Determining meteoroid bulk densities using a plasma scattering model with high-power large-aperture radar data

We present an improved technique for calculating bulk densities of low-mass (<1 g) meteoroids using a scattering model applied to the high-density plasma formed around the meteoroid as it enters Earth’s atmosphere. These plasmas, referred to as head echoes, travel at or near the speed of the meteoroid, thereby allowing the determination of the ballistic coefficient (mass divided by physical cross-section), which depends upon speed and deceleration. Concurrently, we apply a scattering model to the returned signal strength of the head echo in order to correlate radar-cross-section (RCS) to plasma density and meteoroid mass. In this way, we can uniquely solve for the meteoroid mass, radius and bulk density independently. We have applied this new technique to head echo data collected in 2007 and 2008 simultaneously at VHF (160 MHz) and UHF (422 MHz) at ALTAIR, which is a high-power large-aperture radar located on the Kwajalein Atoll. These data include approximately 20,000 detections with dual-frequency, dual-polarization, and monopulse (i.e. angle) returns. From 2000 detections with the smallest monopulse errors, we find a mean meteoroid bulk density of 0.9 g/cm³ with observations spanning almost three orders of magnitude from 0.01 g/cm³ to 8 g/cm³. Our results show a clear dependence between meteoroid bulk density and altitude of head echo formation, as well as dependence between meteoroid bulk density and 3D speed. The highest bulk densities are detected at the lowest altitudes and lowest speeds. Additionally, we stipulate that the approximations used to derive the ballistic parameter, in addition to neglecting fragmentation, suggest that the traditional ballistic parameter must be used with caution when determining meteoroid parameters.     

Meteoroid Bulk Density Determination Using Radar Head Echo Observations

We present the results of a study of meteoroid bulk densities determined from meteor head echoes observed by radar. Meteor observations were made using the Advanced Research Projects Agency Long-Range Tracking And Instrumentation Radar (ALTAIR). ALTAIR is particularly well suited to the detection of meteor head echoes, being capable of detecting upwards of 1000 meteor head echoes per hour. Data were collected for 19 beam pointings and are comprised of approximately 70 min. of VHF observations. During these observations the ALTAIR beam was directed largely at the north apex sporadic source. Densities are calculated using the classical physical theory of meteors. Meteoroid masses are determined by applying a full wave scattering theory to the observed radar cross-section. Observed meteoroids are predominantly in the 10⁻¹⁰ to 10⁻⁶ kg mass range. We find that the vast majority of meteoroid densities are consistent with low density, highly porous objects as would be expected from cometary sources. The median calculated bulk density was found to be 900 kg/m³. The orbital distribution of this population of meteoroids was found to be highly inclined.     

Plasma and Electromagnetic Simulations of Meteor Head Echo Radar Reflections

Recently, meteor head echo detections from high powered large aperture radars (HPLA) have brought new measurements to bear on the study of sporadic interplanetary meteors. These same observations have demonstrated an ability to observe smaller meteoroids without some of the geometrical restrictions of specular radar techniques. Yet incorporating data from various radar reflection types and from different radars into a single consistent model has proven challenging. We believe this arises due to poorly understood radio scattering characteristics of the meteor plasma, especially in light of recent work showing that plasma turbulence and instability greatly influences meteor trail properties at every stage of evolution. In order to overcome some of the unknown relationships between meteoroid characteristics (such as mass and velocity) and the resulting head echo radar cross-sections (RCS), we present our results on meteor plasma simulations of head echo plasmas using particle in cell (PIC) ions, which show that electric fields strongly influence early stage meteor plasma evolution, by accelerating ions away from the meteoroid body at speeds as large as several kilometers per second. We also present the results of finite difference time domain electromagnetic simulations (FDTD), which can calculate the radar cross-section of the simulated meteor plasma electron distributions. These simulations have shown that the radar cross-section depends in a complex manner on a number of parameters. In this paper we demonstrate that for a given head echo plasma the RCS as a function of radar frequency peaks at sqrt (2*peak plasma frequency) and then decays linearly on a dB scale with increasing radar frequency. We also demonstrate that for a fixed radar frequency, the RCS increases linearly on a dB scale with increasing head echo plasma frequency. These simulations and resulting characterization of the head echo radar cross-section will both help relate HPLA radar observations to meteoroid properties and aid in determining a particular radar facility’s ability to observe various meteoroid populations.     

