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.     

A meteoroid stream survey using the Canadian Meteor Orbit Radar: I. Methodology and radiant catalogue

Using a meteor orbit radar, a total of more than 2.5 million meteoroids with masses ∼10⁻⁷ kg have had orbits measured in the interval 2002-2006. From these data, a total of 45 meteoroid streams have been identified using a wavelet transform approach to isolate enhancements in radiant density in geocentric coordinates. Of the recorded streams, 12 are previously unreported or unrecognized. The survey finds >90% of all meteoroids at this size range are part of the sporadic meteoroid background. A large fraction of the radar detected streams have q<0.15 AU suggestive of a strong contribution from sungrazing comets to the meteoroid stream population currently intersecting the Earth. We find a remarkably long period of activity for the Taurid shower (almost half the year as a clearly definable radiant) and several streams notable for a high proportion of small meteoroids only, among these a strong new shower in January at the time of the Quadrantids (January Leonids). A new shower (Epsilon Perseids) has also been identified with orbital elements almost identical to Comet 96P/Machholz.     

Detailed data for 259 fireballs from the Canadian camera network and inferences concerning the influx of large meteoroids

Abstract— We present data for 259 meteoric fireballs observed with the Canadian camera network, including velocities, heights, orbits, luminosities along each trail, estimates of preatmospheric masses and surviving meteorites (if any) as well as membership in meteor showers. Some 213 of the events comprise an unbiased sample of the 754 fireballs observed in a total of 1.51 × 10¹⁰ km² h of clear-sky observations. The number of fireballs and the amount of clear sky in which they were recorded are given for each day of the year. We find at least 37% of the unbiased sample are members of some 15 recognized meteor showers. Preatmospheric masses, based on an assumed luminous efficiency of 0.04 for velocities >10 km s^?1, range from 1 g for some very fast fireballs up to hundreds of kilograms for the largest events. We present plots and equations for the flux, as a function of initial mass, for the entire group of fireballs and for some subgroups: meteorite-dropping objects; meteor shower members; groups that appear to be mainly of asteroidal or cometary origin; and for very fast objects. For masses of a few kilograms, asteroidal objects outnumber cometary ones. Cometary objects attain greater peak brightness than asteroidal ones of equal mass largely due to higher velocity, but also because they fragment more severely. For 66 fireballs, we estimate the meteoroid density using photometric and dynamic masses. Presumed cometary objects have typical densities near 1.0, while asteroidal values show two groups that suggest meteoroids similar to carbonaceous and ordinary chondrites. Our basic data may be used by others for further studies or to reexamine our results using assumptions different from those employed in this paper.     

Video Observations of the 2006 Leonid Outburst

We carried out double station observations of the Leonid meteor shower outburst, which occurred in the morning hours of November 19, 2006. Using image-intensified cameras we recorded approximately 100 Leonid meteors. As predicted, the outburst was rich especially in fainter meteors. The activity profile shows that the peak of the outburst occurred at 4:40 ± 0:05 UT. The maximum reached flux was 0.03 meteoroids km⁻² hod⁻¹ for meteors brighter than +6.5 magnitude.     

The Canadian Meteor Orbit Radar Meteor Stream Catalogue

The Canadian Meteor Orbit Radar is a multi-frequency backscatter radar which has been in routine operation since 1999, with an orbit measurement capability since 2002. In total, CMOR has measured over 2 million orbits of meteoroids with masses greater than 10 μg, while recording more than 18 million meteor echoes in total. We have applied a two stage comparative technique for identifying meteor streams in this dataset by making use of clustering in radiants and velocities without employing orbital element comparisons directly. From the large dataset of single station echoes, combined radiant activity maps have been constructed by binning and then stacking each years data per degree of solar longitude. Using the single-station mapping technique described in Jones and Jones (Mon Not R Astron Soc 367:1050–1056, 2006) we have identified probable streams from these single station observations. Additionally, using individual radiant and velocity data from the multi-station velocity determination routines, we have utilized a wavelet search algorithm in radiant and velocity space to construct a list of probable streams. These two lists were then compared and only streams detected by both techniques, on multiple frequencies and in multiple years were assigned stream status. From this analysis we have identified 45 annual minor and major streams with high reliability.     

