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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, A03304, doi:10.1029/2007JA012531, 2008

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A semi-empirical model of the contribution from sporadic meteoroid sources on the meteor input function in the MLT observed at Arecibo Jonathan T. Fentzke1,2 and Diego Janches1 Received 9 May 2007; revised 26 November 2007; accepted 12 December 2007; published 18 March 2008.

[1] In this paper, we present a modeling and observational study of the micrometeor input

function with a focus on understanding how each of the extraterrestrial sporadic meteoroid sources contributes to the observed meteoric flux in the Mesosphere and Lower Thermosphere (MLT) atmospheric region. For this purpose, we expand the model presented by Janches et al. (2006) using a Monte Carlo technique and incorporating: 1) a widely accepted global mass flux, which is divided into different proportions among the known sporadic meteoroid sources as the initial input above Earth’s atmosphere; 2) contemporary knowledge on the source’s velocity and radiant distributions; and 3) the full integration of the canonical meteor equations that describe the meteoroid entry and ablation physics. In addition, we constrain the initial input through a comparison of our modeled results with meteor observations obtained with the 430 MHz High Power and Large Aperture (HPLA) Arecibo radar in Puerto Rico that covers all seasons. The predicted meteor rates and velocity distributions are in excellent agreement with the observed ones without the need for any additional normalization factor. Our results indicate that although the Earth’s Apex centered radiant source, which is characterized by high geocentric speeds (!55 km/s), appears to be !33% of the meteoroids in the Solar System at 1 AU, it accounts for !60% of the meteors observed by the Arecibo HPLA radar in the atmosphere. The remaining 40% of observed meteors originate mostly from the Helion and Anti-Helion sources, with a very small, but constant during the day, contribution of the South and North Toroidal sources. These results also suggest that particles smaller than !10"3 mg with slow velocities (<30 km/s) will not significantly ablate and never become observable meteors. The motivation of this effort is to construct a new and more precise MIF model needed for the subsequent modeling of the atmospheric phenomena related to the meteoric flux. Citation: Fentzke, J. T., and D. Janches (2008), A semi-empirical model of the contribution from sporadic meteoroid sources on the meteor input function in the MLT observed at Arecibo, J. Geophys. Res., 113, A03304, doi:10.1029/2007JA012531.

1. Introduction [2] The major source of metallic material responsible for a variety of atmospheric phenomena in the Mesosphere and Lower Thermosphere (MLT) originates from the ablation of extraterrestrial particles upon atmospheric entry. The most abundant flux contributions come from sub-millimeter particles in the mass range of 10"11 to 10"4 g from the sporadic meteor background and not from meteor showers [Ceplecha et al., 1998; Baggaley, 2002; Williams and Murad, 2002]. The metallic atoms ablated from these meteors are the source for mesospheric metal layers [Plane, 2003]. They are also believed to be an important source for condensation nuclei, which is a necessary precursor to the formation of 1

NorthWest Research Associates Inc., Boulder, Colorado, USA. Department of Aerospace Engineering Sciences, University of Colorado, Boulder, Colorado, USA. 2

Copyright 2008 by the American Geophysical Union. 0148-0227/08/2007JA012531$09.00

noctilucent cloud particles in the polar mesopause region [von Zahn et al., 2002]. A thorough study of the extraterrestrial meteor flux is necessary to gain a greater understanding of the aforementioned phenomena. Accurate knowledge of the meteoric input function (MIF) including parameters such as the annual, diurnal and geographical variations of meteor rates, global mass distribution, directionality, and velocity distribution are still hotly debated. The relation between the characteristics of the meteoroid population (i.e., total mass flux, velocity distributions) before encountering Earth’s atmosphere (global flux) and those observed at a particular season and geographical location in the MLT (local flux) have also been seldom treated. Most of the previous works that treat the modeling of meteor related MLT (!100 km) phenomena infer global meteoroid influxes from satellites that orbit well above the atmosphere where the meteor phenomenon occurs [Janches and ReVelle, 2005]. The globally and annually integrated measurements of the meteor flux provided by satellites above the atmosphere are not necessarily the true flux

