Research on Orbits of Minor Meteor Streams
V. GUTH 1
4. Shower meteor fluxes
The incident flux for eight showers has been estimated by Weiss (1957a) for meteors with zenithal line densities in excess of K^m"1, using data on hourly rates obtained at Jodrell Bank and Adelaide. From observations made at Sheffield and Jodrell Bank, Kaiser (1953, 1955, 1961a) has determined the incident flux for the three showers, Geminids, Arietids, and Perseids, over a considerable range of limiting
line densities. The results of these various determinations are summarized in table 1, together with estimates of the sporadic flux made by Weiss and Kaiser. I t can be seen from the table that for meteors fainter than MR= +5(5=1014m~1) the sporadic background dominates over any of these major streams.
In order to obtain the rate of incidence of particles above a limiting mass, Weiss (1957a) applied a velocity correction of the form »*e. For meteors whose mass exceeds that equivalent to a zenithal line density of lO^m"1 at a velocity of 60 km/sec, the three showers—Arietids, £ Perseids, and 5 Aquarids—all have a similar flux, which is about 40 percent of the sporadic background. In contrast, the contribution from the three high-velocity showers, Perseids, 17 Aquarids, and Orionids, is in each case only 1 to 2 percent of the sporadic background.
In figure 5 the variation with magnitude of the incident flux of the three showers, Arietids, Geminids, and Perseids, is compared with the variation for sporadic meteors. Here again we consider the mean flux over a sphere. The graphs emphasize the dominant role played by sporadic meteors fainter than radio mag- nitude + 5. For meteors brighter than + 1 0 mag sporadics outnumber any one of the three showers by a factor of 10 or more, and the trend of the graphs suggests that if the magni- tude limit were +13 the sporadics would out- number any of these showers by a factor of the order of 102.
T A B L E 1.—Shower meteor flux
Tvpe of meteor
Sporadic Germinid Perseid Arietid Quadrantid
£ Perseid 5 Aquarid rj Aquarid Orionid
Flux (m->
10» m-1
45X10-18
100X10-"
sec"1) above limiting zenithal line density*
10" m"1
35X10-"
30X 10-"
15X10-"
25X10-"
20X10-"
18X10-"
37X10-"
18X10-"
23X10-"
10" m-i 56X10-"
12X10-"
8X10-"
20X 10-"
10" m-1
90X10-"
5X10-"
13X 10-"
Reference
(1), (2) (2) (1), (2) (1), (2) (1) (1) (1) (1) (1)
*To facilitate comparison between shower and sporadic fluxes the values for the former are given as the mean flux over a sphere (i.e., one-quarter of the flux through a plane normal to the radiant direction).
References: (1) Weiss (1957a), (2) Kaiser (1953, 1955,1961a).
126 SYMPOSIUM ON METEOR ORBITS AND DUST
It should be noted that the ratios of sporadic- to-shower fluxes discussed above refer to the total sporadic flux compared to the flux of an individual shower. The ratio of the total inci- dence per year of sporadic meteors to the total incidence per year of shower meteors will depend on the number of meteor showers per year and their strength and duration. An objective method of defining a meteor stream in terms of the degree of similarity of meteor orbits has been developed by Southworth and Hawkins (1963), and has been applied to 3000 orbits determined from observations made with the Harvard-Smithsonian meteor radar system dur- ing the period January to August 1962 (Haw- kins, Southworth, and Rosen thai, 1964). The radio magnitude limit for these orbital data was estimated as + 1 1 . It was found that 24 percent of the orbits associated into streams (value of association parameter Z>=0.1). A somewhat similar analysis (Nilsson, 1964) has been carried out on 2200 orbits determined from observations of meteors brighter than + 6 mag, made at Adelaide during 1961.
From an examination of real and chance asso- ciations of orbits Nilsson concluded that 17 percent of the total orbits could be classed as definite streams, while a further 8 percent could probably be classed as members of minor streams. An examination of Nilsson's data using the method of Southworth and Hawkins (Elford, unpublished) gave essentially the same result as obtained by Nilsson if the association parameter D was chosen as 0.10 to 0.15. It would thus appear that over the radio mag- nitude range + 6 to +12.5 the ratio of the total annual incidence of sporadic-to-shower meteors is about 3:1.
