the origin).

302-081

loo '0°7[ ATMOSPHERIC I

10- '

CL w m z 3 Z w 2 at- lo-2 IC

I I I. lo3 I

0 I 0 I ECCENTRICIT Y e PERIHELION DISTANCE q

Figures 5-7 and 5-8. Distributions of eccentricity e and perihelion distance q. The plotted numbers are the fractions of the samples within inter- vals of 0.1 in e or q.

23 302-081

io- 7

Id2

U \ w m \ I L’ 3 z zSPACE W -> F a -J W a: IO-^

\ I IO-^

2 3 4 io APHELION DISTANCE q’

Figure 5-9. Distribution of aphelion distance q’. The scale has been broken to show more detail inside 4 a.u. ; this causes an apparent sharp change in the slopes that does not actually exist. The plotted numbers are the fractions of the samples per 1-a. u. interval of aphelion distance.

24 302-081

\ \ \-A4*

...... ,.\ ...... rl \ .. OBSERVED h\ '\ \

\ \ \

ATMOSPHERIC

0 IO 40 I80 INCLINATION i Figure 5-10. Distribution of inclinations i. The scale on the abscissa has been broken twice to permit a convenient representation. The plotted numbers are fractions of the sample per degree of inclination.

Tables 5-1 to 5-3 show relative distributions of l/a versus e, l/a versus i, and e versus i, respectively, for the space sample. Each table was separately scaled to a maximum entry of 800. In Table 5-1, the upper blank area would contain orbits with perihelion outside the earth's orbit, and the lower blank area would contain orbits with aphelion inside the earth's orbit. Border cells of the triangular array are only about half observable from the earth, and scattered values outside the triangle are caused by the earth's orbital eccentricity. The concentration to the top edge of the array reflects the concentration of perihelion distance toward 1.0. Tables 5-2 and 5-3 show small but definite positive correlations between l/a and i and between e and i, respectively. These await interpretation, as do many other prominent features and most details of the distributions. 25 Table 5-1. Relative distribution of l/a versus e for the space sample.

e 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

-0.6 5 -0. 5

-0.4 2 -0.3 2 -0.2 7 -0. 1 11 0.0 37 0.1 79 21 0.2 22 1 74 6 0.3 21 574 358 41 5 0.4 637 557 142 33 5 0. 5 3 463 614 322 88 26 5 l/a 0.6 2 437 800 238 159 59 20 9 0.7 1 496 617 224 145 74 57 21 5 0.8 1 352 569 511 216 137 99 25 35 6 206 603 362 240 235 79 81 48 16 5 1.0 364 436 212 70 103 87 94 54 17 6 1.1 3 112 330 104 68 66 63 27 15 4 1.2 23 86 219 179 42 62 55 19 6 1.3 38 119 80 66 69 21 7 1.4 39 161 129 80 33 7 1. 5 46 71 30 20 3 1.6 57 97 26 9 1.7 10 29 7 1.8 16 4 1.9 2.0

26 Table 5-2. Relative distribution of l/a versus i for the space sample.

i 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

-0.6 4 1 -0.5 -0.4 2 -0.3 21 -0.2 15 -0.1 144 111 0.0 215 7 3431 0.1 18 25 26 15 6 3 2 1 0.2 74 84 78 30 15 5 2 1 0.3 382 304 183 60 21 7 3 1 0.4 425 556 212 88 23 12 3 1 0.5 573 457 302 92 25 9 3 1 0.6 l/a 607 696 220 91 28 11 4 1 0.7 67.3 433 346 81 27 11 5 1 0.8 770 576 365 114 30 15 4 2 0.9 516 800 297 118 46 15 9 3 1.0 324 537 315 118 52 23 13 4 1.1 174 292 130 78 43 27 11 5 1.2 128 286 91 73 43 28 11 3 1 1.3 56 113 48 96 27 30 10 2 1 1.4 27 180 102 53 38 21 7 2 1 1. 5 55 26 8 44 12 9 6 2 1 1.6 1.7 12 53 46 18 28 15 4 4 195119142 1. 8 2 6 3431 1.9 2.0

27 Table 5-3. Relative distribution of e versus i for the space sample.

i

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

105 230 50 15 6 1 1 444 392 169 54 18 6 4 1 OS2 561 491 266 97 29 11 6 2 OS3 605 478 309 125 41 25 8 3 Oe4 417 800 307 124 52 28 10 3 3 e OS5 572 547 333 136 47 25 11 4 OS6 516 666 310 127 52 28 12 3 1 Oa7 277 321 208 104 55 29 12 3 1 Om8 63 86 82 79 42 19 7 5 1 1 1 8 23 30 17 14 11 5 2 1 1 1.0 5 8 21 1.1

28 6. SPACE DENSITY

6.1 Observed Orbits

The space density of meteors observed at Havana from 1962 to 1965, when the radar system was much less sensitive than during the synoptic year, was computed by Southworth (1967). The only other computation of space density (Briggs, 1962) treats an equilibrium distribution of photographic meteors under the Poynting-Robertson effect. The present report follows the methods of Southworth (1967), but it uses the far superior data from the synoptic year and reaches a very different result.

The space density of the observed meteors is computed numerically in straightfor- ward fashion. Space in the solar system is divided into bins, with divisions at inter- vals of 0.1 in log r, of 0. 1 in sin and of 18" in where r is the distance from the 10 p, 1, sun in astronomical units and where p and X are heliocentric latitude and longitude, respectively. The computer follows around each orbit and computes, to a very good approximation, the time spent in every bin traversed. Adding these times (with cosmic weights) and dividing by the bin volumes gives relative space densities. Abso- lute space densities then follow from the local space density derived from meteor influx data.

6.2 Unobservable Orbits

Only orbits with perihelion inside the earth's orbit and aphelion outside it can be observed from earth; clearly, we need to take the unobservable orbits into account. To that end, we extrapolate the element distribution observed at the earth, as follows:

We assume that a and e are independent of the angular elements i, W, and R. Tables 5-2 and 5-3 show that a and e are in fact only slightly dependent on i, while regression of the nodes under planetary perturbations must have randomized w and 0. The two- dimensional relative distribution of l/a and e, shown in Table 5-1, was smoothed and then approximately fitted by

29 P(l/a, e) = BE , where

E = 75- 131 (e-0.775) (le-0.7751) -Os6 ’ i 0.2b if b 5 0 , loglo B= (3b if b > 0 , b= 1.35 - l/a - e . I

Figure 6-1 shows the areas in the l/a-e plane that contain orbits reaching 1 a.u., reaching R a. u., and reaching both. The correction factor F(R) to transform observed space densities at R to total space density was computed as the numerical integral of equation (6-1) in the region reaching R, divided by the integral in the common region. Table 6-1 is the result.

Table 6-1. Correction factor for observed space densities.

loglOR -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15 -0.05

loglOF 1.41 1.35 1.22 1.06 0.90 0.73 0.57 0.39 0.21 0.06

loglOR 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 loglOF 0.21 0.64 1.04 1.40 1.72 2.03 2.34 2.66 2.98 3.24

Jt is evident that the correction factor F must be unreliable when it is large, since large corrections are derived from the extrapolated existence of many unob- servable orbits. Although equation (6-1) was chosen as being a plausible form, as well as being an approximate fit to the observations, the bulk of the mass is in orbits with small e, for which the distribution of l/a can be only poorly extrapolated. Thus, we should treat with reserve the corrected space densities beyond, say, 0.4 and 2 a. u., although the general trends beyond may still have significance.

30 I/a

2

LEE-

I

I/R

0 e 0 I

Figure 6-1. Orbits having l/a and e in the horizontally shaded area can be observed at 1 a.u. from the sun; orbits in the vertically shaded area can be observed at R a.u.

