Icarus 150, 206–218 (2001)
doi:10.1006/icar.2000.6575, available online at http://www.idealibrary.com on
Orbital Properties of the Arecibo Micrometeoroids at Earth Interception
D. Janches
Communication and Space Sciences Laboratory, Department of Electrical Engineering, Penn State University, University Park, Pennsylvania 16802
D. D. Meisel
Department of Physics and Astronomy, State University of New York—Geneseo, Geneseo, New York 14454; and Communication and Space Sciences Laboratory,
Department of Electrical Engineering, Penn State University, University Park, Pennsylvania 16802
and
J. D. Mathews
Communication and Space Sciences Laboratory, Department of Electrical Engineering, Penn State University, University Park, Pennsylvania 16802
E-mail: [email protected]
Received June 8, 2000; revised October 27, 2000
1. INTRODUCTION
Using the Arecibo Observatory (AO) 430-MHz Radar we have
developed a Doppler technique to measure very precise micrometeor instantaneous velocities directly from the meteor head echo. In
addition, a large number of the observed meteoroids show deceleration. With the velocity, the deceleration, and the assumptions of a
spherical shape and a mean micrometeoroid mass density, we have
obtained estimates of in-atmosphere particle sizes. The size estimate, the MSIS model atmosphere, and the measured deceleration
are used to obtain the meteor extra-atmospheric speeds, assuming
these particles undergo little mass-loss prior to and during the time
we detect them (Janches et al. 2000b, Icarus 145, 53–63). Orbital
elements at 1 AU are presented and discussed. These results have
not been corrected for perturbation effects such as radiation pressure, Poynting–Robertson drag, attraction by the giant planets, and
photoelectric charging effects. So far, over 7700 detections obtained
during November 1997 and 3500 during the November 1998 observation campaigns have been analyzed. The observing periods
included the Leonids meteor shower, but none of the orbits are recently derived from it. Out of these detections, we present details
of over 1500 orbits with eccentricities less than unity. These orbits
show (a) a depletion of postperihelion particles with small perihelion distance, suggesting the possibility of collisional and thermal
destruction, and (b) an enhancement of particles with perihelia in
the zone between Mercury and Venus. Also discussed are 40 βmeteoroids (with radii less than 0.5 µm) dynamically related to the
elliptical orbit population with q < 0.7 AU. We interpret the latter
results on the basis of Poynting–Robertson drag and the electromagnetic resonant effects proposed by G. E. Morfill and E. Grün
(1979, Planet. Space Sci. 27, 1269–1282). Comparison with previous
data sets indicates that most of the AO micrometeoroid orbits are
well randomized and that association with a particular parent body
is unlikely. °c 2001 Academic Press
Key Words: interplanetary dust, micrometeoroids; orbits, radar.
The distribution and sources of interplanetary dust particles
(IDPs) in the Solar System are of critical interest for planetary
science. Numerous spacecraft carry dust detectors (DDs) that
are providing fundamental results. Examples of these results include the identification of a significant extrasolar component of
the IDPs (Grün et al. 1997) and the recent detection of dust in
the jovian system (Thiessenhusen et al. 2000). However these
probes only roughly identify orbits and, because of small detector size, exhibit low detection rates. Also, DDs have yet to be
used for long-term exploration of IDP distributions near 1 AU.
Classical low-power meteor radars have historically been used
for these studies and some results can be found in Jones and
Brown (1993), Baggaley (1995), Brown and Jones (1995), and
Taylor et al. (1996).
Current observations of micrometeors at Arecibo Observatory
(AO), Puerto Rico, with the UHF radar uniquely has yielded meteor altitude, velocity, and deceleration, making it possible to estimate radiant, speed, and mass/radius (Janches et al. 2000a,b)
of thousands of particles. This is possible because we detect
and use the highly resolved (in time and height) meteor “head
echo” (in contrast to classical meteor radars that detect the “trail
echo”) to obtain the meteoroid dynamical parameters. These
particles have masses that appear to range from a small fraction of a nanogram to a few tens of micrograms (<1–200 µm
radius), making them the smallest particles reliably observed
with groundbased techniques. In addition, very precise beam
pointing information has provided good radiant information on
large numbers of these IDPs (Janches et al. 2000a). These results combine to make AO uniquely situated and suited for the
study and understanding of interplanetary dust near 1 AU using
groundbased observations.
206
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c 2001 by Academic Press
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ORBITS OF ARECIBO MICROMETEOROIDS
In this paper we present over 1500 orbits derived from radar
meteor detections obtained during the Leonids observation campaigns that took place at Arecibo Observatory, Puerto Rico in
November 1997 and 1998. We will refer to them for the rest of
this work as NOV97 and NOV98 samples. Active Leonids meteor shower took place during both these observing periods but
as we note and discuss in more detail in the following sections,
no apparent association of our results with the modern Leonids
stream or with any other known modern major meteor stream
has been found.
2. METHODOLOGY
The NOV97 data set is an updated version of the sample presented in Janches et al. (2000b). The triple-pulse observational
scheme used to detect this sample was described in Janches et al.
(2000b). The Doppler technique for obtaining the instantaneous
meteor Doppler velocity and deceleration were first described in
Janches et al. (2000a) and amplified in Janches et al. (2000b). In
this paper we use an improved version of our approach. For every
radar interpulse period (IPP) we obtain the real and imaginary
components of the pulse-to-pulse correlation function (Hagen
and Farley 1973, Mathews 1976, Janches et al. 2000a) given by
R j = C(t)C(t + 1t j ) + S(t)S(t + 1t j )
(1)
I j = C(t)S(t + 1t j ) − S(t)C(t + 1t j ),
(2)
where C and S are the normalized real and imaginary returned
voltages of two radar pulses separated by some 1t j ( j = 1,
number of pulses in one IPP-1), and compare them with a set of
predicted components, derived from a set of predicted velocities,
given by the set of equations
4π Vi 1t j
λ
4π Vi 1t j
,
= sin
λ
Ri, j = cos
(3)
Ii, j
(4)
where λ is the radar wavelength (69.7 cm) and i = 1, number
of elements on the predicted velocity vector. We determine the
meteor velocity by minimizing the function
χi2 =
n
X
((R j − Ri, j )2 + (I j − Ii, j )2 ),
(5)
j=1
where n is the number of radar pulses (or samples within a pulse)
in one IPP. We construct the predicted velocity vector around the
velocity given by the meteor altitude difference to duration ratio.
In order to obtain the error of each velocity determination, we
propagate errors in (3) and (4), resulting in
1Vi =
n µ
X
j=1
¶
λ (R j − Ri, j ) + (I j − Ii, j )
.
4π1t j
Rj + Ij
(6)
207
This improvement on the technique avoids the calculation of
the inverse tangent (Janches et al. 2000a) around its singularities,
which introduces errors on the meteor velocity determination
when it is close to the 2π aliasing velocity (34.85 km s−1 for
the 10-µs separation and 17.43, 34.85, and 52.3 km s−1 for the
20-µs separation).
The NOV98 sample is in principle the same as the NOV97 one
with some additional modifications and improvements. During
the November 1998 period we used a double-pulse scheme 1 and
10 µs long respectively separated by 10 µs. This improved pulse
scheme allowed us to have up to 55 estimates of the instantaneous
meteor Doppler speed per IPP instead of the three estimates obtained during the November 1997 campaign. In addition, the
observed altitude range was increased from 89–107 km in 1997
to 89–117 km in 1998. During the NOV98 period we performed
simultaneous UHF/VHF (430 MHz/46.8 MHz) radar observations but due to the limitation of the data-taking/recording duty
cycle for two concurrent radars, the temporal resolution was
decreased to 2 ms (instead of 1 ms used in 1997).
Approximately half of the ∼7700 events detected during the
1997 period have now been fully analyzed (i.e., altitude, velocity, and possible deceleration information was obtained). Out
of these ∼26% showed clear linear deceleration; hence the calculation of the meteor ballistic parameter (BP) and equivalent
size (when meteoroid spherical shape is assumed and canonical meteor mass density adopted, i.e., 3 gm · cm−3 ) is possible
(Janches et al. 2000b). Surprisingly, the NOV98 data set is almost the same size as NOV97, even though it is the result of the
only 6 h (out of a total of almost 90 h) of observation that have
been analyzed so far from this period. During this time, the total
number of events detected is equal to half of the total number observed during the whole 1997 period (∼72 h; see Janches et al.
(2000b)). It is not clear why there was a flux increase between
the two years, but a comprehensive study of this issue will be
given in future papers.
Figure 1 shows the observed dynamical meteor parameters
for both samples while Fig. 2 displays the size distributions for
both years. These results were found in the same manner as that
in Janches et al. (2000b). Note that in addition to the increase
of flux discussed above, the NOV98 is also characterized by
slightly faster events (Fig. 1c) and an increase in the number of
smaller particles (Fig. 2). This is probably due to the fact we
observed higher altitudes during the 1998 campaign, but again
a detailed analysis is needed to sort everything out.
The determination of present-day meteoroid orbits follows
from the determination of the meteor radiant and extraatmospheric velocity (Porter 1952, Dubiago 1961, Danby 1988).
Geocentric and heliocentric velocities include rigorous correction for diurnal aberration, zenith attraction, and Earth orbit ellipticity. The narrow AO beam—300 m in diameter at 430 MHz
in the meteor zone (Mathews et al. 1997)—assures that downthe-beam meteors can be identified. This information, as well as
the precise time, altitude, velocity, and deceleration information,
leads to top-of-atmosphere velocity and mass estimates (Janches
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JANCHES, MEISEL, AND MATHEWS
FIG. 1. (a) Meteor (initial) altitude distributions from the NOV97 and NOV98 (all observations that showed deceleration as discussed in the text). (b) Meteor
total duration distributions. The time resolution for the NOV97 was 1 ms while for NOV98 was 2 ms. (c) Initial velocity distributions from the NOV97/98.
(d) Deceleration distributions for both samples. The technique that is used to obtain these parameters is well described in Janches et al. (2000b).
et al. 2000b). We utilize the MSIS-E-90 model atmosphere (see
http://www.wdc.rl.ac.uk/wdcc1/msis90.html) in our upward integration of the meteor mass and momentum equations. We stop
the integration when the meteor velocity changes are 10−4 of
the final velocity (i.e., at heights of ∼120–130 km). The lack
of evidence for a significant mass-loss regime during the time
the particles are observed by the radar has been already discussed in Janches et al. (2000b). In our previous study of these
head echoes, a picture of single-particle ablation emerged and
has been constantly confirmed (Mathews et al. 1997; Janches
et al. 2000a,b). The number of observed micrometeors is now
reaching 10,000+ objects, but there has been no evidence of
gross fragmentation (i.e., no multiple events or microshowers
separated by more than one 150-m height bin) seen at any deceleration or velocity value, including events with speeds below
11 km/s that were seen. In addition during our two somewhat
limited optical searches (unpublished), no meteors brighter than
11th magnitude were seen in the beam area, although large numbers of micrometeors were observed by radar. To test the effect of
possible mass-loss, an empirical sputtering model with a sputtering yield that increases with energy (Sigmund 1969, Wasa
FIG. 2. Meteor ballistic parameter (BP) and equivalent radius distributions.
The vertical line is the size cutoff for orbital calculation. Note the increase in
the number of small particles between the two years.
ORBITS OF ARECIBO MICROMETEOROIDS
and Hayakawa 1992) was adopted; for the particle orbits discussed here it made little difference whether sputtering was
included.
Observation times and dates introduce orbit sampling bias. In
order to evaluate this sampling bias, a Monte Carlo simulation
program that is based on our orbit determination program was
written. In addition to the AO observing parameters for the radar,
the date and the time interval of actual observations are entered.
The program then uses a uniform distribution, random number
generator to obtain heliocentric velocity values along with a
similar generator to sample randomly in the designated time
interval. The heliocentric velocity generator assumes a range of
0.2 to 42 km/s. Departure of the actual data distributions from the
simulation indicates nonuniform distributions of various kinds,
including different means and/or standard deviations as well as
shifts in distribution types.
3. RESULTS AND DISCUSSION
The corresponding orbital elements for NOV97 and NOV98
are displayed in Figs. 3 to 6. In these figures, only the meteors for which particle radii are greater than 0.5 µm are shown
(see vertical line in Fig. 2). Particles smaller than this usually
show the largest observed decelerations and are excluded for
several reasons. In particular, the calculated possible magnetospheric forces on them due to dust charging are found to be on
the same order as the Earth attraction term or larger. Also it is
unclear how particles of this size have survived such large decelerations, reaching relatively low altitudes, and it is possible
that they are the result of larger meteoroids with some across
the beam component. A paper on this issue as well as details on
the micrometeoroid entry kinetics is in current preparation. The
calculation of evolved orbits has likewise not been attempted
since the majority of the particles we observe are in a size range
such that radiation pressure, Poynting–Robertson drag (P–R)
(Burns et al. 1979, Liou and Zook 1997), and charged particle
electromagnetic effects are likely to be significant (Morfill and
Grün 1979, Mukai 1981, Whipple 1981, Morfill et al. 1986,
Grün et al. 1994). That is, these particles, as we will demonstrate, have significantly evolved orbits and have thus “forgotten” their origins. There is thus little point calculating back
along the orbits without including any EM effects—an arduous
task at best.
3.1. Time to Perihelion, Inclination, and Perihelion
Distance Distributions
Panel (a) in Figs. 3 and 4 give the perihelion times of the
entire IDP set, showing nearly equal pre- and postperihelion
particles (or IDPs) numbers in the case of NOV97 and a lack
of preperihelion particles in the case of NOV98. The absence
of preperihelion IDPs in NOV98 is explained by the bias introduced by using only 6 h of data as shown by the simulation
results (Fig. 4d). The meteoroid orbital inclinations are shown
in panel (b) of both figures—considerable difference can be ob-
209
served between the pre- and postperihelion samples. While both
prograde and retrograde ecliptic concentration of particles are
present for the preperihelion case, the postperihelion IDPs are
dominated by the presence of retrograde orbits with a peak at
∼140◦ . This peak is predicted by the Monte Carlo simulation
for the 1998 time period (Fig. 4e) and is thus likely an artifact of sampling bias. Finally the perihelion distances (q) are
displayed in panel (c) of Figs. 3 and 4 where an asymmetry
can be observed between the pre- and postperihelion samples.
Again the Monte Carlo results are shown. A dramatic reduction
(Fig. 3c) or lack (Fig. 4c) of “sungrazers” in the postperihelion sample, relative to the simulation results, can be seen. This
reduction is presumed to be due to different destruction mechanisms near the Sun. These mechanisms are discussed by Mann
et al. 2000) for the near-solar dust cloud (<10 solar radii) and include collisional destruction (Steel and Elford 1986), erosion by
sputtering or sublimation (Le Sergeant D’Hendcourt and Lamy
1981), rotational bursting (Paddack and Rnee 1975), or thermal
destruction. However the AO data do not yield the information
needed to single out a particular destruction process. Both the
NOV97 and NOV98 data sets show a concentration of orbits
with q between Mercury and Venus (Figs. 3c and 4c), which is
missing in the Monte Carlo results (Figs. 3f and 4f). The large
remaining fraction of postperihelion orbits with q within the orbit of Mercury provides again a strong indication that the AO
micrometeors are particularly durable compared with classical
cometary meteoroids. These results do not statistically change
if our empirical model for sputtering is neglected or if the inatmospheric meteor speeds are used as the velocity at infinity.
3.2. Semimajor Axis and Eccentricity Correlations
Figure 5 and 6 gives the semimajor axis (a) versus the eccentricity (e) distribution for our data set. In addition, the Whipple
K and Pe criteria (Eqs. 3 and 4 respectively, Kresák (1965)) for
particle asteroid/comet origin and the evolutionary path due to
drag effects are shown given by (Kresák 1965)
C = ae−4/5 (1 − e2 ) = const.
(7)
for various values of the constant C. For both criteria, orbits
above the curves (K = 0 and Pe = 2.5) shown in the figures
are cometary orbits and asteroidal for those below (based on
the analysis of large comets and asteroids), suggesting—if the
Whipple criteria carryover to IDPs—that most of the particles detected at AO are concentrated in asteroidal-type orbits
of a ≤ 2 AU at the time of Earth interception. The evolutionary paths or drag contours show the a/e evolution (downward
along the curves) of particles under nongravitation influences
such as P–R drag and radial solar radiation pressure (Wyatt and
Whipple 1950)—the different curves correspond to different initial a/e values. The a/e results indicate that the population of
AO micrometeors are mainly derived from orbits within the distance of Saturn, with the majority coming from within the orbit
of Jupiter. These diagrams also suggest that the particle orbit
210
JANCHES, MEISEL, AND MATHEWS
FIG. 3. Histograms of selected orbital elements just prior to Earth impact for most of the NOV97 IDPs that show atmospheric deceleration—particles <0.5-µm
radius have been excluded. The results of the Monte Carlo simulation for the same time period assuming a uniform heliocentric velocity distribution are also shown.
No correction for planetary perturbations, solar wind pressure and magnetic field effects, PR drag, or solar photo radiation pressure has been applied. (a) The
distribution of perihelion times of AO micrometeors showing nearly equal pre- and postperihelion numbers. (b) The inclination histogram shows a considerable
difference between the pre- and postperihelion samples. The preperihelion impacts show that both prograde and retrograde ecliptic concentrated particles are
present. However, in the postperihelion sample, the inclinations are predominantly retrograde with a peak ∼140◦ . This diagram shows the typical orbital bias in
the AO micrometeor sample since only a comparatively narrow strip of the sky (1/6 degree strip at 18◦ declination ±15◦ ) is covered in any particular time period.
(c) The perihelion distance asymmetry in the pre- and postperihelion samples. As can be seen, there is a dramatic reduction of “sungrazers” in the postperihelion
sample that is presumed to be due to solar evaporation of the particles. Despite this effect, the overall durability of the AO micrometeors is vividly illustrated by
the large fraction of postperihelion orbits with q within the orbit of Mercury. (d, e, f) The same as (a, b, c) but for the Monte Carlo simulation results.
ORBITS OF ARECIBO MICROMETEOROIDS
211
FIG. 4. The same as described in the legend to Fig. 3 but for the NOV98 and the results of the Monte Carlo simulation for that time period.
semi-major axes are reduced to ∼1 AU by P–R drag evolution followed by eccentricity increases (at nearly constant a)
in a manner similar to that of the electromagnetic resonance
(with interplanetary magnetic field sector boundary crossings)
mechanism predicted by Morfill and Grün (1979). The effects
of fluctuating IMF on charged IDPs orbiting around the Sun un-
der solar radiation pressure and P–R drag were also examined
by Wallis and Hassan (1985) and Wallis (1986). These electromagnetic resonance effects appear to be the best framework at
this point to physically explain these results. Electromagnetic
dust interactions are greatest when the particle orbital period is
synchronous with an integer multiple of the solar rotation and/or
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JANCHES, MEISEL, AND MATHEWS
the solar magnetic sector period (25.2, 12.6, or 6.3 days). From
Earth, we can never directly observe particles of these periods
in their initial low-eccentricity states, but only in their evolved,
high-eccentricity states. As Morfill and Grün pointed out, the
main electromagnetic effects are to change the inclination. Such
Lorentz-type forces, where the particle velocity V and the interplanetary magnetic field B (IMF) are in the same plane, occur
without significantly changing a and e. In order to obtain secular
changes on a and e, the particle must be forced synchronously
around the particle orbit. With radiation pressure being radial and
opposite the particle velocity, this synchronization is achieved
automatically. As far as gravitational resonances are concerned,
only Venus has an orbital period that is closely commensurate
with solar rotation. The combination of these effects creates coupling between a, e, and i, making the nature of the dynamical
problem possibly chaotic and difficult to numerically solve. This
is left to a future modeling effort.
The lack of meteor orbits with small perihelion distances for
the postperihelion component of these samples translates into a
region in the a/e diagram (Figs. 5b and 6b) as missing points.
The boundary lines for Earth’s orbit intersection given by
deficiency of orbits in the simulation appears to be the result of
mixing time-period sampling in the observations (two days with
one period and another day with a different one). On the other
hand the observational excess is also weakly present in Fig. 6a
(preperihelion sample). A somewhat lesser group is present in
the NOV97 postperihelion data set (Fig. 5b) at similar (a, e) values. Such behavior is what would be expected if there were one
or more discrete components in the actual heliocentric velocity
distribution. Some vestige of the “clump” around this region in
the a/e diagram is found in all the figures, but is strongest after
perihelion. It is interesting to note that these orbits have perihelion/aphelion distances at approximately Mercury and Mars,
respectively. The NOV98 data also show a clump near a ∼ 1 AU,
e ∼ 0.3, which corresponds to the observed excess of q’s near
the orbit of Venus. Thus most of the observed postperihelion
excess of perihelia between the orbits of Mercury and Venus are
due to orbits lying entirely within the terrestrial planet zone.
We have examined the (a, e) diagram data for possible linear
correlations among log a, log e, and log r , where r is the equivalent particle radius and it is proportional to log mass. There
are no linear correlations of log r with log a and only very weak
ones with log e,
q = a(1 − e) < 1 AU < a(1 + e) = q 0
µ ¶
1
,
log r = (0.62 ± 0.04) + (0.5 ± 0.2) × log
e
(8)
are shown as are the a/e lines for perihelion distance of 0.2 and
0.3 AU. In addition, to better interpret the observed results of
Figs. 5 and 6 we once again present the results of the Monte Carlo
simulation (diamonds in the figures). The limits given by (8)
produce the sideways “wedge” shape shown in the a/e diagrams.
The observed and the simulated postperihelion samples are both
characterized by the lack of orbits with q < 0.2, thus suggesting
that some of this depletion is due to observational bias. However
according to the simulated results, orbits with 0.2 ≤ q ≤ 0.3 AU
should be present in the NOV97 but they are not evident. The
boundary of the depleted region in the observed NOV97 sample
is well defined at q ∼ 0.3 AU while the simulated set show
orbits with q as low as 0.2 AU. These two factors indicates that
there is a real depletion present. For the NOV98 set a similar
depletion is present, but because of sample bias, the q value
cutoff is increased to ∼0.4 AU for the data and ∼0.3 AU for the
simulation. Such a result is not surprising since the NOV98 data
contains 50% more very small particles (below 1 µm in size;
Fig. 2) and ∼50% less large particles (greater than 1 µm). This
is consistent with collisional and thermal destruction of smaller
particles when q is small. This depletion may also be related to
the asymmetry and variability of the the helion and antihelion
sources (Brown and Jones 1995, Poole 1995) seen at much larger
masses, but at this stage we do not have enough information data
to make any sensible connection between the two mass ranges.
One other anomaly is present in Fig. 6b. In the postperihelion
NOV98 data set, the simulation predicts a “gap” that runs from
large (a, e) at the right and sweeps to the left and down until
an inflection is reached in the vicinity of a ≈ 1 AU, e ≈ 0.45.
Here we find a significant number of observed orbits. Part of the
ρ = 0.17, n = 324, NOV97—postperihelion
µ ¶
1
log r = (0.71 ± 0.03) + (0.4 ± 0.2) × log
,
e
ρ = 0.14, n = 268, NOV97—preperihelion
µ ¶
1
,
log r = (0.34 ± 0.04) + (0.3 ± 0.1) × log
e
ρ = 0.13, n = 456, NOV98—postperihelion
µ ¶
1
log r = (0.62 ± 0.04) + (0.5 ± 0.1) × log
,
e
ρ = 0.16, n = 179, NOV98—preperihelion,
(9)
(10)
(11)
(12)
where ρ is the linear correlation coefficient and n is the number of data points in the sample. These indicate a very slight
(ρ < 0.2) tendency for larger particles to have orbits that are
more circularized than smaller particles. Since progressive circularization of orbits is what is expected from pure P–R effects,
the opposite correlation (more circularization for small particles) might be expected from P–R effects alone. This suggests
that the Morfill and Grün effects are indeed operational in this
sample and effectively reverses an expected small size–small eccentricity correlation of P–R to produce what is observed. These
weak correlations also suggest that the AO orbits seem highly
randomized and thus establishing their sources will be difficult.
Finally, an apparent lack of orbits along the upper a, e boundary in the preperihelion set should be noted. The uniform velocity assumption predicts a concentration that is not observed.
FIG. 5. (a) a/e diagrams for the preperihelion component of the NOV97. The observational boundaries due to Earth’s orbit interception are also shown as well
as a/e lines for perihelion distances of 0.2 and 0.3 AU. The diagram shows that according to the so-called Pe criterion, most of the micrometeors are concentrated
in asteroidal-type orbits of 2 AU or less at the time of Earth interception. Other curves are discussed in the text. The crosses are the data points while the diamonds
represents the results of the Monte Carlo simulation described in the text. (b) Same as (a) but for the postperihelion component of the NOV97.
214
JANCHES, MEISEL, AND MATHEWS
FIG. 6. The same as described in the legend to Fig. 5 but for the preperihelion (a) and postperihelion (b) component of the NOV98.
ORBITS OF ARECIBO MICROMETEOROIDS
The velocities of the sampled orbits are obviously not uniformly
distributed, presumably representing an evolution of semi-major
axes due to the Poynting–Robertson effect into the zone where
the Morfill and Grün effect becomes important.
3.3. The Presence of β-Meteoroids
We present a sample of 40 postperihelion events (3 observed
in 1997 and 37 observed in 1998) that were excluded from the
previous statistics both on account of their sizes (radii <0.5 µm)
and their eccentricities (e > 1). The extra-atmospheric properties of these particles were derived in the same way as the elliptical orbits. At the extra-atmospheric size limit of 0.5 µm for
silicates, the ratio of radiation pressure to gravity forces, β, is 0.8
(Wilck and Mann 1996; Landgraf et al. 1999; Wehry and Mann
1999) and presumably near to or in excess of unity down to radii
of 0.1 µm. If one observes such particles after perihelion such
as our sample of 40, they are called β-meteoroids (Grün and
Zook 1980). The detection of β-meteoroids was first reported
by Berg and Grün (1973) and Zook and Berg (1975) using the
dust detectors onboard Pioneer 8 and 9. Since then, other dust
experiments have detected them at different locations in the Solar System. Grün et al. (1980) identified β-meteoroids at 0.31
and 0.98 AU in the ecliptic using the micrometeoroids experi-
215
ments onboard Helios 1 and Grün et al. (1997) and Wehry and
Mann (1999) reported detections of these particles with the dust
detector onboard the Ulysses spacecraft in the ecliptic as well as
during the north and south solar-pole passages. However these
particles have not been detected before by either Earth-orbiting
satellites or groundbased detectors.
β-Particles can originate in different ways. They can be ejected
from comets during their closer approach to the Sun, or they can
be produced whenever a particle in a bound orbit is reduced
in size, increasing the β value. Because β becomes high, the
particle orbits continue to evolve under both radiation pressure
and EM effects, eventually becoming hyperbolic and escaping
the Solar System. Typical mechanisms for a size decrease are
mutual collisions of micrometeoroids, as well as various erosion
mechanisms, such as sputtering or partial sublimation of more
volatile materials (Le Sergeant D’Hendecourt and Lamy 1981,
Mann et al. 2000, Wehry and Mann 1999). These mechanisms
can occur at distances away from the Sun that are too large for
complete particle vaporization (∼distance of Mercury). At this
point, however, without a model we are not able to give a detailed
account of the origin of these particles.
Histograms of some of the properties of the present sample
of β-meteoroids are given in Fig. 7. Figure 7a shows that the
radii are fairly evenly distributed over the range 0.1 to 0.3 µm,
FIG. 7. Distribution of selected properties for the particles with sizes lower than 0.5 µm and eccentricities greater than 1. These meteors have been excluded
from the NOV97 and NOV98 data sets (see discussion in the text). (a) shows the distribution of radii, (b) shows the time of perihelia, (c) shows the distribution of
inclinations, and (d) shows the distribution of q values. These orbital parameters represent the instantaneous orbits at the time of Earth collision.
216
JANCHES, MEISEL, AND MATHEWS
which is where β exceeds unity for 3 g/cc grains. Because β is
so high, the particle orbits continue to evolve under both radiation pressure and EM effects as they escape the Solar System.
At 1 AU, these particles have the orbital properties shown in
panels (b, c, and d). The a and e values of the β particles show
a considerable range, but their C values are all quite close with
hCi = 1.50 ± 0.03. Using arguments similar to the evolution of
a, e along contours of constant C for elliptical orbits, we argue
that the observed β particle population is dynamically related
(at C = constant) to elliptical orbits with q < 0.7 AU when
e < 1. The perihelion distances of these meteoroids seem to be
higher than previous spacecraft detections have shown. Wehry
and Mann (1999) showed that the β-meteoroids detected with
Ulysses seem to have originated within 0.5 AU. As can be observed from Fig. 7d, the AO detections have q values higher
than 0.6 AU. One possible explanation of this difference is that
if these particles are in fact β-meteoroids, they probably originated from collisions between larger meteoroids at Venus-like
distances rather than through sublimation or some other of the
above-mentioned near-Sun destructive mechanisms since their
q’s are at greater distances from the Sun than those considered
by Wehry and Mann.
The previously discussed Morfill and Grün EM effects seem
to be implicated here as well since the β particles have retrograde
orbits with small angles to the ecliptic unlike the orbits of the
elliptical particles. This is in accord with the Morfill and Grün
predictions of solar wind perturbations on dust inside 1 AU.
While complete destruction may explain the observed lack of
postperihelion elliptical orbits at small q (<0.3 AU), it seems
that the depletion seen for the postperihelion elliptical orbits at
larger distances (up to 0.5 AU) can be explained at least in part
by the formation of β particles and their subsequent ejection
from the Solar System.
3.4. Comparison with Previous Data Sets
It is of interest to see if any of our sample is “recently” derived from known, larger mass objects. To investigate this, we
have performed a preliminary comparison of our orbits using
the Drummond D 0 criterion (Drummond 1981) with individual
catalog limits of D 0 scaled from the Hawkins–Southworth D
discriminant (Drummond 2000). The limits we used were calculated from D 0 limit equal to 0.33/N 0.25 , where N is the total
number of entries from each catalog. This allows a 10% statistical margin over the limit adopted by Drummond for near-Earth
asteroids (NEA). When using such discriminants, it is usual to
examine connections between comparison orbits that are reasonably close to the orbits being tested. In particular, the orbital
angular elements involved are usually less than 90◦ . However,
the AO sample contains a higher number of retrograde orbits
than the IAU sample. Thus in addition to a limit on the value
of D 0 , we eliminated all those matches where the computed angular orbital element differences exceed 90◦ . This compensates
for the inclination and nodal quadrant reversals that the small
D 0 itself seems to miss.
In order to test our computations, we also ran 16 known major showers with their presumed parent objects. The Lyrids, Perseids,
Leonids, and Draconids gave D 0 between 0 and 0.01. The Bootids,
Orionids, Andromedids, and the Ursids gave D 0 values between
0.01 to 0.04. Other showers showed matches up to D 0 < 0.11
with their associated objects. The onset of spurious associations
was D 0 = 0.17, where cross matches occur between unrelated
parent objects and other unrelated showers in the list. The limit
where this occurs as predicted by the above D 0 formula is 0.16,
quite in accordance with the results obtained numerically.
Since we were observing at the maximum of the annual
Leonids shower, we first compared our orbit list with the orbit of
Comet Temple–Tuttle. We found no matches for D 0 between 0
and 0.08. Sixteen matches were found for 0.08 < D 0 < 0.15 and
78 matches for 0.15 < D 0 < 0.30. Thus we conclude that few if
any of our orbits are recently derived from the Leonids, although
a remote connection cannot be ruled out until full perturbation
calculations are available.
As our orbits have a high proportion of retrograde orbits, a possible connection with orbits other than Temple–Tuttle (Marsden
1967) was investigated. We first tested for orbit similarity with
the Kreutz family of comets (as suggested by this paper’s referees) and found no matches until D 0 > 0.26. A sample of 25 modern major and minor meteor showers (including the retrograde
Epsilon Geminids and the Leo Minorids) shows no matches until well in excess of D 0 = 0.10 with a number in excess of D 0 =
0.4. Thus we must conclude that our sample is dominated by
sporadic orbits.
Assuming that the IAU database (Lindblad 1992) represents
orbits characteristic of the higher mass sporadic flux, we selected
a cutoff D 0 of 0.04, a number that encompasses the D 0 limits for
the majority of the individual IAU catalogs. From the sample of
65,000 IAU orbits, using a D 0 limit = 0.04 resulted in 117 AO
orbits, out of the 1200+ original set including many multiple
meteor groups, that may be related. When a limit of D 0 = 0.02
was adopted, the number of matches fell dramatically to just 11
orbits with just one multiple AO micrometeor group. A large
number of group matches involving multiple AO micrometeors had D 0 averages around 0.03, but since this number is very
near to the D 0 limit for the IAU catalog component lists averaged together, the connections are considered dubious. While
short-term connections are few, long-term connections are always possible with perturbations serving to make detection of
connections difficult.
4. CONCLUSIONS
In this paper the first orbital study for a large number of AO micrometeors is presented. At this stage, we have considerable confidence that AO detects ecliptic particles down to submicrometer sizes. A large portion of these meteoroids appear to have
orbits lying entirely within the orbit of Mars (Figs. 5 and 6) and
many lying nearly within 1 AU, thus proving AO to be a crucial
217
ORBITS OF ARECIBO MICROMETEOROIDS
instrument for the study of the near-Sun component of the zodiacal dust cloud. In addition, most particles appear to be evolving
from distances up to 4 AU. Thus older particles (i.e., evolved by
P–R drag from other orbits) are predominant in this group.
The apparent excess of particles we observe at the small a,
large e edge of Figs. 5 and 6 can be explained simply by the effect of an increasing number density of particles within 1 AU. To
quantitatively verify the effects described by Morfill and Grün
(1979) with data that are so severely constrained by the observational limits (“wedge lines”) is premature at best. All we know
at this time is that we observe high-eccentricity objects at 1 AU
and the Morfill and Grün effects are a convenient way to produce
(or keep) e high while P–R effects tend to circularize orbits. We
also note that according to Liou et al. (1999) a possible origin
of these particles are retrograde Halley-type comets. In addition, no attempt has been made to discuss the effect of planetary
resonances, collisions, and perturbations, although they most
certainly exist. We actually do seem to see features in our distributions that may be due to the effects of Mercury and Venus,
but it is premature to make these assignments without careful modeling that realistically takes solar wind and interplanetary magnetic field effects into account. Several recent studies
(Gladman et al. (1997), Morbidelli and Gladman 1998, Dones
et al. 1999) concern the transport of planetesimals of size large
compared with our particles to 1 AU from the asteroid belt;
however these studies are not directly applicable here. Collisions have been considered by Steel and Elford (1986), but again
solar wind and IMF effects have not been considered. Thus a rigorous discussion of the interpretation of the dynamical results
presented here must be postponed. The integration back in time
corrected for the various types of perturbations will be done in
the future. However the orbits seem so highly chaotic that almost certainly any history of these particles has been lost, and the
question of their ultimate origin would thus remain unanswered.
Elsewhere in this paper, it is argued that the orbital evolution of these micrometeors outside 1 AU is dominated by the
Poynting–Robertson drag effects, and solar wind and interplanetary magnetic field effects dominate inside 1 AU. In particular,
it is argued that the IMF resonance effect increases the eccentricity while the P–R effects tend to decrease the eccentricity.
Inside 1 AU, both processes together occur without changing
the semi-major axis very much. Thus the orbits have progressively decreasing perihelia distances and therefore become more
prone to destruction and/or ejection. If the orbital subset of 177
objects obtained upon comparison with the IAU Database is
recently derived from the breakup of the listed IAU objects (or
even the progenitors of the IAU objects that are even much larger
in mass), then there should be a correlation between the perihelia distance differences and the eccentricity differences. Indeed
a linear correlation between these quantities was found at the
ρ = 0.65 level for the subsample of 117 points. Only 26 out of
117, however, show the expected solar wind correlation (positive
1e with negative 1q) while the remainder shows the expected
P–R correlation (negative 1e with positive 1q), thus reenforc-
ing our earlier discussion about the a, e diagram as being P–R
dominated. The Morfill and Grün effects may not be dominant in
this subsample because there are a number of orbits with semimajor axes greater than 1 AU. This again indicates that the bulk
of the AO orbits are randomized with little or no memory of
their origins.
ACKNOWLEDGMENTS
We thank E. Grün and D. E. Brownlee for their useful comments on βmeteoroids and B. A. Lindblad for providing a copy of the IAU Database for
comparison with our orbits. This work has been partially supported by NSF Grant
AST 98-01590 to the Pennsylvania State University and to SUNY—Geneseo.
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.
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