For meteors brighter than visual magnitude + 5 , Hawkins (1964) has stated that approxi- mately 50 percent of the meteor flux comes from the major and minor streams. If the stream activity is defined in terms of the sporadic rate by the expression N,=kN cos x, where N, is the shower rate, N the sporadic rate, and x the zenith distance of the shower radiant, Hawkins gives values of & as high as 5.5.
Keay and Ellyett (1961) have pointed out that hourly rates obtained from radio observa- tions of meteor showers are strongly dependent
on the geographical latitude of the observing station and, in general, do not give a reliable indication of the relative fluxes from different meteor showers. They have developed a simple method of determining the relative significance of meteor showers, and have shown that when applied to the shower rates determined at Adelaide, Christchurch, and Jodrell Bank, there is general agreement concerning the relative strengths of showers. They find that the *- Aquarid shower is the strongest of the regular meteor showers.
The latitude variation in optical observations of 24 meteor showers has been investigated by Kresak (1964), who has determined the relative number of meteors from a given shower that penetrate the atmosphere at different geographic latitudes. The proportion of these that can be observed optically has also been determined.
It is of interest to note that the fractional influx into the equatorial zone (±10° latitude) for 17 of the 24 major showers varies by only
± 4 percent. Only those showers with radiants of high declination show a distinct deficiency at the equator, and even among these the effect of zenithal attraction on showers with low geo- centric velocity can partially compensate for the high declination.
5. Annual variation in the incidence of meteors on the earth
The daily echo rate of meteors observed at any point on the earth's surface varies throughout the year. Observations carried out at mid- northern latitudes (Hawkins, 1956; Vogan and Campbell, 1957; Evans, 1960; Millman and Mclntosh, 1963) have shown that the daily echo rate has a maximum between June and Sep- tember and a minimum during February and March. In the Southern Hemisphere the daily echo rate, as determined at Christchurch, 43?5 S (Ellyett and Keay, 1961), and at Adelaide, 35° S (Weiss, 1957b), has a maximum in De- cember and a minimum between June and September. Some features of these annual variations in daily rate can be explained by the occurrence of the major meteor showers. How- ever, even when the effect of the major showers is removed, Hawkins (1956) and Weiss (1957b) have shown that there remains a significant annual variation.
METEOR INCIDENCE ON EARTH FROM RADIO OBSERVATIONS—ELFORD 127 It is generally accepted that the radiants of
sporadic meteors are concentrated in a number of groups. For meteors brighter than MR~ 6 three groups lying on the ecliptic are recognized, one at the apex and two centered on points lying about 70° in longitude from the apex (Hawkins, 1956; Weiss and Smith, 1960;
Davies and Gill, 1960). The last two groups, generally referred to as the sun and antisun groups, have diameters~60° to 70°. At fainter magnitudes there is increased activity from regions lying about 60° north and south of the apex (Davies and Gill, 1960; Hawkins, 1962).
For 10th- to 12th-mag meteors the average strength of this high-latitude activity is about 50 percent of the sun and antisun concentra- tions (Elford, Hawkins, and Southworth, 1964).
Over a period of 1 year the declinations of the various sources of sporadic radiants, as viewed from one locality, vary in a cyclic manner, and it would be expected that the observed echo rate would be a maximum when the apex lies highest in the sky, that is, during March in the Southern Hemisphere and during September in the Northern. The observed rates for the Northern Hemisphere in general follow this pattern. However, the Southern Hemisphere observations contradict the ex- pected annual variation. Weiss (1957b> inter- preted these facts to mean that there is a real variation in the space density of meteors around the earth's orbit, and he derived an annual variation in relative density that was very similar to the results of telescopic studies of meteors by Kresakova and Kresak (1955).
These results indicated that the incidence of meteors on the earth during the second half of the year is about 50 percent greater than during the first half.