6.3 Densities

Table 6-2 shows decimal logarithms of space density in arbitrary units, in three two-dimensional arrays. The top section shows the distribution in r and sin p, averaged for all longitudes, and the bottom section shows the distribution in r and X, averaged for latitudes between -30" and +30°. Both these sections are still affected by the observational selection of meteors with nodes at the earth's orbit and also by appreciable sampling noise, but we anticipate they may be of future interest. The

31 O.J omc91- -#v J- J~NJmm o. e 0) J c a u omo N >rum Y\ Q a c> w- e N...... m P c mowN- NC o - PO o ,J e F - -3 .a J U L7 n In n m m t I) n J I) m m U n

...... Y\ m Y) n "1 m "1 In In In m n In "\In y1 In In n

...... n In Y1 n m In n n n In In VI VI In In In In v. .I\ In ...... nnInInInnnnnnnn*.aInnmInInn ...... m*~annnnoa nInInnInnInnnInnnInnnInnmv)m N N J m m c o o P P m J u, u t m - m ommommo-onmamoocnoo~ ~~DQ~-Q~CCCCQ~CCI-C~QQ...... n~nnnnnn~nnnmntnnan~nn~~~nm ...... m.t-t.tnnInInaa ~nnm~nn~nmm~n~nm~)mnnm~n~nnm J.VYOOSNm.OP D N JN ium o. c 3 J n-~r'om~nmo~...... mt**nnInInnnaonInnnuugm nnInInmnInnnnmInnmnY)nnInIn NPWWUU.fmNO ~ao-~mocmn ...... OtWONmS1-P'1) ...... m.stnnnnInIno...... mnInmnnmnnmInnnnnnnmInIn UQn+Nf-000NO-4NNFOQQQ Q m o J m a m ~nN i NO~O~NU-POJ~V-~-NT-U-~*mm-m4nwmo Or-JNJmCmOPo-OQaI)w0aP...... -ao~.tncmo-...... JJ.rInnnnInaa

FPOOONdIndO J *wt nco. 3 -.u mc,-mmamo~ry...... a-m d3N ca nwP ru I. nmn... a 0-9 no do* 4 Jr *e -om In *--a -I- m ... -4.. NNN... nao a 0.l aaa4

ace t- FP urmNIn L3-U -u- mY m".JJ -4... * .. m... 0 '* v oao O an aooo am emu, cy DOOP om*m-42 cU mn 8,- 3 m -0.mff mmry J rym Urn* v O*PP ...... I. .... OQr .o CJ ua.4 J i) "< m In

MI -0.- Fr-m. n f u r- E m- -ma m IN m -4 tO mm OIViy e ...... I. CQO oooo~c 31) a** 0 o...... o D e Q m J CI N - G c, Q I) 4 F n PO 31I I I118 1'7 Q .-c In

32 central section shows the distribution in r and sin p when the observed value of w for each orbit is replaced by a uniform distribution from 0 to 2~.Regression of the nodes must in fact smear w nearly uniformly in the real interplanetary distribution; accordingly, we have simulated the process as our last correction for observational selection. Because the distribution is now symmetric about p = 0, this portion of the table includes only positive values of sin p.

-22 -3 Figure 6-2 shows the averaged density distribution, using 4 X 10 g cm for

+hn n-mnA ,Innn;Crr -clan +hn nn,r+h nm nn+:-n+nrl ' uicl opabcl uLuu*bj 1ib.cI.L cucI cuy au ~ut,i~~~ucuu i; SCC~~GZ 7. T~c CZTYCS 52~~~CCZ smoothed near r = 1to correct bumps, which were doubtless caused by inexactness in the fit of equation (6-1) to the data. Of course, we could make cosmetic changes to (6-1), but we would make no real advance in reliability. It is not plausible that the earth should have any effect on space density that could be seen on the scale of Figure 6-2, especially at higher latitude.

Figure 6-3 shows, on two scales, the contours of space density in a plane normal to the ecliptic. The less reliable contours are dashed. The meteors are concen- trated to a relatively thin layer about the ecliptic plane. There, the minimum density is 0.7 a. u. from the sun, and the maximum, between 2 and 3 a. u. from the sun.

6.4 Comparisons with Other Data

The distribution of space density just described was a considerable surprise to the authors. Nonetheless, it is in qualitative agreement with two recent results from totally different observing systems: (1) Roosen (1970) was unable to detect the earth's shadow on the gegenschein and deduced that the density of light-scattering particles must increase outward from the earth. (2) Pioneer 10 (Kinard and Soberman, 1972) detected an increase in particle density of larger particles on its way to the asteroid belt.

33 302-081 I 1 1 I Illll I I 1 I IIIII lo-2'

sin p

00-0 I 0 1-02

* 02-03 -I- 03-04 z0) W n 04-05 W 0 05-06 i3 (I) 06-07

\ 0.7 - 0.8 '\ \ \ -.. 0.8- 0.9 \ \ / lo-'4 \ 0.9 - 1.0 -+.> /A/-

--A1. /'

I I1111111 I I I I Illll 0.I 1.0 10 SOLAR DISTANCE (a u 1 Figure 6-2. Space density of meteors, corrected for unobservable orbits. Curves are plotted for 10 ranges of heliocentric latitude p and have been smoothed near 1 a.u. in dotted lines.

34 35

7. COLLISIONS IN SPACE

7. 1 Significance of Collisions

The drastic revision of meteor masses and orbital distributions communicated in earlier sections of this report led to a reappraisal of the importance of collisions between meteors in space compared to other loss processes, primarily the Poynting- Robertson effect. Formerly, it had appeared that collisions were important only for retrograde orbits, for large meteoroids, and for meteoroids near the sun. Now, after revision of the masses and therefore of the total flux by means of the new ionizing efficiency, it appears that collision is at least competitive with the Poynting-Robertson effect for ordinary orbits near the earth.

The last previous estimate of radio meteor space densities (Southworth, 1967) had shown density decreasing monotonically outward from the sun, entirely in harmony with dominance of the Poynting-Robertson effect over all other loss mechanisms for meteors (except near the sun). The run of space density found in Section 6, however, can be maintained as a stationary distribution only if collisions are significant.

7.2 Theoretical Collision Model

A simple theoretical model for the distribution of space density when both collisions and the Poynting-Robertson effect are significant can be constructed as follows: Con- sider particles all of one size and in nearly circular orbits at small inclinations to the ecliptic. At some distance from the sun, the particles are supplied to the system at a uniform rate and then spiral in under the Poynting-Robertson effect, while preserving their respective orbital inclinations. Some of the particles at each distance from the sun undergo mutual collisions; we shall suppose that they are eliminated from the sys- tem through solar radiation pressure that blows their fragments away. The Poynting- Robertson effect reduces the radius r of each orbit at the rate

11 -1 - -5x lo cm sec (%)pR s6r , (7-1)

37 where t is time and s and 6 are particle radius and density in cgs units; the particles are taken to be spheres. If there were no collisions, the Poynting-Robertson effect would set up a density distribution inversely proportional to r (Southworth, 1967) because the orbital planes near the sun are more densely concentrated to the ecliptic. Thus,

Two particles collide if their centers approach closer than 2s, so that each 2 particle sweeps out a volume 4rr s v dt in the time dt, where v is the mean relative velocity. Consequently, collisions diminish the space density at the rate

3 where m= (4/3)~s 6 is the particle mass.

To determine v, consider first the mean relative velocity resulting from the orbital inclinations. Since these inclinations are small, the relative velocities are primarily normal to the ecliptic, and the mean absolute velocity component is

-1 v = 7.3 ir-'l2 cm sec n x , (7-4)

where r is in centimeters and i is in radians. The mean relative velocity between particles is of the order of vn, but depends on the distribution of inclinations. For this model, it will be sufficiently realistic to assume that inclinations are distributed from 0 to I so that the space density at the ecliptic plane is uniform for each interval of inclination. It can then be readily shown that the frequency of particles with inclination i is proportional to i itself, that the mean inclination is - i = (2/3) I , (7-5)

38 and that the mean relative velocity normal to the ecliptic is

v.==ivn64 I . (7 -6) 1

Orbital eccentricity introduces relative velocity components parallel to the ecliptic plane, both radial from the sun and parallel to the circular velocity. The mean parallel component is approximately one-half the radial component. Since eccentricity also gives rise to collisions between particles at different mean distances irom the sun, we must assume that the space density does not vary substantially between perihelion and aphelion of most of the particles. If we assume a con- tinuous distribution of eccentricities, it has not proved possible to obtain an analytic value for the mean relative velocity caused by eccentricity, but for a single eccen- tricity e we find the mean component parallel to the ecliptic plane to be

e ve = 1.57 v -in (7-7)

For a distribution of eccentricities, the numerical coefficient in (7-7) would be larger, because the faster particles collide more frequently and are therefore more highly weighted in the mean. When the mean velocity for a distribution of inclinations is com- pared with the mean for a single inclination, it appears that the coefficient should be increased by roughly a factor of 2. We therefore use

where e is the mean eccentricity. Then for the total mean relative velocity, we have

-2 1/2 -1/2 v= 7.3X 10l2 (4.6i2 + 9 e ) I: (7-9)

Since there is a constant rate of particle supply, there is an equilibrium density distribution. As each group of particles supplied within a small interval of time spirals in toward the sun, the density within that group traces out the general run of density with respect to distance from the sun. Combining collisional losses (7-3)

39 with orbital shrinkage (7-1), and adding the effect (7-2) of the clustering of the orbital planes, we thus find that the space density obeys

(7-10)

Substituting (7-l), (7-2), (7-3), and (7-9) gives

(7-11) where

-2 1/2 A= 93 (i2 + 2 e ) (7-12)

We now obtain the model density distribution in the ecliptic as the solution of (7-1 1):

(7-13) which has a density minimum pmin at distace rminfrom the sun given by

1 pmin = A- --3 (7-14) rmin 2

and

1 + 2 r1’2>” , (7-15) ’min= (3A po ro 30 where p is the density at a given distance from the sun. Figure 7-1 shows the 0 r 0 theoretical distribution (7-13).

