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Astron. Astrophys. 357, 777-781 (2000)

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4. Mass distributions and flux

The hourly echo rates obtained as described at the beginning of the previous section were used for the mass-distribution analysis. To eliminate fluctuations of fainter echoes the echo duration [FORMULA] s corresponding to a radio magnitude, [FORMULA], of +1.3 calculated from Eq. (5) (cf. Simek 1987)


was chosen as the lower limit for the mass-distribution analysis. The mass-distribution index, s, for overdense meteor echoes was inferred from the conventional formula (cf. Kaiser 1955)


where [FORMULA] is the cumulative number of echoes having durations of at least T seconds. From the theory it follows that Eq. (6) is valid when ambipolar diffusion is the only process acting inside the ionized meteor path. Jones et al. (1990) recognized two principal regions corresponding to different dissipative processes operating in the ionized trail. While diffusion alone is dominant for echoes of shorter duration appearing at greater heights in the atmosphere, longer echo durations from meteors at lower heights are controlled mainly by different chemical and physical processes resulting different from the simple formula (6). Therefore, the mass-distribution index, s, is according to this model represented well by the slope of the initial linear portion of the [FORMULA] vs [FORMULA] curve.

When the observations lasted only a fraction of an hour, [FORMULA] applied for calculation of s were recalculated for 60 minutes. Particular hours during which the observing time was less than 30 minutes were not used for the analysis.

The diurnal variation of the mass-distribution index, s, was described by Simek (1993), Simek & Pecina (1999), Pecina & Simek (1999). The resulting diurnal patterns of s-parameter for shower echoes (i. e. the Perseids and the Geminids) and those for relevant sporadic background are characterized by similar patterns of relevant pairs. It is apparent that in all cases, s for the background in all particular hours are related to corresponding mean of the full cycle values of s by the same multiplying coefficient as that for the shower meteors. It indicates that such diurnal variation is neither due to the stream character nor the nature of sporadic radiants. This effect could be explained by diurnal variations of chemical and physical reactions in the atmosphere controlled by the solar radiation (cf. Jones et al. 1990). The mean background mass index s for the Perseids and the Geminids have the same value of 2.17. We know the mass-distribution of the Leonid background for a fraction of the diurnal cycle between 23h and 14h only giving [FORMULA]. Therefore, the above mean value [FORMULA] was ad hoc applied for the Leonids period, too. To obtain real s for the shower corrected for the diurnal variation, values of s calculated from observed shower data were multiplied by the ratio of 2.17/background value of s for each particular hour of observations. Correction factors, [FORMULA], Leonid zenith radiant angle, [FORMULA], at the middle of the interval, and multiplying factors, [FORMULA], discussed in the Sect. 4, are listed in Table 2.

The resulting patterns of the Leonid mass distribution index, s, vs the solar longitude, [FORMULA] (J2000.0) in 1965 and 1966 are presented in Figs. 4-5.

[FIGURE] Fig. 4. The mass distribution index, s, for 1965 drawn as triangle, as a function of solar longitude (J2000.0). Horizontal lines designate the error bars

[FIGURE] Fig. 5. The same as in Fig. 4 but for 1966

4.1. 1965

Mass-distribution indices indicate particular difference in both analyzed years. Leonids 1965 are characterized by generally lower mass-coefficient indicating higher content of large particles shown already by McIntosh (1973). An average value on November 16 in the period 02h-07h (i.e. six hours before maximum hourly rate) is [FORMULA], and [FORMULA] one day later. Comparable results were derived from radar observations at Springhill published by McIntosh (1966, Fig. 11) which yields [FORMULA] and [FORMULA] at the same days. The maximum observed hourly rate of 111.7 for echo duration [FORMULA] s appeared at Ondejov on Nov. 17 at 7h LT with [FORMULA].

4.2. 1966

Observation in 1966 resulted in a higher average s-values of 1.63 on November 17 (calculated similarly as in 1965), and of 1.57 on November 18 when the missed 11h value was approximated by [FORMULA]. A maximum hourly rate of 38.6 at 12h is associated with [FORMULA]. Mass-index derived from McIntosh & Millman (1970, Fig. 8) for Leonid echo counts for November 17, 1966 gives [FORMULA] which perfectly fits with our result. Such values of s correspond with "slightly higher content of intermediate sized particles" (McIntosh 1973).

The differences of s indicate higher contribution of longer echoes in 1965 while in 1966 the activity of shorter echoes is dominant. The cluster of Leonid meteoroids encountering the Earth's atmosphere in 1965-66 is characterized by non-uniform structure along the parent comet orbit.

4.3. 1967

Because of low recorded hourly echo counts mean mass indices for November 15/16 [FORMULA], November 16/17 [FORMULA], and November 17/18 [FORMULA] are determined. These results indicate s-values on both marginal days close to [FORMULA] for sporadic background. Lower s on November 16/17 supports above conclusion that the culmination of the shower activity could appear after [FORMULA] when the radiant was below the horizon.

4.4. The flux

The flux was computed according to Pecina (1982). Its determination is based on the comparison of observed hourly rates with the theoretical rates as expressed by the formula


where [FORMULA] represents theoretical rates corresponding to those observed during the time interval [FORMULA] within the duration interval [FORMULA], s is the mass distribution index, [FORMULA] is the limiting mass to which the flux, [FORMULA] is related, and the function [FORMULA], expressed by the integral, bears the information of mutual orientation of the shower radiant with respect to the antenna pattern. The time dependence of [FORMULA] is due to the dependence of integration limits within the echo plane on this configuration. The function [FORMULA] takes also into account the fact that the region within the echo plane contributing to N differs for different duration classes. The flux is nonlinear function of s. The higher the value of s the higher value of flux. We were interested in the hourly course of the Leonid's flux so we have computed these quantities. Since hourly values of s are determined on one hour base only for 1965 and 1966 the hourly flux was computed for these years. The mass distribution indices from Figs. 4 and 5 were employed. Other parameters we needed for computation were the ablation parameter, [FORMULA], and shape-density coefficient, [FORMULA]. The ablation parameter was set to [FORMULA] (Spurný et al. 2000) while [FORMULA] (in SI units). The s-values corrected for diurnal variation were used for flux computation. All values of flux are related to [FORMULA] kg. This value is close to the lower duration value of the duration interval considered. The flux is drawn in Figs. 6 and 7. The higher values of flux in 1966 are mainly due to higher values of s as compared with corresponding values in 1965 (compare Fig. 5 with Fig. 4), as it was mentioned above. The standard deviations of the flux values depend mainly on standard deviations of mass distribution index, s. The resulting relative standard deviations of flux grouped around [FORMULA] of their values.

[FIGURE] Fig. 6. The 1965 Leonid flux as a function of solar longitude, [FORMULA] (J2000.0). It is expressed in units of [FORMULA]

[FIGURE] Fig. 7. The same as in Fig. 6 but for 1966

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© European Southern Observatory (ESO) 2000

Online publication: June 5, 2000