Meteor head echo radar data: Mass-velocity selection effects

High-power, large-aperture (HPLA) radars detect the plasma that forms in the vicinity of a meteoroid and moves approximately at its velocity; reflections from these plasmas are called head echoes. For over a decade, HPLA radars have been detecting head echoes with peak velocity distributions >50 km/s. These results have created some controversy within the field of meteor physics because previous data, including spacecraft impact cratering studies, optical and specular meteor data, indicate that the peak of the velocity distribution to a set limiting mass should be <20 km/s [Love, S.G., Brownlee, D.E., 1993. Science 262, 550-553]. Thus the question of whether HPLA radars are preferentially detecting high-velocity meteors arises. In this paper we attempt to address this question by examining both modeled and measured head echo data using the ALTAIR radar, collected during the Leonid 1998 and 1999 showers. These data comprise meteors originating primarily from the North Apex sporadic meteor source. First, we use our scattering theory to convert measured radar-cross-section (RCS) to electron line density and mass, as well as to convert modeled electron line density and mass to RCS. We subsequently compare the dependence between mass, velocity, mean-free-path, RCS and line density using both the measured and modeled data by performing a multiple, linear regression fit. We find a strong correlation between derived mass and velocity and show that line density is approximately proportional to mass times velocity^3.1. Next, we determine the cumulative mass index using subsets of our data and use this mass index, along with the results of our regression fit, to weight the velocity distribution. Our results show that while there does indeed exist a bias in the measured head echo velocity distribution, it is smaller than those calculated using traditional specular trail data due to the different scattering mechanism, and also includes a bias against the low-mass, very high-velocity meteoroids.     

Some Aspects of Meteoric Head Echo Velocity Determination

Velocity determination of 131 head echoes recorded during Perseid meteor shower observations by the Canadian 2 MW radar, has been performed under the assumption of either their constant velocity or of its linear change with time. Even though the constant velocities concentrated at 60 km s-1 generally accepted for the Perseids, a substantial number of echoes had velocities either lower than 60 km s-1 or greater than this value. The inclusion of variable velocity into considerations led to surprising result that a great portion of the head echoes accelerated (3 possibly decelerating echoes in comparison with 33 accelerating cases on the level of relative standard deviations of output parameters not exceeding 10%). It seems that the allocation of the ionization responsible for the head echo is not entirely identical with the instantaneous meteoroid position. As a consequence, the velocity derived from the measured head echo coordinates can differ from the velocity of parent body. We are not able to explain this finding at present. This revised version was published online in July 2006 with corrections to the Cover Date.     

Determination of the meteoroid velocity distribution at the Earth using high-gain radar

Plasma formed in the immediate vicinity of a meteoroid as it descends through Earth's atmosphere enables high-gain radars such as those found at Kwajalein, Arecibo, and Jicamarca to detect ablating meteoroids. In the work presented here, we show that these head echo measurements preferentially detect more energetic meteoroids over less energetic ones and present a method of estimating the effects of this bias when measuring the velocity distributions. To do this, we apply ablation and ionization models to estimate a meteoroid's plasma production rate based on its initial kinetic energy and ionization efficiency. This analysis demonstrates that, almost regardless of the assumptions made, high-gain radars will preferentially detect faster and more massive meteoroids. Following the model used by Taylor (1995, Icarus 116, 154-158), we estimate the biases and then apply them to observed meteoroid velocity distributions. We apply this technique to observations of the North Apex meteoroid source made by the Advanced Research Project Agency Long Range Tracking and Instrumentation Radar (ALTAIR) at two frequencies (160 and 422 MHz) and compare results from the Harvard Radio Meteor Project (HRMP) at High Frequency (HF, 40.9 MHz). Both studies observe a peak in the distribution of North Apex meteoroids at approximately 56 km s⁻¹. After correcting for biases using Taylor's method, the results suggest that the mass-weighted peak of the distribution lies near 20 km s⁻¹ for both studies. We attribute these similarities to the fact that both radar systems depend upon similar ablation and ionization processes and thus have a common mass scale.     

