Meteor observations by the Arecibo 430 MHz incoherent scatter radar. II. Results from time-resolved observations

Journol of Almospherrc and S&r-Terresrrial

Pergamon

PII: SOO21-9169(96)00103-l

Physics, Vol. 59, No. 7, pp. 739 -752, 1997 C’ 1997 Elsewer Science Ltd reserved. Pnnted 1” Great Britain 1364-6826/97 $17.00+0.00

All nghts

Review Paper Meteor observations by the Arecibo 430 MHz incoherent scatter radar. II. Results from time-resolved observations Qihou H. Zhou’ and Michael C. Kelley’ ‘Arecibo

Observatory, National *School of Electrical

Astronomy Engineering,

and Ionosphere Center, Arecibo, PR 00613-0995, Cornell University, Ithaca, NY 14853, U.S.A.

U.S.A.;

(Received 11 March 1996; accepted 10 May 1996)

Abstract-We report high time resolution

observations using the powerful Arecibo incoherent scatter radar (ISR). The majority of the meteor-like echoes observed lasted less than 50ms at one range gate, although echoes lasting for a second were also occasionally observed. The latter may not necessarily be associated with meteors. Most of the meteor echoes in our observations have an effective radar cross-section of the order of 3 x lo-*m2, and an estimated electron line density (ELD) of the order of 4 x 109/m. The visual magnitude is approximately + 16, which is about two orders of magnitude fainter than the meteor echoes found in our time-integrated data (Zhou et al., 1995). The average echo power is positively correlated with the number of range bins in which an echo is detected. This characteristic, along with other experimental evidence, strongly suggests that the Arecibo 430 MHz radar is more sensitive to head-on meteors than to those arriving at an oblique angle. Although classical underdense scattering mechanisms may account for echoes having short range extensions, it is clear that they are insufficient lo explain echoes having long range extensions. Some possible mechanisms are discussed. In particular, we suggest that Bragg scattering due to the irregular structure existing in a meteor trail is the most important scattering mechanism for the latter type of echoes in our observations. A plasma instability operating near the Arecibo wavelength is required. 0 1997 Elsevier Science Ltd. All rights reserved

oes only come from a region very close to the meteor head and, like VHF echoes, are most easily observed when the meteor trajectories are nearly perpendicular to the radar line of sight direction. This is the classical meteor echo geometry. However, recent observations by more sensitive UHF radars appear to suggest different characteristics from earlier observations. At Arecibo, we found such a large number of meteor echoes in our conventional ionospheric observations that the Arecibo 430MHz radar qualifies as one of the most sensitive ground-based meteor observing instruments (Zhou et al., 1995, henceforth referred to as Paper 1). Furthermore, contrary to classical observing schemes, observations carried out both at EISCAT (Pellinen-Wannberg and Wannberg, 1994) and Arecibo (Paper 1) seem to suggest that perpendicularity between radar beam and meteor trajectory is not essential for meteor detection. New meteor observations near Jicamarca seem to imply that plasma instabilities can sometimes be generated by meteors as well (Chapin and Kudeki, 1994). The recent experiments at Arecibo reported in Paper 1, however, were not ideal for meteor observations since they were primarily designed for observ-

INTRODUCTION It is well established that radio echo power from an ionized meteor trail is steeply proportional to the radar wavelength. In order to obtain the most signal from a meteor trail, one would thus prefer to have a radar operating at the lowest frequency possible. On the other hand, background noise and interference increase as the frequency decreases. In general, most of the meteor radars, for either astronomical or aeronomical applications, operate within the frequency range from 15 to 50 MHz. A systematic treatment on VHF scattering of meteoric ionization can be found in McKinley (1961). As the radar frequency increases to the UHF range (30&3 000 MHz), observation of meteor echoes becomes difficult even for a moderately powerful radar. For instance, in an early UHF observation, Greenhow et al. (1962) were only able to observe 14 meteors during 20 hours of a meteor shower observation using a 1.3 GHz radar, which had a forward gain of 47 dB and a 2.5 MW transmitter. Observations made by Greenhow and Watkins (1964) at 300 MHz and Evans (1965, 1966) using the Millstone Hill 440 MHz ISR system show that UHF ech739

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ing incoherent scatter from the ionosphere. The long time average necessary for incoherent scatter observations makes it impossible to study the duration time of a meteor echo. Another disadvantage of the previous observation is the coding technique employed for incoherent scatter observations. The technique boosts the effective transmitter power by more than 10 fold for relatively stationary targets, but makes it difficult to distinguish a fast moving meteor head from a long stationary trail. Although one can infer from the diurnal meteor rate and the altitude distribution that perpendicularity is not essential for meteor detection and argue that the inability to decode an echo means that it must possess a considerable radial velocity, more complete and accurate characterization of UHF meteor echoes is only possible with a simple transmitter pulse. In this study, we report observational results from three dedicated meteor experiments carried out in 1993 in concurrence with three major meteor showers. All three observations were conducted with 2 or 3 ms time resolution and a simple square transmitter pulse. Because no integration is performed on the data, the meteors reported here are in general smaller than the meteors found in our time-integrated data (Paper 1). Our current observation demonstrates that the Arecibo 430MHz system is more sensitive to head-on meteors than to those traveling at a right angle with respect to the radar beam. In this report, we describe our meteor detection technique and present observational results. We also discuss the data in the light of various scattering mechanisms.

