SOME STATISTICAL CHARACTERISTICS OF METEORS DETECTED BY THE RADAR METHOD

E. I. FIALKO

(Presented by the scientific seminar of the Radio Engineering Faculty)

Systematic radar observations of meteors in the city of Tomsk, begun in the middle of 1957, made it possible to obtain certain statistical characteristics of meteors.

The systematic observations carried out during the International Geophysical Year and the International Geophysical Cooperation were preceded by intensive work by the staff of the Department of Radio Engineering Equipment of the Tomsk Polytechnic Institute to create an installation for the radar detection of meteors and to conduct trial observations.

The Radio Engineering Test Range of the Tomsk Polytechnic Institute

In 1950, preparatory work was begun at the Tomsk Polytechnic Institute (TPI), preceding the organization of a group capable of designing and constructing equipment for meteor radar, operating it, and processing the results of observations.

Development of the preliminary design of an installation for radio investigation of meteors began in 1953, mainly through the efforts of graduating students of the Radio Engineering Faculty of TPI, who, after graduating from the institute, formed the core of the emerging group.

The preliminary design was completed in July 1954. The technical design work that followed was completed with the creation of the station “TPI-1” in August 1956 and the station “TPI-2” in August 1957.

The station “TPI-1,” intended for meteor observations at a wavelength \(\lambda = 10\) m, emits pulses of duration \(\tau = 5\ \mu\text{s}\), with power \(P_i \simeq 100\ \text{kW}\), at a frequency \(F_i = 300\) pulses/s and \(F_i = 600\) pulses/s (in the latter mode, single pulses alternate with paired ones). In addition to the transmitter, receiver, and range markers, the station includes a meteor-velocity indicator (recording the diffraction pattern observed during trail formation) and a meteor-trail drift indicator (a conical range indicator).

In developing the station “TPI-1,” account was taken of the results of work connected with measuring meteor velocity [1], meteor-trail drift velocity [2], increasing the interference immunity of meteor radars [3], and so forth.

The “TPI-1” station was deployed in August 1956 at the TPI radio-engineering test range (the first stage of which had been built in the summer of 1956). In September 1956, trial observations of meteors were carried out, confirming the great possibilities of meteor radar at \(\lambda = 10\) m.

The “TPI-1” radar was then transferred to the customer—the Institute of Atmospheric Physics of the USSR Academy of Sciences (IFAN). Tests of the “TPI-1” installation, carried out in December 1956 in the region of Murmansk with the participation of TPI staff members, assistants F. I. Peregudov and V. A. Fedorov, demonstrated the suitability of the apparatus that had been created for operation under polar conditions.

The “TPI-2” station includes, in addition to a range finder, an angle-measuring unit. The range-finding part of the “TPI-2” installation is essentially an improved “TPI-1” station (in addition to a simple drift indicator, it has a coherent-pulse drift indicator, etc.).

In addition to the “TPI-2” radar, modernized “P-2M” radars (\(\lambda \simeq 4\) m), “Most-2” (\(\lambda \simeq 1.5\) m), and the original “M-3” radar (\(\lambda \simeq 4\) m\(^1\)) were installed at the radio-engineering test range. In addition, for the study of polarization effects observed upon reflection of radio waves from a meteor trail, a directional antenna was constructed (radiating in two mutually perpendicular planes), analogous to the antennas used in well-known experiments [4, 5].

The design and construction of the apparatus, carried out under the author’s direction, were actively participated in by assistant F. I. Peregudov (chief designer of the transmitters of “TPI-1” and “TPI-2” and of the “M-3” station), assistant E. K. Nemirova (chief designer of the receiving-indicating installations “TPI-1,” “TPI-2,” and also of the antenna for studying resonance effects in the meteor trail), senior engineer I. D. Zolotarev (chief designer of the angular-coordinate channel of the “TPI-2” station), docent G. S. Zubarev (who directed the work of creating the test range and setting up observations on the “P-2M” radar, etc.), assistant L. P. Serafinovich, assistant L. A. Pokrovskii. Also participating in the work were assistant V. A. Fedorov, senior instructor I. Sh. Solomonik, postgraduate student A. N. Kolesov, postgraduate student V. P. Denisov, docent G. B. Kats, engineer L. G. Shoshin, junior research associate G. V. Noskova, A. V. Saenko, and others.