Sputtering and high altitude meteors

Conventional ablation theory assumes that a meteoroid undergoes intensive heating during atmospheric flight and surface atoms are liberated through thermal processes. Our research has indicated that physical sputtering could play a significant role in meteoroid mass loss. Using a 4th order Runge-Kutta numerical integration technique, we tabulated the mass loss due to the two ablation mechanisms and computed the fraction of total mass lost due to sputtering. We modeled cometary structure meteoroids with masses ranging from 10⁻¹³ to 10⁻³ kg and velocities ranging from 11.2 to 71 km s⁻¹. Our results indicate that a significant fraction of the mass loss for small, fast meteors is due to sputtering, particularly in the early portion of the light curve. In the past 6 years evidence has emerged for meteor luminosity at heights greater than can be explained by conventional ablation theory. We have applied our sputtering model and find excellent agreement with these observations, and therefore suggest that sputtered material accounts for the new type of radiation found at great heights.     

Eccentricities of Planets in Binary Systems

The most puzzling property of the extrasolar planets discovered by recent radial velocity surveys is their high orbital eccentricities, which are very difficult to explain within our current theoretical paradigm for planet formation. Current data reveal that at least 25% of these planets, including some with particularly high eccentricities, are orbiting a component of a binary star system. The presence of a distant companion can cause significant secular perturbations in the orbit of a planet. At high relative inclinations, large-amplitude, periodic eccentricity perturbations can occur. These are known as “Kozai cycles” and their amplitude is purely dependent on the relative orbital inclination. Assuming that every planet host star also has a (possibly unseen, e.g., substellar) distant companion, with reasonable distributions of orbital parameters and masses, we determine the resulting eccentricity distribution of planets and compare it to observations? We find that perturbations from a binary companion always appear to produce an excess of planets with both very high (?0.6) and very low (e ? 0.1) eccentricities. The paucity of near-circular orbits in the observed sample implies that at least one additional mechanism must be increasing eccentricities. On the other hand, the overproduction of very high eccentricities observed in our models could be combined with plausible circularization mechanisms (e.g., friction from residual gas) to create more planets with intermediate eccentricities (e? 0.1–0.6).     

Influence of fast interstellar gas flow on the dynamics of dust grains

The orbital evolution of a dust particle under the action of a fast interstellar gas flow is investigated. The secular time derivatives of Keplerian orbital elements and the radial, transversal, and normal components of the gas flow velocity vector at the pericentre of the particle’s orbit are derived. The secular time derivatives of the semi-major axis, eccentricity, and of the radial, transversal, and normal components of the gas flow velocity vector at the pericentre of the particle’s orbit constitute a system of equations that determines the evolution of the particle’s orbit in space with respect to the gas flow velocity vector. This system of differential equations can be easily solved analytically. From the solution of the system we found the evolution of the Keplerian orbital elements in the special case when the orbital elements are determined with respect to a plane perpendicular to the gas flow velocity vector. Transformation of the Keplerian orbital elements determined for this special case into orbital elements determined with respect to an arbitrary oriented plane is presented. The orbital elements of the dust particle change periodically with a constant oscillation period or remain constant. Planar, perpendicular and stationary solutions are discussed. The applicability of this solution in the Solar System is also investigated. We consider icy particles with radii from 1 to 10 μm. The presented solution is valid for these particles in orbits with semi-major axes from 200 to 3000 AU and eccentricities smaller than 0.8, approximately. The oscillation periods for these orbits range from 10⁵ to 2 × 10⁶ years, approximately.     

A search for interstellar meteoroids using the Canadian Meteor Orbit Radar (CMOR)

Using the CMOR system, a search was conducted through 2.5 years (more than 1.5 million orbits) of archived data for meteoroids having unbound hyperbolic orbits around the Sun. Making use of the fact that each echo has an individually measured error, we were able to apply a cut-off for heliocentric speeds both more than two, and three standard deviations above the parabolic limit as our main selection criterion. CMOR has a minimum detectable particle radius near 100 μm for interstellar meteoroids. While these sizes are much larger than reported by the radar detections of extrasolar meteoroids by AMOR or Arecibo, the interstellar meteoroid population at these sizes would be of great astrophysical interest as such particles are more likely to remain unperturbed by external forces found in the interstellar medium, and thus, more likely to be traceable to their original source regions. It was found that a lower limit of approximately 0.0008% of the echoes (for the 3σ case) were of possible interstellar origin. For our effective limiting mass of 1×10⁻⁸ kg, this represents a flux of meteoroids arriving at the Earth of 6×10⁻⁶ meteoroids/km²/h. For our 2σ results, the lower limit was 0.003%, with a flux of 2×10⁻⁵ meteoroids/km²/h. The total number of events was too low to be statistically meaningful in determining any temporal or directional variations.     