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observed in the MLT (!100 km) [Plane, 2003, 2004; Megner et al., 2006]. One could argue, for example, what is the validity of using the total mass flux derived from satellite measurements obtained over long periods of time (months/years), in order to obtain sufficient count statistics due to small collecting area and integrated over the whole planet, as the material responsible for a metal layer observed over one particular night at a specific geographical location. [3] In order to understand the origin and global distribution of metallic layers, it is crucial to understand not only how much meteoric mass is deposited in the upper atmosphere but also what portion of that input is deposited at a particular season and latitude. For example, to model the mesospheric Na layer Plane [2004] modulated the meteoric input with a seasonal and diurnal function resulting from the radio meteor survey reported by Yrjo¨la¨ and Jenniskens [1998], which for a given local time (i.e., geographical longitude) had no latitudinal variability. However, Janches et al. [2004] and Singer et al. [2004] reported meteor observations from the Antarctic and the Arctic showing that the activity is antisymmetric. In particular, when the observed maximum occurs at one hemisphere, the minimum occurs at the opposite pole of the planet. Recently, Gardner et al. [2005] reported lidar observations of Na and Fe at the South Pole and compared them with detailed chemical models of these species. These observations reveal an almost complete absence of Na and Fe below 90 km during the middle of the summer that results in layers with higher peaks, narrower widths and lower abundances than those observed at midlatitudes. The authors concluded that an additional source of gas-phase metallic species that must be comparable to the meteoric input is required during winter in order to correctly model the Na and Fe abundances. This source appears to arise from the wintertime convergence of the meridional flow over the South Pole. Thus knowing precisely how much, when and where the meteoric material is deposited in the MLT is crucial to set limits on transport models. [4] Most aeronomical models that utilize meteoric flux contributions to study atmospheric phenomena such as, metallic layers, meteor ablation and PMC formation rarely consider the directionality of the incoming flux and adopt a constant average incoming entry angle as if the sporadic meteoroid radiant distribution is isotropic [McNeil et al., 1998, 2002; Plane, 2004; Pesnell et al., 2004; Megner et al., 2006], which is not representative of the observed meteoric flux [Jones and Brown, 1993; Galligan and Baggaley, 2005; Chau et al., 2007]. In the same manner models tend to misrepresent the geocentric velocity distribution of the incoming meteoric mass by either using a single low value [Plane, 1991; Love and Brownlee, 1991; McNeil et al., 1995] or by considering a range of only slow particles between 15 to 25 km/s [Hunten et al., 1980; Pesnell et al., 2004; Megner et al., 2006] unless a particular meteor shower is being modeled. [5] As noted by Ceplecha et al. [1998], the main contribution of meteors in the Earth’s atmosphere comes from sporadic meteoroids, that is, particles not associated with a particular known shower. These sporadic meteoroids originate from six known radiant distributions (i.e., orbital families), which are: the North and South Apex, composed mainly of dust from long period comets; the Helion and

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Anti-Helion, composed of dust from short period comets; and the North and South Toroidal composed of dust from Halley-family type comets with the radiants near the ecliptic poles being from asteroidal sources [Jones and Brown, 1993; Taylor, 1997; Taylor and Elford, 1998]. These radiant source distributions have been also observed by recent surveys using both specular meteor radars (SMRs) and HPLA radars [Galligan and Baggaley, 2005; Chau et al., 2007]. The fact that meteors come from specific regions in the sky in a heliocentric frame of reference translates into a very specific set of incoming directions in a geocentric frame of reference that highly depend on time of day, season, and geographical location. While a particular radiant source can be high in the local sky above Arecibo at sunrise, it will be below the horizon at another geographical location. This type of variability will be accentuated at polar latitudes [Janches et al., 2006]. [6] In order to understand how much, when and where micrometeor mass is deposited in the Earth’s atmosphere we investigate how these different meteoroid populations contribute to the local diurnal and seasonal meteor rates, in particular those observed at Arecibo, Puerto Rico (18!N, 66!W). Janches et al. [2006] showed that different meteoroid sources are responsible for producing distinct diurnal and seasonal variability in the observed meteor flux by HPLA radars at different latitudes. We follow up on that work by assuming an initial input and divide it among the six known meteoroid radiant sources. We assign a radiant and velocity to each particle using Monte Carlo simulation techniques based on the current knowledge of the meteoroid populations and integrate each meteoroid case using canonical meteor physics equations in order to determine which portion of the initial flux is detected by the Arecibo radar. This methodology allows us to understand how each source contributes to the local observed flux as the radar beam scans through the sky at different seasons [Janches and Chau, 2005]. Furthermore, it permits us to estimate what portion of the incoming flux remains undetected. This effort is intended to provide a better estimate of the amount and associated properties of meteoric material that will be deposited in a given small volume placed on the MLT at a particular time, given a known extraterrestrial flux and geographical location.

2. Model Description 2.1. Modeled Sporadic Meteor Radiant and Velocity Distributions [7] As done by Janches et al. [2006], we begin by assuming that each meteoroid source has a 2-dimensional Gaussian distribution in the ecliptic coordinate frame of reference based on earlier observations [Jones and Brown, 1993; Galligan and Baggaley, 2005; Chau et al., 2007]. The modeled parameters are presented in Table 1. In this work there are only minor radiant source differences from those observed and reported in the past. For example, the North and South Apex radiant sources are modeled as a single Apex radiant source with the combined attributes of both sources [Chau and Woodman, 2004; Janches and Chau, 2005; Janches et al., 2006]. The modeled values of the Apex source, which are taken from Galligan and Baggaley, [2005] who used the 26 MHz Advanced Meteor Orbit Radar

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Table 1. Gaussian Fitting Parameterization of Radiant Source Distribution Geocentric Velocity Distribution s, km/s

V , km/s

A!