This variability in the space density of meteors encountered by the earth during the course of the year has been confirmed by precise hourly rate observations carried out over a period of 1 year at Christchurch, 43?5 S (Ellyett and Keay, 1963; Keay, 1963). These observations were made with a 70-Mc/sec-wide aperture system that could detect meteors down to +8.2 mag. The response function for this system has already been discussed and is given in figure 2. From a comparison of the
observed echo rate and the expected echo rate based on a triple-source radiant distribution (apex, sun, and antisun), Keay (1963) has shown that the increase in meteor flux in the second hah* of the year is due primarily to an increase in the strength of the antisun group and, to a lesser extent, to an increase in the strength of the apex group. The strength of the sun group remains essentially constant throughout the year. In a recent investi- gation of meteor streams based on measure- ments made at Adelaide (35° S) of orbits of meteors of + 6 mag or brighter, Nilsson (1964) has shown that the antisun group predominates during the 6 months July to December, in agree- ment with the conclusion reached by Keay for somewhat fainter meteors. Moreover, as shown in figure 6, the predominance of the antisun group during these months is due to a large number of minor streams through which the earth passes during the second half of the year. When meteors that are members of these streams are removed, the strengths
l40r
100
60
o u 20 -
0l_c£3=C i 180 2"
all orbits
270
ac UJ ffl 40 z 30
90 180
nonshower
180 270 0 90 180
LONGITUDE RELATIVE TO THE APEX FIGURE 6.—The distribution of meteors with ecliptic longitude
as observed at Adelaide (35° S) for 4 months, July-October 1961 (Nilsson, 1964).
128 SYMPOSIUM ON METEOR ORBITS AND DUST
of the sun and antisun groups over this period are essentially the same. If it is assumed that there is no marked change in the radiant dis- tribution as the limiting magnitude is lowered from + 6 to + 8 , the increase in the incidence of meteors of + 8 mag or brighter during the second hah* of the year is most likely due to the occurrence of a large number of unresolved meteor showers.
Additional evidence for the presence of minor showers during the second half of the year comes from the results of an extensive investi- gation of hourly echo rates carried out at the Springhill Meteor Observatory, Ottawa (45° N) over a period of 5 years 1958 to 1962 (Millman and Mclntosh, 1963). These observations were made with a 33-Mc/sec-wide aperture system omnidirectional in azimuth. The re- sponse function for this system has already been given in figure 1. There is no published information on the minimum signal that can be detected with this equipment, but, if it is assumed that the equipment will just detect a signal equal to the average cosmic noise, it is estimated that the radio brightness threshold for the equipment is +7.5. This is very close to the threshold level for the Christchurch equipment. Thus it appears that the two precise echo-rate surveys carried out at Ottawa and Christchurch have investigated essentially the same portions of the meteor population.
Further, these two surveys have been made from two points almost equally spaced either side of the equator, 45° N and 43?5 S. In publishing the statistics of the survey, Millman and Mclntosh have compared the daily rate of all echoes with the daily rate of echoes with duration greater than 8 sec. The percentage of echoes with durations > 8 sec shows strong correlation with the major meteor showers, the percentage for the Perseids and Geminids rising to as much as 10 percent compared with a nonshower value of 1 to 2 percent. It is of interest to note that the average value of the percentage of long-duration echoes during February and March is 1.22 ±0.20 percent, and the average value during September and the first half of October is 1.76±0.20 percent. If it is assumed that the percentage of long- duration echoes is an index of meteor shower activity, this result adds weight to the sugges-
tion made earlier that during the second half of the year the earth passes through a large number of minor meteor streams.
Since the Christchurch and Ottawa surveys refer to essentially the same portion of meteor population, it is of interest to compare the meteor influx deduced from the two sets of observations. The average meteor influx for each month of the year has been determined from the Ottawa hourly rate data by a com- parison of the observed diurnal rates with those predicted when the radiant distribution is approximated by a triple-source model and the response function is that given in figure 1 for c= —1.0. The three sources, each of diameter 65°, were centered on the ecliptic, one at the apex and the other two at points
±70° from the apex. The relative strengths of the sources and the uniform background were adjusted to give the best match between the pre- dicted and the observed diurnal rates. Using a similar procedure, Keay (1963) has deduced the average meteor flux for each month of the year from the Christchurch data. The radiant- distribution model assumed by Keay consisted of three point sources on the ecliptic and a uni- form background. The strength and position of the sources were as follows: Source of strength 1 unit at the apex, two sources each of strength 2 units at points ±60° from the apex, a uniform background of integrated strength 1 unit. The results are shown in figure 7 together
°1
Mar | »DI
l a « A0CLAI0C.1T SlaCISS.ItST) •
» • » CMOI5TCMU«CH. 4S»» S («eAY.i»«si
A J
Ho, 9 0 * J»» 1 J.l •<g
1 8 0 * Sap ' Oet Nc>
2 7 0 * i | OT X Dae | Ja» | ' a » j Mar j
FIGURE 7.—The incidence of meteors on the earth as a function of ecliptic longitude; observed at mid-northern and mid- southern latitudes.