Radar observations of meteors in Tomsk

The first radar observations of meteors in Tomsk were carried out in August 1953, during the Perseid stream [6].

For this purpose, the “P-2M” radar station was used, with an additional brightness marker and a photographic attachment. Earlier, this installation had been used by B. Yu. Levin for meteor observations organized by him in the region of Moscow.

In December 1953, the Geminid stream was observed in Tomsk [6]. Observations were conducted from 11 to 14 December during the night and morning hours, for a total of 31 hours 10 minutes.

In all, 209 meteors were recorded; the mean hourly number was \(N \simeq 7\). The greatest number was noted at \(2^h\) and \(3^h 30^m\) on 12 December (Tomsk local time), when the hourly number reached 36.

\(^1\) The “TPI-2,” “M-3,” and “Most-2” radars have approximately identical parameters \(P_i, F_i, \tau_i\).

In setting up observations of the Geminid stream, account was taken of the experience of work carried out by B. Yu. Levin [7], I. S. Astapovich [8], P. O. Chechik [9], and also by foreign investigators [10, etc.].

However, these observations were conducted with the aim of solving certain instrumental questions, and not for the accumulation of statistical material.

For the first time in the USSR, observations at wavelength \(\lambda = 10\) m were carried out from 6 to 13 September 1956 with the “TPI-1” station at the radio-engineering test range of the Tomsk Polytechnic Institute. During the observations, which lasted a total of 41 hours, more than 7000 meteors were recorded; the mean hourly number was \(N \simeq 170\). Photographic recording of the screen of the range bright-spot indicator was carried out for 6 hours 40 minutes (from \(1^h\) to \(7^h 40^m\) on 13 September 1956). On 7–8 September the apparatus operated around the clock (with two one-hour interruptions), which made it possible to determine the diurnal variation of the hourly number, whose maximum reached \(\simeq 300\) at \(5^h\)–\(6^h\), and whose minimum was \(\simeq 60\) at \(18^h\)–\(19^h\) local time [11].

The distribution of meteor radio echoes by durations and ranges was also obtained [12, 11].

In December 1956, as already mentioned, F. I. Peregudov, with the participation of V. A. Fedorov, observed the Geminid stream in the region of the city of Murmansk (also with the “TPI-1” station).

Beginning in July 1957, observations were started at the “TPI-2” station, installed at the TPI radio-engineering test range.

During the period from July 1957 to December 1958, more than 325 thousand meteors were registered (the mean hourly number was 177), of which about 43,700 gave reflections with durations \(> 1\) sec.

In August 1957 diffraction patterns were recorded, and at the beginning of 1958 the drift velocity of meteor trails was measured by the coherent-pulse method.

Meteor heights were measured during the activity periods of the Geminid, Ursid, Quadrantid, and other streams.

The radar observations carried out during the IGY period made it possible to accumulate extensive statistical material.

Variation of the hourly number of meteors registered by radar at \(\lambda = 10\) m

As is known, the number of meteors registered by a locator during one hour (the hourly number \(N\)) does not remain constant. Diurnal, as well as seasonal, changes in the hourly number \(N\) are associated with the rotation of the Earth about its axis and around the Sun, with the distribution of meteoric matter in space, etc. In addition, the magnitude and character of the variation of \(N\) are determined by the parameters of the radar (wavelength, transmitter power, antenna radiation pattern, pulse repetition frequency, etc.).

Some idea of the level of meteor activity over a definite time interval \(T_\Sigma\) can be given by the mean hourly number \(\overline{N} = \dfrac{N_\Sigma}{T_\Sigma}\) (where \(N_\Sigma\) is the total number of meteors registered during the observing time \(T_\Sigma\)).

But in this case it remains unclear how often (and by how many times) the hourly number may exceed the level \(\overline{N}\), or, conversely, how often a decrease in the hourly number may be expected.

Clarification of the problem under consideration is also important in the interests of rational design of radar devices: in a number of cases it is necessary to know what the probability is of registering a very large or a very small number of meteors by a radar designed for \(N\). In this connection, an experimental study of the law of distribution of hourly numbers is of interest.