Sun Centered Width

Sun Location Width

Source Name

Fast Part

Slow Part

Fast Part

Slow Part

Fast Part

Slow Part

l, deg

s, deg

sl, deg

sb, deg

Apex Helion Anti-Helion N. Toroidal N. Toroidal

0.8

0.2 1.0 1.0 1.0 1.0

55

17.3 30.0 30.0 30.0 30.0

2.5

2.60 2.57 2.57 2.57 2.57

270 350 190 270 270

0 0 0 60 "60

19 8 8 17 17

32 20 20 17 17

(AMOR) in New Zealand, are within !10% of previous reported values resulting from the Harvard Radar Meteor Project (HRMP) [Jones and Brown, 1993; Taylor, 1997; Taylor and Elford, 1998], and interferometric meteor headecho observations using the 50 MHz Jicamarca radar (JRO) in Peru [Chau et al., 2007]. In addition, the Helion and Anti-Helion source values used in the model are a composite of past observations. The center and width in ecliptic latitude (sb) of the sources are in close agreement with Jones and Brown [1993], Galligan and Baggaley [2005], and Chau et al. [2007], while the width in ecliptic longitude (sl) is narrower. As with the Apex source case, the values for the North and South Toroidal source distributions are also directly taken from Galligan and Baggaley [2005], and in agreement with those values reported by Jones and Brown [1993], Taylor [1997], Taylor and Elford [1998], and Chau et al. [2007]. [8] As is the case for any astronomical object, the position of a given meteoroid source in the local sky at a particular geographical location will vary with time of the day and season, thus altering the atmospheric entry angle for particles originating from that population. In this work, we define the entry angle as the angle between the meteoroid traveling direction and the local zenith (complement of elevation angle). [9] Furthermore, the orbit of a particle in the solar system determines the particle’s velocity in a given frame of reference. Consequently, each of the meteoroid radiant sources will have specific distributions of incoming geocentric velocities since, as discussed earlier, each of these sources is determined by a family of orbits. In particular, the velocity distribution of meteoroids originating from the Apex source is characterized by a bimodal shape dominated by a fast retrograde component and a slower less dominant prograde velocity component. For this model we assume that the geocentric velocity distribution is bimodal with approximately !80% of the population centered at !55 km/s and !20% of the population centered at !17.3 km/s. The chosen distribution is taken from AO observations when the radar beam is pointed directly into the direction of the Apex [Janches et al., 2003; Sulzer, 2004; Janches and Chau, 2005]. This distribution is well supported by different investigations including observations with the ALTAIR system [Hunt et al., 2004]; the AMOR system [Galligan and Baggaley, 2005] and the HRMP survey [Jones and Brown, 1993; Taylor, 1997; Taylor and Elford, 1998]. The rest of the radiant sources are modeled with Gaussian geocentric velocity distributions with a peak at 30 km/s also taken from radar measurements.

2.2. Modeled Extraterrestrial Mass Input [10] The estimated daily amount of meteoric mass deposited globally into the upper atmosphere ranges from !7 to 210 tons of material per day over the whole planet [Hughes, 1978; Gru¨n et al., 1985; Wasson and Kyte, 1987; Love and Brownlee, 1993; Taylor, 1995; Mathews et al., 2001; Cziczo et al., 2001]. Figure 1 displays different estimates of the total mass flux. The curve represented by triangles in Figure 1 was compiled by Gru¨n et al. [1985] from work conducted using satellite space probes and lunar microcraters, and lead to one of the first widely used extraterrestrial model mass inputs. Also shown in this figure is the mass influx obtained using measurements from the Long Duration Exposure Facility (LDEF) mission [Love and Brownlee, 1993]. LDEF estimated a significantly larger mass flux of sub-millimeter particles resulting in approximately 120 ± 60 tons/day over the whole earth. Because of limitations on individual instruments by factors such as, sensitivity, observing volume, and location, it is difficult to deduce the exact global mass input over the broad size range from micrometeoroids to large bolides using a particular observing technique. However, Ceplecha et al. [1998] combined the results of photographic meteors, meteor radar, space probe, and lunar microcrater results to determine a cumulative global mass flux in the range of 10"21 to 1015 kg. The portion of this estimate in the mass range of interest to this work is also shown in Figure 1. Also, for comparison purposes, we depicted in Figure 1 an extrapolation to small masses of the flux derived by Brown et al. [2002] using Department of Defense satellite measurements for large bolides (10"1 –103 m size range). Although the constant power law fit determined by Brown et al. [2002] is close to the curve of Ceplecha et al. [1998] and Gru¨n et al. [1985] at the extrema of the mass range of interest, the overall linear nature, in a log-log scale, of the Brown et al. [2002] fit does not replicate the results determined by Ceplecha et al. [1998], Gru¨n et al. [1985], and others in the sub-millimeter size range. [11] Because the data for the smaller particles was integrated for long periods of time and were obtained in large part from instruments that lie well above the MLT region, these results represent to a degree the global influx of mass at the very highest extent of the Earth’s atmosphere where the interaction between meteoroid and air molecules is negligible if the particle size is small, and thus there is no significant ablation and ionization and micrometeors are not produced [Janches and ReVelle, 2005]. Although satellites and space probes have measured extraterrestrial flux at 1

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Figure 1. (a) Cumulative particle flux per year over the whole earth. (b) Total mass flux per year over the whole Earth per d(log10(mass)). AU, the actual meteor flux detected in the MLT at an altitude of !100 km at a particular geographical location and time of day and year is of greater interest for the study of atmospheric meteor related phenomena. We refer to this particular quantity as a local flux. Generally, local fluxes are estimated by assuming an isotropic meteoroid environment and dividing the global mass, determined outside earths atmosphere integrated globally and annually, equally over the whole earth. This results on an overestimation of the local flux (specific location and time) at MLT altitudes as demonstrated by Mathews et al. [2001] who determined the flux in the range of 10"11 to 10"4 g observed by the HPLA radar at Arecibo. This was also shown by ReVelle [2005a], who modeled this difference. [12] For the model presented in this work, we adopt as initial global input the mass flux reported by Ceplecha et al. [1998]. We then convert the adopted cumulative flux to the

