Icarus 145, 53–63 (2000)
doi:10.1006/icar.1999.6330, available online at http://www.idealibrary.com on
Micrometeor Observations Using the Arecibo 430 MHz Radar
I. Determination of the Ballistic Parameter from Measured
Doppler Velocity and Deceleration Results
D. Janches and J. D. Mathews
Communication and Space Sciences Laboratory, 316 EE East, Penn State University, University Park, Pennsylvania 16802-2702
D. D. Meisel
Department of Physics and Astronomy, SUNY Geneseo, 1 College Circle, Geneseo, New York 14454-1401; and Communication
and Space Sciences Laboratory, 316 EE East, Penn State University, University Park, Pennsylvania 16802-2702
and
Q.-H. Zhou
Arecibo Observatory, Box 995, Arecibo, Puerto Rico 00613
Received May 24, 1999; revised September 15, 1999
for the study of radar meteors. Zhou et al. (1995) first reported
the use of this system for meteor observation, and soon afterwards Mathews et al. (1997) reported the detection of a “possible new class” of sporadic meteors utilizing a high-resolution
(150-m and 1-ms range and time resolutions, respectively) observation mode. Zhou et al. (1998) discussed common volume
46.8/430-MHz radar meteor observations at AO, and Janches
et al. (2000) report first observations of antapex micrometeors,
using the same high temporal and range resolution, with the
addition of a multi-pulse Doppler technique. This approach permitted the first direct measurement of Doppler velocities from
the micrometeor leading-edge and in some cases micrometeor
deceleration. These authors associated the leading edge of the
radar meteor with the classical head-echo, and by inference the
head-echo with “plasma” moving at the speed of the meteroid.
The AO radar has now been routinely used in high-resolution,
multi-pulse mode since 1995 to study the November Leonids
shower period. Mathews et al. (1998) presented a preliminary
sample of meteors, detected during the Leonids 1997 period,
in which a very distinct deceleration is present during the time
when the particles are observed by the radar. Velocity/deceleration measurements are essential for understanding the interaction processes occurring when the meteoroid enters
Earth’s atmosphere, as we discuss in some detail here.
The classical theory of the physics of the meteoroid entry
into Earth’s atmosphere has been described by many authors
(Opik 1958, McKinley 1961, Evans 1966, Bronshten 1983). We
will adopt their approach in this paper. Since, as we will describe, these particles are believed to be much smaller than the
We present a sample of radar meteors detected during the November 1997 Leonids shower period using the narrow-beam, high-power
Arecibo Observatory 430-MHz radar. During this period ∼7700
events were detected over 73 h of observations that included six
mornings. Near apex-crossing, 6–10 events per minute were observed in the ∼300-m diameter beam. From these events a total
of 390 meteors are characterized by a clear linear deceleration as
derived from the radial Doppler speed determined from the meteorecho leading-edge (head-echo). We interpret our results in terms of
the meteor ballistic parameter—the ratio of the meteoroid mass to
cross-sectional area—yielding a physical characterization of these
particles prior to any assumptions regarding meteoroid shape and
mass density. In addition, we compare these measurements with
the results of a numerical solution of the meteor deceleration equation and find them in good agreement. The size and dynamical
mass of the meteoroids are estimated considering these particles to
be spheres with densities of 3 g/cm3 . We also discuss atmospheric
energy-loss mechanisms of these meteroids. We believe these are
the first radar meteor decelerations detected since those ones reported by J. V. Evans (1966, J. Geophys. Res. 71, 171–188) and
F. Verniani (1966, J. Geophys. Res. 71, 2749–2761; 1973, J. Geophys. Res. 78, 8429–8462) and the first ones for meteors of this size.
c 2000 Academic Press
°
Key Words: meteors; meteoroids; radar; ionosphere; Leonids.