Radar surveys of meteoroid orbits

Summary Radar facilities providing routine measurements of the heliocentric orbits of meteoroids are valuable in providing a data-base of the orbital characteristics of the solar system small body population in the mass range about 10^–2 down to 10^–6 g. Such an orbital information background is essential for an understanding of the evolutionary processes of this component.An outline is presented of orbit-finding systems; their inherent limitations and associated selection effects with some emphasis given to the on-going southern hemisphere routine survey provided by the AMOR facility which provides orbits down to a limiting magnitude +13.     

The Effect of Tidal Interaction with a Gas Disk on Formation of Terrestrial Planets

We have performed N-body simulation on final accretion stage of terrestrial planets, including the effect of damping of eccentricity and inclination caused by tidal interaction with a remnant gas disk. As a result of runway and oligarchic accretion, about 20 Mars-sized protoplanets would be formed in nearly circular orbits with orbital separation of several to ten Hill radius. The orbits of the protoplanets would be eventually destabilized by long-term mutual gravity and/or secular resonance of giant gaseous planets. The protoplanets would coalesce with each other to form terrestrial planets through the orbital crossing. Previous N-body simulations, however, showed that the final eccentricities of planets are around 0.1, which are about 10 times higher than the present eccentricities of Earth and Venus. The obtained high eccentricities are the remnant of orbital crossing. We included the effect of eccentricity damping caused by gravitational interaction with disk gas as a drag force (“gravitational drag”) and carried out N-body simulation of accretion of protoplanets. We start with 15 protoplanets with 0.2M⊕ and integrate the orbits for 10⁷ years, which is consistent with the observationally inferred disk lifetime (in some runs, we start with 30 protoplanets with 0.1M⊕). In most runs, the damping time scale, which is equivalent to the strength of the drag force, is kept constant throughout each run in order to clarify the effects of the damping. We found that the planets' final mass, spatial distribution, and eccentricities depend on the damping time scale. If the damping time scale for a 0.2M⊕ mass planet at 1 AU is longer than 10⁸ years, planets grow to Earth's size, but the final eccentricities are too high as in gas-free cases. If it is shorter than 10⁶ years, the eccentricities of the protoplanets cannot be pumped up, resulting in not enough orbital crossing to make Earth-sized planets. Small planets with low eccentricities are formed with small orbital separation. On the other hand, if it is between 10⁶ and 10⁸ years, which may correspond to a mostly depleted disk (0.01-0.1% of surface density of the minimum mass model), some protoplanets can grow to about the size of Earth and Venus, and the eccentricities of such surviving planets can be diminished within the disk lifetime. Furthermore, in innermost and outermost regions in the same system, we often find planets with smaller size and larger eccentricities too, which could be analogous to Mars and Mercury. This is partly because the gravitational drag is less effective for smaller mass planets, and partly due to the “edge effect,” which means the innermost and outermost planets tend to remain without collision. We also carried out several runs with time-dependent drag force according to depletion of a gas disk. In these runs, we used exponential decay model with e-folding time of 3×10⁶ years. The orbits of protoplanets are stablized by the eccentricity damping in the early time. When disk surface density decays to ?1% of the minimum mass disk model, the damping force is no longer strong enough to inhibit the increase of the eccentricity by distant perturbations among protoplanets so that the orbital crossing starts. In this disk decay model, a gas disk with 10⁻⁴-10⁻³ times the minimum mass model still remains after the orbital crossing and accretional events, which is enough to damp the eccentricities of the Earth-sized planets to the order of 0.01. Using these results, we discuss a possible scenario for the last stage of terrestrial planet formation.     