appropriate binned flux by calculating the difference between successive mass bins in order to estimate the number of meteoroids contained in each mass bin for the whole planet in a year, or per minute per km2 by a simple time/area product conversion factor. In addition, we initially constrain the minimum mass Arecibo will observe by using Bronshten [1983] critical meteoroid radii estimates for which ablation can occur upon atmospheric entry as a function of velocity and bulk density, assuming a spherical particle (Table 2). Although the exact composition and distribution of bulk densities for the meteoroid influx is still uncertain and will strongly depend on their origin (i.e., asteroidal or cometary) we adopt for the model ‘‘typical’’ values of 1 g/cc for the cometary case and 3 g/cc for the asteroidal case, but we note that the model is not particularly sensitive to meteoroid density. Thus if a micrometeroid does not have a sufficient combination of mass, velocity, and

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Table 2. Characteristic Dimensions of Meteoroids [Bronshten, 1983] Meteoroid Type Stony Iron

Velocity, km/s 15 30 60 15 30 60

Rmelt, cm 3.3 4.6 5.8 1.2 7.0 2.2

( ( ( ( ( (

"3

10 10"4 10"5 10"3 10"4 10"5

momentum (Mdv) lost by the meteoroid is proportional to the momentum of oncoming airflow

Mcritical, kg 4.5 1.2 2.5 2.2 4.3 1.3

( ( ( ( ( (

M

"10

10 10"12 10"15 10"11 10"12 10"16

entry angle to ablate due to frictional heating it will decelerate without depositing material along its path and will not produce enough ionization for the meteor to occur. If this is the case then this particular incoming particle will not be detected since a radar observes meteors and not meteoroids. (Table 2). [13] Finally, using the binned flux derived from Ceplecha et al. [1998] in conjunction with the minimum mass range constraints determined from Bronshten [1983], an extraterrestrial flux is determined for each source by assigning a percentage of the total global flux for each particular mass bin to each meteoroid radiant source. This represents the flux originating at 1 AU that enters the top of the atmosphere over Arecibo from all of the radiant sources. Once this extraterrestrial flux is determined for each radiant source, individual meteors from each mass range are randomly assigned an initial velocity and entry angle based upon the radiant source velocity and angular distributions discussed in section 2.1. Then detectability of each particle is determined by integrating the meteor equations, as described in the next section. We note that, although there is a small diffuse background of meteors [Chau et al., 2007] over the entire range of ecliptic coordinates, for this model we assume that all meteors originate from one of the six known radiant sources. 2.3. Integration of the Single Body Meteor Motion/ State Equations [14] Once a given meteoroid mass, entry angle, and velocity are chosen at random from the characteristics of the individual source radiants it is necessary to determine if the Arecibo radar will detect a meteor event based on the ability of the meteoroid to ablate and thus produce enough ionization. We note that the highly sensitive radar at Arecibo detects meteor events in the form of head-echoes,

! "2 dV REarth cosðqÞ ¼ "GSrair V 2 þ gM REarth þ z dt

ð1Þ

where S and M are the meteoroid cross-sectional area and mass, V is the meteor velocity, rair is the air density, G is the drag coefficient (!1), q is the entry angle (vertical entry is 0!). Additionally, the effects of gravity (g) are included for completeness although this term is negligible. The second equation gives the meteor vertical component of the velocity: dz ¼ "V cosðqÞ dt

ð2Þ

[15] The third equation gives the meteor mass loss: dM Ch Srair V 3 ¼" 2QHeat dt

ð3Þ

[16] Equation 3 is derived assuming that a fraction (Ch) of the kinetic energy from the impinging air molecules (1/2SrV3) is expended on ablation of the meteoroid in the form of vaporization or fusion [Bronshten, 1983]. Also, we use in this model QHeat = 8'106 J/kg for the latent heat of vaporization or fusion, which corresponds to non-fragmenting stone or iron meteors [Lebedinets, 1973]. The adopted QHeat value represents pure vaporization of the meteor, which has been suggested by Bronshten [1983] to be the main process observed for photographic and fast radio meteors. [17] The meteor energy equation is derived assuming that the energy of the meteoroid is lost through radiation and heating. # 4 $ 4 1 dTMet 4 þ RMet rMet Csh " TAir Ch rair V 3 ¼ ssb R! TMelt dt 2 3

ð4Þ

Where R is 4 (fast rotating body) and represents the ratio of instantaneous total surface area of the meteoroid to its frontal drag and heat transfer cross-section [Janches and ReVelle, 2005]. The normalized heat transfer coefficient, normally referred to as L [Bronshten, 1983] is given by ReVelle [1979] as Ch.

