DISTRIBUTION OF STABLE METEOR RADIO ECHOES BY DURATION

E. I. FIALKO

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

Introduction

Several methods are known for determining the exponent \(s\), which characterizes the distribution of meteor bodies by mass [1]:

\[ P_m(m)\sim \frac{1}{m^s}. \tag{1} \]

Kaiser [2] used the dependence of the number of detected meteors \(N\) on the parameters of the radar and on the value of \(s\)

\[ N\sim \left(\frac{P_u \lambda^3}{\varepsilon}\right)^{\frac{s-1}{2}}, \tag{2} \]

where \(P_u\) is the transmitter pulse power; \(\varepsilon\) is the threshold-signal power; \(\lambda\) is the wavelength. Using the experimental data of McKinley [3], Kaiser found that in the case of sporadic meteors \(s\simeq 2\). Brown, Bullough, Evans, and Kaiser [4] proposed using the duration distribution of stable echoes: according to Kaiser [5]

\[ P_\tau(\tau)\sim \tau^{-\frac{3s+1}{4}}; \tag{3} \]

according to Williams and Brown [6]

\[ P_\tau(\tau)\sim \tau^{-\frac{6s-1}{5}}. \tag{4} \]

It appears possible to determine the value of \(s\) from the previously obtained approximate expression for the integral law of the duration distribution of stable-type meteor echoes [7]:

\[ \frac{N}{N_\Sigma}=\left(\frac{\tau_{\min}}{\tau}\right)^{s-1}, \tag{5} \]

where \(N\) is the number of echoes with duration exceeding \(\tau\); \(N_{\Sigma}\) is the total number of echoes with duration \(\tau>\tau_{\min}\).

As was shown in [7], formula (5) is in satisfactory agreement with experiment.

The refined expression for the integral distribution has the form

\[ \frac{N}{N_{\Sigma}}=\left(\frac{\tau_{\min}}{\tau}\right)^{\frac{3}{4}(s-1)}, \tag{6} \]

which is in agreement with (3).

Experiment

To construct the distribution of meteor echoes according to echo duration, we used the results of observations carried out on July 28 and 29, 1957, with the aid of the range-measuring section of the radar “TPI-2,” built by the staff of the Department of Radio Engineering Equipment of the Tomsk Polytechnic Institute specifically for meteor investigations.

The apparatus data were as follows: wavelength \(\lambda=10\) m; pulse power \(P_u \simeq 100\) kW; pulse repetition frequency \(F_u=600\) pulses/sec; the apparatus operated in the mode of “coded” pulses (single pulses alternated with paired ones); a nondirectional antenna was used (a half-wave vibrator at a height \(h\simeq \frac{\lambda}{3}\) above ground level).

Fig. 1. Photocopy of a section of film. \(t\) — local time; \(R\) — slant range from the locator to the section of the meteor trail reflecting radio waves.

The screen of the range brightness indicator was photographed on a continuously moving film; the film speed was 17 mm/min. Fig. 1 presents a photocopy of a section of the film. The time axis \(t\) is directed opposite to the motion of the film (\(t\) is local time).

Along the slant-range axis \(R\), a range scale was recorded every minute. The interval between range marks corresponds to 10 km;

The fifty-kilometer marks had increased brightness; the “250 km” mark was the brightest (this facilitates processing of the film).

On the screen of the range indicator the interval \(R = 50\text{–}350\) km was viewed (in the photograph the interval \(R = 80\text{–}350\) km is shown). During the action of the probing pulse the receiver was blocked, as a result of which a wide dark band is visible in the photograph (at \(R = 250\) km).

Short-lived reflections from meteors are obtained in the form of a “colon,” while long-lived ones are in the form of two bands. In the case when the slant range from the locator to the meteor lies within \(50\ \text{km} < R < 100\ \text{km}\) and \(300\ \text{km} < R < 350\ \text{km}\), in addition to the paired mark a single mark is visible, the distance between them corresponding to 250 km.