DATA TAKING AND METEOR DETECTION PROCEDURES

The instrument parameters used for our observations are listed in Table 1. In order to avoid decoding difficulties, we used a simple square pulse with a width of 8~s corresponding to a height resolution

Table 1. Experiment Operating Frequency Gain at 15” Zenith Angle Beam Width at Half Power Peak Transmitter Power System Temperature Transmitter Pulse Length Inter-Pulse-Period IF Filter Bandwidth Zenith Angle

parameters

430 MHz 60 dB l/6” 2.0 MW 80K 8 ps 3 ms (July) 2 ms (August, December) 250 kHz (July, August) 500 kHz (December) < 20”

of 1.2 km. We experimented with two intermediate frequency filters (IF), one at 250 kHz for July and August observations and the other at 500 kHz for the December observation. The 250 kHz bandwidth rejects signals moving at a line of sight velocity above 44 km/s while the 500 kHz bandwidth has its cut-off velocity at 88 km/s, and thus permits the reception of the fastest moving meteors. The time resolutions were 3 ms for the July 1993 observation and 2 ms for the August and December 93 observations. In-phase and quadrature voltage samples were digitized to 12 bits signed integers, and recorded without performing any average. The sampling region was mainly confined to the 70-125 km altitude range. Our meteor detection procedure requires that a meteor echo must possess three qualities. It has to be well above background noise, it must possess a certain time duration and it should be coherent in nature. For the purpose of meteor study, we used the samples derived from the 120-125 km altitude range as our noise base line. Because of the short period between two adjacent pulses, the received power for each sample is the summation of system noise, incoherent scattering from the background ionosphere and, possibly, a meteor echo. For 3ms inter-pulse-period (IPP) meteor experiments, total noise temperature is the system temperature (- lOOK) plus the incoherent scattering from the E-region, which is about equal to the system temperature at daytime and is negligible during the night-time. For 2ms IPP meteor experiments, however, the noise temperature can be as high as 300 K due to height aliasing with the F-region ionosphere. The minimum meteor signal-to-noise ratios (S/N) used for this study are 15 and 20, for 2ms and 3ms IPP observations respectively. The reason for using different S/N thresholds is to make the absolute brightness of the meteors approximately the same for different noise levels. The second criterion in our meteor detection technique is the meteor time duration, which is the time period during which the power was continuously above the S/N thresholds. The minimum time duration used in this study is 12 ms, which practically eliminates all sporadic interference. Our third detection criterion, i.e., the coherence test, mainly deals with the strong background ion layers often present at Arecibo latitude. Zhou and Mathews (1994) have demonstrated that the ratio of the standard deviation of the power spectrum to its average is an excellent test for coherence. This test also holds true in the time domain if a proper sampling window is chosen. In order to do this, we took 128 consecutive power returns from the same height and calculated the ratio (R) of the standard deviation to the average. For a raw data taking experiment without

Meteor observations by incoherent scatter radar. II performing any average, R is very close to unity for uncontaminated incoherent scattering processes, which include the scattering from sporadic E. On the other hand, R will deviate significantly from unity if there is a coherent scattering process present. In general, if R is significantly smaller than one (say 0.Q it suggests the presence of a coherent mechanism over most of the 128 data samples. If R is significantly larger than one, it usually suggests the presence of a coherent mechanism in less than half of the data points in the averaging window. Our meteor selection criterion requires that R has to be outside the range from 0.8 to 1.2, in addition to that the minimum time duration of an echo at one range gate has to be 12 ms and the signal-to-noise ratio has to be at least 15.

OBSERVATIONS

We conducted three sets of observations in July, August and December 1993. Although there was at least one major meteor shower present at each period, we have found (to our surprise) that the observed characteristics are not significantly affected by the presence of meteor showers. During the July and August observing periods, we also ran the time-integrated program that we used for Paper 1. The meteor rate obtained in that mode during the shower periods was essentially the same as that reported in Paper 1, which applies to sporadic meteors. No detectable increase in meteor rate was observed whether we pointed the radar beam perpendicularly to or directly toward the shower radiant direction. Due to upgrading of the Arecibo telescope, the observations were carried out primarily at night-time. Types of echoes observed Three types of echoes have been identified from our raw data taking experiments. The first type appears essentially at only one range gate and has a duration typically less than 20ms. The second type of echoes appears at multiple range bins and their duration time in most of the range bins is typically above 20ms. Some of them have been observed to appear over a vertical distance of more than 6 km. The second type of echoes is usually stronger in power than the first one. The third type of echo lasts much longer than the either of the first two types of echoes. These long duration echoes typically have a duration longer than several hundred milliseconds, and are much less frequent than the first two types of echoes. In Figs la, b and c, we plot an example for each type. In this paper, we concentrate on the first two types of echoes. The third type may not even be related to meteor ablation