8 > <1 Ch ðV Þ ¼ ð"0:0253ðV " 25Þ þ 0:73Þ ( CCF > : 0:0975 ( CCF

i.e., a cloud of electrons moving at or near meteoroid speeds [Janches et al., 2000, 2003]. We integrate the full set of equations governing the interaction of the meteoroid with the air molecules [Whipple, 1950, 1951] to determine the initial altitude at which ablation of the mircometeoroid produces the required amount of ionization to be detected [Janches and ReVelle, 2005]. The first equation assumes the

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if V < 29:5 km=s; if 29:5 km=s ) V ) 50 km=s; if V * 50 km=s:

ð5Þ

[18] The value of Ch is normally assumed to be !1, however, ReVelle [1979] showed that Ch for chondritic type meteors (CCF of 1.62) can vary by an order of magnitude depending on velocity. By integrating this set of equations, particle parameters (i.e., temperature, deceleration, mass loss, etc.) can be determined along the trajectory of the meteor. [19] The last fundamental modeling equation accounts for electron production per unit path length resulting from an

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Table 3. Average Annual Modeled Source Contributions Above Arecibo Source Name

Input (%) (1 AU)

Model Avg. (%) (MLT)

Yearly Min (%) (MLT)

Yearly Max (%) (MLT)

Combined N&S Apex Helion Anti-Helion North Toroidal South Toroidal

33.0 22.0 22.0 11.5 11.5

56.17 19.26 19.44 4.32 1.16

49.93 15.15 15.13 3.65 0.25

58.85 23.43 23.43 4.98 2.05

ablating meteor. This equation is derived under the assumption that the energy used to ionize ablating particles is proportional to the transfer of kinetic energy from the ablated atoms [McKinley, 1961] and is given in the form stated by Janches and ReVelle [2005] as: " t ion rAir ð zÞAsð zÞG M ð zÞ 2=3 4 qline ð zÞ ¼ V ð zÞ 2h rMet !

ð6Þ

where A is the shape factor (1.21 for spherical particles) and s(z) is the ablation coefficient given by Bronshten [1983]. sð zÞ ¼

Ch 2QHeat G

ð7Þ

[20] The dimensionless ionization efficiency factor t ion in equation (6) is proportional to the probability (b) that an ablated atom produces an electron resulting from the ionization process carried out by collisional impacts with air and it is given by: t ion ¼

2h b mV 2

ð8Þ

[21] A description of theoretical, experimental, and observational values of b are given by Bronshten [1983] and a series of closed form analytic solutions for the determination of this parameter based on velocity are given by Jones [1997]. The ionization probability b is strongly dependent on the material that is being ablated and although a mean value is used for the model, a full thermodynamical treatment of the ablation process for each meteor constituent is necessary to determine the total ionization coefficient properly (Plane, personal communication, 2007). Although t ion is velocity dependent, estimates given by Revelle [1980, 2005b] and Revelle and Ceplecha [2001, 2002] support a numerical value of t ion = 0.001 over a broad range of velocities. Because of the aforementioned uncertainty in the determination of t ion we use in this work a value equal to 0.001, noting that using a velocity dependent treatment of t ion proposed by Jones [1997] does not show significant differences in the modeled results at Arecibo that are discussed in section 3. The mean ionization potential per atom (h) is approximately 11.092 eV and can be calculated based on the assumed composition of a chrontitic meteor as ¨ pik [1958] and the weighted average of the discussed by O individual ionization potential for each neutral. Thus after a conversion from eV to Joules (1 eV = 1.6'10"19 J) the total weighted value of h is approximately 1.7747'10"18 J. Because the radar detects the ionization per unit volume, the line density (qline(z)) must be converted to a volume density by assuming some head-echo shape and size. In this work we followed a somewhat similar approach to that

reported by Close et al. [2002] and assume the head-echo to be spherical with a radius equal to the atmospheric mean free path as is given by: qvol ð zÞ ¼

qline ð zÞ 2 prmfp

ð9Þ

[22] An example of the full integration is illustrated in Figure 2 for a 1 microgram particle, with a 0! entry angle moving at 20 km/s. If we assume a meteor event must produce a certain electron volume density for a given radar to detect it, then it is possible for a meteoroid to ablate but never reach such a detection threshold, thus remaining undetected as a meteor. This is illustrated in Figure 3 where the electron volume densities for different sets of initial conditions are plotted. It can be observed from this figure that ablation and, thus electron production, has a strong dependence on mass, velocity, and entry angle. [23] In Figure 4 we present modeled initial altitude of detection as a function of meteor velocity assuming different volume density thresholds and compare them with Arecibo observations. In Panel (a) it can be seen that for a threshold of 1 ( 108 e"/m3 good agreement between model and radar observations is found from almost the entire velocity range, although for very slow velocities the model predicts a detection significantly higher than it is actually observed. It can also be observed from this figure that larger electron thresholds seem to reproduce only the lower initial altitudes of slower particles and that detection is predicted at significantly lower altitudes for almost the entire velocity range. These results suggest that at Arecibo, and probably the other HPLA radars, detection occurs before the maximum ionization is produced. While electron threshold is directly related to meteor detection, the radar cross-section (RCS) is the true measure of how the radar observes the incoming meteors [Hunt et al., 2004; Close et al., 2005, 2007]. This sensitivity function is not yet well determined for Arecibo, however, preliminary results [Janches et al., 2008] show that the Arecibo radar is very sensitive, with a minimum detected RCS of "90 dBsm compared to, for example, only "50 dBsm for the VHF ALTAIR system [Close et al., 2007]. On the basis of the results presented in Figure 4, we adopt a minimum detection threshold for the Arecibo HPLA radar of 1 ( 108 e"/m3 for all subsequent simulations presented herein. If a modeled meteor event does not produce enough ionization to reach this minimum detection threshold, then we assume it will not be detected and is therefore ignored. It should be noted that while this value is not completely certain, changing it by an order of magnitude does not currently present a large change in the results between modeled and observed flux shown in the next section. We are currently working on

