The radiant distribution of AMOR radar meteors

Transcription

1 Mon. Not. R. Astron. Soc. 359, (2005) doi: /j x The radiant distribution of AMOR radar meteors D. P. Galligan 1 and W. J. Baggaley 2 1 Defence Technology Agency, Private Bag 32901, Auckland, New Zealand 2 Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand Accepted 2005 February 11. Received 2005 January 27; in original form 2004 August 5 ABSTRACT A large data set provided by the highly sensitive Advanced Meteor Orbit Radar (AMOR) facility is used to investigate the structure of the sporadic meteor complex. The helion, antihelion and apex apparent sources are clearly found. Observational bias is then removed to reveal the true source distributions as observed on Earth. A long-standing problem in meteor science has been the difference in observed meteor flux between the helion and antihelion source directions. Consideration of the effects of atmospheric interference and Faraday rotation is found to lead to a closer balance between these. The orbital distributions present within the different regions are also discussed. The apex region is found to have a strong retrograde component and a weaker prograde component that exists at high southerly latitudes and that contains orbits with particularly high inclinations. The retrograde component reduces substantially after inclusion of observational bias corrections. Care should be taken in comparing the results presented here with those from other radar systems: AMOR is sensitive to dust as small in diameter as 40 µm, while the limiting sensitivity of most contemporary systems is an order of magnitude larger. Keywords: meteors, meteoroids. 1 INTRODUCTION Many studies have been conducted over the past century into the large-scale clustering in the radiant (apparent upstream flow direction) position of meteors as observed on Earth. The radiant distribution describes the apparent geocentric inflow of meteoroids, and the various features of this arise from the true orbital distribution of the solar system dust cloud, the Earth collision probability and the particular radar response function. As such it may be useful for predictions (at any latitude) of, for example, radio forward scatter conditions. The so-called sporadic source regions within the radiant distribution comprise useful groupings of orbital types. For many years the principal groupings were thought to be concentrated about the ecliptic in the directions of the apex of the Earth s way, the antihelion and the helion (Hawkins 1956; Hawkins & Prentice 1957; Weiss & Smith 1960). Later, other off-ecliptic sources were added to this list. For example, the Harvard Radio Meteor Project (HRMP) found another apex source located about +60 ecliptic latitude and surveys at Adelaide found a complementary source at 60 ; these were named the northern and southern toroidal sources, respectively. Jones & Brown (1993) present an excellent summary of this work and provide inter-comparisons of the radiant distributions in 10 photographic and radar meteor data sets. d.galligan@paradise.net.nz (DPG); jack.baggaley@canterbury. ac.nz (WJB) Recently, the large data set amassed by the AMOR facility has been studied to determine and remove observational biases in order to obtain the true meteoroid orbital distribution at 1 au of detectable meteoroids (Galligan & Baggaley 2004). A useful outcome of this work is the opportunity to examine the apparent (geocentric) non-stream source regions within this data set, both as directly observed and also as corrected for in-atmosphere bias effects. Of particular interest here is the strength of the helion source relative to the antihelion. Studies have generally found that the antihelion is stronger than the helion source, but both are made up of meteoroids from the same orbital types (e.g. Keay 1963; Stǒhl 1968). (The only difference between the orbits detected in the antihelion and helion regions is whether the meteor impacted the Earth pre- or post-perihelion in its orbit.) It has been suggested that this difference may be attributable to atmospheric effects that differ between the day and night, when the helion and antihelion sources are visible, respectively (e.g. Jones & Brown 1993). The effects of sporadic-e and Faraday rotation signal attenuation are discussed in Ceplecha et al. (1998), and are corrected to the degree 1 possible in the AMOR 1 The effect of sporadic-e is partially represented in the correction process by including a record of the times during which AMOR was effectively not operational (as evidenced by a negligible meteor detection rate). Such periods resulted either from genuine physical system down-time or from ionospheric conditions that prevented unique meteor detections from being identified such as during strong E-region scatter. C 2005 RAS