METEOR INCIDENCE ON EARTH FROM RADIO OBSERVATIONS—ELFORD 129 with an earlier result obtained by Weiss (1957b)
from observations made at Adelaide. No at- tempt was made to remove the effect of meteor showers from the original rate data for either Christchurch or Ottawa. Keay justified this approach for the Chr.stchurch data on the basis that for wide-aperture systems the ratio of shower to sporadic rates is greatly decreased as compared with observations made when narrow- beam antennas are used, and that faint shower meteors are swamped by the sporadic back- ground. However, the Ottawa observations (Millman and Mclntosh, 1963) do not support the latter contention. During May and June the echo rate from the daytime streams is com- parable to the sporadic rate, and as a result the flux estimates based on the Ottawa data show an anomalous peak in June. The absence of a similar peak in the Christchurch result is due to the fact that the response functions of the Ottawa and Christchurch systems for shower meteors (c=—0.4 to —0.6) are markedly dif- ferent from the response functions for sporadic meteors (c= —1.0). As a consequence, the probability of detecting Arietid and £-Perseid meteors at Ottawa is enhanced compared with sporadics, while the reverse is true at Christchurch.
With the exception of the 3 months, April, May, and June, there is good agreement be- tween the three estimates of the relative meteor influx throughout the year as shown in figure 7.
It is therefore of interest to compare the abso- lute values of the meteor flux determined from the Ottawa and Christchurch data. This has been carried out for the month of March 1960.
The limiting zenithal line density of the Ottawa system was estimated by assuming that the minimum detectable echo power was 7.0X10"14 watts. This gave a limiting density of 8.9 X lO12!!!"1, or radio magnitude +7.5. The inci- dent flux was determined from a comparison of observed and predicted diurnal rates with the use of the triple-source radiant distribution discussed earlier. It was assumed that all trails were uniform in electron density along their length and that the difference in heights between the beginning and the end of the trails was 6 km. A similar analysis was carried out with the Christchurch data, and the results are shown in table 2. The Christchurch result is
Station
TABLE 2.—Sporadic meteor flux
Ottawa, 45° N Christchurch,
43 ?5 S
X(m)
9.2 4.3
Limiting
8. 9X 1012
5. 1X1012
Limit- ing MR
+ 7.5 + 8.2
Flux (m-2
sec"1) (March
1960)
1.25X7O-"
1 . 0 8 X 1 0 "
very close to the previous estimates shown in figure 5, but the Ottawa result is a factor of 2 higher. Since the response functions for these two systems can be calculated accurately and the assumed model radiant distribution is the same for the two calculations, this discrepancy between the two estimates of flux reflects either an incorrect estimate of the limiting zenithal line density for the Ottawa system or the failure to account properly for the effect of wavelength on the echo rate. This point should be examined further when the actual value of the minimum detectable echo power for the Ottawa system is known.2
In comparing measurements of meteor flux made by different workers at different times one should note that the maximum in the diurnal echo rate averaged over 1 month can show year-to-year variations of as much as 50 percent (Millman and Mclntosh, 1963; Ellyett and Keay, 1964; Mclntosh and Millman, 1964).
6. Selection effects due to meteor velocity, trail diameter, and diffusion
Estimates of meteor fluxes down to a given limiting mass from radio echo-rate data are subject to considerable error due to the severe selection effect of velocity and to uncertainties in the dependence of the ionizing probability /3 on velocity. In a recent review of the ionizing efficiency of meteors, Verniani and Hawkins (1964) conclude that /3ocy40 with an uncertainty in the exponent of about ± 0 . 5 . A velocity correction of v* was applied to shower fluxes by Weiss (1957a), and it was shown in section 4 that this greatly reduces the significance of the high-velocity showers.
2 Recently B. A. Mclntosh (private communication) has pointed out that the minimum detectable echo power for the Ottawa system is probably closer to 2X1(H« watts. This would bring the Ottawa and Christchurch fluxes into closer agreement.
130 SYMPOSIUM ON METBOR ORBITS AND DUST
Recently (Elford, Hawkins, and Southvvorth, 1964), an estimate has been made of the mass limit for sporadic meteors observed in March 1963 with the Harvard-Smithsonian meteor radar system. From the observed velocity distribution and the value of the ionizing proba- bility given by Verniani and Hawkins, it was estimated that the flux of sporadic meteors with mass greater than 1.3X10"8 g is 1.0X lO-^n"2 sec"1.