1. INTRODUCTION
The 430-MHz narrow-beam radar located at Arecibo Observatory (AO) in Puerto Rico has proven to be a crucial instrument
53
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c 2000 by Academic Press
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54
JANCHES ET AL.
atmospheric mean free path (MFP; ∼14 cm at 100 km) at the
altitudes at which they are observed, we have assumed that the
meteoroid interacts with the air molecules through individual inelastic collisions without the formation of “air caps” (Bronshten
1983). The meteor deceleration equation assumes that the loss
of momentum by a meteoroid is proportional to the momentum
of the impinging air flow and can be expressed as
to-radiant separation at 1047 UTC (0647 LT). Figure 1 displays
the observed fluxes during the six mornings. Note that no apparent increase of the flux was observed at any time during the
reported Leonid visual meteor maximum (November 16 and 17)
(Brown 1999). Thus the question of which portion of these meteors are members of the shower and which are the micrometeor
sporadic background remains unanswered. This question will be
addressed further in the conclusions.
dV
2
Our observational methods are similar to those presented in
M
= −0Sρa V ,
(1)
dt
Janches et al. (2000). In this case we utilize a triple (coherent
where M is the meteoroid mass, V the meteor speed, 0 the drag radar) pulse scheme, allowing the determination of three indecoefficient, S the meteoroid cross-sectional area, and ρa is the pendent estimates of the pulse-to-pulse Doppler phase shift of
atmospheric mass density at the altitude at which the meteor the returned echo. This technique provides very accurate meais observed. Assumptions regarding mass-loss, energy transfer surements of the meteor instantaneous Doppler velocity directly
efficiency, and meteor mass densities can be made in order to from the highly resolved head-echo. The reader may refer to
Mathews et al. (1997) for a complete description of the system
reduce the number of unknowns in (1).
In addition, if the observed meteor velocity (V ) and decel- and methodologies.
Our Doppler technique is summarized in Fig. 2. Figure 2a
eration (dV /dt) are utilized, (1) can be rewritten solving for
shows
the three returns from a strong and (relatively) long-lived
unknown parameters in terms of measured parameters, yielding
meteor. The head-echo is taken to be the leading-edge of each
return. The range-spreading is due to the decaying transmitρa V 2
,
(2) ter pulse and the wide dynamic range of the return. Figure 2b
BP = −
dV /dt
displays the same event where each diamond represents one
where BP is the meteor ballistic parameter—the ratio of the me- range/time (150 m/l ms) resolution cell belonging to the meteoroid mass to cross-sectional area taking 0 = 1 (Opik 1958, teor region and the asterisks indicate those pixels that belong
Ceplecha et al. 1998). Note that Vrad and dV /dt are measured to the meteor head-echo. Since we record the in-phase and inwhile ρa is taken from the MSIS-90 model atmosph- quadrature voltages for each cell of the three echoes, three estiere (http://nssdc.gsfc.nasa.gov/space/model/models/msis.html). mates (one from each pulse-pair) of Doppler phase shift between
This approach yields a physical characterization of the me- the returns can be obtained (Mathews 1976, Janches et al. 2000).
teoroid with no assumptions regarding meteoroid density and Figure 3 displays the instantaneous Doppler velocity obtained
from the phase shift, where each data point is an average of the
shape.
In this paper we present a study of 390 meteors detected dur- three estimates at the given 1-ms interval. It is very clear from
ing the 1997 Arecibo Leonids campaign that display a clear, this figure that the meteor was decelerating during the time it
linear deceleration. The majority of these meteors are believed was visible to the radar. We use a linear least-squares fit to obtain
2
to be unrelated to the Leonids shower itself. A description of the the deceleration yielding 50.4 ± 0.2 km/s for this example. We
observations is presented in Section 2. In Section 3 we present present other examples in Fig. 4. A linear fit is used as no signifour results and compare them with those derived from numeri- icant curvature is present in 389 of 390 of the sample discussed
cal solution of (1). In addition, we discuss different scenarios of here. The remaining meteor perhaps displayed a small curvature
the physical processes that the meteoroid undergoes in its entry term in the deceleration (Fig. 3).
The average range-rate velocity of the meteor can also be obinto the atmosphere. Finally we infer meteroid sizes and masses
tained from the time-range trajectory if the duration of the event
from both the deceleration results and observed fluxes.