2 552 D. P. Galligan and W. J. Baggaley data set debiasing of Galligan & Baggaley (2004). We examine here whether these effects are sufficient to explain the source strength difference. We then examine each of the source regions to determine the different orbital types that make up these regions. 2 THE AMOR DATA SET The AMOR facility, located near Christchurch, New Zealand, has been operational since Over the intervening time approximately one million high-quality meteoroid orbits have been added to the data set. Over the period 1995 May to 1999 October, AMOR was operated with a high-level of continuity. During that time, careful attention was paid to the long-term stability of the system orbits were reduced over this 5-yr period. The technical aspects of the AMOR system have been discussed in depth elsewhere (Baggaley et al. 1994; Baggaley 1995; Baggaley & Bennett 1996; Baggaley et al. 2001; Galligan & Baggaley 2004). Briefly, the system as operated prior to 2000 consisted of a central station with a dual-interferometer, transmitter and receiver systems (the system transmitted radiation due-north and South using a broad-side array, the beam shape was similar to afan with narrow azimuthal extent ( 2 ) and broad extent in elevation); and two remote stations, each with a receiving antenna, separated from the central station and each other by 10 km. The remote stations communicated via radio telemetry with the central station. Each meteor s velocity vector was determined based upon the time-of-flight obtained from echo signal profile timing at each site, the elevation angle from the dual-interferometer, range from echo timing, and knowledge of the azimuthal angle owing to the narrow azimuthal extent of the transmitted beam. Using this measurement, and knowledge of the time of detection, the heliocentric orbit of the meteoroid was determined. AMOR is more sensitive (limiting grain-size 40 µm) by an order of magnitude in meteor grain size than are most other meteor radar systems. The reader is cautioned that this size-difference requires a cautious approach to any comparisons with other data sets. This is because the dominant processes that evolve meteoroid orbits vary with meteoroid size and therefore the dust population that can be observed with AMOR could differ significantly from that which could be observed with another system. 2.1 Data set preparation Several steps are taken to filter the data set used in this study. Meteoroids having non-elliptic eccentricities are removed as we are concerned here only with gravitationally bound Solar system bodies. Overdense trains are removed because the radar response function used does not allow for these. Major shower meteors (which also form a minor constituent of the data set) are removed so that the data set consists of non-stream dust-cloud grains; the meteoroid stream definitions of Galligan & Baggaley (2002) are used to facilitate this filtration. After these processes are completed, out of the original meteoroid orbits remain. 3 DEBIASING THE DATA SET We begin by summarizing an all-collision-direction correction method used previously in Galligan & Baggaley (2004). We then extend this method to allow discrimination of whether the impacting meteoroid was pre- or post-perihelion in its orbit at impact. The reader should note that it is this extended method which is used for the correction of the AMOR data set presented in this paper, the method summarized from Galligan & Baggaley (2004) is only provided as a foundation to this extension. 3.1 All collision direction correction method Galligan & Baggaley (2004) describe the various bias effects found to influence the radar meteoroid orbit data set provided by AMOR. Three output sets are produced in that study: a directly observed set, 2 an atmospheric set corrected for all known in-atmosphere effects and a space set which is additionally corrected for meteoroid Earth collision. Here, we are interested in the first two of these outputs. The response of the radar to meteors with different speeds and radiant positions in the topocentric frame is termed the radar response function (Elford 1964). Taylor & Elford (1998), in their revision of the corrections applied to the HRMP data set, applied an additional correction to account for the diurnal response of the radar as geocentric radiants were moved through the topocentric frame over a 24-h period. Galligan & Baggaley (2004) extended this correction by looking at the particular topocentric radiant positions a given orbit, defined by a particular perihelion distance (q), eccentricity (e) and inclination (i) combination, could take at sub-hourly intervals throughout the 5 yr of AMOR observation. The outcome of this study was a time-integrated response function that gave the total response for a given orbit. It should be noted that this function, which is discussed below, does not discriminate whether a meteor was preor post-perihelion in its orbit at impact as that did not concern the study of Galligan & Baggaley (2004). Section 3.2 follows with a discussion of how such a discrimination is achieved and applied in the current study. For each orbital element set, (q, e, i), there are four possible orientations for intersection with the Earth at any given time; these arise owing to the possibility of ascending or descending node collision and the symmetry of the orbit about the perihelion