The effect of diffusion and finite initial trail radius on the radar echo rate of meteors has been discussed by a number of workers (Peregu- dov, 1958; Fialko, 1960; Greenhow and Hall, 1960; Lebedinets, 1964), who have predicted that equipment operating on short wavelengths
« 1 0 m) will detect only a fraction of the meteor population. Lebedinets estimates that for equipment operating on a wavelength of S m and at an effective minimum detectable line density of 1012m~', the true sporadic rate is about a factor of 30 greater than the observed echo rate. Greenhow and Hall (1960) estimate that the percentage of the true influx of meteors detected by a radio system varies from 1.5 at 4-m wavelength to 40 at 17 m. However, the estimates of sporadic flux discussed in section 5, which have been derived from observations at frequencies of 70, 38, and 17 Mc/sec, do not differ by more than a factor of 2 to 4. The lack of agreement between the predicted and the observed variations in rate as a function of wavelength has been attributed to the effect of a decrease in fragmentation among meteors fainter than + 5 mag (Hawkins, 1964).
References
BBOWNE, I. C ; BULLOUQH, K.; EVANS, S.; and KAISER,
T. R.
1956. Characteristics of radio echoes from meteor trails, II: The distribution of meteor magnitudes and masses. Proc. Phyg.
Soc. London, vol. 69B, pp. 83-97.
DAVII!8, J. G., and GILL, J. C.
1960. Radio echo measurements of the orbits of faint sporadic meteors. Monthly No- tices Roy. Astron. Soc., vol. 121, pp.
437-462.
ELFORD, W. G.
1964. Calculation of the response function of the Harvard Radio Meteor Project Radar System. Harvard Radio Meteor Project Res. Rep., no. 8.
ELFORD, W. G., and HAWKINS, G. S.
1964. Meteor echo rates and the flux of sporadic meteors. Harvard Radio Meteor Pro- ject Res. Rep., no. 9.
ELFORD, W. G.; HAWKINS, G. S.; and SOUTHWORTH,
R. B.
1964. The distribution of sporadic meteor radi- ants. Harvard Radio Meteor Project Res. Rep., no. 11.
ELLYETT, C , and KEAY, C. 8. L.
1961. All-sky meteor rates in the Southern Hemi- sphere. Journ. Geophys. Res., vol. 66, pp. 2590-2591.
1963. S o u t h e r n H e m i s p h e r e m e t e o r r a t e s . Monthly Notices Roy. Astron. Soc., vol.
125, pp. 325-346.
1964. Meteors: An unexpected increase in 1963.
Science, vol. 146, p. 1458.
EVANS, G. C.
1960. Radio echo observations of metoor activity between 1054 December and 1958 De- cember. Astron. Contr. Univ. Man- chester (1), Jodrell Bank Ann., vol. 1, pp. 280-337.
FIALKO, E. I.
1960. The dependence of the mean hourly rates of recorded meteors on the parameters of meteoroids, the atmosphere, and the radar system. Sov. Astron.—AJ., vol.
4, pp. 711-721.
GREENHOW, J. S., and HALL, J. E.
1960. The importance of initial trail radius on the apparent height and number distribu- tions of meteor echoes. Monthly No- tices Roy. Astron. Soc., vol. 121, pp.
183-196.
HAWKINS, G. S.
1956. A radio echo survey of sporadic meteor radiant?. Monthly Notices Roy. Astron.
Soc., vol. 116, pp. 92-104.
1962. Radar determination of meteor orbits.
Astron. Journ., vol. 67, pp. 241-244.
1964. Interplanetary debris near the earth. Ann.
Rev. Astron. Astrophys., vol. 2, pp.
149-164.
HAWKINS, G.S.; SOUTHWORTH, R. B.; and ROSENTHAL,S.
1964. Preliminary analysis of meteor radiants and orbits. Harvard Radio Meteor Project Res. Rep., no. 7.
HAWKINS, G. S., and UPTON, E. K. L.
1958. The influx rate of meteors in the earth's atmosphere. Astrophys. Journ., vol. 128, pp. 727-735.
KAISER, T. R.
1953. Radio echo studies of meteor ionization.
Adv. Phys., Phil. Mag. Suppl., vol. 2, pp. 495-544.
1955. The incident flux of meteors and the total meteoric ionization. In Meteors, ed. by T. Kaiser, Pergamon Press, New York, pp. 119-130.