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and certainly deserves further study elsewhere. The leading edge of the echo progresses down the radar beam at a speed of about 60 km/s in Fig. 1b. There is a hint of deceleration if, for example, the arrival times in the lower range gates are compared to those in the upper ones. This deceleration is potentially of interest for future studies as is the ability we have to determine unambiguously the velocity distribution in the high velocity tail of the meteor distribution. Before we delve into details, a comment on terminology seems in order. The classic meteor literature notes the term “long duration” to refer to echoes lasting of the order of seconds. To a UHF radar, several tens of milliseconds is a long time. Also the term “duration” used here represents mostly the meteor flight time within the radar beam, rather than the time constant for the decay of an underdense trail echo. For reference, the beam/range gate geometry of our experiments can be approximated as a cylinder of 300 m radius with a length of 1.2 km. Taking a typical length scale as 1 km and typical meteor velocity as 50 km/s, the time scale for a meteor to remain in the beam is 20ms. Another time scale of interest is the diffusive time constant z = 12/(16x2D,), where 1 is the radar wavelength and D, the ambipolar diffusion constant. This time scale is roughly proportional to the atmospheric density and is about 2 ms at 100 km for the Arecibo radar wavelength. Aspect sensitivity of meteor echoes Practically all the meteor echoes observed by VHF and UHF radars at other locations show strong aspect sensitivity (e.g., McKinley, 1961; Greenhow and Watkins, 1964; Evans, 1965). In general, meteor echoes are most easily detected when the radar line of sight is perpendicular or nearly perpendicular to the meteor trail, which is commonly referred to as the specular condition. In order to be concise, let us define aspect angle as the angle between the radar line of sight and the trajectory of a meteor. We will use the terms specular, radial and oblique for the situations where the aspect angle is, respectively near 90”, 0” and otherwise. We also refer to a meteor trail with a 90” aspect angle as a perpendicular or orthogonal trail. Although most radio meteor studies involve perpendicularity, there is a class of events referred to as head echoes in which this condition is not necessary. A head echo is defined as “an instantaneous echo apparently moving with the velocity of the meteor” (McKinley and Millman, 1949). For example, in the study of visual meteors and radar head echoes, roughly 40% of visual meteors had associated head echoes and they were distributed uniformly across the

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sky (Jones and Webster, 1991). Head echoes are not well understood after nearly 50 years of study. Conventional wisdom attributes the signal to an overdense region near the meteor head which mysteriously disappears right behind it. The most recent attempt to explain the disappearance invokes copious amounts of water vapor released by the meteor which creates a large local recombination coefficient (Jones et al., 1988). Echoes such as those in Fig. lb have some similarities to head echoes in that they are observed far from perpendicularity and seem to follow the meteor head down the beam. In the center of the plot, echoes remain in a given range gate for a relatively long period of time, e.g. 50 ms at 100 km in Fig. 1b, similar to some examples of head echoes accompanied by diffuse subsequent echoes (McIntosh, 1961). In the recent EISCAT work at 933MHz, 73% of their meteor echoes are of the head echo type and display an altitude distribution nearly identical to that reported for Arecibo in Paper 1 (and here in Fig. 8). Pellinen-Wannberg and Wannberg (1994) report no aspect sensitivity for the head echoes, but their flux rate is nearly two orders of magnitude lower than reported here, so the statistics are not very great. The rest of the EISCAT echoes are termed “trail” echoes and ascribed to incoherent scatter from trails left by meteors larger than 3 mm in diameter, which corresponds to I 10e4 g (Pellinen-Wannberg and Wannberg, 1994). The Arecibo scattering type shown in Fig. lc may be related to these. In Fig. 2, we show our relative echo count as a function of range extension, which is the height range that an echo is continuously detected along the radar line-of-sight direction. Any echo that is detected in three or more range bins, i.e. range extension equal to or larger than 3.6 km in Fig. 2, we refer to as radial. On the other hand, an echo with one or two range bins can be a specular echo, or alternatively a short oblique or radial echo. From Fig. 2, we conclude that at least 10% of all echoes are radial or oblique echoes. In order to study aspect sensitivity further, we plot the echo power, which is measured in signal-tonoise ratio, as a function of range extension in Fig. 3. One reason for the nonlinearity at high S/N values of each curve is due to the saturation of the receiving system.

It is seen that on average the stronger echoes have longer range extensions. This implies that a meteor is more likely to be detected when its aspect angle is small, just the opposite of conventional meteor radar echoes in which the 90” angle is preferred. Consequently, we believe that most of the meteors appearing in one or two ranges are more likely to be weak radial or oblique meteors than specular ones. That the Arecibo 430 MHz radar is more sensitive to radial meteors than to specular ones is discussed further in the following sections as we examine the diurnal and altitudinal characteristics. Diurnal characteristics

qf UHF meteor echoes

In this subsection, we present and discuss the diurnal variation of the hourly meteor rate, echo height, range extension and time duration. In Fig. 4, we plot the diurnal variation of the hourly meteor rate for the three observing periods. Although we used the same S/N threshold for the August and December periods, the meteors observed in the December period were likely to be brighter because the wider bandwidth filter used in this period resulted in a higher noise power level. Yet, the hourly rate for the December period during the dawn hours is significantly greater than the other two periods. We believe that the difference is due to the fact that the filter cut-off velocity for the July and August observations (250 kHz filter) was 44 km/s while the filter cut-off velocity for December (500 KHz) was 88 km/s. During the dawn hours, the heliocentric motion of the earth shifts many of the meteors to velocities larger than 44 km/s. If the scattering medium moves at approximately the meteor velocity, echoes visible to a 500 kHz bandwidth system may not be visible to a 250 kHz bandwidth system. On the other hand, if most of the meteors entering the atmosphere have a velocity less than 44 km/s, a 250 kHz system excludes very few fast moving meteors and may detect more meteors than a 500 KHz system because of the lower noise level. This can explain the higher hourly rate between 2&04 hours for the July and August observations. The difference in filter bandwidth may also account for the much slower variation in hourly rate for the July and August observations

Fig. 1, (a) A relatively weak meteor echo, which lasted for only 12 ms at only one range gate. The echo was observed at 07:21 LT on July 29, 1993. (b) A strong echo observed at 06:45 LT on December 14, 1993 using a 500 kHz filter, which permits the reception of practically all the echoes associated with meteor entries. The apparent echo velocity shown in this plot is 55 km/s. (c) A long enduring echo observed at 20:50 LT on July 28, 1993. Echoes with duration time longer than 100 ms were only occasionally observed. They may not necessarily be related to meteoric ablation.

