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Radar Meteors Range Distribution Model Contrib. Astron. Obs. Skalnat´ePleso 37, 147 – 160, (2007) Radar meteors range distribution model III. Ablation, shape-density and self-similarity parameters D. Pecinov´aand P. Pecina Astronomical Institute of the Czech Academy of Sciences 251 65 Ondˇrejov, The Czech Republic, (E-mail: [email protected]) Received: January 23, 2007; Accepted: July 3, 2007 Abstract. The theoretical radar meteors Range Distribution of the overdense echoes developed by Pecinov´aand Pecina (2007 a) is applied here to observed range distributions of meteors belonging to the Quadrantid, Perseid, Leonid, Geminid, γ Draconid (Giacobinid), ζ Perseid and β Taurid streams to study the variability of the shape-density, ablation, and self-similarity parameters of meteoroids of these streams. We have found in accordance with results of photographical observations that ablation parameter σ is higher for members of showers of clearly cometary origin, and is lower for Geminid and daytime shower meteoroids. Levin’s self-similarity parameter µ was found to be much greater than the classical value 2/3 for all investigated streams with the exception of Geminids, for which the value found is almost classical, i. e. 0.66 ± 0.01. The method of getting µ by means of fitting the light curve of faint TV meteors is also suggested. Key words: physics of meteors – radar meteors – range distribution – ablation, shape density and self-similarity parameters 1. Introduction At the very beginning, our aim was to develop a model allowing for the com- putation of fluxes and mass distribution indices of meteor showers. To achieve this goal, we developed the radar meteors range distribution model (RaDiM) (Pecinov´aand Pecina, 2007 a) which we will refer to as Paper I. The results of the application of RaDiM concerning the flux Θm0 and mass distribution indices s on some showers have been published by Pecinov´aand Pecina (2007 b) (here- inafter as Paper II). It turned out, however, that the whole problem is much more complicated. The computation of two quantities describing the inner struc- ture of meteor showers (Θm0 , s) proved to be intimately connected with several physical parameters of meteoroids. These are the shape-density parameter K, the ablation coefficient σ, and Levin’s self-similarity parameter µ. This paper is a follow-up to Papers I and II. In this work, we present results on the above listed quantities and discuss the results we have arrived at. The next paper in this series will deal with the ionization coefficient β. 148 D. Pecinov´aand P. Pecina 14 20 18 12 16 10 14 12 8 10 6 8 SHOWER RATE SHOWER RATE SHOWER 4 6 4 2 2 0 0 100 120 140 160 180 200 220 240 260 280 300 100 120 140 160 180 200 220 240 260 280 300 RANGE [KM] RANGE [KM] Figure 1. Left: the range distribution of meteors belonging to the ζ Perseid meteor shower observed between 3 and 7 UT on 8th June 2003. The vertical axis shows shower rates in 5-km-wide range intervals, which are represented by their mid-points on the horizontal axis. The observed range distribution is represented by squares which are connected by the full line. Both theoretical range distributions were computed using the fundamental formula (7) from Paper I. The former one, depicted by the horizontal lines and the dashed line, results from computations under the assumption µ = 2/3. The latter one, represented by the stars and the dotted line, was obtained when the parameter µ was allowed to vary in the RaDiM. The result gives µ = 1.92 ± 0.04 (see Table 6). Right: the same but for the Geminid meteor shower observed between 0 and 4 UT on 14th December 1991. The result gives µ = 0.66 ± 0.08 (see Table 4). 