position. Galligan & Baggaley (2004) define the total response function, n t, as tf n t (q, e, i) = W (t) [n s (Asc., ω pre ) + n s (Asc., ω post ) + t i n s (Desc., ω pre ) + n s (Desc., ω post )] dt, (1) where n s, fully defined in Galligan & Baggaley (2004), is the topocentric static radar response function at time, t, for radiants and speeds corresponding to the particular (q, e, i) triplet and to the argument of perihelion (ω) and longitude of the ascending node (ω). Corrections are included in n s for echo amplitude attenuation effects related to initial radius, finite velocity, pulse repetition frequency and Faraday rotation. The appropriate weightings for each of these are based on those suggested in Ceplecha et al. (1998), who determined them from a survey of the best data currently available in the literature on the subject. More details on their specific application here are to be found in Galligan & Baggaley (2004). In equation (1), ω pre and ω post are the arguments of perihelia corresponding to pre- and post-perihelion detection, respectively. Asc. and Desc. correspond to detections at the ascending and descending nodes, respectively. is equal to the longitude of the sun (λ ) for descending node collisions and differs by 180 from λ for those at the ascending node. The argument of perihelion 2 The directly observed set does contain some inherent correction as part of the reduction process. Corrections are applied for zenithal attraction and atmospheric deceleration.

3 Radiant distribution of AMOR meteors 553 Table 1. Argument of perihelion range appropriate in equation (2) for particular orbital orientations at impact. Ascending node Descending node Pre-perihelion arc 0 ω ω 360 Post-perihelion arc 180 ω ω 180 is defined by a required relationship between q, e and ω for Earth collision: cos ω = q [r E(1 + e)] 1, (2) ±e where ± is + for ascending node collision and for descending node collision; r E is the Earth s orbital radius at a given time. The presence of cos ω allows two solutions for ω for each nodal collision: ω 1 and (360 ω 1 ). Table 1 shows the appropriate ω range to use for a given circumstance. Galligan & Baggaley (2004) proceed to correct the AMOR data set for the in-atmosphere bias effects by weighting each orbit by n t (q, e, i) 1.(Asmall number of orbits that have very marginal probability of detection are removed at this stage, i.e. <0.3 per cent of total number.) While this approach allows for different day- and night-time atmospheric effects, by including the Faraday rotation attenuation and radar system operational status at each time step, it necessarily produces a combined probability of detection for each orbit without allowing differences between the helion and antihelion sources to emerge. 3.2 Source direction separated correction method applied here Whether a meteoroid appears from the helion or antihelion source direction is decided by which of the symmetric positions about perihelion in its orbit it impacts the Earth: impacts from meteoroids on the pre-perihelion arc have radiants with 90 < (λ λ ) < 270 and those on the post-perihelion arc have (λ λ ) > 270 or (λ λ ) < 90. (The geocentric ecliptic reference frame is used, with longitude λ being referenced to the solar longitude λ, toavoid longitudinal motion of the source regions throughout the year.) An adaptation of the method shown in Section 3.1 is adopted here to allow any differences between helion and antihelion meteor detection conditions to emerge. The method is to determine the orbital arc (pre- or post-perihelion) each meteoroid was on at impact and then to only use the sum of the two corresponding nodal solutions in equation (1) to derive the associated n t value. Equations (3) and (4) show the correction equations for pre- and post-perihelion impacting meteoroids, respectively. tf n t (q, e, i) = W (t) [n s (Asc., ω pre ) + n s (Desc., ω pre )] dt, t i (3) and for post-perihelion impacts we use n t (q, e, i) = tf t i W (t) [n s (Asc., ω post ) + n s (Desc., ω post )] dt (4) 4 DIRECT SOURCE OBSERVATIONS Fig. 1 shows the radiant distributions of all meteors detected between 1995 May and 1999 October. Three main source regions are evident in this diagram. The helion source is centred 20 off the solar direction and the antihelion source is centred a similar angular Figure 1. The radiant distribution of meteors detected by AMOR between 1995 May and 1999 October. Ecliptic longitude (λ)is referenced to the solar longitude (λ ) toavoid longitudinal motion of the source regions throughout the year. On this diagram the Sun is at 0 and the apex of the Earth s way is at 270. distance off the anti-sun direction. A broad source is present about the direction of the apex of the Earth s way (λ λ = 270 ). This source is mainly made up of retrograde orbiting meteoroids, with a small prograde component at higher southerly latitudes. In order to determine the strengths of, and orbital distributions within, the given source regions: it is necessary to begin by having a clear definition for each of the regions. Fig. 2 shows the meteoroid population partitioned