40 302-081

SOLAR DISTANCE (a.u. 1

Figure 7-1. Radial distribution of space density. The model distribution given by equation (7-13) is drawn as the smooth curve labeled "Simplified Theory" referred to the top and left-hand scales. The asymptotes are dashed. The top curve of Figure 6-2, labeled "Meteors" referred to the bottom and right-hand scales, has been positioned to make an approximate fit to the model.

The model distribution (7-13) has a vertical asymptote at r = 2.25 rdn, corres- ponding to dominance of collisions over the Poynting-Robertson effect; but this part of the solution must be neglected because it violates the assumption that space density does not vary steeply with distance from the sun. The model distribution is also asymptotic at small r to

41 (7 - 16) which corresponds to dominance of the Poynting-Robertson effect over collisions.

We note that, in this simple model, if collisions eliminate most of the particles, then the asymptotic density at small r is related to the distance of the particle supply from the sun. Substitution of (7-14) and (7-15) into (7-16) shows that if

(7 - 17) Pasy rasy << Psup rsup 9 then

r-sup- (2A Pasy r asyr2 , (7-18) where subscripts sup and asy, respectively, denote the point of supply and a point on the asymptote. If we relax the condition (7-17), then the right-hand side of (7-18) is an upper bound to rsup.

7.3 Comparison with Observation

For an order-of-magnitude comparison of the model distribution with observation, we can take Whipple's (1967) influx distribution and a mean geocentric velocity of -1 9 km sec (derived from our observed mean v, of 14.5 km sec-l) to estimate a total space density of small particles (smaller than meteorites) of

(7-19) at the earth's orbit; thus,

r = 1.5~ cm . (7-20) 0

Our observed inclination and eccentricity distributions give

As66 , (7-2 1)

42 and substitution into (7-15) gives

13 r = 1.2X10 cm min , = 0.8 a.u. . (7 -22)

Figure 7-1 also shows the space density on the ecliptic as derived in Section 6.3, positioned to match at po and r min' We concentrate our attention on the interval from 0. 5 to 1.5 a. u. (and we must ignore the derived density at 0.9 a. u. , as explained in Section 6). Within these limits, the fit between model and observation is better than might have been expected. In particular, the match along the r axis, given by (7-22), shows that we have been lucky in our estimates of A and po. Nonetheless, observa- tion seems to support the approximate validity of the model in this interval.

7.4 Sources of Meteors

Comparison of the observed run of density in Figure 7-1 leads directly (if we accept the assumptions of the model and the reliability of the data analysis) to con- clusions concerning where the particles are supplied. No significant number of particles enter the system in the range where the model distribution fits the observa- tions - that is, from 0.5 to 1.5 a. u. Most of the particles enter between 1.5 and roughly 4 a.u. -that is, in the region of the asteroid belt. However, this is also the region most densely populated by short-period comets and also by particles that are captured by Jupiter from long-period orbits, so that we cannot identify the source of this supply in an easy fashion. If we take the "observed" curve in Figure 7-1 at face value, there is a further supply of particles in the neighborhood of 0.2 a. u., which tempts us to identify them with particles ejected from bright long-period comets near perihelion. However, because of the limitation on the observations, it would not be safe to place any reliance on such a source at this time from this set of data. For the same reason, we cannot safely say anything about particle sources or their absence beyond 4 a. u.

7.5 Further Research

Our recognition that collisions are very important in the evolution of meteor orbits requires us to recast the theory of orbital distribution. This is both an important

43 Opportunity and a considerable task. The theory will need to include particle density, breaking strength, and fragment size distribution., as well as space density and flux distribution, because these are the parameters that determine the loss of most particles from the system and also the gain of collisional fragments to the system. Considerable computation will doubtless be necessary, but careful formulation is even more important. One result to be hoped is that the physical properties of individual particles can to some extent be determined from the other parameters, such as orbital distribution, that we now know to be linked with them.

The simplified model in Section 7.2 neglects differences in collision rate that depend on particle size or orbital inclination or eccentricity. One effect of these differences is a difference in the average age of particles in the system, depending on size and orbit; large particles and those in highly inclined or eccentric orbits are much younger. Now that a meaningful space density distribution is available, it may well be possible to find collisional ages for meteor streams.

At least three kinds of observational data are at hand for comparison with a theory including collisions, so that we have reason to expect that the comparisons can in fact tell us some things we should like to know, such as particle properties. First, the space density distribution is approximately as concentrated to the ecliptic plane as are the short-period comets, even though the long-period comets are the known source of both a substantial proportion of the observed large (photographic) and small (radar) meteors and almost all the observed dust input. Both Jupiter per- turbations (which are independent of the physical properties of the particles) and collisions and the Poynting-Robertson effect (which depend on the physical properties) are important to the present distribution. Second, there is vast observational literature on the mass distributions of the whole cloud and of individual meteor streams. The mass distributions of new streams are important input data to a general study of I collisions; the overall mass distribution is a function of the physical properties of I the particles. Third, the observed distribution of masses and orbits within individual , meteor streams (including the 290 new streams announced in this report) makes it possible to compare dynamical and collisional ages of the streams.

44 Theoretical study of collision processes is, in fact, an essential step in improving our knowledge of interplanetary density distributions, because the emprical extrapola- tion of the observed orbital distribution in Section 6 needs theory if it is to be im- proved. At the same time, we would extend our knowledge of both general space distributions and the physical properties of individual meteors. (In particular, we might find that mass distributions depend on mean distance from the sun and perhaps from the ecliptic plane.) We should also expect new results on the history of the sources of the interplanetary cloud.

45

8. COMPUTERIZED SEARCH FOR RADIO METEOR STREAMS

8.1 Two-Phase Computerized Stream Search in the Synoptic-Year Sample

The stream search performed by us on the sample of 19,303 radio meteor orbits from the years 1961 to 1965 was based on the statistical model of meteor streams (Sekanina, 1970a; referred to hereafter as Paper I). The model provides parameters of the distributions of meteor orbits in a stream and in the surrounding sporadic back- ground in terms of the Southworth-Hawkins (1963) D-criterion, which tests the similarity of meteor orbits in terms of the differences in their Keplerian elements.

The search procedure starts from an initial orbit, which is assumed to be known, and iterates the elements of the stream's mean orbit by weighting them with the use of the elements of individual meteors until the orbit converges. The method is very convenient for searching for members (in a sample) of known meteor streams (see Sekanina, 1970b; Paper 11) or for meteor streams associated with objects of known orbits (see Sekanina, 1973; Paper ID). Searching for new streams, for which of course no orbital information is available in advance, becomes more difficult as the size of a meteor sample to search grows.

Theoretically, one should have to take the orbit of every single meteor in the sample as the initial set of elements, which for extensive samples is practically impossible, even with the aid of a powerful computer, because of the enormous number of calculations associated with the particular search procedure.

From the synoptic-year data, 19,698 radio meteor orbits have been successfully processed. This is far more than the number for which the orbit-to-orbit approach would be reasonable. Fortunately, it proved possible to use the original Southworth- Hawkins (1963) search program in the place of a preparatory search to supply the required initial orbits for further analysis by the statistical-model search program. Prnctical calculations have confirmed that the two computer programs complement each other excellently and have shown that the two-phase technique is the most effec- tive stream-search method in existence, particularly for a huge sample of orbital data.

47 We also used the orbits of previously known meteor streams and other objects as additional initial orbits, in part to check the completeness of the list of initial stream orbits supplied by the Sauthworth-Hawkins search program.