Meteor

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during the dawn hours and the sharper variation for the December period. If we believe that the higher hourly rate at dawn observed in the December period is indeed due to the reception of meteors having radial velocities larger than 44 km/s, we are accepting that a significant portion of meteors are radial ones since only those radial or nearly-radial meteors can possess velocities larger than 44 km/s. Further, the diurnal variation of the hourly rate also suggests that the specular echoes cannot dominate the meteor population in our observation. If the Arecibo radar mainly saw specular meteors, we would expect that the hourly rate at midnight to be higher than at 06 LT because, with the

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4 8 12 Local Time Fig. 4. Diurnal variation of meteor hourly rate for the three observing periods. The higher hourly rate for the December period is believed to be due to the wider filter bandwidth used which allowed the acceptance of fast moving meteors. Note there is no data between 09OG1200 hours for the December period.

radar beam being nearly vertical, meteor trajectories are more likely to be perpendicular to the radar beam at midnight vs dawn. Therefore, from the diurnal variation of the hourly rate, we conclude that the Arecibo radar is either not significantly aspect sensitive or perhaps even more sensitive to radial meteors. In Fig. 5, we plot the mean echo altitude as a function of local time. The echo altitude for a meteor appearing in several range bins is defined as the altitude where the maximum S/N is found. If our above

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6 6 Range ixtension (km) Fig. 3. Average echo signal-to-noise ratio vs range extension. At the lower range of S/N, the signal power is essentially linearly proportional to the range extension.

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_____---= ___--____---_________------_----_______-----

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Fig. 2. Relative number of meteors detected plotted vs the number of range gates in which they are detected. Each range gate is 1.2 km long. The total number of meteors selected is 1632, 6522, 1675 for July, August and December observations respectively.

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Time Fig. 5. Diurnal variation of average altitude of meteor echoes. The higher echo altitude for the December period suggests that the detected meteors had a higher average meteor velocity during this period than during the other two periods. Local

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observations by incoherent scatter radar. II

argument about the velocity filtering effect is correct, the echo height for the December period at dawn hours is expected to be higher than the heights for the other two periods because of the generally larger velocity of the dawn meteors. This can indeed be seen from Fig. 5. However, we cannot explain why the difference in echo height for the period O&O4 LT between the December observation and the other two periods is even larger than the difference near 04-08 LT. For the time period between O&O4 LT, the choice of either 250 kHz or 500 kHz filter should make less difference because of the generally lower meteor entry velocity than at the dawn hours. Since the total number of meteors observed during 20-04 LT in December is far less than the number observed during 0408 LT, it is possible that statistical uncertainty may play a role here. It is generally known that a meteor with a larger entry velocity ablates at a higher altitude. In Fig. 5, however, the maximum meteor echo height does not occur at 06 LT when the average entry velocity is believed to be the largest. For the July and August periods, it is interesting to note a local maximum echo height appears at two time periods, each about 4 hours apart from the expected time at about 06 LT. The December curve at least partially suggests the same although there is no data after 08 LT. We also examined the height variation for each individual day and found that the feature was very consistent. We, therefore, believe that the higher echo height at about 02 and 10 LT is physical instead of being due to statistical fluctuations. One possible explanation lies in considering the effect of the meteor entry angle on the ablation height. For meteors with similar physical characteristics, the ablation and ionization profiles are determined by both the meteor velocity and the integrated atmospheric content a meteoroid has to pass through. If the velocity is the same, vertically penetrating meteoroids will have the lowest ablation altitude because they encounter less friction with the atmosphere than obliquely falling meteors for the same vertical distance they traverse. It is possible that the composite effect of velocity and obliqueness of the meteor path makes the ablation height highest at 0200 and 1000 hours respectively. However, we do not have an explanation why the maximum ablation height data (Paper does occur at 06 LT in our time-integrated 1) other than suggesting that meteor size and mass may make a difference. We show the diurnal variation of the average meteor range extension in Fig. 6. The shorter range extension in December is believed to be due to the fact that the wider bandwidth used in this period allows the acceptance of fast moving meteors. In general, the

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ablation of high velocity meteors is more rapid and consequently shorter in length than low velocity meteors having the same mass. The larger range extension at 06 LT present in each curve is likely to be due to the fact that dawn meteors tend to fly straight down into the radar beam and thus make the radial extension appear longer. The range extension reported here using a simple square pulse is shorter than our timeintegrated results using coded pulses (Paper 1) although they have similar local time variation. It is almost certain that some of the echoes in the transmitter pulse coded data cannot be decoded properly, contributing to the artifact that longer range extension was observed. On the other hand, it is possible that the power due to the relatively stationary trail may exceed that due to the fast moving scattering medium under some circumstances, which is further discussed in Section 4.4. In Fig. 7, we plot the average time duration of