on the basis of orbital direction. The clear differences in the sub-populations are visible in the ecliptic longitude with respect to the Sun: the retrograde population forms a welldefined and narrow peak about the apex of the Earth s way; the prograde population forms three sub-peaks close to the antihelion and helion and about the apex directions. In order to partition the prograde population, Gaussian distributions have been fitted to both the antihelion and helion peaks and cut-offs at 3σ on the outer edges and 2σ on the apex-ward edges have been established as marked. The prograde apex region has been assumed to lie between these inner limits. The prograde sources are defined as antihelion (λ λ [150, 250 ]), apex (λ λ (240, 300 )) and helion (λ λ [300,30 ]). No limits are applied in the case of the retrograde population owing to the uni-modal nature of its longitude distribution. 4.1 Motion of the sources within the ecliptic frame While studies such as Sekanina & Southworth (1975) and Jones & Brown (1993) present static radiant distributions similar to those shown in Figs 1 and 3, it is interesting to look at the monthly changes in the radiant distributions. Fig. 4 shows this, with a month being defined as 30 of solar longitude and a virtual year being formed between vernal equinoxes. All data from 1995 to 1999 have been used in these graphs with weighting being applied to remove the effect of radar facility outages the intention being that all years make equal contribution to each virtual month s distribution. Fig. 4 shows that all of the source regions experience large changes in latitudinal distribution with each month. For example, the helion source region is close to the ecliptic at the vernal equinox, moves to its furthest Southerly position halfway to the autumnal equinox, moves back to the ecliptic at the autumnal equinox, then proceeds North of the ecliptic halfway back to the vernal equinox and finally returns to the ecliptic at the following vernal equinox. The antihelion source acts similarly, but half a year out of phase. The use of a logarithmic density scale in this figure is necessary, as otherwise the retrograde apex and antihelion sources tend to

4 554 D. P. Galligan and W. J. Baggaley ANTIHELION APEX HELION Distribution Fitted Gaussians 2.5 Apex Source Number [x10 4 ] Number [x10 4 ] Number [x10 4 ] Ecliptic Longitude J (w.r.t Sun) Ecliptic Latitude J Number [x10 4 ] Ecliptic Longitude J (w.r.t Sun) Ecliptic Latitude J Figure 2. Gross distributions of the geocentric Sun-referenced ecliptic coordinates for all five years of meteor observations. The data set is partitioned according to the orbiting direction of the meteoroids: prograde meteors are shown on the left and retrograde on the right. The sporadic source regions are identified on the longitude distribution plots; the antihelion region is defined by (λ λ ) [150, 240 ], the helion region by (λ λ ) [300,30 ] and the prograde apex region by (λ λ ) (240, 300 ). Retrogrades are not partitioned by longitude as they only appear in the apex region. Figure 3. As for Fig. 1, but with the in-atmosphere observational biases removed as described in Section 3. dominate at the expense of the prograde apex and helion sources. It should be noted that when the sources travel far from the ecliptic their strength is reduced markedly, for example, the helion source is extremely weak in the 3rd to 4th virtual months, when it is furthest South. A simple explanation is available for the motion of the sporadic sources. Fig. 5 shows the same information as Fig. 4, but uses equatorial rather than ecliptic coordinates; here, similarly to the use of sun-referenced ecliptic longitude, right ascension is referenced to the solar longitude to prevent motion of the source regions. This figure shows that there is little change in the declination coverage of the sources within 30 of the celestial equator: the strengths of the sources do change but not their locations. This is in direct contrast to the ecliptic picture and shows that the motion of the sources within the ecliptic system is solely an observational effect caused by the Earth s orbital motion in conjunction with the effective fixed declination coverage of the radar system. These results show that sporadic source distributions derived from a year, some months or even several years of data, must be influenced by the changes in the positions of the main sources in the ecliptic reference frame over time. Unless correction is applied for this effect comparison of source structure from different studies proves difficult. Inter-comparison becomes even more challenging when one considers that different radar systems have very different radiant declination coverage. For example, the present data set covers little North of the celestial equator. This means that the retrograde apex source in Fig. 1 is not symmetrical about the ecliptic, which would have been otherwise expected. Likewise, most of the prograde source strength is South of the ecliptic. Few meteoroids are detected at their descending nodes by AMOR because of this coverage situation. In contrast, the HRMP survey (e.g. Sekanina & Southworth 1975) was sensitive to mostly northern declinations in that particular study southern declination meteors were deliberately removed as the authors felt that incomplete coverage of the hemisphere made it inappropriate to include those data. 4.2 Corrected radiant distributions The original sporadic source distribution of Fig. 1 consists of a true underlying distribution distorted by inherent biases related to the method of observation. By using the method discussed in Section 3, these observational biases have been removed to produce the