For the observations, the “TPI-2” station was used (\(\lambda = 10\ \mathrm{m}\)) with nondirectional transmitting and receiving antennas (half-wave vibrators at a height \(\simeq \dfrac{\lambda}{3}\) above ground level); the pulse power was \(P_i \simeq 100\ \mathrm{kW}\), the pulse duration \(\tau_i = 5\ \mu\mathrm{s}\), and the pulse repetition frequency was \(600\) pulses/sec. To increase the interference immunity of the system and to ensure unambiguous range measurement, double pulses alternating with single ones were used. Meteor radio echoes were recorded on photographic film moving at a speed of \(\simeq 30\ \mathrm{mm/min}\).

In July–December 1957, observations were carried out for \(602.5\) hours. Both showers (including the Perseids, Geminids, etc.) and sporadic meteors were observed. During this time, 134,280 meteors were registered. The differential distribution of hourly numbers (Fig. 1) has an extremal character.

The mode of the distribution lies within the range of 150–200 meteors per hour; the mean hourly number is \(\overline{N} \simeq 222\).

Fig. 1.

Figure 2 presents the normalized integral distribution of hourly numbers. The median value of the hourly number is \(\simeq 200\). The probability of exceeding twice the mean level (that is, \(N \gtrsim 440\)) is less than 4% (see Fig. 2). The probability that \(N\) will be greater than 500 does not exceed 1%. Let us note that over the entire observation time the largest hourly number only once reached the value \(N_{\max} = 650 \div 700\).

It is quite natural that the results obtained are preliminary in character. To refine them, it is necessary to analyze

also the first half-year and to consider time intervals that are small in comparison with 1 hour.

When low-efficiency or low-sensitivity apparatus is used, the differential distribution of hourly numbers has a monotonically decreasing character. To confirm this statement, let us use the summary sent out by the Engelhardt Astronomical Observatory (Kazan) to participants in the work under the IGY program. During August, September, and November 1957, observations at the station

Fig. 2.

“P-2M” (modernization by K. V. Kostylev) were conducted for 1088 hours; during this time 1075 meteors were recorded (thus, the mean hourly number is approximately 1). The differential distribution of hourly numbers is shown in Fig. 3.

Although the results obtained over a comparatively short period are preliminary in character, it seems possible to draw a number of conclusions.

1. The distribution of hourly numbers has an extremal character if sufficiently sensitive and highly efficient apparatus is used.

2. At \(\lambda = 10\ \mathrm{m}\), with transmitter power \(P_i \approx 100\ \mathrm{kW}\), it is possible to record on average about 200 meteors per hour. In this case, during approximately half of the observing time more than 200 meteors per hour will be detected.

3. The time during which an hourly number twice exceeding the mean level \(\overline{N}\) may be observed is \(\approx \frac{1}{25}\) of the total observing time.

1. The probability that (at \(\lambda=10\) m) the hourly number will exceed \(N=500\) is only \(\approx 1\%\).

Fig. 3.

Distribution of meteor radio echoes by duration

For the period from July to December 1957, as already indicated, 134280 meteor radio echoes were recorded, belonging both to meteor streams and to sporadic meteors. Of these, 22180 reflections had a duration \(\tau \geqslant 1\) sec.

The integral distribution of radio echoes by duration is presented in Fig. 4 on a logarithmic scale (for \(\tau \geqslant 1\)); \(N(\tau)\) is the number of reflections with duration \(\geqslant \tau\).

It is not difficult to see that in the region of long-lasting echoes the character of the dependence \(N(\tau)\) is somewhat different than in the region \(\tau \simeq 1 \div 10\) sec.

The character of the dependence \(N(\tau)\) is determined by the law of distribution of meteoric bodies by mass and by the peculiarities of reflection of radio waves from meteor trails [13].

As is seen from Fig. 4, in the interval \(\tau \simeq 1 \div 10\) sec the integral distribution \(N(\tau)\) is satisfactorily approximated by the hyperbola \(N(\tau)\sim \tau^{-0.86}\), and in the interval \(\tau \simeq 10 \div 60\) sec by the hyperbola \(N(\tau)\sim \tau^{-1.55}\).

Using the distribution of radio echoes by duration that characterizes the entire set of recorded meteors (both sporadic and belonging to streams) for the second half of 1957, we find a certain averaged value of the exponent \(s\).