is sufficiently long. This calculation confirms the Doppler speed
determination. In addition, if the altitude at which the meteor has
2. OBSERVATIONS
been observed is higher than 104 km or lower than 90 km only
The observations we report here were performed at Arecibo one or two echoes will be present—46% of our observed meteObservatory (AO; astronomical coordinates, 18◦ 210 13.700 north ors had sufficient duration to estimate the meteor speed from the
latitude, 66◦ 450 18.800 west longitude) during the November 1997 trajectory and were within the range where three returns were
Leonids shower period. During this time more than 7700 radar detected. Of this portion only 390 (5%) meteors showed decelermeteor events were detected over six mornings (November 15, ation within reasonable errors limits. The remaining meteors that
16, 17, 18, 19, and 20; 73 h total observation), yielding of or- showed no deceleration are interpreted as having masses larger
der 6–10 events per minute near apex-crossing (∼0600 LT) and that the mass limit for which we can detect deceleration, as will
over the 88- to 106-km altitude range. The antenna was directed be discussed in more detail in Section 3. The measured decelertoward the shower radiant transit point (Zenith Distance = 3.9◦ ations range from a few km/s2 to 200–300 km/s2 (Fig. 5b), with
looking toward the geographic north) yielding minimum antenna- meteor average velocities between a few km/s to a maximum of
FIG. 1. Observed fluxes by the AO 430-MHz radar during the Leonids 1997 meteor shower period.
PHYSICAL CHARACTERIZATION OF MICROMETEOROIDS
55
56
JANCHES ET AL.
FIG. 2. (a) UHF radar meteor—relative received power (grayscale)—is plotted versus time and altitude with 1-ms and 150-m resolutions, respectively. Three
images of the meteor are seen due to the use of three, 1-µs-duration, radar pulses separated by 10 µs (b) Detail of the same event where the diamonds represent a
1 ms/150 m resolution cell and asterisks indicate the meteor leading edge (head-echo).
∼70 km/s (Fig. 5a). The distribution of observed altitudes are
presented in Fig. 5c.
3. DISCUSSION
We begin our discussion by estimating the average mass of
these particles from the observed fluxes (Fig. 1). Using the system parameters given in Mathews et al. (1997) and assuming
1 µgm/meteor, an observed rate of 300 meteors/h yields an incident flux on the whole Earth of the order of 1.7 × 109 g/year. This
value is in good agreement with the observed fluxes for masses
between 10−8 and 10−6 g, given in Hughes (1978, Fig. 17),
confirming that these particles are in fact small. Theoretical results, discussed later in this section, show that a spherical 1 µg
particle—86 µm in diameter if 3 g/cm3 is assumed to be its
density—will experience a deceleration close to our detection
limit. This potentially explains why we observe deceleration in
only 5% of our measurements.
The numerical calculations performed by Love and Brownlee
(1991) suggested that particles smaller than 50 µm in diameter
PHYSICAL CHARACTERIZATION OF MICROMETEOROIDS
57
FIG. 3. Meteor Doppler speed (asterisk, left-hand scale) and signal-to-noise ratio (line, right-hand scale) plotted versus time for leading edge (head-echo)
return of Fig. 2 meteor. Each data point is the average of three estimates (one from each pulse-pair combination) of the velocity derived from the pulse-to-pulse
Doppler phase shift.
do not have noticeable loss of mass due to heating effects.
Their results also suggest that the time interval from when the
particles begin experiencing heating effects due to their interaction with the atmosphere to the time when they reach the
temperature necessary to ablate by vaporization or melting are
of the order of a few seconds. In addition, they showed that
maximum temperatures and mass loss are achieved between
85 and 90 km. Since the events we report are visible by our
radar over time intervals 3 orders of magnitude shorter than
the Love and Brownlee results and are observed above the altitudes for which they report significant mass-loss (Fig. 5c), we
assume that no mass loss due to evaporation or melting occurs (also see Bronshten 1983; Section 8). In addition, we have
never observed fragmentation in spite of the fact that the observed altitudes are quite low for particles of these velocities
according to Porter (1952, Table 20)—this again indicates very
durable particles. We believe, as will be mentioned later, that
sputtering of single atoms/molecules is the dominant mass loss
mechanism. This process is too slow to produce significant mass
reduction during the relatively short observation times. Hence
we assume a low mass-loss regime for the remainder of this
paper.
As we mentioned in Section 1, we next describe our determination of the ballistic parameter given by Eq. (2). In Eq. (2)
we use ρa as given by the MSIS-90 model atmosphere and the
initial velocity of the meteor. We determine the meteor deceleration, also as input to Eq. (2), by linear (least-squares) fit of the
Doppler velocity versus flight-time curve. The distribution of the
resultant meteor BP for all 390 meteors is displayed in Fig. 6.