5 Radiant distribution of AMOR meteors 555 Figure 4. The radiant distributions (ecliptic coordinates) for the twelve virtual ( λ = 30 wide) months in the AMOR data set. Data from all five years are used with the normalized rates per region being used to form this composite picture. Each pixel is 3 by 2 and the ecliptic longitudes are given with respect to that of the Sun. Figure 5. The average monthly radiant distributions (equatorial coordinates) in the AMOR data set. The declination of the celestial equator is marked by a horizontal white line. See Fig. 4 for further details. radiant distribution shown in Fig. 3. Comparison of these figures shows that the helion source increased in strength relative to the antihelion source. This change is more clearly shown by Fig. 6, where the original longitudinal distribution is compared with that after correction. Table 2 lists the changes in population distribution between source regions after the correction is applied. The statistics of the defining parameters of each source region before and after correction are provided in Table 3.

6 556 D. P. Galligan and W. J. Baggaley Figure 6. Radiant distribution in longitude with respect to the Sun. The original distribution curve is shown with square symbols and that for the in-atmosphere bias corrected sample is shown with triangular symbols. Table 2. The original and corrected number fractions of the total meteoroid population residing in each of the source regions is shown. The ratio of the corrected number fraction to the original shows that all prograde regions increase at the expense of the retrograde population. Note that the total number fraction of all of the four sources does not add to one because of cut-off limits imposed in selecting the source regions. Source region Original Corrected Ratio Helion Antihelion Prograde apex Retrograde apex Table 3. Statistics for key parameters defining the population of each of the main source regions, before and after correction for observational biases. Angles are measured in degrees and speed is measured in km s 1. Source region λ λ β V G x σ x σ x σ Helion Uncorr Corr Antihelion Uncorr Corr Prograde apex Uncorr Corr Retrograde apex Uncorr Corr As shown in Table 3 there is no change in the mean ecliptic latitude of any of the source regions when correction is applied for observational bias. Correction causes a clear decrease of approximately 4 km s 1 in the mean geocentric speeds of the prograde populations, but no change to that of the retrograde apex population. The mean ecliptic longitude with respect to the Sun of the two apex sources is unchanged upon correction but that of the antihelion and helion sources moves 5 further from the apex of the Earth s way. The latter change is consistent with the decrease in geocentric speeds in the prograde meteoroid population after correction. There is no change in the standard deviations of the various source population defining parameters after correction is applied. The relative strengths of the source regions change significantly upon correction. The helion source almost doubles in strength, and the antihelion source increases to a lesser extent. The end result of this correction is that the helion source changes from having 60 per cent of the antihelion strength to having 80 per cent. This shows that the inclusion of Faraday rotation and allowance for radar down-time (with some of the effective down-time resulting from ionospheric E-region scatter) has a positive effect in bringing these sources closer to balance. The fact that these two sources do not present exactly the same strength after correction is most likely due to an incomplete correction: effects such as ground scatter via the E-region may not prevent all meteors from being detected. We assume here that if one meteor was detected in an hour then the radar was operational: in fact its rate may have been greatly diminished beyond the effects predicted by Faraday rotation alone. Dealing with this problem is very difficult as we effectively have a low number of meteors per hour about midday arriving at random times some days this number will be lower, but not necessarily zero, owing to atmospheric interference. Hence, we have multiple Poisson distributions in operation and are unable to determine easily whether a low number over several hours on a particular day is due to randomly low numbers in a higher expectation value Poisson distribution or, instead, that the rate is low due to strong interference conditions. The