Eccentric Extrasolar Planets: The Jumping Jupiter Model

Most extrasolar planets discovered to date are more massive than Jupiter, in surprisingly small orbits (semimajor axes less than 3 AU). Many of these have significant orbital eccentricities. Such orbits may be the product of dynamical interactions in multiplanet systems. We examine outcomes of such evolution in systems of three Jupiter-mass planets around a solar-mass star by integration of their orbits in three dimensions. Such systems are unstable for a broad range of initial conditions, with mutual perturbations leading to crossing orbits and close encounters. The time scale for instability to develop depends on the initial orbital spacing; some configurations become chaotic after delays exceeding 10⁸ y. The most common outcome of gravitational scattering by close encounters is hyperbolic ejection of one planet. Of the two survivors, one is moved closer to the star and the other is left in a distant orbit; for systems with equal-mass planets, there is no correlation between initial and final orbital positions. Both survivors may have significant eccentricities, and the mutual inclination of their orbits can be large. The inner survivor's semimajor axis is usually about half that of the innermost starting orbit. Gravitational scattering alone cannot produce the observed excess of “hot Jupiters” in close circular orbits. However, those scattered planets with large eccentricities and small periastron distances may become circularized if tidal dissipation is effective. Most stars with a massive planet in an eccentric orbit should have at least one additional planet of comparable mass in a more distant orbit.     

Frequency of hyperbolic and interstellar meteoroids

Hyperbolic meteor orbits from the catalog of 64,650 meteors observed by the multistation video meteor network located in Japan (SonotaCo 2009) have been investigated with the aim of determining the relation between the frequency of hyperbolic and interstellar meteors. The proportion of hyperbolic meteors in the data decreased significantly (from 11.58% to 3.28%) after a selection of quality orbits, which shows its dependence on the quality of observations. Initially, the hyperbolic orbits were searched for meteors unbound due to planetary perturbation. It was determined that 22 meteors from the 7489 hyperbolic orbits in the catalog (and 2 from the selection of the orbits with the highest quality) had had a close encounter with a planet, none of which, however, produced essential changes in their orbits. Similarly, the fraction of hyperbolic orbits in the data, which could be hyperbolic by reason of a meteor's interstellar origin, was determined to be at most 3.9 × 10^?2. From the statistical point of view, the vast majority of hyperbolic meteors in the database have definitely been caused by inaccuracy in the velocity determination. This fact does not necessarily assume great measurement errors, since, especially near the parabolic limit, a small error in the value of the heliocentric velocity of a meteor can create an artificial hyperbolic orbit that does not really exist. The results show that the remaining 96% of meteoroids with apparent hyperbolic orbits belong to the solar system meteoroid population. This is also supported by their high abundance (about 50%) among the meteor showers.     

The origin of the Kuiper Belt high-inclination population

I simulate the orbital evolution of the four major planets and a massive primordial planetesimal disk composed of 10⁴ objects, which perturb the planets but not themselves. As Neptune migrates by energy and angular momentum exchange with the planetesimals, a large number of primordial Neptune-scattered objects are formed. These objects may experience secular, Kozai, and mean motion resonances that induce temporary decrease of their eccentricities. Because planets are migrating, some planetesimals can escape those resonances while in a low-eccentricity incursion, thus avoiding the return path to Neptune close encounter dynamics. In the end, this mechanism produces stable orbits with high inclination and moderate eccentricities. The population so formed together with the objects coming from the classical resonance sweeping process, originates a bimodal distribution for the Kuiper Belt orbits. The inclinations obtained by the simulations can attain values above 30° and their distribution resembles a debiased distribution for the high-inclination population coming from the real classical Kuiper Belt.     

The Canadian Meteor Orbit Radar: system overview and preliminary results

This paper describes the Canadian Meteor Orbit Radar (CMOR) that has been in operation since late 2001. CMOR is a 3 station meteor radar operating at a frequency of 29.85 MHz near Tavistock, Ont. To avoid bias against fragmenting meteoroids that is inherent in the traditional multi-station method of Gill and Davies (Mon. Not. R Astron. Soc. 116 (1955) 105), we use a completely geometrical method similar to that used in the AMOR system (Quart. J. R. Astron. