On the Question of the Distribution of Intervals Between Meteor Radio Echoes

E. I. Fialko, G. L. Kalinichenko

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

Introduction

In processing observations of meteor radio echoes, attention is drawn to the fact that meteor reflections appear in groups: at times radio echoes are not observed for several minutes, while at other times their number in one minute reaches ten (or more). In other words, if by an interval we understand the time span between the appearances of two neighboring radio echoes, and if we find the mean interval \(\overline{T}\) from the formula

\[ \overline{T}=\frac{T_{\Sigma}}{N_{\Sigma}}, \]

where \(T_{\Sigma}\) is the total observation time, and \(N_{\Sigma}\) is the number of radio echoes recorded during the time \(T_{\Sigma}\), then we see that during the time \(\overline{T}\) not one but several meteor radio echoes appear, and intervals \(< \overline{T}\) occur more often than intervals \(> \overline{T}\). It should be noted that, although very rarely, intervals with a duration up to \(10\overline{T}\) do occur.

These, as well as other facts of grouping of meteor radio echoes described in the literature, testify to the grouping of meteors in time. The question arises as to whether this fact is the result of grouping of meteoric bodies in space [1], or of the fragmentation of meteoric bodies in the atmosphere, or whether it is the result not only of grouping of meteoric bodies in space but also of the random entry of meteoric bodies into the atmosphere [2, 3].

In other works [4, 5] a hypothesis is advanced concerning the completely random entry of meteors into the atmosphere; the observed groupings confirm this hypothesis.

In works [6, 7], from the results of normal sounding of meteor trails at the wavelength \(\lambda = 10\) m, the distribution of intervals between neighboring radio echoes over a time interval of 2 and 3 hours was constructed. Good agreement was shown between the experimental distribution and the theoretical one, constructed under the assumption that meteoric bodies enter the Earth’s atmosphere at random.

In the present work we are interested in comparing the distributions of intervals between recorded meteor radio echoes with theoretical-

...with the distribution obtained under the assumption of a completely random entry of meteors into the atmosphere, for time intervals with different character of variation of the hourly number.

Results of the observations

The observations were carried out at the “TPI-2” station at a wavelength \(\lambda = 10\) m [6, 7]. Observations for 1959 were processed from 2 to 9 hours on January 5, from 0 to 11 hours on January 9, from 0 to 3 and from 5 to 8 hours on January 11, from 0 to 2 hours on February 12, from 2 to 12 hours on February 17,

Fig. 1. Distribution of intervals between meteor radio echoes over 70 hours, taken selectively from January through April 1959. The solid line is the theoretical distribution. The histogram is the experimental distribution of intervals between radio echoes. The theoretical distribution is

\[ N_m = 10262 \cdot 0.4072 \cdot e^{-0.04072 \cdot T}. \]

from 3 to 11 hours on April 7, from 0 to 9 hours on April 8, from 1 hour to 12 hours 45 minutes on April 11, and from 0 to 6 hours on April 12 (Tomsk standard time). In all, the material was processed for 70 hours.

Then histograms were constructed for the experimental distributions and curves for the theoretical distributions under the assump-

in the assumption of an entirely random entry of meteors into the Earth’s atmosphere; in the latter case the differential law of the distribution of time intervals has the form [4, 5]:

\[ p(T)=\frac{1}{\overline{T}} e^{-\frac{T}{\overline{T}}}, \tag{1} \]

where \(\overline{T}\) is the mean interval between radio echoes.

Since the histograms are constructed not for frequencies, but for counts, the theoretical distribution of intervals under our assumption will have the form

\[ N_m=N_\Sigma p(T)\Delta T=\frac{N_\Sigma e^{-\frac{T}{\overline{T}}}\Delta T}{\overline{T}} . \tag{2} \]

Fig. 2. Same as in Fig. 1, for observations from 3 to 9 o’clock on February 17, 1959.
Theoretical distribution

\[ N_m=788\cdot 0.03648\cdot e^{-0.03648\cdot T}. \]

Fig. 2a. Variation of the hourly numbers from 3 to 9 o’clock on February 17, 1959.