Finding \(s\) for the interval \(\tau \simeq 1 \div 10\) sec from the formula \(s=1+\dfrac{4\lg N_1/N_2}{3\lg \tau_2/\tau_1}\),

and \(s_2\) for the interval \(\tau \approx 10 \div 60\) sec from the formula

\[ s = 1 + \frac{2}{3}\,\frac{\lg N_1/N_2}{\lg \tau_2/\tau_1} \]

(see [13]), we obtain \(s_1 \approx 2.15\) and \(s_2 \approx 2.05\).

As is known, for sporadic meteors the characteristic value is \(s \approx 2\) [14].

Such agreement of the results apparently indicates that the greater part of the meteoric matter belongs to the sporadic background. It is also possible that the contribution of meteor streams with distributions of the masses of meteoroid bodies differing from the sporadic background in both directions (i.e., with \(s > 2\) and with \(s < 2\)) to the Earth’s atmosphere is the same.

Fig. 4.

Distribution of Meteoroid Bodies by Mass

From the distribution of meteor radio echoes by duration in the interval \(\tau \approx 1 \div 10\) sec, for each hour the index \(s\), characterizing the distribution of meteoroid bodies by mass, was found (see [15, 16, 13]):

\[ s \approx 1 + \frac{4}{3}\,\frac{\lg \dfrac{N_1}{N_2}}{\lg \dfrac{\tau_2}{\tau_1}}, \]

where \(N_1\) (and \(N_2\)) is the number of reflections with durations \(\geq \tau_1\) (and \(\tau_2\)).

Strictly speaking, the index \(s\) should be determined for a group of meteors with identical velocities. However, it is also of interest to determine \(s\) for the entire set of observed meteors. In this case both an approximate value of \(s\) and the degree of its dispersion will be determined.

From the distribution of radio echoes by durations (in the interval \(\tau = 1 \div 10\) sec) for 1957, a value \(s = 2.3\) was found; the value of the exponent \(s\) varied within the limits from 1.25 to 4.25 (Fig. 5).

Fig. 5.

The value of \(s\) obtained in this way characterizes the entire set of observed meteors; some of the recorded meteors belong to sporadic meteor matter, while another part belongs to large meteor streams.

Despite the fact that the value of \(s\) corresponding to some meteor streams differs considerably from the mean value of \(s\) for the entire set of meteors [14, 17], the dispersion of \(s\) in the histogram (Fig. 5) is relatively small (\(\Delta s_{qf} \approx 0.55\)), which probably indicates a predominance of sporadic material.

Distribution of intervals between meteor radio echoes

When meteor reflections are observed on indicator screens, and also when films with records of meteor radio echoes are inspected, the impression is created that meteors are grouped in time. A similar effect has also been noted in visual observations of meteors.

Such grouping of meteors in time may be the result of grouping of meteoric bodies in space. However, even when the entry of meteoric bodies into the Earth’s atmosphere is completely random, groups of meteors may appear from time to time, including groups with equal intervals between meteors.

Some investigators have concluded that the grouping of meteor radio echoes in time is a consequence of the fact that meteors enter the Earth’s atmosphere in groups [18].

The opinion has also been expressed that the appearance of echoes in the form of “chains” is explained chiefly by the presence of ascending electrical discharges [19]. In a number of works, both the possibility of grouping of meteoric bodies in space and the random character of the entry of meteoric bodies into the Earth’s atmosphere are admitted [20, 21].

In some works it has been shown that, under conditions of both normal [22] and oblique [23] sounding of meteor trails, there is no evidence in support of the theory according to which meteoric bodies enter the atmosphere in groups.

In view of the contradictory opinions on the question discussed, it seems advisable to compare the distribution of intervals between recorded meteor radio echoes with the theoretical distribution obtained under the assumption of a completely random entry of meteors into the Earth’s atmosphere.

Results of observations. The epoch of the Perseid stream was used for the investigation. Observations were carried out with the aid of the “TPI-2” station.

During the first half of the day on August 12, 1958, an increase in the hourly number of meteors was observed twice: from \(2^h\) to \(4^h\) (caused by the Perseid stream) and from \(6^h\) to \(9^h\) (apparently caused by an increase in the sporadic background), according to Tomsk standard time.