8.2 Phase I: Major Source of Initial Orbits

With the synoptic-year sample of 19,698 radio meteors, the Southworth-Hawkins search program would require a computer memory capacity several times larger than that of a CDC 6400, on which this phase was carried out. It was therefore necessary to divide the whole sample into smaller sets a.nd to search for streams in each of them. The sets had to overlap each other significantly to ensure that PO stream was lost because of the dividing lines. This brought the estimated number of necessary subsets to at least 10. The longitude of perihelion and the inclination were taken as the dividing parameters, although the perihelion distance and the eccentricity were another possible pair. Only the nodal longitude and the argument of perihelion were felt to be less convenient, since for certain types of orbits, fairly large spreads in the two elements have only slight effects on the magnitude of the D-criterion.

Table 8-1 shows the division of the sample into 12 sections by inclination and longitude of perihelion. For each section, we list the number of streams detected by the Southworth-Hawkins program at two different rejection levels, Ds. The rejection levels were established in accordance with Lindblad's (1971) paper. The average number of meteors per section was about 3800, which, with Lindblad's formula (2), gives D = 0.10. We also made an independent search with Ds = 0.08 S in an effort to increase our ability to separate streams. For low-inclination sections, the rejection levels were decreased to 0.08 and then 0.06, because the major, broad streams are well known (we used the known orbits of these streams as the initial orbits to collect their members) and because we more urgently wished to separate possible minor showers.

Table 8-1 indicates that 90 to 98% of the detected streams had no more than five members. We considered these streams as fortuitous groupings of nonrelated meteors and discarded them. By so doing, we reduced the total numbers of streams from 6019 to 502 for the higher rejection levels and from 4763 to 167 for the lower.

48 m a* or- A NO wr- 4 + 32cd c, 0 4m mw B+ 4N mr- moo 22 ++

000 "2 4m

000 ww mm r-m Nm m*

wo N* m -I*

oom -N moo or- m* **

NW mm 3m +*

-4w a34 am -0 *w *m

oom mo -4*

*o or- Nu3 m* X$

am a00 00.. 04 00 Od

0 0 0 0 * 00 4 I I 0 0 0 *m

49 The remaining 669 streams went through a second screening: rejection of streams that were multiply listed because the 12 sections overlapped (Table 8-1) and because two rejection levels were used. We discarded all the multiple entries that differed from each other by less than 0.06 (but keeping the limit somewhat flexible in individual cases). We also discarded entries that indicated a clear identity with a stream detected in Paper I1 or III. We refrained from being too harsh in reducing the number of stream entries because multiple entries still surviving in the list would be rejected anyway in the following phases of screening. The present phase brought the number of streams down to 285.

8.3 Phase I: Other Sources of Initial Orbits

Besides the initial orbits provided by the Southworth-Hawkins program, we used a number of orbits of previously known streams and of potentially related objects as additional initial orbits for Phase 11. Specifically, the entries are as follows:

A. Orbits of the radio meteor streams detected in the 1961-1965 set of data, as published in Papers It and III. B. Predicted orbits of twin showers (i.e., daytime branches) of low-inclination streams of Papers I1 and I11 (see below for details).

C. Orbits of periodic comets with perihelion distances q <, 1.2 a.u., approaching the earth's orbit within a few tenths of 1 a. u.

D. Orbits of earth- and Mars-crossing asteroids (with q 5 1.2 a. u. ).

E. Orbits of meteorites and bright fireballs.

Since verification of the existence of meteor streams detected in the 1961- 1965 list of orbits is one of the primary aims of this investigation, orbits A permit this to be done most easily. Also, the problem of stream associations with periodic comets, asteroids, and related bodies can be solved most directly by applying orbits C, D, and E, respectively.

Orbits B deserve special attention. As pointed aut by Whipple (1940) in the case of the Taurids, a broad meteor stream moving in a low-inclination orbit meets the earth at two points: on its way to as well as on its way from the sun. It is observed

50 as two apparently independent but actually closely related showers. In Paper 111, we suggested that such a pair be called the twin showers. If the motion of the stream is direct, one of the twin showers (preperihelion branch) must be nighttime, and the other, daytime. In Table XIV of Paper 111, we listed seven pairs of twin showers, of which three had been established a long time ago and the remaining four were detected in the 1961- 1965 collection of radio orbits.

In an effort to increase the chance of discovering more twin showers to the previously known nighttime low-inclination showers, we predicted approximate orbits of the former from the 1961- 1965 orbits of the latter, using a criterion based on Figure 8-1.

A stream moving in the plane of the ecliptic intersects the earth's orbit on the way to the sun at point R, and on the way from the sun at point R,.

For some members of the stream, S2 is actually the ascending node and w is the argument of perihelion; these meteors could cause a nighttime shower. For some other members of the stream, R* is the ascending node and W* is the argument of perihelion; they could produce a daytime shower. Obviously, the two elements of the twin showers are related to each other by

w*= 360" - w ,

n*=n+2w ,

while,for the other three elements, we have i, = i 0, q, = q, e, 5 e. The predicted elements of the twin showers served as additional initial orbits in the Phase II calculations.

8.4 Phase It: The Weighting System

The technique developed in Paper I and previously applied in Papers It and III was used in Phase It with only one minor change.

51 301-052

Figure 8-1. The orbits of twin showers (schematic). Here, w and s1 are the argument of perihelion and the longitude of ascending node, respectively, of the nighttime (preperihelion) shower, and W* and a*, the same elements of the daytime (postperihelion) shower.

52 The search in the synoptic year sample for meteors belonging to 40 streams detected in the 1961- 1965 collection was carried out with four different weighting systems. The system used for the 1961- 1965 set,

w = 1 - D/O. 2 for D i 0.2 ,

w= 0 for D 2 0.2 , was generalized to

h w= (1 - D/DO) for D < Do , (8-3) w=o for D ?Do , and, with use of the same initial orbits, the mean orbits of the streams were cal- culated for the following combinations of (Do, h): 0.20, l; 0.20,2; 0.25, l; 0.25,2. It was found that the four resulting sets of elements were in very good agreement for a number of streams and in reasonable agreement for most streams.

There were, however, several instances where the mean orbits appeared to depend more substantially on the weighting system, and these were the key cases for deciding which of the four (Do, h) pairs to prefer in searching for new streams.

To illustrate the following arguments, we list a few examples in Table 8-2. For high-inclination streams, the mean elements from different weighting systems com- pare with each other quite favorably (December Draconids and X Draconids). At moderate and low inclinations, a high degree of consistency exists only for concen- trated streams (Geminids, Southern 6 Aquarids, and Monocerids).

The system with Do = 0.2 and h = 2 tends occasionally to give somewhat erratic results for very extended streams (Piscids, Southern Arietids, and to some extent 5 Perseids), apparently because it gives too much weight to orbits with very low D's and too little weight to those with relatively large D's.

The system with Do = 0.25 and h = 1, on the other hand, seems to give too much weight to orbits with large D's, which may result in suppressing dispersed,

53 Table 8-2. Comparison of mean orbits of several streams calculated with different weighting systems (Do, h) .

Equinox 1950.0 a Stream n 1. 0 (a. u. ) (1950)

5 Perseids 0.20 1 60: 1 81?2 6Y6 0.361 0.757 1.486 141?3 0.20 2 62.9 76.8 4.8 0.385 0.748 1. 524 139.8 0.25 1 60. 1 82.7 7.6 0.364 0.751 1.465 142.8 0.25 2 60.5 80. 8 6.5 0.365 0.755 1.492 141.4

p Taurids 0.20 1 232.1 282.9 0.7 0.269 0.841 1.694 155.0 0.20 2 53.0 102.5 0.6 0.280 0.828 1.627 155.5 0.25 1 59.9 83.0 7.6 0.363 0.752 1.462 142.9 0.25 2 52.3 102.0 0. 3 0.274 0. 834 1.653 154.3

Southern 0.20 1 155.3 305.7 28.3 0.070 0.957 1.633 100.9 6 Aquarids 0.20 2 155.4 305.4 28.6 0.067 0.960 1.669 100.8 0.25 1 155.3 306.2 27.7 0.071 0.955 1.577 101.5 0.25 2 155.4 305.7 28.2 0.069 0.958 1.630 101.0

Pi scids 0.20 1 306.4 172. 5 3.8 0.311 0.769 1.344 118.9 0.20 2 297.0 166.3 5.6 0.368 0.779 1.667 103.2 0.25 1 306.7 174.8 2.0 0.306 0.777 1.371 121.4 0.25 2 306.3 172.8 3.5 0.311 0.769 1.349 119.1

X Draconids 0.20 1 155.9 195.6 66.4 0.967 0.537 2.087 351.6 0.20 2 157.6 195.9 66.0 0.973 0.499 1.944 353.4 0.25 1 154.5 195.5 67.3 0.962 0. 566 2.215 350.0 0.25 2 156.0 195.7 66.6 0.967 0.530 2.060 351.7

