THE INCIDENCE OF METEOR PARTICLES UPON THE EARTH By A. A. WEISS· [Manuscript received May 10, 1957] Summary R,adio echo rates for both shower and sporadic meteors, measured at Adelaide with the 27 Mcls C.W. equipment, are applied to the calculation of the incident flux of meteors above limiting brightnesses in the range M R < + 7·5. On the hypothesis of a strongly velocity.dependent ionizing probability, reached after a critical evaluation of the observational material, the meteor flux above prescribed limiting meteor particle masses, and the space densities of meteor particles, are also calculated. These fluxes and densities agree reasonably well with independent evaluations from visual meteor rates. The amount of meteoric matter falling on the whole Earth per day within particle mass limits 10-1 to 10-& g, for sporadic meteors and some showers, is also estimated. I. INTRODUCTION This paper is the third of a series dealing with meteor observations at Adelaide with the 27 Mc/s C.W. equipment. Paper I (Weiss 1957a) discusses the sporadic background. Paper II (Weiss 1957b) is concerned with shower meteors and presents an overall picture of the meteor activity. The present paper, based on the data of the preceding two, deals with the influx of meteor particles over the whole surface of the Earth, and with their density in space. Meteors are counted by radio equipments in terms of the line density or the equivalent radio brightness-an equipment will detect in a given direction all meteors which satisfy the geometrical conditions for specular reflection and whose line densities exceed the threshold appropriate to the equipment. Similarly, visual observers record all meteors above the visual threshold brightness which fall within a prescribed field of view. These brightness counts are not necessarily simply related to the total influx of meteors above a prescribed radio brightness (because of the influence of aerial aperture and polar diagram, and trail aspect) or a prescribed visual brightness (visual aperture and subjective factors), nor to the total influx of meteors above a prescribed limiting mass. Several estimates have been made (Kaiser -1955, p. 119; Levin 1955; Hawkins 1956b; Davies 1957) of the number of meteor particles, above a given limiting brightness,-radio or visual, falling on the whole Earth. Meteor brightness is directly measurable, and the above estimates of the numbers of incident particles and the flux found from the Adelaide counts are reasonably concordant. The extension of these results to the determination of the influx of meteors above a prescribed limiting mass, or of the density of meteor particles iIi space, can * Division of Radiophysics, C.S.I.R.O., at Department of Physics, University of Adelaide. 398 A. A. WEISS only be made if the ionizing probability and the luminous efficiency, i.e. the efficiencies of production of free electrons and radiation, are known. This further analysis has been made for the visual counts by Levin, who concluded that the maximum particle densities in shower orbits are considerably lower than the density of sporadic meteors. Although the question of the dependence of ionizing probability upon meteor velocity is not fully resolved, there is a growing body of evidence which suggests that this parameter is strongly dependent on meteor velocity. Interpretation of the Adelaide r:adio counts on this basis leads to the conclusion already reached by Levin from the visual data: above the liJniting mass corresponding to the visual threshold brightness for a meteor with a velocity of 60 km sec--:!, the sporadic meteor density is higher than th:tt in the most dense portions of all the major day-time and iught-time meteor streams. This agreement is, in itself, rather convincing evidence for the correctness of the forms of velocity dependence, weak for luminous efficiency and strong for ionizing probability, which emerge from the discussion of the relevant observa­ tional material in Section V. II. THE BRIGHTNESS AND MASS DISTRIBUTIONS The maximum value of the line density of electrons in the meteor trail is IXmax.~(4/9!J.H)m~(v) cos X, .............. (1) where X is the zenith angle of the-radiant, !J. the atomic weight of the (average) meteor atom, H the atmospheric scale height, and ~(v) the ionizing probability, i.e. the probability that a single evaporated meteor atom will produce a free electron. The analogous parameteI' in visual detection is the luminous intensity 1. According to Levin (1955) the brightness estimated by a visual observer may characterize some average luminous intensity loc(Imax.)z, !