The range is read from the first point of the paired mark. In the case \(100\ \text{km} < R < 300\ \text{km}\), only a double mark is obtained on the film. When the distance from the locator to the meteor exceeds 350 km, a single mark is recorded on the film; in this case a weak meteor is difficult to distinguish from interference. In the unlikely case of the appearance of a meteor at \(R < 50\) km, a single mark could appear in the 250–300 km zone.

In processing the films, only double marks were taken into account.

Fig. 2. Distribution of meteor radio echoes by duration for \(\tau \ge 0.5\) sec. \(N\) is the number of reflections with duration exceeding \(\tau\). The approximating line is solid. The experimental results are marked by points.

In Fig. 1, 6 short-lived reflections are recorded, two reflections with durations of several seconds (at \(R\) about 100 km), and one reflection with \(\tau > 1\) min.

Over 5 hr 38 min of photographic recording, 1356 reflections were recorded (table).

Figure 2 presents the distribution of reflections by duration on a logarithmic scale for \(\tau > 0.5\) sec (the experimental results are marked by points).

Table

Distribution of meteor radio echoes by range
\(N\) — number of recorded reflections with durations \(\ge \tau\);
\(\tau\) — duration in seconds.

Determination of the Value \(s\)

Approximating the experimental dependence by the function

\[ N \sim \frac{1}{\tau^n}, \tag{7} \]

we obtain

\[ n = \frac{\lg N_2 - \lg N_1}{\lg \tau_1 - \lg \tau_2}. \tag{8} \]

Comparing (5) and (7), we find \(s = 1 + n\),

or, from (6) and (7),

\[ s = 1 + \frac{4}{3} n. \tag{9} \]

Formulas (5) and (6) are valid only for the case of a linear electron density \(\alpha > 2.4 \cdot 10^{12}\) el/cm. Such a value of \(\alpha\) will correspond to echoes with durations exceeding a certain minimum value that depends on the magnitude of the diffusion coefficient \(D\).

For an average meteor velocity \((\overline{v} \simeq 45\ \text{km/sec})\), stable echoes with \(\alpha > 5 \cdot 10^{13}\) el/cm will have a duration \(> 0.5\) sec.

It is therefore necessary to exclude from consideration echoes with \(\tau < 0.5\) sec.

Approximating the dependence \(\lg N(\lg \tau)\) by a straight line, we obtain, for \(\tau < 0.5\) sec, the value \(n \simeq 0.51\), and consequently \(s \simeq 1.51 \div 1.68\).

Remark

On July 28 and 29, 1957, both sporadic meteors and meteors of streams—the \(\delta\)-Aquarids, Perseids, and others—could have been observed. Therefore the obtained value of \(s\) characterizes the distribution of the aggregate of meteoroid bodies (both sporadic and belonging to streams).

The value found above, \(s \simeq 1.51 \div 1.68\), differs substantially both from the value \(s \simeq 2\) for the sporadic background [2, 5] and from \(s \simeq 2.2\) for the \(\delta\)-Aquarids [1].

As a result, it may be assumed either that the majority of meteors recorded on July 28 and 29, 1957, belong neither to the \(\delta\)-Aquarid stream nor to the sporadic background, or that the observed sporadic background has a distribution different from that found earlier [2, 5].

LITERATURE

1. Levin B. Yu. Physical Theory of Meteors and Meteoritic Matter in the Solar System, Publishing House of the Academy of Sciences of the USSR, 1956.
2. T. R. Kaiser, M. N., 114, 39, 1954.
3. D. W. R. McKinley, Canad. Journ. Phys., 29, 403, 1951.
4. I. C. Browne, K. Bullough, S. Evans, T. R. Kaiser, Proc. Phys. Soc., B 69, 83, 1956.
5. T. R. Kaiser, Advanc. Phys., 2, 495, 1953.
6. K. B. Billam, I. C. Browne, Proc. Phys. Soc., B 69, 98, 1956.
7. Filko E. M., Astronomicheskii Zhurnal, 34, 247, 1957.