Southern 0.20 1 122.1 18.7 2. 9 0. 337 0.765 1.434 140.8 Arietids 0.20 2 133.2 359.3 2.8 0.239 0.828 1.389 132.5 0.25 1 124.6 14.2 1.9 0.315 0.780 1.433 138.7 0.25 2 122.5 17.8 2.9 0.333 0.768 1.435 140.3

Triangulids 0.20 1 270.2 218.4 18.6 0.603 0.645 1.699 128.6 0.20 2 275.0 215.6 16.8 0. 563 0.665 1.679 130.6 0.25 1 264.2 219.6 18.7 0.649 0.627 1.740 123.8 0.25 2 269.6 218.6 18.3 0.606 0.647 1.718 128.2

Monocerids 0.20 1 135.4 71.9 22.3 0.155 0.977 6.626 207.3 0.20 2 136.6 71.4 22.1 0. 147 0.978 6.621 208.0 0.25 1 135.2 72.1 22.6 0. 160 0.970 5.372 207.3 0.25 2 135.8 71. 8 22.3 0.153 0.975 6. 199 207.6

December 0.20 1 185.1 253.7 42.1 0.981 0.586 2.370 78.8 Draconids 0.20 2 184.5 253.6 42.8 0.983 0.589 2.393 78. 1 0.25 1 183.3 255.4 41.8 0.981 0.569 2.276 78.7 0.25 2 184.6 254.2 42.2 0.981 0.582 2.346 78. 8

Geminids 0.20 1 325.3 261.3 23.4 0. 139 0.894 1.307 226.6 0.20 2 325.3 261.9 23.1 0.139 0.893 1.301 227.2 0.25 1 325.2 260.6 23.4 0.140 0.893 1.312 225.8 0.25 2 325.2 261.4 23.2 0.139 0.893 1.306 226.7

54 low-population streams and lead relatively often to spurious convergences. Sur- prisingly, our calculations showed that this weighting system suppressed the p Taurid stream in favor of the ( Perseids.

The two remaining weighting systems used give practically identical results in almost all cases. One of the very few exceptions was again the p Taurid stream, where the (0.2, 1) system gave the opposite node to that given by the other systems. The (0.25,2) system appeared to be slightly preferable for more dispersed streams because of being somewhat faster in their delineating, and just as good as the (0.2, 1) one for more concentrated streams. Also, the quadratic form of the former approxi- mates a Gaussian-type curve, which is the postulated stream-membership probability function, much better than does the plain linear form of the (0.2, 1) system. As a result, we found the (0.25,2) weighting system most convenient and applied it throughout.

55

9. RESULTS OF THE STREAM SEARCH

9. 1 List of the Detected Radio Streams

Detection of any particular stream in different samples depends on the degree of compatibility of the corresponding observing schedules. The observing schedule of the synoptic year is given in Table 9-1, for comparison with the 1961- 1965 observ- ing schedule (see Table I of Paper I).

The orbits of possible streams provided by the Sauthworth-Hawkins search program, plus the orbits of potential parent or related bodies, of the streams detected in the 1961- 1965 sample, and of suspected twin showers, produced a total of 473 entries for Phase I1 of our search and resulted in detecting in the synoptic-year sample 256 streams, 200 of which were not found in the previous radio meteor sample.

The orbital elements and related parameters of the streams detected in the synoptic-year sample are listed in Table 9-2. The individual columns give the follow- ing information (all angular data are referred to the standard equinox 1950.0):

Column 1. Designation of the stream.

Column 2. Argument of perihelion w and its mean error (degrees).

Column 3. Longitude of ascending node s2 and its mean error (degrees).

Column 4. Inclination i and its mean error (degrees).

Column 5. Perihelion distance q and its mean error (a. u. ).

Column 6. Eccentricity e and its mean error.

Column 7. Semimajor axis a (a. u. ) and revolution period P (years).

Column 8. Longitude of perihelion TT = w + s2 (degrees) and the date of passage through the node (UT and days in 1950).

Column 9. No-atmosphere velocity V, and its mean error (lun sec-l).

57 Column 10. Right ascension of the corrected mean radiant from individual a R meteor radiants and its mean error (degrees).

Column 11. Declination 6 of the corrected mean radiant from individual meteor R radiants and its mean error (degrees).

Column 12. Right ascension and sun-oriented celestial longitude X of aR RO-1 the corrected mean radiant from the stream's mean orbit (degrees).

Column 13. Declination 6 and celestial latitude pR of the corrected mean radiant R from the stream's mean orbit (degrees).

Column 14. Geocentric V and heliocentric velocity at the node (km sec-l). G VH Column 15. The node (A - ascending; D - descending), and the type of stream (C - circumpolar, with the mean radiant permanently above the horizon at Havana; D - daytime; M - mixed, with the mean radiant never more than 10" below the horizon; N - nighttime).

Column 16. Height at maximum ionization hmax and its mean error (km).

Column 17. Number of meteors in the sample with D < 0.25 with respect to the mean orbit, with an asterisk to indicate that the stream was detected in the 1961-1965 sample.

9.2 Identification of Streams Detected in the 1961- 1965 Sample

The D-test was used to identify in the synoptic-year sample the streams previausly found in the 1961- 1965 sample. With an identification threshold of Di = 0.2, we were able to identify 55 of the 83 streams of the 196 1- 1965 sample; 1 more stream was probably detected, though with D. = 0.26; and 27 streams were not found. The doubt- 1 ful case is the Quadrantid shower. With the radar network idle during the period of the shower's maximum activity, the search program detected a minor stream with the mean orbit similar to that of the Quadrantids, but with the node shifted by 13" for- ward, thus matching the nearest operational period of the radar. Of the 27 streams apparently absent in the synoptic-year sample, positively three (January Scutids, Andromedids, and December Ursids) and probably two more (p Geminids and November Cepheids) could not be detected, because of gaps in the operational schedule in the critical periods. In 5 cases of the 22 remaining unidentified streams (Equuleids,

58 ~ ~~~ ~~~

Table 9-1. Observing schedule of the Havana meteor radar during the synoptic year.

Number of Number of successfully successfully Date (CST) reduced meteors (%) Date (CST) reduced meteors (%)

1968 -1969 (cont.) December 2 - 6 498 2.53 June 16-21 701 3. 56

IA 1 no TI.-- 9A- A A OC n----.L,.- Y919 An T-.l-- "V UGbG.ILIUG?L A1 A. vu "Uric. vu uury 1 9?? *. December 16-20 269 1.37 July 14-19 1059 5.38 July 21 3 0.01 -1969 July 25-26 11 0. 06 January 13-17 808 4.10 July 28 -August 1 1272 6.46 January 27-31 6 18 3.14 August 11- 15 1373 6.97 February 10- 14 4 96 2.52 August 17- 18 175 0.89 February 24 75 0.38 August 25-30 892 4.53 February 26-28 89 0.45 September 7 2 19 1. 11 March 10-14 557 2.83 September 9-12 1239 6.29 March 17-19 25 0.13 September 18 49 0.25 March 23-28 404 2.05 September 22-26 1210 6.14 April 7-9 4 97 2.52 October 6- 10 1369 6.95 April 11-12 39 0.20 October 14- 15 44 0.22 April 17 109 0.55 October 20-24 1117 5.67 April 20-21 71 0.36 November 3- 8 1124 5.70 April 24- 25 133 0.67 November 14 8 0.04 May 5-9 490 2.49 November 16 39 0.20 May 19-23 573 2.91 December 12- 14 157 0.80 June 2-6 6 94 3.52 June 11- 12 3 0.01 Total 19,698 100.00 I

59 IC 4 nm NN8

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72 Je r-r- Or- -m -n ar- NN 00 me mr- -4 NN mm n~ nm o ...... oe d e- N- n m d- n mc. r- m o -4 N- 9- o- 4 eeeeee~emaee~ee~

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74 r- o N* m m o r- n oc o nr mr r-r ,or r-L r. nm ruN-.m~o~em- N e nw.... oe r-.r-. r..om mawo eo...... ne N* eo *e r-0 r.m QI r-o eo .. - r-N n N mr. .t e- -4 m N- o o a e- r. m- 0 o~bmoomoomommowm

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u) 0 n z 0

75 x Piscids, April Draconids, K Cygnids, and p Cetids), the search revealed streams that must have been classified as new, but that differed significantly from the corres- ponding 1961- 1965 streams in only one element other than the nodal longitude.