prograde apex population is seen to make up 5 per cent of the overall population both before and after correction. In contrast, the retrograde population falls from just under 50 to 18 per cent of the population on correction. This indicates that the retrograde population is exaggerated in significance in directly observed radar meteor data sets. 4.3 Orbital distributions within source regions All meteors Fig. 7 shows key orbital element distributions of all meteoroids within the selected AMOR data set. The original distributions are shown overlaid with the in-atmosphere bias corrected distributions for each element. The semi-major axis length distribution shows little change upon correction: most orbits have 0.5 a < 3auwith the hard-limit at 0.5 au being caused by the condition for Earth impact. The original eccentricity distribution is strongly biased towards the more eccentric orbits, with most orbits having e > 0.5 and with a peak between 0.8 and This high eccentricity tendency is tempered somewhat by the bias correction, where the peak is moved towards mid-eccentric regions. The inclination distribution originally observed is fairly uniform for inclinations greater than 30, with a strong increase as the inclination approaches 0 from there. The correction enhances the i < 30 population markedly with 50 per cent of all meteoroids then being found within this region. The retrograde population, which was sizable when directly observed ( 50 per cent) is strongly reduced upon correction. The geocentric speed distribution also shows the effect of this ionization assumption, where the original bi-modal distribution (the lower speed mode being composed of prograde meteors and the higher one of retrogrades) is reduced to a single dominant mode that peaks lower than the original prograde peak and a much diminished mode for the retrogrades that also peaks lower than the original Antihelion and helion sources The antihelion and helion source regions, identified earlier, contain much of the prograde population within the AMOR data set. Figs 8 and 9 show the orbital distributions in these regions, respectively. It is clear that these regions contain very similar orbital populations. As discussed earlier we expect this, as these sporadic source regions

7 Radiant distribution of AMOR meteors 557 Figure 7. Orbital element distributions of all meteoroids within the AMOR data set between 1995 May and 1999 October. Distributions are shown for the semi-major axis length, eccentricity, inclination and the geocentric speed at impact. Squares denote data points from the uncorrected distribution and triangles denote those from the distribution corrected for in-atmosphere bias effects. Figure 8. As for Fig. 7, but with only prograde antihelion source meteors selected. should sample the same types of meteoroid orbit at intervals six months out of phase with each other. In fact, it is interesting to study the change in orbital types that are detectable in these regions as the solar longitude changes. This is out of the scope of the current study with the interested reader being referred to Galligan (2000) for complete coverage of this matter. In these source regions, it is found that little change occurs to the semi-major axis length distribution upon correction. Most meteoroids here have 0.5 a < 3auwith a pronounced peak about a 1 au. The eccentricity distribution is biased towards high values with correction producing a flatter and less eccentric peak: low-eccentricity orbits become more noticeable upon correction, a small proportion of such orbits were directly observed by the radar. The inclination distribution is biased towards orbits with i < 30. Correction increases this tendency and removes a significant number of the higher-inclination prograde population. A smaller fraction of

8 558 D. P. Galligan and W. J. Baggaley Figure 9. orbits are found to have inclination >30 here than in the all source population of Fig Apex region Two separate populations exist in this region the prograde and retrograde apex sources. The orbital element distributions for these sources are shown in Figs 10 and 11, respectively. The retrograde population has a directly observed distribution in semi-major axis length that is narrower by about 1 au than is that As for Fig. 7, but with only prograde helion source meteors selected. for the antihelion/helion sources: most orbits have 0.5 a < 1.5 au. Conversely the eccentricity distribution is much broader than these: there is a fairly flat distribution for e > 0.4 with a gradual falloff towards circular eccentricities. Correction of these distributions clearly has little effect. The exception is for orbital inclination where the peaked distribution at i 160 has had all points displaced by about 10 further away from the ecliptic. The peak in inclination is purely a matter of chance caused by the retrograde meteoroids appearing from a fairly narrow region about the apex, and because of this the observed inclination distribution changes throughout the Figure 10. As for Fig. 7 but with only prograde apex source meteors selected.