Let us note that the distributions of intervals between meteor radio echoes (1) and (2) were given earlier [2—5].

In the work, 5 histograms are considered:

1) For all intervals observed over 70 hours, taken selectively from January through April 1959, with the mean hourly number for this

interval, that is, over 70 hours, \(\overline{N}=147\) meteors with a change in hourly numbers from 70 to 299 meteors.

2) For the intervals from 3 to 9 hours on February 17, with a characteristic monotonic decrease of the hourly number from 170 to 84, with a mean hourly number \(\overline{N}=131\) and intervals from 0 to 150 sec.

The theoretical distribution law in this case has the form

\[ N_m=788\cdot 0.3648\cdot e^{-0.03648\cdot T} \qquad \text{(see Fig. 2).} \]

3) For the intervals from 2 to 7 hours on April 7, with the following change in the hourly number: a small change over two hours, then a rapid

Fig. 3a

Fig. 3. Distribution of intervals between meteor radio echoes from 2 to 7 hours on April 7, 1959.
Theoretical distribution

\[ N_m=937\cdot 0.5205\cdot e^{-0.05205\cdot T} \]

Fig. 3a. Change in hourly numbers from 2 to 7 hours on April 7, 1959.

increase over two hours from 156 to 222 and again a small change (see Fig. 3a); the mean hourly number \(\overline{N}=182\), with intervals from 0 to 170 seconds.

Theoretical distribution law

\[ N_m = 937 \cdot 0.5205 \cdot e^{-0.05205 \cdot T}. \]

(see Fig. 3).

4) For intervals from 0 to 9 hours on April 8 with a gradual, but not monotonic, increase in the hourly number.

The hourly number varied from 118 to 177. The mean hourly number was \(\overline{N}=154\), with intervals from 0 to 160 sec.

Theoretical distribution law

\[ N_m = 1389 \cdot 0.4287 \cdot e^{-0.04287 \cdot T}. \]

(see Fig. 4).

Fig. 4. Distribution of intervals between meteor radio echoes from 0 to 9 hours on April 8, 1959. Theoretical distribution

\[ N_m = 1389 \cdot 0.4287 \cdot e^{-0.04287 \cdot T}. \]

Fig. 4a. Change in hourly numbers from 0 to 9 hours on April 8, 1959.

5) For intervals from 1 hour to 5 hours 54 minutes, with an increase in the hourly number from 127 to 197, then with a decrease to 157 meteors (see Fig. 5a).

The mean hourly number is \(\bar N=160\), with intervals from 0 to 200 seconds.
The theoretical distribution law is

\[ N_m=782\cdot 0.4433\cdot e^{-0.04433\cdot T}. \]

(see Fig. 5)

From Figs. 1–5 we see that the agreement between the experimental and theoretical distributions is satisfactory. At the same time, we note that for \(T<10\) sec, in 4 cases out of 5 the frequency of occurrence of intervals exceeds—though only slightly—the expected number of inter-

Fig. 5a.

Fig. 5. Distribution of intervals between meteor radio echoes from 1:00 to 5:54 on April 11, 1959. Theoretical distribution

\[ N_m=782\cdot 0.4433\cdot e^{-0.04433\cdot T}. \]

Fig. 5a. Change in hourly numbers from 1:00 to 5:54 on April 11, 1959.

vals. Thus, the percentage of intervals exceeding the expected number of intervals is 8% in Fig. 1, 5% in Fig. 3, 5% in Fig. 4, and 7% in Fig. 5.

Conclusions

1. Based on the results of normal sounding of meteor trails at wavelength \(\lambda=10\) m, a distribution of intervals between neighboring radio echoes was constructed for time periods lasting up to 9 hours, with differing behavior of the hourly numbers.

1. These distributions are in satisfactory agreement with the theoretical distribution constructed under the assumption that meteoric bodies enter the Earth’s atmosphere at random.

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