Of the remaining 17 streams of the 1961- 1965 sample missing in the synoptic- year sample, 11 were found to be "absorbedI1 by one of the 55 identified streams

(X Capricornids, (T Leonids, May Librids, May Herculids, v Librids, Taurids- Perseids, y Aquarids, a Cygnids, 6 Cygnids, X Draconids, and October Camelopar- dalids); 2 by the sporadic background (June Draconids and Andromedids); 1 by a new stream (TCepheids); and in 3 cases, no or only a few possibly associated meteors were found (Lyrids, r) Aquarids, and Halleyids).

9.3 New Streams: Toroidal Group, Short- and Long-Period Streams, Twin Showers, and the "Cvclid'' Svstem

A great number of the new streams belong to the so-called toroidal group (Hawkins, 1963). They have direct but high-inclination orbits with low to moderate eccentricities. For example, we find 10 streams with i > 70°, of which all have q > 0.6 a.u., but only 3 have semimajor axes significantly larger than 1 a.u. Their radiants lie at high northern latitudes, mostly in the constellations of Draco, Ursa Major, Camelopardalis, Cassiopeia, Cepheus, and Ursa Minor. The traditional system of stream designation used in Paper I11 proved insufficient to provide names for all the new streams in that area of the sky so heavily populated by radiants. We therefore expanded the previous system of designation by adding capital letters before the name of the radiant's con- stellation wherever the original system proved inadequate. Also, streams coming from the constellation of Ursa Minor have been called Umids to distinguish them from streams from Ursa Major, which are called Ursids.

There are only two retrograde streams in the sample, the Orionids and the Perseids. The latter were not classified as a detected stream in the 1961- 1965 sample, since only two probable members were found there.

A total of 26 streams have their perihelia less than 0.2 a.u. from the sun, and 9 streams less than 0. 1 a. u. from the sun, the record being 0.045 a. u. for the November Orionids.

76 Nine streams have semimajor axes shorter than 0.8 a.u., and three shorter than 0.7 a.u. Two of these, the J Camelopardalids and f3 Andromedids, actually cross the earth's orbit almost at their aphelion points (aphelion distances 1. 02 and 1.06 a. u., respectively).

On the other hand, there are 12 streams in the sample with semimajor axes of 3 a.u. or longer. Surprisingly, neither the Perseid stream, nor the Orionid, nor the Monocerid holds the record. Rather, a new, very rich stream with q = 0.86 a.u., inclination almost 50°, and revolution period of more than 30 years, appears to he the most extended, not only in the synoptic-year sample, but probably among all radio streams known so far. It is called the September Ursids, and it is associated with neither a known comet nor a photographic stream.

We now know 14 pairs of twin showers with confidence and 4 more pairs possibly related. Two of the seven pairs listed in Paper III as detected in the 1961- 1965 sample were not found in the synoptic-year sample: the Orionid-Halleyid pair because of the absence of the Halleyid stream; and the o Capricornid-X Capricornid pair because of the absence of the X Capricornid stream. The E Arietids replaced the X Piscids as the twin shower loosely associated with the Triangulids. The new list of detected twin showers is in Table 9-3; the D values for the uncertain cases are in parentheses.

Nine of the new streams have inclinations less than 10" and eccentricities less than 0.4. We find that there is a fairly close relationship among most of them in terms of D despite an apparent variety in their orbits (Table 9-4). A similar relation- ship detected by Southworth and Hawkins (1963) among orbits of this type of photo- graphic meteors led the two authors to call such a tTstreamt'the Cyclids and interpret it as a result of a high probability that meteors in these orbits meet the earth.

9.4 Distribution of Radiants

The computer plots of radiants of the 19,698 radio meteors of the synoptic-year sample are exhibited in Figures 9-1 and 9-2. Figure 9-1 is a plot of the ecliptical coordinates, longitude X versus latitude p, in Hammer's equal-area projection.

77 Figure 9-2 is a plot, in the same projection, of the sun-oriented ecliptical longitude A -Ao versus latitude p. Except for a few details, the plots are almost identical with the corresponding plots of the individual meteor radiants from the 1961- 1965 sample (see Figures 4a and 4b of Paper III).

Table 9-3. Twin showers detected during the synoptic year.

~~______Twin showers - D i Pr eper iheli on Postperihelion

Southern Arietids 5 Perseids 0.108 5" Scorpiids-Sagittariids Capricornids-Sagittariids 0.119 4" X Orionids K Aurigids 0.135 3" Southern r) Virginids $ Virginids 0.136 2" 6 Leonids August Lyncids 0.144 10" January Cancrids August Cancr ids 0.148 3" p Leonids T Leonids 0.150 1" Ophiuchids January Sagittariids 0.150 2" Piscids May Arietids 0.154 3" Taurids p Taurids 0.157 0" p Geminids 5 Leonids 0.164 2" y Piscids A Capricornids 0.182 5" Librids ( Sagittariids 0.198 3" a Taurids p Cancrids 0.202 1" 6 Cancrids y Leonids (0.285) 4" a Capricornids E Aquarids (0.288) 7" f; Aurigids March Andromedids (0.320) 12"

Triangulids E Arietids (0.388) 11"

The mean radiants of the detected streams (both new and known from the previous sample) are plotted in Figures 9-3 and 9-4. They show rwch the same pattern as the plots of individual radiants. At least, there is much better agreement between Figures 9-2 and 9-4 than between Figures 4b and 5b of Paper III. This is of cuurse

78 due to the fact that the present search was much more complete than the former. Although we have not yet been able to determine the population and dispersion coeffi- cients of the streams found in the synoptic-year sample, we can estimate that the total number of meteors in the detected streams is of the order of 6000, or approxi- mately 30%, as compared to 1400 or 7.5% in the 1961- 1965 sample.

Table 9-4. The Cyclid system of streams in the synoptic year (the numbers are D values in units of 0.001).

am m m 2 3k m m m a M .r( 3 z z z -8 5 m m m uh 4 s s s Stream d +J, W Q

~~ ~ ~~~~~ ~ 5 CYgnidS 0 188 370 254 442 493 272 266 260 K Geminids 188 0 266 93 238 267 229 216 165 March Virginids 370 266 0 324 404 387 269 244 252 X Aurigids 254 93 324 0 164 236 322 306 252 a Aurigids 442 238 404 164 0 149 424 466 379 June Aurigids 493 267 387 236 149 0 449 427 309 5 Ursids 272 229 269 322 424 449 0 87 182 z Ursids 266 216 244 306 466 427 87 0 127 (3 Ursids 260 165 252 252 379 309 182 127 0

9.5 Comparison with Cook's Working List of Meteor Streams

Of Cook's (1972) working list, 16 streams were closely matched by radio streams from the synoptic-year sample (D 5 0. l), and 18 more streams were probably identi- fied (D 6 0.2). However, we were not able to separate the northern and the southern branches of the Taurids and the X Orionids. Because the radar system did not operate early in January, we found only a remote branch of the Quadrantids. The remaining 21 streams of Cook's list, many of them either retrograde in motion or nearly para- bolic or ones in southern hemisphere, were not found in the synoptic-year sample.

79 W 0

0 3 cd k

al

b .r(ki Fr k

. 0

81 82 m E

0 zcd k

0 0

83

10. COMET- METEOR AND ASTEROID-METEOR ASSOCIATIONS

10.1 Associations with Periodic Comets

Table 10-1 lists the detected associations between the meteor streams of the synoptic-year sample and the potential parent objects within D = 0.3.

We find that the following periodic comets are likely to have associated streams in the synoptic-year sample: Encke, Pons-Winnecke, Giacobini-Zinner, Halley, Schwassmann-Wachmann 3, Swift-Tuttle, and Mellish. Possible associations have also been found for some other comets (Honda-Mrkos-Pajdus&ova/, Gale, Helfenzrieder, Blanpain, and Lexell), but these are. suspected to be fortuitous, because of the comets' orbit instabilities in some cases or because of relatively loose relationships in others.