During two night hours (\(2^h\)—\(4^h\)), 508 meteors were recorded, with the intervals between neighboring radio echoes lying between 0 and 70 seconds. In the morning hours (\(6^h\)—\(9^h\)), 852 meteors were registered, with intervals from 0 to 120 sec.

Fig. 6.

The differential distribution of intervals between meteor radio echoes is plotted in the form of histograms in Figs. 6 and 7.

The theoretical distribution of intervals \(T\) for random entry of meteors into the atmosphere, as is known [22, 23], has the form

\[ n_m = f(T)\Delta T = \frac{N_\Sigma}{\overline{T}} e^{-\frac{T}{\overline{T}}}\Delta T, \tag{1} \]

where \(f(T)\Delta T\) is the number of intervals with duration from \(T\) to \(T+\Delta T\); \(N_\Sigma\) is the total number of meteors recorded during the observation time \(T_\Sigma\); \(\overline{T}=\dfrac{T_\Sigma}{N_\Sigma}\) is the mean interval between radio echoes.

For the two time intervals under consideration (\(2^h\)—\(4^h\) and \(6^h\)—\(9^h\)), formula (1) takes the form

\[ n_m = f(T)\Delta T = 358e^{-\frac{T}{14.2}} \tag{2} \]

and

\[ n_m=f(T)\Delta T=670e^{-\frac{T}{12.7}} \tag{3} \]

(\(T\) in seconds).

These distributions are shown by the solid lines in Figs. 6 and 7. As can be seen, the agreement between the experimental and theoretical interval distributions is quite satisfactory in both cases.

Let us consider the region of small intervals \(T\). Figure 8 presents the distribution of intervals in the region \(0<T<10\) sec for the night hours (\(2^h\)—\(4^h\), 12 August 1958). The theoretical distribution (1), for \(N_\Sigma=508\), \(\overline{T}=14.2\) sec, and \(\Delta T=1\) sec, takes the form

\[ n_m=f(T)\Delta T=35.8e^{-\frac{T}{14.2}}. \tag{4} \]

As can be seen from Fig. 8, in the region of small intervals there is also satisfactory agreement between the experimental and theoretical data.

The result obtained permits the following conclusion.

Apparently, some part of the meteor trails is formed by meteoroid bodies that enter the region of intense meteor ionization in groups. Such grouping of meteors may be a consequence of the effect of grouping of meteoroid bodies in space, and also a consequence of the breakup of loose meteoroid bodies into separate parts moving in the Earth’s atmosphere with different velocities. However, apparently, the appearance of most groups of meteor radio echoes is the result of the random coincidence of the moments of entry of meteors into the Earth’s atmosphere.

Fig. 7.

Conclusions

At a wavelength \(\lambda=10\) m, with transmitter power \(P_i \approx 100\) kW and pulse repetition frequency \(F_i \approx 300\div 600\) pulses/sec, the differential distribution of hourly numbers has an extremal character. The mean value of the hourly number is approximately equal to the average hourly number.

According to observations carried out in 1957, the average hourly number of recorded meteors was \(\overline{N}\approx 200\).

The probability that more than 500 meteors will be detected during an hour does not exceed 1%.

According to the observations of 1957 and 1958, \(\overline{N}\approx 177\).

The integral distribution of meteors by durations of radio echoes, recorded in the second half of 1957, satisfactorily

is approximated by parabolas \(N(\tau)\sim \tau^{-0.86}\) in the interval of durations \(\tau \simeq 1\div 10\) sec and \(N(\tau)\sim \tau^{-1.55}\) in the interval \(\tau \simeq 10\div 60\) sec, which corresponds to the exponent \(s \simeq 2.05\div 2.15\).

As follows from the differential distribution law for the exponent \(s\) (from the observations of 1957), the value of \(s\) varied within the limits from 1.25 to 4.25; the mode of the distribution is in the interval \(s \simeq 2\div 2.25\); \(\bar{s} \simeq 2.3\); the root-mean-square deviation (from \(\bar{s}\)) \(\Delta s_{\mathrm{eff}}\simeq 0.55\).