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Figure 2. (a) Velocity evolution starting at 20 km/s. (b) Temperature evolution starting at 300 K. (c) Mass evolution starting at 1 mg. (d) Electron volume density (solid), Mean free path (dotted). including a full treatment of the RCS calculation in the model and we expect to report results in future papers. [24] Finally, the integration results are included on the model using 3-dimensional lookup tables containing the resulting initial altitude of ablation for each case covering: 1 ( 10"5 – 1 ( 103 g mass range, 11 – 72 km/s velocity range, and 0 – 89! in entry angle were created to reduce the overall computational time. The resolution in each table is: 10 divisions per decade log10(mass), 1 km/s, and 1! for the mass, velocity, and entry angle respectively.

3. Meteor Input Function Model Results and Discussion [25] The radar observations presented in this paper and utilized in the comparison with the model results were obtained during 2002 and are representative of each month. The observations were planned to start in the early evening at 18:00 Arecibo Local Time (ALT) and to end at 08:00 ALT of the following day. The data sets, which cover shorter periods are due to either technical or scheduling problems during that particular observation. The details of the AO observations are given by Janches et al. [2003]. 3.1. Model and Observational Flux Comparisons: Individual Source Contributions [26] Figure 5 shows a comparison between the predicted and observed meteor rates at Arecibo for 2 – 3 October 2002. In Panel (5a) we compare the observed results with

the overall modeled flux, while in Panel (5d) we present the modeled individual source contributions. The black curve in Panel (5a) is the sum of the curves in Panel (5d). The observed and modeled counts per minute are compared with no additional normalization factor. As suggested by the observations and shown by the modeled results (Figure 5a), for this particular month the flux rates are characterized by the presence of two maxima with a dip in the center. These features are explained by an increase of the Apex and a decrease in the amount of meteors associated with each of the Helion/Anti-Helion radiant sources. [27] The individual source strengths of the global meteor flux at 1 AU that produced this result are: 33% of the counts for a given mass bin are assigned to the Apex source, 22% to the Helion, 22% to the Anti-Helion, 11.5% to the North Toroidal, and 11.5% to the South Toroidal. These percentages that represent a best fit to the data, are similar to previously published values [Jenniskens, 2006]. This modeling effort shows for the first time the difference between the relative source strengths outside the Earth’s atmosphere and those observed by HPLA radar in the MLT (See Table 3). From Panel (5d), it is clear that the flux observed at the MLT by the Arecibo radar is composed of a somewhat different intensity than the global input distribution at 1 AU from each source. The diurnal variability of the simulated meteor flux rates from the Apex, Helion and Anti-Helion sources rise and fall in the local Arecibo sky in accordance to their relative location with respect to the radar beam and provide the majority of the total modeled flux rate. They

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Figure 3. (a) Case 1: 0.01 mg, 0.1 mg, and 1 mg for 20 km/s at 0! entry angle. (b) Case 2: 20 km/s, 40 km/s, and 60 km/s for 0.1 mg at 0! entry angle. (c) Case 3: 0!, 45!, and 80! entry angle for 0.1 mg at 20 km/s. have a rapid increase in the detected meteors, reach their respective peaks that are visible for only part of the day, and then quickly decrease. While the distinct rise and fall of the Helion and Anti-Helion sources contributes to the small temporal scale variability (two peaks present in the October observations), the Apex source provides the majority of the counts detected between 02:00 ALT and 10:00 ALT as expected [Ceplecha et al., 1998] and produces the large temporal scale shape of the meteor diurnal rate curve. This occurs because smaller particles can be detected from the Apex source according to the values presented in Table 2. That is, the minimum meteoroid mass for the

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flux originating from the fast Apex source is approximately 10"5 mg, while for the other sources it is approximately 10"3 mg. The North and South Toroidal sources provide a small and nearly constant number of counts (!1 – 2 counts per minute) based on the Arecibo radar beam path through these two radiant sources during this time of the year [Janches and Chau, 2005]. [28] While the individual contributions that provide the total flux shown in Panel (5d) are in excellent agreement between the observed rates and the total modeled flux shown in Panel (5a), it is natural to consider how unique the chosen set of percentages (or relative source strengths) are at 1 AU that result in the modeled flux. That is, can agreement between model and observation be reached using different initial source contributions? To further investigate the validity of the results in Figure 5, other source combinations, taken from Jenniskens [2006], are explored. These percentages are derived from SMR observations [Jones and Brown, 1993; Taylor, 1997] and lead to the modeled meteor rates shown in Panels (5b) and (5e) as well as Panels (5c) and (5f). Panels (5b) and (5e) represent a large Helion and Anti-Helion source contribution as reported by Jones and Brown [1993] and Taylor [1997], and Panel (5c) and (5f) represent a more uniform contribution from each source. Figure 5 shows that while small changes in the percentage of each source can simulate small scale features, such as the dip at 06:00 ALT, without the right combination of sources the overall flux at Arecibo is not easily replicated. The observed results at Arecibo, cannot be reproduced by assuming that the majority of particles originate mainly from the Helion and Anti-Helion sources as it is suggested by measurements using SMRs. We believe that the reason why these two sources are more dominant in SMR observations is explained by the height-ceiling effect inherent to SMR systems that detect the specular reflection of meteor trails. As pointed out by Steel and Elford [1991], this effect prevents SMRs, which utilize frequencies in the 25– 50 MHz range, from detecting trails formed above !105 km of altitude independently of particle mass. According to the authors, in this region the vast majority of meteoric input ablates, which is in agreement with HPLA meteor headecho observations and the modeled results presented here. Altitude distributions resulting from SMR data peak at !90 km of altitude with few detections above at !110 km, while altitude distributions resulting from HPLA radars observations of head-echoes peak at !100 –110 km [Close et al., 2000; Janches et al., 2003; Chau and Woodman, 2004; Westman et al., 2004; Chau et al., 2007]. Furthermore, as shown in Figure 4 [see also Janches et al., 2003, 2008; Janches and ReVelle, 2005; Chau et al., 2007], most of the meteors detected at higher altitudes are associated with higher geocentric velocities (>40 km/s). Thus as indicated by Steel and Elford [1991], SMRs fail to detect a large portion of meteors originating from the Apex source. Thus relating atmospheric phenomena with meteor rate variability resulting from SMR observations can potentially lead to large errors because 50% of the input mass (or more) is unaccounted for. Haldoupis et al. [2007] recently suggested that the seasonal variation of sporadic E layers correlates well with the annual sporadic meteor deposition. However, the authors used observations from a SMR showing a strong seasonal peak in June but did not