9 Radiant distribution of AMOR meteors 559 Figure 11. year as the declination of the apex changes. The location of the final peak therefore depends on the time-coverage of the radar throughout the year more than anything else. The geocentric speed distribution changes a little upon correction with a translation of the distribution downwards by 5 kms 1. This decrease is not so dramatic as is the comparable antihelion/helion speed decrease: the inclusion of atmospheric attenuation effects in the response function, in combination with the higher average heights of the retrogrades, leads to a tempering of the biasing influence of the ionization efficiency velocity effect. The prograde apex region differs greatly from the antihelion and helion regions. While there is a distinct enhancement in retrogrades close to the apex owing to the large Earth impact speeds that can exist, the opposite is true for progrades, with the Earth overtaking such meteoroids. The directly observed semi-major axis length distribution about 1 au is the tightest of all; correction widens the peak a little away from 1 au. The eccentricity distribution shows the opposite trend from all of the other sources with a tendency towards low-eccentricity orbits: the correction increases the tendency still further with a peak extending from e = 0.1 to 0.3. The inclination distribution is biased towards high-prograde angles with few having i < 40 ; this is in marked contrast to the antihelion and helion sources, which had few meteors with i > 40. The corrected inclination distribution shows a sharper peak than does the relatively flat original distribution. This is due to the decrease in the average geocentric speeds of meteoroids upon correction: meteoroids on high-inclination orbits generally impact with higher than average geocentric speeds. 5 COMPARISONS AND CONCLUSIONS 5.1 Radiant distributions Two relevant studies suitable for comparison of the radiant distributions obtained here are those presented in the reappraisal of the HRMP survey data by Taylor & Elford (1998) and the summary of several radar and optical surveys by Jones & Brown (1993). Taylor As for Fig. 7 but with only retrograde apex source meteors selected. & Elford s (1998) radiant distribution, which has been corrected for in-atmosphere bias, shows coverage over all ecliptic latitudes they note that incomplete coverage South of the ecliptic has necessitated the assumption that the radiant distribution is symmetric about the ecliptic. Six sources are identified. Additional to those discussed in the current study, there are the North and South toroidal sources, which appear above 60 and below 60, respectively, and also the North and South apex sources, which represent a split of the retrograde apex population about the ecliptic. The AMOR source distributions (see Fig. 3) share many of the same features. The South apex source is clearly visible, but more disperse across a range of longitudes, while the North source is only slightly visible owing to the incomplete coverage above the ecliptic. The helion and antihelion sources are also located similarly, but the correction for Faraday rotation and radar down-time/atmospheric interference has substantially increased the strength of helion source here. In contrast, Taylor & Elford s (1998) helion source is 50 per cent of the strength of the antihelion source. The toroidal sources are not present as far South here as they were in Taylor & Elford s (1998) results. It should be noted that the region South of 60 was not covered by the HRMP survey, and their assumption of symmetry with the North toroidal source may not be true. There is a source at a higher latitude than the main South apex source, however, and it is from this that the prograde apex meteors arrive. This source, in addition to the antihelion, helion and main apex sources, produces a picture that is similar to those in the uncorrected Kharkov (northern latitudes only) and Adelaide (southern latitudes only) radio survey results displayed by Jones & Brown (1993). 5.2 Orbital distributions The uncorrected antihelion and helion regions have orbital distributions very similar to those shown by Jones & Brown (1993). After applying corrections for observational biases it is found that high inclination, high eccentricity and high geocentric speed meteors are overemphasized in the observed distribution. Accordingly, all of