The distribution of intervals between radio echoes observed at \(\lambda=10\) m is in satisfactory agreement with the theoretical distribution constructed under the assumption of the random entry of meteoric bodies into the terrestrial atmosphere. This confirms the conclusion obtained earlier [22, 23] that the grouping of meteor echoes in time may not be a consequence of a group intrusion of meteoric bodies into the atmosphere.

Fig. 8.

LITERATURE

1. J. G. Davies, C. D. Ellyett. The diffraction of radio waves from meteor trails and the measurement of meteor velocities, Phil. Mag., Ser. 7, 40, N 305, 614, 1949.

2. J. S. Greenhow. A radio echo method from investigation of atmospheric winds at altitudes of 80 to 100 km., Journ. Atm. Terr. Phys., 2, N 5, 282, 1952.

3. A. Aspinall, J. A. Clegg, A. C. B. Lovell. The day-time meteor streams of 1948, part I, Measurement of the activity and radiant positions, M. N. R. A. S., 109, 352, 1949.

1. E. R. Billam, I. C. Browne. Observations of polarization effects in radio echoes from meteor trails, “Meteors,” Ed. by T. R. Kaiser, p. 73, 1955.

2. E. R. Billam, I. C. Browne. Characteristics of radio echoes from meteor trails. IV. Polarization effects, Proc. Phys. Soc., Sec. B, 69, Part 1, No. 433, 98, 1956.

3. E. I. Fialko, G. I. Galibin, G. S. Zubarev, R. P. Chebatarev, and others. Restoration and transfer of the Slabozhaninna station to a directional antenna. Report on stage 3 of theme 300. Tomsk Polytechnic Institute, 1953.

4. B. Yu. Levin. Observations of the Draconids by the radiolocation method, Astr. Circ., No. 57, 2, 1946.

5. I. S. Astapovich. Radio observations of the meteor shower of the Geminid stream, 1953, A. Ts., No. 169, 17, 1956.

6. P. O. Chechik. Radio Engineering and Electronics in Astronomy, Gosenergoizdat, 1953.

7. J. A. Clegg. Determination of meteor rediants by observation of radio echoes from meteor trails, Phil. Mag., 39, 578, 1948.

8. E. I. Fialko, F. I. Peregudov, E. K. Nemirova. Preliminary results of radiolocation observations of meteors at \(\lambda = 10\) m, Bulletin of the Commission on Comets and Meteors of the Astronomical Council of the Academy of Sciences of the USSR, No. 2, 39, 1957.

9. E. I. Fialko. Radiolocation observations of meteors at wavelength \(\lambda = 10\) m, Astr. Circ., No. 175, 21, 1956.

10. E. I. Fialko. Distribution of meteor radio echoes by duration. 1. Reflection from persistent trails, Astr. Journal, 36, issue 5, 867, 1959.

11. T. R. Kaiser. Radio echo studies of meteor ionization, Phil. Mag. Suppl., 2, No. 8, 495, 1953.

12. E. I. Fialko. Some results of a study of the distribution of meteoric bodies by mass, Astr. Circular, No. 195, 22, 1958.

13. E. I. Fialko. A method for studying the law of distribution of meteoric bodies by mass, Astr. Journal, 36, issue 6, 1058, 1959.

14. I. C. Browne, K. Bullough, S. Evans, T. R. Kaiser. Characteristics of radio echoes from meteor trails. II. The distribution of meteor magnitudes and masses, Proc. Phys. Soc., B, 69, 83, 1956.

15. L. R. Wylie, H. T. Castillo. Ohio J. Sci., 6, 339, 1956.

16. G. A. Isted. Marconi Rev., 17, 37, 1954.

17. C. A. Shain, F. J. Kerr. A note on factors affecting the interpretation of transient echoes from the ionosphere, J. Atm. Terr. Phys., 6, No. 5, 280, 1955.

18. B. H. Briggs. Observations of short bursts of signal from a distant 50 c/s transmitter, J. Atm. Terr. Phys., 8, No. 3, 171, 1956.

19. K. R. Bowden, J. G. Davies. The time distribution of meteors, J. Atm. Terr. Phys., 11, No. 1, 62, 1957.

20. T. J. Keary, H. J. Wirth. The random occurrence of meteors in the upper atmosphere, J. Geoph. Res., 63, No. 1, 67, 1958.