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Figure 4. Observational and model comparison of initial altitude of detection as a function of velocity with 5 km/s binning. The dotted diamonds with 1 standard deviation error bars are Arecibo Observations obtained on 21 January 2002 while the solid symbols are modeled results assuming: " " " of 1 ( 108 e"/m3, (b) ethreshold of 1 ( 109 e"/m3, (c) ethreshold of 1 ( 1010 e"/m3, and (a) ethreshold " 11 " 3 (d) ethreshold of 1 ( 10 e /m .

Figure 5. (a), (b), and (c) display the total diurnal variation of observed and simulated meteor events per minute for 2 – 3 October 2002 for different source strengths, while (d), (e), and (f) display the input from each individual source. The sum of the curves in the bottom panels result in the modeled curves in the upper panels. The source intensities are also shown in the bottom panels. Note that the modeled contribution of each source to the overall MLT flux is in a much different proportion than the source contribution at 1 AU. 9 of 13

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Figure 6. Comparison between the modeled flux and the 2002 observed flux data for each month of the year using the Arecibo 430 MHz radar. The input percentages at 1 AU are those from Figure 5d and are the same input percentages at 1 AU for all months. account for the large portion of undetected meteors at high altitudes. The reported seasonal peak is 3 months earlier than what is suggested by an earlier version of this model validated through HPLA observations at somewhat similar latitudes [Janches et al., 2006]. Thus either only part of the meteoric influx (slower particles ablating at lower altitudes) is responsible for the seasonal variability of sporadic E layers or this correlation may be non-causal. [29] It is also important to consider the detected mass range being observed when comparing Arecibo results to those of other radars, particularly SMR. The Arecibo radar detects smaller particle sizes than, for example, CMOR and HMRS. As shown by Mathews et al. [2001] the largest estimated mass of a particle typically observed at AO in a day is on the order of 10 mg. If the sporadic sources have different mass distribution indexes (which seems reasonable given their different orbital histories) they will have different relative strengths in different size ranges. [30] Additionally, the results of our model suggest that the Arecibo observed diurnal rates have an additional component of particles originating from the Apex with very small masses in the 10"5 to 10"3 mg range. Particles with

these masses but slower velocities (<30 km/s) are not as likely to ablate, according to Bronshten [1983], and will not become meteors, thus remaining undetected by Arecibo, or any other radar. [31] Figure 6 shows a comparison between modeled and observed meteor rates collected for each month of 2002 at Arecibo. It can be observed from this figure that the seasonal variability of the overall shape of the observed meteor rates is in very good agreement with the modeled one. The Apex source is responsible for the large temporal scale characteristics of the rate curves throughout the year, while the contribution from the Helion and Anti-Helion sources show a more pronounced variability that results in a seasonal change of the small temporal scale features of the observed and modeled rates. That is some months show two comparable peaks, some months show a single peak and the rest show two peaks but one that is more dominant than the other as discussed by Janches et al. [2006]. An important factor of the comparisons shown in Figure 6 is that the model simulates the actual number of detected meteors, unlike Janches et al. [2006] in which an additional normalizing factor was introduced to match the counts per minute