10 560 D. P. Galligan and W. J. Baggaley these distributions are displaced downwards. The definition of the source regions based solely upon ecliptic longitude range and orbital direction has included more higher-inclination orbits than did Jones & Brown (1993) (who used a tighter definition, also based on ecliptic latitude, which resulted in meteoroids being excluded that were further from the ecliptic). Meteors appearing in the antihelion and helion regions have orbits similar to short-period comets and also some Earth-crossing asteroids. The apex region has been shown to be mainly composed of retrograde meteoroids, which diminish in significance upon correction. The orbital distributions presented by Jones & Brown (1993) differ somewhat from the uncorrected distributions in Fig. 11. Jones & Brown (1993) show a strong peak at the parabolic limit, while no such peak is visible in the AMOR data. The prograde apex meteors are mainly present further South than 30.Asnoted above, these are the closest to the southern toroidal source shown by Taylor & Elford (1998). Much of the high-inclination prograde population is present in this region and the effect of applying Opik s (1951) collision probability to the data, to obtain the true space distribution, is to magnify this population (Galligan & Baggaley 2004). The bias towards near-circular eccentricities, seen in Fig. 10, is confirmed by Jones & Brown (1993), as are the other orbital element distributions, which are very similar. Davies & Gill (1960) also find this population: they suggest that meteoroids with such high inclination might have originally come from a long-period comet and have been circularized over time by the Poynting Robertson effect. ACKNOWLEDGMENTS This meteoroid influx monitoring survey is being undertaken as part of the ESOC Upgrade of Meteoroid Model to Predict Impacts on Spacecraft Contract ESOC RFQ/3-9528/99/D/CS and under Contract UOC911 to the Marsden Fund of New Zealand. Financial support from these sources is gratefully acknowledged. REFERENCES Baggaley W., 1995, Earth, Moon and Planets, 68, 127 Baggaley W., Bennett R., 1996, in ASP Conf. Ser. Vol. 104, Physics, Chemistry and Dynamics of Interplanetary Dust. Astron. Soc. Pac., San Francisco, p. 65 Baggaley W., Bennett R., Steel D., Taylor A., 1994, QJRAS, 35, 293 Baggaley W., Marsh S., Bennett R., Galligan D., 2001, in Warmbein B., ed., ESA SP-495, Meteoroids ESA, Noordwijk, p. 387 Ceplecha Z., Borovička J., Elford W., Revelle D., Hawkes R., Porubčan V., Šimek M., 1998, Space Science Reviews, 84, 327 Davies J., Gill J., 1960, MNRAS, 121, 437 Elford W., 1964, Calculation of the response function of the Harvard Radio Meteor Project radar system, Harvard Radio Meteor Project Research Report No. 8. Smithsonian Astrophysical Observatory Galligan D., 2000, PhD thesis, Univ. Canterbury, Christchurch, New Zealand Galligan D., Baggaley W., 2002, in Green S., ed., Proc. IAU/COSPAR Colloquium 181, Dust in the Solar System and Other Planetary Systems Galligan D., Baggaley W., 2004, MNRAS, 353, 422 Hawkins G., 1956, MNRAS, 116, 92 Hawkins G., Prentice J., 1957, AJ, 62, 234 Jones J., Brown P., 1993, MNRAS, 265, 524 Keay C., 1963, MNRAS, 126, 165 Öpik E., 1951, Proc. R. Irish Acad. Sect. A, 54, 165 Sekanina Z., Southworth R., 1975, Physical and dynamical studies of meteors. NASA CR-2615, Smithsonian Institution, Cambridge, MA, USA Stǒhl J., 1968, in Proc. IAU Symp. 33, Physics and Dynamics of Meteors. Reidel, Dordrecht, p. 298 Taylor A., Elford W., 1998, Earth Planets Space, 50, 569 Weiss A., Smith J., 1960, MNRAS, 121, 5 This paper has been typeset from a TEX/LATEX file prepared by the author.