Meteoroid structure from radar head echoes

The Advanced Research Project Agency (ARPA) Long Range Tracking and Instrumentation Radar has recorded thousands of head echoes from small meteoroids, which include detailed trajectory information as well as ionization measurements. In total, 25 complete ionization curves have been matched using a detailed model of meteoroid ablation, though the solutions are not necessarily unique. While measurements of the spread along the trajectory of the echoes indicate that most meteors in this size range do not have large separations among fragments, the ionization curves are consistent with fragmenting bodies in the most cases. Very precise radar measurements of meteors can be a valuable source of data on the chemical and physical properties of small meteoroids.     

THE METEOR FLUX: IT DEPENDS HOW YOU LOOK

In this paper, we use radar observations from a 50 MHz radar stationed near Salinas, Puerto Rico, to study the variability of specular as well as non-specular meteor trails in the E-region ionosphere. The observations were made from 18:00 to 08:00 h AST over various days in 1998 and 1999 during the Coqui II Campaign [Urbina et al., 2000, Geophys. Rev. Lett. 27, 2853–2856]. The radar system had two sub-arrays, both produced beams pointed to the north in the magnetic meridian plane, perpendicular to the magnetic field, at an elevation angle of approximately 41 degrees. The Coqui II radar is sensitive to at least two types of echoes from meteor trails: (1) Specular reflections from trails oriented perpendicular to the radar beam, and (2) scattering, or, non-specular reflections, from trails deposited with arbitrary orientations. We examine and compare the diurnal and seasonal variability of echoes from specular and non-specular returns observed with the Coqui II radar. We also compare these results with meteor head echo observations made with the Arecibo 430 MHz radar. We use common region observations of these three types of meteor echoes to show that the diurnal and seasonal variability of specular trails, non-specular trails, and head echoes are not equivalent. The implications of these results on global meteor mass flux estimates obtained from specular meteor observations remains to be examined.     

Quantitative Comparison of a New Ab Initio Micrometeor Ablation Model with an Observationally Verifiable Standard Model

The Arecibo UHF radar is able to detect the head-echos of micron-sized meteoroids up to velocities of 75 km/s over a height range of 80–140 km. Because of their small size there are many uncertainties involved in calculating their above atmosphere properties as needed for orbit determination. An ab initio model of meteor ablation has been devised that should work over the mass range 10⁻¹⁶ kg to 10⁻⁷ kg, but the faint end of this range cannot be observed by any other method and so direct verification is not possible. On the other hand, the EISCAT UHF radar system detects micrometeors in the high mass part of this range and its observations can be fit to a “standard” ablation model and calibrated to optical observations (Szasz et al. 2007). In this paper, we present a preliminary comparison of the two models, one observationally confirmable. Among the features of the ab initio model that are different from the “standard” model are: (1) uses the experimentally based low pressure vaporization theory of O’Hanlon (A users’s guide to vacuum technology, 2003) for ablation, (2) uses velocity dependent functions fit from experimental data on heat transfer, luminosity and ionization efficiencies measured by Friichtenicht and Becker (NASA Special Publication 319: 53, 1973) for micron sized particles, (3) assumes a density and temperature dependence of the micrometeoroids and ablation product specific heats, (4) assumes a density and size dependent value for the thermal emissivity and (5) uses a unified synthesis of experimental data for the most important meteoroid elements and their oxides through least square fits (as functions of temperature, density, and/or melting point) of the tables of thermodynamic parameters given in Weast (CRC Handbook of Physics and Chemistry, 1984), Gray (American Institute of Physics Handbook, 1972), and Cox (Allen’s Astrophysical Quantities 2000). This utilization of mostly experimentally determined data is the main reason for calling this an ab initio model and is made necessary by the fact that individual average meteoroid mass densities are now derivable from Arecibo observations.     

Estimated Visual Magnitudes of the EISCAT UHF Meteors

We have investigated the conditions for simultaneous meteor observations with the EISCAT UHF radar system and telescopic optical devices. The observed characteristics of 410 meteors detected by all three UHF receivers are compared with model simulations and their luminosity is calculated as a part of a meteoroid ablation model using a fifth order Runge–Kutta numerical integration technique. The estimated absolute visual magnitudes are in the range of +9 to +5. The meteors should therefore be observable using intensified CCD or EMCCD (Electron Multiplying CCD) cameras with telephoto lenses. A possible setup of a coordinated radar and optical campaign is suggested.     