<x<1. However, Browne et al. (1956) find x,...."l and it is sufficient to put x=1. Then the maximum value of the luminous intensity is (2) where T(V) is the luminous efficiency, i.e. the fraction of the total energy dissipated which is emitted as visible radiation. The velocity-dependence of the parameters ~ and 't" is examined in Section V. In the meantime, attention may be drawn to the factor v3 which already appears in (2). The visual and radio brightnesses are now, as usual, taken to be M v=const. -2·5 loglOImax_ M R = const. -2 ·5 loglolXmax. The frequency distribution of both radio and visual magnitudes will be assumed to have the form vMocaM , ••••••••••••••••••••.•.• (3) INCIDENCE OF METEOR PARTICLES UPON THE EARTH 399 where v~M is the incident flux of meteors with magnitudes between M and M +dM. The corresponding flux of meteors with masses between m and m +dm is then assumed to be vmdm ocm -'dm, .................... (4) where8=1+2·510g10a=1+x, if X=2·510g10a. Detailed investigations of the structures of several showers by Browne et al. indicate that the distributions (3) and (4) do not hold exactly over extended ranges of brightness and mass. They do, however, form a useful first approxi­ mation, and in the present paper mass distributions are, with one exception, discussed with 8=constant over the range of interest. Values of 8 adopted for showers are listed in Table 1. For sporadic meteors 8=2 ·0. III. SHOWER METEOR FLUX ABOVE A PRESCRIBED RADIO BRIGHTNESS From equations (1) and (4), assuming ~ to be independent of the mass m, the incident flux of meteors, across unit area of a plane. normal to the meteor paths, with zenithal line densities greater than ocz=(Xa/cos X, is 0(ocz }={O/(8-1)}oc!-B. .••............ (5) The zenithal line density is the maximum number of electrons per unit length which the meteor would produce if it travelled vertically downwards. (Xa is the minimum detectable line density in the direction 6, which is the direction of the reflection point of the meteor trail in the echo plane, following the geometry and notation of Kaiser (1955, p.1l9). From (5) it follows that 0(oco/cos X)=0(oco/cos X)(OCo/(Xa)B-l, where 0C0 is the minimum detectable line density on the axis of the aerial beam, which for the Adelaide equipment is directed to the zenith. Kaiser (loc. cit.) has given expressions for the total radio echo rate in terms of the equipment geometry and parameters, and the incident flux. Shower fluxes have been computed using these expressions and the radio counts at zenith angles X=70° given in paper II. At this zenith angle collection is confined to the major lobe; the limiting sensitivity contours are given in paper I. A horizontal collecting surface for meteors, at a height of 90 km, has been assumed; this introduces an error of less than 1 per cent. The further approximation is mada that only short, decay type echoes are observed (oc<2 X 1012 cm-1); this is true over most of the major lobe. With these approximations, the echo rate integrated over the whole aperture of the major lobe is N x = 700 =0(3 ·5 X 1011) .15001(8), .......••••...•• (6a) 1(8)=:=(8-1·14)-1 I (OCo/(Xa),-l cos-26 d6. (6b) major lobe The integral (6b) is illustrated in Figure 1. For a given flux 0 the echo rate is evidently quite sensitive to the mass distribution within the stream. E ~ o o TABLE 1 SHOWER METEOR FLUXES AND STREAM DENSITIES --- Hourly Rates Fluxes above Fluxes above Observed Limiting Brightness Limiting Mass Stream Densities Shower Velocity Radio Visual (lon-2 sec-I) (km- 2 sec-I) (lon-3) v 8 x* Radio (lon sec-I) ------ Visual* 8(1012) 8(4·3) V(1012) I v(4'3) D(1012) D(4'3) -. J.B.R. A.W. X lOB X lOB X lOB X lOB X lOB X lOB Perseids · . 60 1·6 1·0 47 55 58 310 58 310 1·0 5·1 ~ Geminids · . 36 1·7 1·3 70 24 60 110 330 470 2500 13 68 ~ Quadrantids .. 40 1·8 1-0 92 40 78 220 290 760 7· 19 Arietids 38 2-5 - 61 24 100 1600 41 · . ~rn rn ~.Perseids · . 29 2·5 - 40 16 67 5200 180 2·0 81 1500 51 8.Aquarids · . 40 2·5 1·4 23 140 1600 41 2·0 150 780 20 1·75 150 500 13 7)-Aquarids · . 64 2·0 0·9 11 36 72 200 56 170 0·9 2·6 Orionids · . 66 2·5 1·5 14 10 86 56 49 37 0·7 0·6 2·0 95 1·0 I 65 - * After Levin. INCIDENCE OF METEOR PARTICLES UPON THE EARTH 401 Using (6) and the average echo rates at maximum. activity given in paper IIt the following fluxes are obtained: Geminids 0( IX) =3·6 X 102 IX-O. 7 km-2 sec-I June day-time showers =2·4 X 10I21X-I.