10.2 Adonis Meteor Streams

Among the asteroid-meteor associations, the most obvious one is again the case of Adonis. The CJ Capricornids, a prominent stream in the 1961-1965 sample, were found to match the asteroid's orbit less satisfactorily in the synoptic-year sample, partly because of smaller perihelion distance and partly because of higher inclination. However, it seems increasingly likely that the Scorpiids-Sagittariids, a very broad stream undoubtedly related to Hoffmeister' s (1948) Scorpiid-Sagittariid complex, is associated with Adonis. We note that both the June nighttime stream and its twin shower, the C apricornids-Sagittariids appearing in January and February, are in terms of D within 0.2 from the asteroid's orbit, and that a minor stream, the X Sagittariids, closely related to the Scorpiids-Sagittariids (actually its component), is within 0.09 of the asteroid's orbit. Hoffmeister did notice a resemblance between the orbits of Adonis and his Scorpiid-Sagittariid system, but left open the possibility of a real association between both. This was the correct approach because his results were based on inaccurate visual observations; also, he found a discouraging difference of almost 25" between the longitudes of perihelion of the asteroid and of the middle of the meteor complex. Our radio meteor samples suggest that the difference is

85 Q, mm aeaw eamm mmw co ma cnmm **Q, 0 44 4" z2Ei eawhl d dd 600 ddd Odd

d 0m Q, 4

Q, m 0 m ea @a d 0

m z8 m 0 .d 0 z uii 8 cc

F: .e h cd al a H 9 4 E9 \6! \ PI PI

86 actually much less than that. In the synoptic-year sample, the Capricornids- Sagittariids indicate a difference of 13", and the Scorpiids-Sagittariids, only 8".

10.3 Possible Associations with Other Minor Planets of the Apollo and Amor Types and with Meteorites and Bright Fireballs

Besides Adonis, there is a definite possibility of the existence of associations of meteor streams with the minor planets Apollo, Hermes, Toro, and 1950 DA, and to a lesser degree also with Icarus and: surprisinglyj Gengraphos x~c!PBPE Ercs. The last two must, however, be taken with much caution: The would-be associated streams belong to the group of Cyclids. We know that these orbits have high probability of encounter with the earth, and detection of any well-established associa- tions is most difficult if not impossible. Besides, the perihelion distance of Eros is 1.13 a.u., so that detectable meteors could only be fairly loosely related to the asteroid anyway.

Of the meteorites and bright fireballs, the Pslbram meteorite and the Prairie Network fireball 40617 may be associated with some of the detected streams (see Table 10-1). No streams were found to move in the orbit of the Lost City meteorite, but the radar system was not operating at and around the node of that object. No streams seem to be associated with a few other fireballs, among them Prairie Network 40503 and Mt. Riffler (in the latter case, the radar was, however, again idle).

87

11. HEIGHT-VELOCITY DIAGRAM

11.1 Introduction

Ceplecha (1967, 1968) detected three discrete levels of beginning height on height- velocity plots of photographic meteors and interpreted them in terms of the composition 226 frzg;.r=zztztio:: sf the mete~rciids, this s-%-gesiirlp ihai ihe buik ciensiiy of the iaiker is important. Cook (1970) applied Ceplecha's criterion to classify 25 photographic streams.

Height-velocity computer plots have been used in this study to search for the dis- crete height levels in the synoptic-year sample. Since for radio meteors the height at maximum ionization is much easier to define than the beginning height, we used essentially the former. A few check plots with the beginning height have confirmed that it makes little difference which of the two heights is used, except that the begin- ning height is subject to a larger dispersion.

11.2 Height-Velocity Plots for Individual Radio Meteors

The plot of 16,322 radio meteors of the synoptic year with zenith distance of radiant less than 60" (to eliminate a possible effect of nearly Wmgential" meteors) has failed to show the discrete levels detected by Ceplecha among the photographic meteors (Figure 11-1). Nothing has been gained by dividing the whole sample into graups according to the meteor luminosity and perihelion distance (Figures 11-2 to 11-7). Dispersion seems to be large enough to mask completely the double-peak dis- tribution in height. However, we have been able to detect some of the features of the height-velocity plots known for the photographic meteors.

First, there is a clear separation between the major concentration (at low V,) and the minor concentration (at high V,) in the velocity axis at V, 5 48 km sec-l. The effect is obvious from all figures except Figure 11-4. In Ceplecha's terms, the gap separates the minor C2 group from the major C1 (plus A) group. The separation was originally recognized by Jacchia (1958).

89 Figure 11-1. Height-velocity plot of 16,322 radio meteors of the synoptic year with zenith distances of radiant less than 60".

90 I I I I I 1 II

I I 1 I I I II IO 20 30 50 80 NO-ATMOSPHERE VELOCITY (km sec-' )

Figure 11-2. Height-velocity plot of 8487 radio meteors of the synoptic year with zenith distances less than 60" and "brighter" at maximum ionization than 11.5 mag.

91 I I I I I I 11

I I I I I I II 10 20 30 50 80 NO-ATMOSPHERE VELOCITY ( km sec-'

Figure 11-3. Height-velocity plot of 7835 radio meteors of the synoptic year with zenith distances less than 60" and "fainterffat maximum ionization than 11.5 mag.

92 I I I I 1 I II

70

h 5 80 Y z 0- I- a -N z 0- I 3 90 -I X a I 2 I- r a- g IOC

I IC

I I I 1 I I II IO 20 30 50 80 NO-ATMOSPHERE VELOCITY ( km sec-l 1

Figure 11-4. Height-velocity plot of 2877 radio meteors of the synoptic year with zenith distances less than 60" and perihelion distances less than 0.25 a.u.

93 1 I 1 1 I I I1

70

c

I I I I I1 LAIO 20 30 50 80 NO-ATMOSPHERE VELOCITY ( km sec-' )

Figure 11-5. Height-velocity plot of 3008 radio meteors of the synoptic year with zenith distances less than 60" and perihelion distances between 0.25 and 0.50 a.u. Figure with 0.50

95 I I I I I I II IO 20 30 50 80 NO-ATMOSPHERE VELOCITY (km sec-l

Figure 11-7. Height-velocity plot of 7181 radio meteors of the synoptic year with zenith distances less than 60" and perihelion distances larger than 0.75 a.u.

96 Second, the vertical dispersion in the major concentration (V, < 48 km sec-l) is definitely larger than that in the minor concentration (V, > 48 km sec-l). From Ceplecha's results, we actually expect this, because the dispersion in the major con- centration is a sum of the dispersions of the two groups (A + C1) several kilometers apart, while the dispersion in the minor concentration represents that of the C2 group alone.

Third, the minor concentration is more pronounced (relative to the major concen- tration) among the brighter meteors. Ceplecha found the same effect among the photographic meteors, although the magnitude scale was naturally shifted by about 10 mag.

Finally, Figure 11-4 (meteors with perihelion distances less than 0.25 a. u.) is the only one that shows but one cluster of meteors with the cutoff at V, = 60 km sec-l rather than 70 to 75 km sec-' (as the other figures do). Among the photographic meteors, the group with q < 0.25 a. u. also indicated only one concentration; Ceplecha classified these meteors as forming an intermediate height level, which he called the B group.

11.3 A Height-Velocity Plot for Radio Streams

The last attempt to separate the discrete levels d radio meteor heights was a height-velocity plot for the meteor streams from the synoptic-year sample. Only streams with a mean error in height not exceeding f 1 km were plotted. The idea was that with individual heights grauped into the stream heights, the dispersion within each of the two parallel levels A and C1 may be lowered, so that the two levels show up. That did not, however, turn out to be the case, as can be seen from Figure 11-8. The major concentration remains structureless, despite a decrease in the overall dis- persion along the height axis, as compared to the individual height-density plots. An interesting point, possibly worth pursuing further in the future, is a clear indica- tion that the area of the main cluster with maximum heights (=93 to 96 km at 25 km sec-', -95 to 98 lun at 35 lun sec-l) is not populated by ecliptical high-eccentricity streams, as one might expect by analogy to Ceplecha's conclusions, but mostly by high-inclina- tion, -low-eccentricity streams. A question to be answered is whether a possible selection effect exists, since these streams consist of meteors whose radiants are most favorably located for the main beam of the radar system.

97 301 -OS2 . - 80 - . E x Y . . z 0 ... t I-a 85- N z . 0 f 90- z . X a 5 5 95- . I- r +.. (3 W = 100-

1 IIIIIIIIII IIIIIIIIII I I I I 1 IO 20 30 40 50 60 70 NO -ATMOSPHERE VELOCITY ( km sec-'1

Figure 11-8. Height-velocity plot of 145 radio meteor streams with reliably deter- mined mean heights (mean error in height not exceeding *l. 0 km).

Another feature of Figure 11-8 is a drastic drop in the height dispersion at velocities below about 18 km sec-l. At the other end of the velocity range, the C2 group has reduced to only two points: the Orionids and the Perseids.