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0

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Rate Fig. 8. Normalized altitudinal distribution of meteors detected for the three observing periods.

meteor echoes as a function of local time. The duration time is the overall time interval between the first detection of a meteor echo and its disappearance irrespective of the gate number where it is detected. The time duration is affected by many parameters including the meteor entry velocity and degree of difficulty in detection. In general, slowly moving meteors tend to make the duration time longer but at the same time they are more difficult to detect, which shortens the duration time. For the time interval between 2&24 LT, the longer time duration is most likely to be due to the slower entry velocity. The local maximum at 06 LT in all three data sets is more likely to be due to the generally longer range extension as seen in Fig. 6. Although the duration time at each range bin at 06 LT is shorter due to the generally faster entry velocity compared with other time periods, dawn meteors tend to extend over a longer height range, which makes the overall time duration longer. Altitudinal

characteristics

weak echoes and the other at 107 km for strong echoes. The altitudinal distributions of the July and August observations in this study are in good agreement with that of the fainter meteors in the timeintegrated data. Since meteors yielding higher S/N in the time-integrated data appear to ablate at higher altitude, it is desirable to know if this is still true with the time-resolved data. We examined the altitudinal distribution for various ranges of S/N but did not find any significant deviation from the distribution shown in Fig. 8. Therefore, either the power in the timeintegrated data is not correlated with that in the timeresolved data, or the higher S/N echoes in the timeintegrated data belong to a different group of meteors, which are not statistically significant in our current observation. We present the average time duration of meteor echoes as a function of altitude in Fig. 9. The tendency we see for longer durations at lower altitudes is expected for two reasons. If an echo is closely associated with the meteor head, the time duration is inversely proportional to the radial velocities of the meteors. Since it is known that slower meteors ablate at lower altitudes, the time duration at lower altitudes is expected to be longer. On the other hand, if the echo power is predominantly due to the scattering from the irregular structures existing in the trail, its time duration is mainly controlled by the diffusion rate. In general, since diffusion occurs faster when the atmosphere is less dense, higher atmospheric density can also be responsible for the longer echo duration time at lower altitudes. At present, we are not certain whether the time duration is predominantly controlled by meteor velocity or diffusion rate. In Fig. 10, we plot the altitudinal variation of the range extension averaged for all the echoes observed during each period. Since range extension varies with local time

of UHF meteor echoes

In this subsection, we discuss meteor probability distribution, time duration and radial range extension as a function of altitude. In Fig. 8, we plot the normalized altitudinal distribution of the meteors detected in each observing period. The generally higher meteor height of the December observation has been anticipated in Fig. 5 and discussed in the above subsection. It is of interest here to compare the altitudinal distributions of the July and August observations with that of the time-integrated observation (Paper 1, Fig. 7) since all of the observations used a 250 kHz filter. In our time-integrated observation, the altitude distribution has two peaks, one at 97 km for

‘\

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Fig. 9. Average time duration of meteor echoes vs altitude.

Meteor observations by incoherent scatter radar. II

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and the three observing periods were not conducted during the same time of the day, the altitudinal variation for each period is differently biased and subsequently inter-period comparison may not be reliable. In general, however, Fig. 10 indicates that the range extension is positively correlated with the probability distribution function shown in Fig. 8. This is consistent with the characteristic that the Arecibo radar is more sensitive to radial than to specular meteors, as discussed in Section 3.2. DISCUSSION

Estimation of effective scattering cross section, electron line density and visual magnitude The sensitivity of the Arecibo ISR can be accurately estimated from conventional ionospheric experiments. The relation between the signal temperature S, and the effective radar scattering cross-section 0 at with a 250 kHz filter is range r for our observations found to be

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about 15 dB above their noise level. Large antenna area, low receiver noise temperature, and short range make our observation far more sensitive. In order to estimate the equivalent visual magnitude and electron line density (ELD), we assume the effective half beam width as 0.2”, at which offset angle the attenuation reaches 1OdB with respect to the beam center. With this assumption, the detected daily average flux rate was about 1000 meteors/hour/km2 or 3 x lO~‘/m*/s. The true flux rate was likely higher because, as we discussed in the above, the Arecibo radar is sensitive to only part of the meteors that intercept the radar beam. Using the meteor flux rate (N in /hour/km’) and visual magnitude (M) relation log N = 0.538M -5.17 derived from optical observations (Hawkins and Upton, 19%) the visual magnitude of the meteors in our observation is estimated to be in the order of + 15. VHF radio observations suggest that the relation between line density and visual magnitude for a meteor with a velocity of 40 km/s can be approximately expressed as in (McKinley, 1961) M = 40-2.510g*oc(

(2)

where we use tl to represent the electron line density (ELD). Using M = 15 as derived from the flux rate estimation, we have a = 8 x 109/m. As discussed in the following subsection, a more direct way of estimating the ELD is to utilize the signal power. Using an effective scattering length of 4 m, we estimate that the average ELD is 4 x lO’/m. Corresponding to this ELD, we have the visual magnitude as + 16, again via equation (2). Since the signal power can be accurately determined from observation, this approach yields more accurate results. In any event, the two independent methods do not differ very much. We take M = 16 and a = 4 x 109/m as characteristic values for our observation. The mass of the meteoroid at such a visual magnitude is about 10P6g according to Hughes (1978).