Note that two distinct distributions are observed at 2 × 10−3 and
6 × 10−3 g/cm2 , perhaps suggesting the presence of different
classes of objects.
To interpret our results we numerically solve (2) assuming no
mass loss, for various assumed meteor BP, velocity, and altitude
values. We then calculate the average deceleration experienced
by the particle over a period of 100 ms. A comparison of the dependency of the meteor deceleration with the meteor BP, given
initial meteor velocity and altitude, derived from both observation and numerical solution of (2) is given in Fig. 7. Each data
point in Fig. 7 represents the observed meteor deceleration and
meteor BP (as calculated from the observed decelerations, velocities, and altitudes) for those meteors with the initial measured
velocity and observed altitude indicated in the plots. The curves
show the results determined from the numerical integration of
(2). The results of this comparison are in good agreement, thus
supporting the validity of the theoretical description.
We now use the drag equation to illustrate the range of sizes
and masses of these objects. Using the same approach as Evans
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JANCHES ET AL.
FIG. 4. Examples of radar meteor deceleration. The symbols and scales are the same as in Fig. 3. The straight lines are the best linear (least-square) fit to the
Doppler speeds. The meteor deceleration is given by the slope of the lines.
59
PHYSICAL CHARACTERIZATION OF MICROMETEOROIDS
(1966), and lacking a basis for another approach, we assume
the meteoroid to be of spherical shape and define the meteor
equivalent-radius (Opik 1958, Chapter 4) as a function of the
meteor BP as
rδ =
3
BP,
4
(3)
where r is the meteor equivalent-radius and δ the meteor mass
density (g/cc). Note that we do not consider the approach used by
Verniani (1966, 1973) since he derived the meteor speeds from
the rate of development of the Fresnel pattern of the received
meteor trail-echo. As seen in Fig. 6, a surprising characteristic of our BP results is the wide range, 10−4 –10−1 g/cm2 , of
the distribution with a peak at 10−3 g/cm2 . This distribution is
1–2 orders of magnitude lower than the average r δ given by
Evans (0.08 g/cm2 ). Taking the meteor density to be 3 g/cm3 ,
this distribution yields masses between 10−12 and 10−6 g. Note
that Evans (1966) used δ = 1 g/cm3 to calculate the mass of the
meteors. The range of our results will not change significantly
if we use 1 g/cm3 or other common meteor densities (Whipple
1952, Murrell et al. 1980 McDonnell et al. 1998).
Finally we can verify our previous assumptions by modifying
(1) to take into account mass-loss and thus obtain an estimate
of how much mass the meteoroid loses during the time it is
observed by our radar. This can be done by considering the total
loss of momentum as d(M V )/dt and rewriting (1) as
µ
¶
dM
M dV
dt
= − 0Sρa V +
.
(4)
dt
V
FIG. 5. (a) Distribution of meteor initial Doppler velocities of the 390
events for which deceleration was detected. (b) Distribution of meteor deceleration. (c) Distribution of meteor observed altitudes. The horizontal lines indicate
the range for which the three echo returns are present.
Since the deceleration is clearly constant over our interval of
observation (Figs. 3 and 4) and we know the meteor altitude and
velocity for every millisecond, we can integrate numerically (4)
using as initial conditions the initial observed meteor velocity
and altitude and the mass estimated from the initial meteor BP.
We emphasize the fact that this is a very simple approach and is
done with the purpose of obtaining an estimate of the mass loss
to validate our previous assumptions. A more rigorous approach
to this issue will be given in a future paper. Figure 8 displays
the percentage of mass loss found using (4) for those meteors
presented in Fig. 4. Four of these events lost less than 2% of their
mass while the other two lost less than 6%. Figure 9 displays
a histogram of the total mass loss—as deduced from (4) over
the time duration during which the meteors are observed—of
the 390 meteors utilized here. As seen from Fig. 9 most of these
particles lose less than 2% of their mass. The resultant decrease
in the BP due to the Fig. 9 mass-loss calculated as the ratio of
the estimated initial and final meteor masses and cross-sectional
areas is of the order of 0.5% (Fig. 10).
Information on how these particles interact with the atmosphere can also be drawn from these results. These considerations are necessary in order to elucidate the mass-loss mechanism(s) encountered by the meteoroid in its path through the
atmosphere. The atmospheric mean-free-path (MFP) at the
60
JANCHES ET AL.