98 12. SPACE DENSITY IN RADIO METEOR STREAMS

12.1 Mean Space Density in a Stream in Terms of the Sporadic Density

In Papers 11 and 111, we derived the two parameters of the statistical model of meteor streams - the population coefficient A and the dispersion coefficient cr - for a number of streams from the 1961- 1965 sample, and we commented that the popula- tion coefficient gives essentially the flux ratio of the stream meteors relative to the sporadic background in a limited vector space (i. e., the stream-to-background flux ratio of meteors from within a particular solid angle related to particular limits of the geocentric velocity). By varying the value of the D-test, we change the "volume" of the vector space and thereby can study the variations in the stream-to-background flux ratio along a given section of the earth's orbit. By extending the vector space to cover all directions and all velocities, we could derive the stream-to-background space-concentration ratio.

The parameters of the statistical model are derived from the cumulative D-distri- bution of meteors, not of meteor masses. This makes no difference within any stream, because the total range of D is then fairly narrow. Selection effects caused by both the observing conditions and the physical processes are, however, of considerable importance in assessing the overall concentration of meteoric matter in space, as shown elsewhere in this report.

The mean space density in a meteor stream, in units of the mean space density of the meteoric matter in the sporadic background, was derived by us with the use of the stream's population and dispersion coefficients and with the use of the overall distribution of the orbital elements of meteor masses from the synoptic year, corrected for all selection effects (see Figures 5-5 to 5-10). In Paper I, we defined the outer limit D of a stream by a condition of equal population the stream and background 11 of meteors between D = 0 and D = Dn. The expression for D and its graph are also I1 given in Paper I. Papers II and 111 list DII for 83 streams of the 1961- 1965 sample.

99 For each stream, a Monte Carlo method has been applied to simulate the distribution of 10,000 sporadic meteors of equal mass with orbital characteristics distributed as given in Figures 5-5 to 5-10. This distribution gives us the background noise for each stream in terms of the overall distribution of meteor masses. Specifically, for D = D we can immediately find the fraction of the sporadic meteor masses that falls 11' within DII from the mean orbit of the stream. From the definition of DII, this is also the fraction of the number of meteors (or meteor masses) of the stream that falls within Dn, which covers practically all the stream members. Since the space density is proportional to the total of meteor masses swept up by the earth within a certain period of time, this method gives us the space density in the meteor stream within D in terms of the overall space density of the sporadic background. II

12.2 Space-Density Gradient in a Stream

In any meteor stream that can be distinguished from the sporadic background, there exists a measurable space-density gradient. The method described gives actually a laver limit for the space density in a stream, because D is much larger I1 than the stream's characteristic dimension (" on). We do not know the profiles of most streams, because there were gaps in the observing schedule, but we can estimate the density gradient from the shape of the D-distribution curves in the following way.

The number of meteors with D < Di, JSpi), swept by the earth during a pass through a stream is

Ts(Di) = const p(D ) (12- 1) i -VE

where p(Di) is the mean space density in the stream for D 5 Di; W(Di) is the charac- teristic width of the stream for the same range in D; E is the elongation of the corrected radiant from the apex of the earth's motion; and V and VE are the comet's H and earth's heliocentric velocities, respectively. For p independent of D, we would have from equation (12-1), Ts W. From Paper I, we know that the number of meteors would then vary as DP (where P = 3.8), so that W - D P . In the case of a variable space density in the stream, equation (12- 1) can be written thus:

100 (12-2)

It is convenient to replace Di as the argument by Ei = Di/(odZ) and to write, with the use of equation (6) of Paper I, the ratio d the mean space density in the stream within Di to that within or/2 :

where

erf (E) = - e dz . (12-4) 0

The function p(E)/p(l) is plotted in Figure 12-1. It can be shown that for E e 1, this expression simplifies to

(12-5)

and for E >> 1, to

= 2.34 E -3.8 3 (12-6)

Also plotted in Figure 12-1 is the relative number of meteors in a stream as a function of E. We note that the statistical model predicts that only 0. 1%of the total mass of a stream move in orbits with D I 0.15 (T, so that the mean density within E = 0.1 is perhaps a realistic estimate for the actual maximum central space density in meteor streams.

12.3 Numerical Results

The results of the Monte Carlo simulation, described earlier in this section, and those of the subsequent space-density calculations are summarized in Table 12-1 for several of the more important streams of the 1961-1965 sample.

10 1 We conclude that mean space densities in meteor streams are small compared with the space density of the surrounding sporadic background, but that central densities in some major streams can significantly exceed the background density.

301-052

- 100 c----- 00 010 / v) / sa / I- w 5 IO 010 % U !4w 22 I % SF p 05 +a 0.1% uK

LZ 0- 0.01% 5 I- aO a \ LL 0.001%

0.01 0.I I IO E

Figure 12-1. Space-density variation (solid curve, left-hand scale) in meteor streams versus E = D/(oJZ) (a is the dispersion coefficient) predicted from the statistical model, and a relative cumulative number of a stream's mem- bers (dashed curve, right-hand scale) as a function of E.

With an average overall space density of 4 X g cmm3in the vicinity of the earth (see Section 7.3), the results of Table 12-1 suggest that mean densities in meteor streams are typically several times 10-24 g cm-3 and that the central density in some streams could be as high as almost g ~m-~.In meteoric storms, the 19 density must be still at least 1 to 2 orders of magnitude higher, i. e. , some 10 - to 10-l~g cm-3.

102 Table 12-1. Mean and central space densities in radio meteor streams.

Space density in stream

Stream (in units uf sporadic density = 4 X g ~m-~) mean (at D 2 Drr) central (at D 5 0.15 cr)

Scorpiids -Sagittariids 0.06 30 in Ge mi nid s !?- nn5 A" cr Capricornids 0.05 8 Piscids 0.03 3 Monocerids 0.01 3 Taurids 0.02 2 Southern Arietids 0.02 2 July Draconids 0.006 2 Triangulids 0.02 1 o Cetids 0.006 1 Southern 6 Aquarids 0.003 1 Lyrids 0.0002 0.4 Arietids (Daytime) 0.002 0.3 X Orionids 0.003 0.2 5 Perseids 0.002 0.2 p Taurids 0.002 0.1 a Leonids 0.002 0.1 Southern Virginids 0.001 0.05 Quadrantids 0.00002: 0.01: Orionids 0.000002: 0.005:

12.4 Space Density from Cometary Production Rates of Solid Material; Comparison of the Two Methods

It is of interest to compare the above conclusions with independent evidence avail- able from the study af cometary type I1 tails. Finson and Probstein's (1968a) model of dust comets makes it possible to estimate the total mass of the solid material lost

103 by a comet during an approach to the sun. The results from the regular dust tails are unfortunately inconclusive for the particle sizes that produce radio meteors (" 0.1 cm in diameter), since the method is based on photometric considerations and the effect from heavy particles is always masked by the much stronger light-scattering power of micron and submicron particles. Consequently, the size-distribution function, which is also determined by the Finson-Probstein model, is uncertain for large masses. However, the "spikett tail of comet Arend-Roland 1957 ID, studied by Finson and Probstein (1968b), appeared to be composed of only heavy particles (2, 0.01 cm in diameter). The two authors showed that the spike had been formed as a result of an outburst abuut 2 months before the comet reached the perihelion point and that the 14 total mass ejected during the outburst had been of the order of 1013 to 10 g. It seems that this is the only quantitative estimate to date of the emission rate of dust particles approaching the radio meteor range of masses.

With a characteristic dispersion in their velocity distribution along the orbit of some 10 m sec-l, the particles ejected from a short-period comet in an isolated outburst wauld form, after one revolution around the sun, a filament some 0.2 a. u. long.

With a width of s 0.001 a.u. (corresponding to the duration of less than 0.1 day, 32 3 typical for meteoric storms), the volume of the filament is = 5 X 10 cm , and with - 19 the mass of s 1014 g, its space density comes out to exceed 10 g ~m-~,in total agreement with the estimate given in the previous section.

To estimate the space density in old streams dispersed along the whole arc of orbit around the sun, we can adopt the orbital length 15 a.u. and the width = 0.5 a. u., so that the volume of the stream is = 1040 cm3 . The total mass involved can be 3 inferred either from the order-of-magnitude estimate of the age (" 10 revolutions), assuming that the comet is ejecting meteoroids at a more or less constant rate, or from the total mass of the parent comet (if the latter is presumed defunct), assuming that a significant fraction of the comet disintegrated into the stream. Both estimates 16 -23 give fairly consistently a mass of = 10 to 1017 g and a space density = 10 to g crnm3, again consistent with the results of Section 12.3.

104 13. REFERENCES

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106 NASA-Langley, 1973 - 30 CR-2316