Surface slope probabilities from the spectra of weak radar echoes: Application to Mars

Slope probability densities were derived from the power spectra of radar echoes from Mars using integral inversion. The inverse problem is ill-posed; that is, small changes in the data can lead to large changes in the solution. We describe a method of stabilizing the inversion, which was necessary for echoes with signal-to-noise power spectral densities on the order of unity, and for those with broad spectral distributions. The resulting slope probabilities usually consisted of a component due to quasi-specular reflection which decreased rapidly with tilt, plus a broad, slowly decreasing, “diffuse” component due to scattering from (1) surface scales small compared with a radar wavelength, or (2) larger features with high slopes. In the absence of more complete polarization measurements, we are unable to In the absence of more complete polarization measurements, we are unable to distinguish between these possibilities. Root mean square tilts have been determined separately for the two cases. For case (1), values of rms tilt associated with surface features responsible for the quasi-specular echo are normally less than 3°; for case (2), values greater than 8° are common. Knowledge of the depolarization of radar returns would help distinguish between these possibilities.     

Improving the Accuracy of Meteoroid Mass Estimates from Head Echo Deceleration

This paper examines current techniques used to determine meteoroid mass from high-power, large aperture (HPLA) radar observations. We demonstrate why the standard approach of fitting a polynomial to velocity measurements gives inaccurate results by applying this technique to artificial datasets. We then suggest an alternate approach, fitting velocity data to an ablation model. Using data taken at the Jicamarca Radio Observatory in July 2005, we compare the results of both methods and demonstrate that fitting velocity data to an ablation model yields a reasonable result in some instances where alternate methods produce physically unrealistic mass estimates.     

The rings of Saturn: Two-frequency radar observations

Observations of 3.5- and 12.6-cm radar echoes from the rings of Saturn suggest that no significant difference in scattering properties exists in this wavelength interval. The echoes are largely unpolarized at both wavelengths, and yield a radar cross section at 3.5 cm of 7.32 ± 0.84 × 10⁹ km² for each polarization. The combined radar cross sections for both polarizations correspond to 1.37 ± 0.16 times the optically observed projected A- and B-ring areas (excluding that part of the rings shadowed by the planet). The shape of the echo spectrum is compatible with a homogeneous ring scattering model, except in having excess power at frequencies near the center of the spectrum. A number of possible explanations for the observed scattering properties are explored.     

A comparison of detection sensitivity between ALTAIR and Arecibo meteor observations: Can high power and large aperture radars detect low velocity meteor head-echoes

Meteor head-echo observations using High Power and Large Aperture (HPLA) radars have been routinely used for micrometeor studies for over a decade. The head-echo is a signal from the radar-reflective plasma region traveling with the meteoroid and its detection allows for very precise determination of instantaneous meteor altitude, velocity and deceleration. Unlike specular meteor radars (SMR), HPLA radars are diverse instruments when compared one to another. The operating frequencies range from 46 MHz to 1.29 GHz while the antenna configurations changes from 18,000 dipoles in a 300 m×300 m square array, phase arrays of dipoles to single spherical or parabolic dishes of various dimensions. Hunt et al. [Hunt, S.M., Oppenheim, M., Close, S., Brown, P.G., McKeen, F., Minardi, M., 2004. Icarus 168, 34-42] and Close et al. [Close, S., Brown, P., Campbell-Brown, M., Oppenheim, M., Colestock, P., 2007. Icarus, doi:10.1016/j.icarus.2006.09.07] recently showed, by utilizing a head-echo plasma-based model, the presence of instrumental biases in the ALTAIR VHF radar system against detecting meteors produced by very small particles (<1 μg) moving at slow (∼20 km/s) velocities due to the low head echo radar cross-section (RCS) associated with these particles. In this paper we apply the same methodology to the Arecibo 430 MHz radar and compare the results with those presented by Close et al. [Close, S., Brown, P., Campbell-Brown, M., Oppenheim, M., Colestock, P., 2007. Icarus, doi:10.1016/j.icarus.2006.09.07]. We show that, if the methodology applied by Hunt et al. [Hunt, S.M., Oppenheim, M., Close, S., Brown, P.G., McKeen, F., Minardi, M., 2004. Icarus 168, 34-42] and Close et al. [Close, S., Brown, P., Campbell-Brown, M., Oppenheim, M., Colestock, P., 2007. Icarus, doi:10.1016/j.icarus.2006.09.07] is accurate, for particles at least 1 μg or heavier, while the bias may exist for the ALTAIR measurements, it does not exist in the Arecibo data due to its greater sensitivity.     