FIG. 6. Distribution of the meteor ballistic parameter. Two distinct distributions can be observed at 2 × 10−3 and 6 × 10−3 g/cm2 , suggesting the presence of
different classes of objects.
altitudes where these meteors are observed is on the order of
10 cm with an average atmospheric intermolecular spacing of
∼0.4 µm. The MFP is several orders of magnitude greater than
the meteoroid sizes suggested by our calculations. This indicates
that the meteoroid encounters the atmosphere via collisions with
individual air molecules rather than aerodynamically. That is, it
seems unlikely that an “air cap” forms.
The mass of air per second that the meteoroid encounters
during its flight can be rewritten from (1) as Sρa V . A 50-µmradius, 3 g/cc (∼1 µg) meteoroid with a speed of 55 km/s observed at an altitude of 100 km will encounter 2.6 × 10−10 kg/s
or 5.5 × 1015 molecules of air per second. Taking 80 ms as an
average meteor flight-time through our radar and 30 km/s2 as
the average deceleration, the meteoroid encounters only 1%
of its mass, undergoes 4.3 × 1014 collisions, and loses 1.4 J of
its kinetic energy. Table I summarizes these results for different meteoroid parameters. The correlation between the meteor
mass-loss and the atmosphere mass-encountered suggests that
sputtering is the dominant mechanism for the ablation of these
particles.
We have observed dV /dt to be relatively constant. It is natural
to ask under what conditions is this physically correct and not
just the result of a short time of observation. Since the mass-loss
is small over our observational time intervals, we can return to
(1) and solve for ρa V 2 , the aerodynamic pressure:
ρa V 2 = −0BP
dV
.
dt
(5)
TABLE I
Expected Collisional Frequencies
Collision Freq.
(×1014 s−1 )
(V = 60 km/s)
Collision Freq.
(×1014 s−1 )
(V = 30 km/s)
Collision Freq.
(×1014 s−1 )
(V = 11.7 km/s)
Radius
(µm)
Altitude
(km)
50
120
100
95
90
1.9
60
155
372
0.9
29
77
186
0.4
11
30
72
10
120
100
95
90
0.07
2.4
6.2
14.9
0.03
1.1
3.1
7.4
0.01
0.4
1.2
2.9
1
120
100
95
90
0.0007
0.024
0.062
0.14
0.0003
0.011
0.031
0.074
0.0001
0.004
0.012
0.029
PHYSICAL CHARACTERIZATION OF MICROMETEOROIDS
61
FIG. 7. Comparison between the experimental and numerical results of the dependency of the meteor deceleration with the BP, for different combinations of
meteor initial speed and initial altitude. The data points represent the observed meteor deceleration and meteor BP, as calculated from the observed decelerations,
velocities, and altitudes, for those meteors with initial measured velocity and observed altitude indicated in the plots. The curves show the results determined from
the numerical integration of (2).
FIG. 8. Mass loss as a function of time for the events presented in Fig. 4
as given by the numerical integration of (4).
FIG. 9. Distribution of the total mass loss of the 390 events.
62
JANCHES ET AL.
CONCLUSIONS
FIG. 10. Distribution of the magnitude of the change on the meteoroid
ballistic parameter due to the change of mass. Note that this change is negative
(i.e., the final BP value is lower than the initial value).
In order for dV /dt to be truly constant then ρa V 2 must be rigorously constant. This in turns leads to the condition (by differential) that the velocity be low, i.e., that it covers two atmospheric
scale heights per second which at these altitudes (90–100 km)
means V ≈ 12 km/s. We thus conclude that the constancy of
dV /dt occurs only because of our short radar visibility time and
not through any physical mechanism.
Previously we noted that the bimodal distribution of BP values may be the result of two density or size classes in our sample.