14 6 12 5 10 4 8 3 SHOWER RATE SHOWER 6 RATE SHOWER 2 4 1 2 0 150 170 190 210 230 250 270 290 100 120 140 160 180 200 220 240 260 280 300 RANGE [KM] RANGE [KM] Figure 2. Left: the same as in Figure 1 but for the Giacobinid meteor shower observed between 12 and 14 UT on 8th October 1998. The result gives µ = 1.94 ± 0.11 (see Table 5). Right: the same but for the Perseid meteor shower observed between 10 and 12 UT on 12th August 1980. The result gives µ = 1.01 ± 0.22 (see Table 2). Radar meteors range distribution model; III. Ablation, shape-density, self-similarity parameters149 10 12 9 10 8 7 8 6 5 6 4 SHOWER RATE SHOWER RATE SHOWER 4 3 2 2 1 0 0 100 120 140 160 180 200 220 240 260 100 120 140 160 180 200 220 240 260 280 300 RANGE [KM] RANGE [KM] Figure 3. Left: the same as in Figure 1 but for the Leonid meteor shower observed between 0 and 2 UT on 17th November 1998. The result gives µ = 1.80 ± 0.19 (see Table 3). Right: the same but for the Quadrantid meteor shower observed between 12 and 14 UT on 3th January 1987. The result gives µ = 1.80 ± 0.19 (see Table 1). S/S∞ 1 0.8 0.6 1 g 0.4 0.01 g 0.2 70 80 90 100 110 120 h [km] Figure 4. The dependence of the ratio S/S∞ on the value of preatmospheric mass m∞ is depicted in accord with (2). Both curves that are marked by the relevant value of mass, m∞, (in grams) are computed for the case of Geminids radiant culmination and −3 2 the following values: µ = 2/3, H = 5.409 km, %o = 56.803 kg m and K· σ = 0.01 s km−2. 150 D. Pecinov´aand P. Pecina 18 1.5 16 14 2/3 12 10 0.1 8 6 4 THEORETICAL SHOWER RATE SHOWER THEORETICAL 2 0 100 120 140 160 180 200 220 240 260 280 300 RANGE [KM] Figure 5. The theoretical range distribution as a function of Levin’s parameter µ. The relevant curves are marked with the chosen value of µ. The computations were performed for the Geminids between 1 and 2 UT, on the 13th of December 2000. The constants and quantities used for the theoretical calculations were the following: −5 −1 2 −2 mass mo = 10 kg, v∞ = 36 km s , K · σ = 0.01 s km , s = 1.5, β = 0.100, 2 −3 Dr = 4.2 m s (height of 93 km), H = 5.409 km and %o = 56.803 kg m . S/S∞ 1 0.8 2/3 0.6 0.4 1.5 0.2 90 100 110 120 h [km] Figure 6. The dependence of the ratio S/S∞ of a meteoroid on the height h, for two values of µ, computed according to (2). The constants and quantities used for the theoretical calculations were the same as in Fig. 5. Radar meteors range distribution model; III. Ablation, shape-density, self-similarity parameters151 α [m−1] e 0.1 1.4·1014 1.2·1014 · 14 1 10 2/3 8·1013 6·1013 1.5 4·1013 2·1013 70 80 90 100 h [km] Figure 7. The ionization curve changes as Levin’s parameter µ varies while the other parameters are kept constant. The relevant curves are marked by the corresponding value of µ, the value 2/3 being valid for the classical theory. The computations were performed for the same constants and quantities as in Figure 5. 200 0.001 180 160 140 120 100 80 60 THEORETICAL SHOWER RATE SHOWER THEORETICAL 40 0.01 20 0 100 120 140 160 180 200 220 240 260 280 300 RANGE [KM] Figure 8. The theoretical range distribution as a function of the product K· σ. Both curves that are marked by the corresponding value of K · σ were computed for the radiant of Geminids between 1 and 2 UT, on the 13th December 2000. The constants −5 and quantities used for the theoretical calculations were the following: mass mo = 10 −1 2 kg, v∞ = 36 km s , s = 1.5, µ = 2/3, β = 0.100, Dr = 4.2 m s (height of 93 km), −3 H = 5.409 km and %o = 56.803 kg m . 152 D. Pecinov´aand P. Pecina −1 αe[m ] 0.01 0.001 1·1014 8·1013 6·1013 4·1013 2·1013 70 80 90 100 h [km] Figure 9. The ionization curve changes as the product of K· σ varies while the other parameters are kept constant. The relevant curves are marked by the corresponding value of K· σ. The constants and quantities used for the theoretical calculations were the same as in Fig. 8. 2. Self-similarity parameter µ The physical theory employed so far usually considers µ = 2/3 as a standard. When we tried to develop a simple model of the range distribution with this assumption, it turned out that it did not describe the observed reality very well (as already mentioned in Paper I). To improve our model, we introduced µ in accordance with relation (11) from Paper I. Allowing µ ≥ 0 in our computations, we achieved a substantial improvement between the observed range distributions and the theory. This fact can easily be seen in Figs. 1 - 3. This finding, and the fact that the observed and theoretical range distributions computed under Levin’s assumption correspond to each other (better correspondence for smaller distances) justifies this assumption. We now focus on Levin’s assumption in a greater detail.
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