Meteoric head echoes

Results of the analysis of 3261 radar meteor head echoes observed during the Orionid and Lyrid periods by the high-power radar of the Springhill Meteor Observatory are given. Dependence of the occurence of head echoes on the geometrical factors and physical properties of the meteoroids has been studied. Increas of the head echo rates with the elevation of the shower radiant and with the velocity of meteoroids has been observed.     

The initial train radius of sporadic meteors

The height distributions, velocity distributions and flux measurements of underdense echoes determined from meteor radar observations are significantly affected by the attenuation associated with the initial radius of meteor trains. Dual-frequency radar observations of a very large set of sporadic radar meteors at 29 and 38 MHz yield estimates of the initial train radius and its dependence on height and meteoroid speed as determined by the time-delay method. We provide empirical formulae that can be used to correct meteoroid fluxes for the effect of initial train radius at other radio frequencies.     

Geminid Meteor shower activity 2003–2005 as observed by Gadanki radar

The distribution of meteor signals reflected from a backscatter radar is considered according to their duration. This duration time (T) is used to classify the meteor echoes and to calculate the mass index (S) of different meteoroids of shower plus sporadic background. Observational data on particle size distribution of the Geminid meteor shower are very scarce, particularly at low latitudes. In this paper the observational data from Gadanki radar (13.46°N, 79.18°E) have been used to determine the particle size distribution and the number density of meteoroids inside the stream of the Geminid meteor shower. The mean variation of meteor number density across the stream has been determined for three echo duration classes, T<0.4, T=0.4–1 and T>1 s. We are more interested in the appearance of echoes of various durations and therefore meteors of various masses in order to understand more on the filamentary structure of the stream. It is observed that the faint particle flux peaks earlier than the larger particles. We found a decreasing trend in the mass index values from the day of peak activity to the next observation days. The mass index profile was found to be U-shaped with a minimum value near the time of peak activity. The observed minimum s values are 1.64±0.05 and 1.65±0.04 in the years 2003 and 2005, respectively. The activity of the shower indicates the mass segregation of meteoroids inside the stream. Our results are best comparable with the “scissors” structure model of the meteoroid stream formation of Ryabova [2007. Mathematical modeling of the Geminid meteoroid stream. Mon. Not. R. Astron. Soc. 375, 1371–1380] by considering the asteroid 3200 Phaethon as an extinct comet.     

Small scale structures of a mesospheric dusty plasma

A dusty plasma model is presented to study the small scale structures of plasma densities in mesopause region associated with polar mesosphere summer echoes (PMSE). The heavy dust grains (ice particles) are treated as a flowing background of negative charge. Numerical results show that the electron and ion densities drop rapidly while the electric field increases dramatically within a short distance of several meters. The scalelengths of the electron density are comparable to the typical wavelength of the PMSE radars, which may be responsible for strong radar backscatter. Furthermore, the increase of the ice particle concentration results in the reduction of the density gradient and electric field.     

On the shape of meteor light curves, and a fully analytic solution to the equations of meteoroid ablation

The shape and characteristics (beginning and end heights, and height of maximum brightness) of meteor light curves are investigated under the constraint that the surface area S that a meteoroid presents to the oncoming air flow varies as a power law in the meteoroid mass m such that   S ∼ m ^α  . We investigate the meteoroid ablation for a range of values of α, and find that the  α= 1  condition allows for a fully analytic solution to the coupled differential equations of meteoroid ablation when the density profile is that of an isothermal atmosphere. The possible geometrical properties of Geminid meteoroids are discussed in terms of the  α= 1  ablation model and it is shown that they are consistent with being derived from an asteroidal, rather than cometary, parent body.     

Power Fluctuations in Meteor Head Echoes Observed with the EISCAT VHF Radar

We present observations and preliminary results from a meteor experiment carried out with the 224 MHz EISCAT VHF radar in Tromsø, Norway, which was run for 6 h on November 26, 2003. The data set contains echoes with peculiar pulsations in received power in the frequency range 20–200 Hz, limited by instrumental parameters. The process causing the echo power pulsations has not yet been identified. Plasma effects are the most likely cause, a possible mechanism is for instance asymmetrical dust grains in rotation causing a modulation of the ionization rate.