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Figure 7. Comparison between observed and modeled geocentric velocity distributions for 6 months of data between 04:00 and 06:00 ALT (UT-4) during 2002. (a) January, (b) February, (c) March, (d) April, (e) May, and (f) June. between modeled and observed data. Thus we have successfully modeled the overall shape of the detected diurnal and seasonal meteor rate curves observed at Arecibo as well as the small scale variability without normalization. What appears to be a noise like fluctuation in the model is a result of the inherent variability in the number of meteors simulated per minute based on a Monte Carlo treatment of the input particles typical of a counting experiment. It must be noted that, January and June observed fluxes are higher than those modeled. One of the main assumptions made in this model is that the extraterrestrial micrometeor flux is constant throughout the year. The disagreement between the data from these two months and the model suggests that this may not be the case. In fact Campbell-Brown and Jones [2006] shows that significant source activity variability seems to be present in multiyear CMOR surveys. Future observations at Arecibo are planned during these months to investigate the uniformity, or lack thereof, of the extraterrestrial flux. It is also important to note that in order to get the agreement between model and observed rates an atmospheric filtering parameter was needed. That is, meteor radiants that are at an elevation angle lower than 20! are neglected. This value is in agreement with the previous work [Janches et al., 2006] that showed the modeled

atmospheric filtering angle to be in the range of 15! to 26! in elevation. This parameter has little effect on the number of counts detected, but rather the shape of each detected source. Another effect that needs further exploration is the ‘‘knee’’ that is present in the modeled results sometimes in the early morning hours (January, February, November, and December), sometimes during the afternoon (May, June, July, and August) and some other times during both periods (March and April). This effect results from an excess of particles originating from the Anti-Helion and Helion sources (depending on time of the day) with respect to the measured rates. It is not clear at this time exactly what causes this difference between model and observation, but it is probably due to a combination of the Gaussian shape of the simulated radiant sources and the fact that we are currently modeling the radar beam pattern as uniform through its volume instead of a more realistic treatment. We are also, as discussed earlier, not yet including a full treatment of the RCS meteor head-echo calculation. These modifications will be included in future versions of the model. 3.2. Model and Observational Velocity Comparisons [32] Representative radial (i.e., line-of-sight component) velocity distributions derived from the Arecibo radar obser-

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vations for different months are presented in Figure 7. Because of the limited observing period for the observations presented herein, the model is only run between 04:00 ALT and 06:00 ALT (UT-4) in order to compare the observed radial velocity distributions with those modeled. If different periods between observed and simulated results were to be compared, then velocities from other radiants not present between 04:00 ALT and 06:00 ALT would skew the modeled results. [33] It can be seen from this comparison that the resulting modeled radial velocity distributions are in excellent agreement with observations. Also, it is important to note again, that the panels in Figure 7 show actual number of meteors as opposed to a comparison between modeled and observed velocity distributions that are normalized. Hence the model accurately accounts for each detection, given the initial flux input, as well as the directionality reflected in the seasonal variation of the detected radial velocity distribution as the Arecibo beam scans through different sources during the course of a year.

4. Summary [34] In this work, we have presented an improved semiempirical model of the micrometeor input function (MIF) into the MLT initially reported by Janches and Chau [2005] and Janches et al. [2006]. We have investigated in detail how each meteoroid radiant source contributes to the overall local meteor input and how they manifest in the diurnal variability of the meteor rate observed by the 430 MHz Arecibo radar in Puerto Rico. We improved upon the initial model of Janches et al. [2006] by including a widely used global meteoric mass flux at 1 AU in the 10"5 to 103 mg mass range, which is divided into different proportions among all the known sporadic meteoroid radiant sources and use this as the initial input above the Earth’s atmosphere. We then used the complete integration of the equations that describe the meteoroid atmospheric entry and ablation physics to determine radar detectability. The simulated results presented from this model, including meteor rates and velocity distributions at different seasons, are in excellent agreement with Arecibo HPLA radar observations. This modeling effort demonstrates the current ability to reproduce meteor observational results using the 430 MHz Arecibo radar in Puerto Rico. However, given the necessary system parameters this model can be, and will be, generalized to any HPLA radar. The agreements found between modeled and observed results indicate that, although the Earth’s Apex centered radiant source, which is characterized by high geocentric speeds (!55 km/s), appears to be !33% of the meteoroids in the Solar System at 1 AU, it accounts for !60% of the meteors observed in the atmosphere by Arecibo. The remaining 40% of observed meteors originate mostly from the Helion and Anti-Helion sources, with a very small, but constant during the day, contribution of the South and North Toroidal sources. These results suggest that HPLA radars detect head-echoes long before maximum ionization occurs and also that the differences in the observed distributions between HPLA and SMR radars are due to two factors: 1) the height-ceiling effect inherent in SMR systems, which results in the lack of sensitivity to faster particles occurring at higher altitudes,

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independent of particle mass, thus missing a very large portion of the incoming flux as suggested by Steel and Elford [1991] and 2) very small particles in the 10"5 to 10"3 mg mass range with slow velocities (<30 km/s) will not significantly ablate according to Bronshten [1983] and never become meteors. This results in an additional component of faster and very small particles in the observed Arecibo distributions. Finally, it also needs to be pointed out that when comparing Arecibo results to those of other radars, specially SMRs, differences in mass range sensitivity can easily introduce differences in relative abundances of the sources. This is due to the fact that the sporadic sources may have different mass distribution indexes due to their different orbital histories which would result in different relative strengths for different size ranges. [35] Acknowledgments. 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. In addition, the authors wish to thank Naomi Edelberg for her help on the analysis of the AO meteor data. The authors have been supported under NSF Grants ATM-05311464 and ATM-0525655 to NorthWest Research Associates, Inc. [36] Wolfgang Baumjohann thanks M. Campbell-Brown, Lars Dyrud and another reviewer for their assistance in evaluating this paper.

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J. T. Fentzke and D. Janches, NorthWest Research Associates Inc., CoRA Division, 3380 Mitchell Lane, Boulder, CO 80301, USA. (jonathan. [email protected]; [email protected])

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