(1) Underdense scattering from smooth trails For meteor detection purposes, assuming that the minimum detectable signal temperature is 1200 K, which is at least 3 times the noise level, the minimum detectable scattering cross-section at a range of 100 km is 3 x lop9 m’. Since most of the meteors reported here have a S/N larger than 30, the effective scattering cross-section of the average echo in our observations is on the order of 3 x 10~*m2. For reference, in the UHF observation made by Evans and Brockelman (1964) using a less sensitive radar at essentially the same frequency, the average cross-section at 300 km range was l-2 x 10P2m2, which was

Most applicable to classical meteor echoes is the underdense scattering mechanism. In the “underdense” situation, i.e., when the plasma frequency of the meteor trail is below the probing radar frequency, the radio wave can penetrate the plasma and be reradiated by individual electrons. For underdense trails, it is usually most efficient to scatter radio wave energy back if the radar beam forms a right angle with the meteor trail. In the following, we estimate the electron line density assuming that underdense scattering from a uniform trail is the sole mechanism operating.

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Fig. 11. Diagram depicting the effective scattering length L, for a meteor trail undergoing rapid expansion. The dashed

lines are the radar wavefronts separated by a quarter of the wavelength. L, is the trail length within the Fresnel zone immediately behind the meteor head.

The underdense scattering theory is well established for VHF radars (McKinley, 1961). Because of the initial rapid expansion of the trail radius (i.e., the socalled initial radius effect), the VHF theory cannot be readily applied to UHF. To estimate approximately the electron line density for underdense scattering, a convenient way is to assume that all the energy comes from the portion of the trail where all the electrons are in the same Fresnel zone. As depicted in Fig. 11, the total energy radiated from the rear part of the trail is approximately zero because of destructive interference from different Fresnel zones. The energy received is roughly the energy radiated by the front portion of the trail with a length L,, where all the electrons are within one Fresnel zone. Again denoting the ELD of the trail by c(, the effective scattering cross-section can be written as e = (~&)*a,, where 6, = 10-28m2 is the classical electron scattering crosssection. For the moment, we have ignored an exponential term describing interference within the trail itself (exp( - 8n’?/1’)). The diameter of a meteor trail after the initial rapid expansion is thought to be 0.3-1.5 m, which is the order of the radar wavelength at UHF. When viewed from 90” aspect angle, destructive interference will render the trail portion with a diameter greater than a quarter of the radar wavelength essentially invisible due to the exponential term mentioned above. Consequently, the effective underdense scattering region is dominated by the portion where the trail radius is less than n/8. Since the initial expansion process is thought to occur at a speed of 1 km/s, for a typical velocity of 50 km/s, the trail radius is n/8 at 4 m behind the meteor head. Using L, = 4m and (r = 3 x lo-* m’, we have

the characteristic ELD as 4 x lO’/m, which is the value we quoted in the last subsection. If a meteor trail forms an arbitrary angle with the radar beam, the effective scattering length will be considerably reduced due to interference. When the meteor flies straight into the radar beam, the effective scattering length becomes smaller than n/4. Thus it is possible that some of the echoes in our observation are detected by virtue of underdense near perpendicular scattering at the principal Fresnel zone alone. However, underdense scattering does not at all explain why we get radial echoes nor why the echo power in our observation even appears to be enhanced in the head-on direction. This suggests that, other than the underdense scattering mechanism, there is at least a second mechanism in operation. In the following, we discuss scattering from an overdense plasma and scattering due to irregular structures existing in a meteor trail. Overdense scattering In the “overdense” situation, i.e., when the plasma frequency of the meteor ionization is above the probing radar frequency, an incident radio wave is reflected by the plasma. An overdense echo is not aspect sensitive since high density ionization can only be confined in a very small region near the meteor head. To estimate the importance of overdense scattering, let us assume that the meteoric ionization is initially confined in an infinitely small space at the meteor head and gradually expands without going through any loss process. For a fixed ELD, the largest overdense scattering cross-section is obtained at an expansion size such that the plasma density just equals the radar frequency. For a radar frequency of 430 MHz and an ELD of 8 x 109/m, the maximum overdense trail radius is found to be 0.01 m, which is much smaller than the wavelength (0.7m). Clearly, overdense scattering for our observation belongs to the domain of Rayleigh scattering. Using the Rayleigh scattering coefficient curve for a metallic sphere found in Skolnik (1980, p.34), we estimate that the scattering coefficient for our case is of the order of lo-‘, which makes the effective scattering cross-section from the overdense part to be of the order of 3 x lo-l2 m2 which is well below our typical cross-section. Rough trail scattering McIntosh (1962) and Greenhow (1961) have discussed rough trail mechanisms to explain bright VHF head echoes and longer duration echoes which sometimes accompany them. The rough trail scattering that they envisioned is mainly due to the overdense part of

149

Meteor observations by in coherent scatter radar. II a meteor trail, which is not likely to apply for our observations. In the following, we consider scattering from a rough underdense trail. Consider first a dynamic rough trail model, in which the Bragg scattering structure moves at a speed well above the atmospheric thermal velocity. Let us consider the following plausible meteor ablation process. When the outer layer material is shredded from a meteoroid, the debris may well consist of a swarm of neutral and charged dust, molecules and atoms. As the meteoroid continues its plunge in the atmosphere, more and more such debris is produced and an efficient Bragg scattering structure is created by turbulence or a plasma instability. Because the debris can still be much more massive than neutral air particles and have a much higher velocity than the atmospheric thermal velocity, it will not diffuse into the ambient atmosphere. Since the debris structure behind the meteor head is driven by turbulent processes, a Bragg structure could maintain its structure for a much longer time than that allowed by ambipolar diffusion. The Bragg scattering structure can be extended far behind the meteor head. The long Bragg structure can result in not only strong echoes in the head-on direction, but also makes it possible to observe echoes far behind the meteor head. We develop the model based on turbulence scattering theory for the lower atmosphere which we apply to the ablation zone behind a meteor head. At the heights of the observation, normal atmospheric turbulence does not create a detectable echo for a 430 MHz radar since the wavelength of the system is smaller than the Kolmogorov microscale, $

1’4

(1

q=

-

E

where v is the kinematic viscosity and E is the energy dissipation rate. For atmospheric levels of E, q is tens of m at the echoing heights of interest here. This means that no structure is developed at half the probing radar wavelength, which is the Bragg scattering scale. But in a steady-state model of turbulence E is also equal to the energy input rate which we hypothesize will be much larger than atmospheric levels for an ablating meteor traveling at several tens of km/s. Following Tennekes and Lumley (1972) c=-

2 km trail shown in Fig. lb. At the 101 km center of the same trail, v is about 40 m’js (Banks and Kockarts, 1973) and using V = 60 km/s we find that q = 1.4 cm. This puts the Arecibo 430MHz radar backscatter wavelength of 34 cm well into the inertial subrange. This does not mean that the region will be detectable, only that the turbulent spectrum will have structure at the scattering wavelength. To estimate the scattering cross-section we follow the Booker formula for the scattering cross-section per unit volume, m-’

): = 4xa,AN2(k) (

>

where AN(k) is the spectral density of the three-dimensional turbulent spectrum at the Bragg wavenumber k,. For a turbulent spectrum we use a three-dimensional inertial subrange, the integral of which for k greater than k, is equal to the total fluctuation strength. For convenience we use a standard model (Rufenach, 1975) for a three-dimensional isotropic spectrum to the inertial suband set yP = 1 l/3 corresponding range of a passive scalar electron gas.

(6) where k, = 27-c/1, is the break point in the spectrum and can be considered as the energy injection wavenumber. Fork > k, the three-dimensional spectrum will decrease as k- “I3 in this model. The integral of equation (6) over all f yields (AN/N)2, the total fluctuation strength. Examples of this function are plotted vs lkJ fork, = k, = 0 in Fig. 12 with AN/N = 0.5 and different values of k,. The extension of the spectrum to

k, m-’

V’ L

where V is the characteristic velocity and L the characteristic scale of the turbulence process. Again following Lumley, we take L = (l/16), the physical length of the ablating region, or about 125 m for the

Fig. 12. Turbulent scatter spectra for AN/N = 0.5, c( = 1 and &=O.l8m (#l), 1.8m (#2), 18m (#3) and 180m (#4).

750

Q. H. Zhou and M. C. Kelley

k << k, is not physical since we expect that the energy input scale will fall within one order of magnitude of the break point to the inertial subrange. However, since most of the integral lies within ko/5 < k < co, we are not making much of a compromise in using this convenient expression. The vertical line corresponds to the Arecibo backscatter wavenumber k, = 4n/i = 18m-‘. Note that by taking k, = ky = 0, we have oriented the coordinate system such that z lies along the radar line-ofsight. The plot shows that the larger the energy input scale the smaller the fluctuation strength at the Arecibo wavenumber. To estimate the scattering cross-section the relative spectral density must be multiplied by mean electron density and the scattering volume. As we shall see these are not unrelated quantities. Consider a radial meteor trail which produces a electrons per meter initially. Let D be the diameter of the trail and H the length of the range gate (H = 1.2km in our case). Then the total number of electrons in the trail is aH and the number density is 4a/nD2. Since the scattering volume is nD2H/4, the total scattering cross-section is then

Using AN/N = 0.5, and a diameter of 0.5m, (ANiN)* from Fig. 12 is 7.2x lo-’ and 0 = 3.4 x 10-‘OmZ. This value is too small to explain our results by about a factor of 400. As a final possibility we turn to an unspecified plasma instability with k vectors aligned with the meteor axis. An extreme case can be modelled by an anisotropic Gaussian spectrum such as presented in Equation (4) of Rufenach (1975). (8) where k, is a characteristic scale, k, is the wavenumber parallel to the meteor velocity, k, is the wavenumber perpendicular to the meteor flight and a is an anisotropy factor. If the spectrum is peaked near the Arecibo wavenumber and the most intense waves are parallel to the meteor velocity, then, k. = k, and a is large. Evaluating equation (8) at k = (k,, k,) = (k,,O) yields

For a = 20 and k, = 18 mm’ this yields 2.2 x 10m4 and rr = lo-‘m*.

Researchers at Jicamarca, where the geometry favors plasma instabilities with kl_&, have invoked the two-stream Farley-Buneman instability due to currents along the meteor trail to explain anomalous meteor echoes (Chapin and Kudeki, 1994). But this process will not work at the roughly 45” angle to B,, over Arecibo. What could this instability be? We do not know, but are willing to speculate. The field of dusty plasma physics is developing rapidly. An enhanced 430 MHz echo was reported over Arecibo which may be related to charged ice. When the Space Shuttle engines were burned over Arecibo, an expected plasma depletion was formed, but in addition, a short enhanced echo was registered by the radar (Bernhardt et al., 1995). Several candidate echoing processes involving charged ice formed in the supercooled expanding water vapor cloud were proposed in that paper to explain this signal. One of the proposed sources involved the motion of the charged ice relative to the background plasma. Something like this may be occurring in the meteor environment as well. Rosinski and Snow (1961) and Hunten et al. (1980) have shown that when meteors ablate, they rapidly form dust by accretion. This dust will charge in the high temperature ionized cloud around the meteor. Perhaps dust-acoustic waves (de Angelis et al., 1988; D’Angelo, 1990; Rao et al., 1990; Shukla and Silin, 1992; Rosenberg, 1993) are generated in this process at wavelengths matched to the Arecibo radar. The fact that many echoing regions display a very large line-of-sight velocity suggests the dynamic rough trail scattering mechanism may be the most important mechanism responsible for what we have observed at Arecibo. However, examination of meteor echoes from our transmitter pulse coded experiment suggests that it is possible that a stationary Bragg scattering structure may also play a part. The effect of a Barker coding scheme on fast-moving meteors is such that the decoded echoes are not randomly smeared in range but appear to be symmetrically split with mirroring peaks displaced from the center, as shown by Pellinen-Wannberg and Wannberg (1994) using the EISCAT UHF radar. Similarly decoded echoes at Arecibo, however, often show a single peak and are not necessarily symmetric. This leads us to believe that the echo power is a superposition of the power from a fast-moving medium as well as from a relatively stationary one. The echo from a stationary medium can be perfectly decoded and in the case of 13-baud Barker code, its power is increased by a factor of 13 and may dominate the power from the fast-moving portion of the trail for some instances.

Meteor Incoherent

observations by incoherent scatter radar. II

scattering

CONCLUSIONS

Incoherent scattering is unimportant for practically all the meteors in our observation. However, for some very large meteors, incoherent scattering can become observable. Using equation (1) and the fact that each electron has an equivalent incoherent scattering crosssection of 0.5 x lo-** m2, the incoherent scattering signal temperature due to a meteor trail with an ELD CI is: s

= 2000G~H T

751

(10)

r4

where His the height resolution and G, is the gain due to coding, which, for instance, is 13 for a 13-baud Barker code experiment. Let G, = 13, r = 100 km and H = 1 km, it requires an ELD of 5 x 10i4/m to produce an echo of 130 K, which is about the minimum signal temperature one can detect for short duration echoes. Pellinen-Wannberg and Wannberg (1994) arrive at an ELD of 5 x 1015/m for their trail echoes which is consistent with this estimate. Using equation (2) the faintest visual magnitude in our case has to be + 3.25 in order for incoherent scattering to become visible at Arecibo. In the absence of a meteor shower, we estimate that it takes about 2500 hours of observing time in order to see one such meteor for the Arecibo ISR. In spite of the fact that all of our observations reported here were conducted during strong shower periods, we have not seen any signature of incoherent scattering following a strong coherent echo for hundreds of strong meteor echoes visually examined. We are puzzled a bit by the high percentage of such echoes observed by the EISCAT radar (Pellinen-Wannberg and Wannberg, 1994). A more thorough and systematic search may reveal some incoherent scattering echoes in our data. Even the observation of very few incoherent scattering echoes could be significant to study recombination processes involving meteoric ions.

We have conducted meteor observations during three shower periods using the Arecibo 430 MHz incoherent scatter radar system. The time resolutions of those observations range from 2 ms to 3 ms while the height resolution was 1.2 km. The altitudinal and diurnal characteristics of meteor echoes from three observing periods are presented. In general, the echo characteristics observed in the time-resolved experiment are comparable with those observed from the time-integrated data except for the diurnal variation of the average echo height and the height extension of meteor echoes. Most of the echoes have an effective scattering cross-section above 3 x 1O-’ m2 although the theoretical limit is as low as 3 x 10m9m2. The visual magnitude of meteors reported here is estimated to be at + 16 and the electron line density is believed to be in the order of 4 x lO’/m. We show that, unlike a conventional meteor radar, the Arecibo 430 MHz radar is more sensitive to headon meteors than to meteors flying into the radar beam obliquely. We have discussed overdense and incoherent scattering mechanisms and deemed they are unimportant in our observation. Although underdense scattering from a smooth trail may be responsible for some of the echoes, it is our belief that the scattering due to the Bragg structure existing in a meteor trail is of foremost importance to UHF radar observations of faint meteors. The mechanism that maintains the irregular structures has yet to be investigated and quantified, but it seems that some plasma instability is required since a turbulent mixing process is too weak. Acknowledgements-We thank Drs. Mike Sulzer, John Cho, John Mathews, and Wes Swartz for various beneficial discussions and Dr. Phil Erickson for help with the data taking program. Arecibo Observatory is part of the National Astronomy and Ionosphere Center, which is operated by Cornell University under a cooperative agreement with the National Science Foundation.

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