In the past (McKinley 1961, p. 185) it was argued that meteors,
which were “dust balls” and subject to fragmentation, would
break up at ρa V 2 = 2 × 103 N/m2 . Since we know ρa and V 2 we
can predict at what altitudes we should have seen fragmentation, if our objects were made up of aggregates of high density
small particles instead of just single ones. Using the MSIS-90
atmosphere, calculation shows that the fragmentation zone ends
at about 102 km high for 70 km/s particles and drops at about
2 km/10 km/s until it reaches ∼90 km for 15–20 km/s. Since
we do not observe any fragmentation at any altitude or at any
speed, it can be concluded that we are observing particles that
were single objects prior to atmospheric entry or broke up long
before they entered our zone of detectability. From (3) and due
to the fact that BP is bimodal we infer that there are two classes
of particles present, each with its own average value of r δ which,
according to our observations, differ by only about a factor of
three. If it is assumed that the two peaks represent a difference
of density and the size distribution is the same for both densities, then if those with BP higher than average have density
of 3 g/cm3 (“asteroidal”), the other class has a density of about
1 g/cm3 (cometary?). If the lower BP objects are indeed cometary,
then our results imply that the fundamental units of “fluffy” meteors have density of the order of 1 g/cm3 , within our derived
ranges of sizes.
We have reported physical details of that sample of meteors
displaying deceleation as observed during the November 1997
Leonids shower period using the Arecibo Observatory UHF
radar system. Over 7700 meteor events were detected during
a period of six mornings. About 46% of these meteors had sufficient duration to calculate their radial speed from both the
range-time trajectory and the Doppler phase shift of the meteor head-echo and were within the altitude range for which the
echo-return from all three pulses were present. Of this portion
only 390 radar meteor events showed clear (linear) deceleration.
The accurate measurement of the instantaneous Doppler velocity and the deceleration allowed us to interpret our results in
terms of the meteor ballistic parameter (BP), yielding a physical
characterization of these particles prior to assumptions of meteor
shape and mass density. This distribution covers a wide range
(10−4 to 10−1 g/cm2 ) and suggests the presence of two classes
of BP characteristics and thus of meteors. The consistent linear
behavior of the observed deceleration suggests that these particles undergo low or negligible mass loss. This result agrees
with those obtained by the theoretical work done by Love and
Brownlee (1991). We numerically integrated the meteor drag
equation, expressed in terms of the meteor BP, for various values of meteor BP, initial velocity, and initial altitude and find
this calculation to be in good agreement with the results derived
from the observations. We note the range of sizes and masses
that these results represent, when the meteroid is assumed to be a
sphere of density 3 g/cm3 , give radii of ∼104 –10−2 cm. We also
obtained an estimate of the mass loss using a simple approach
that indicates that almost all the particles will not lose more than
2% of their mass. This confirms our previous assumptions.
Two questions remain unanswered. First, it is not clear which
portion of the overall observations are in fact Leonids meteors.
The observed meteor fluxes did not show an increase toward
the reported Leonids maximum (Fig. 1) in spite of fact that
the maximum occurred when the antenna was closest to the
shower radiant. In addition, the observed fluxes reported during
nonshower times by Mathews et al. (1997) and Zhou and Kelly
(1997) using the AO radar are of the same order as those reported
here. This suggests that the micrometeoroid component of the
Leonids 1997 shower was negligible compared with that of the
daily sporadic influx. This result is not surprising since IRAS
studies of comet trails suggest particle sizes greater than 1 mm
(Sykes et al. 1990, Brown 1999). Observations during periods
away from known meteor showers are essential to address this
problem.
Finally, it is uncertain how or if these meteors disintegrate.
We observe them disappearing from our radar beam, but yet
we do not see any evidence of significant mass-loss mechanism
that indicates the meteor is slowly being ablated. Therefore, we
propose as a possibility that the meteoroids catastrophically disintegrate, depositing the majority of the micrometeoroid mass in
the 90- to 100-km altitude region, before any significant melting
PHYSICAL CHARACTERIZATION OF MICROMETEOROIDS
or evaporation process begins. Planned common-volume with
the radar, time-resolved, synchronous with the radar, optical/IR
observations of the meteor zone at Arecibo may well yield further information on these issues.
ACKNOWLEDGMENTS
This work has been partially supported by NSF Grant AST 98-01590 to The
Pennsylvania State University and to SUNY—Geneseo and by the SUNY—
Geneseo Foundation’s 1997 Roemer Senior Research Fellowship to D.D.M.
The Arecibo Observatory is part of the National Astronomy and Ionosphere
Center, which is operated by Cornell University under cooperative agreement
with the National Science Foundation. The authors thank David Garmire for his
help in the analysis of the data and the referees for their useful comments.
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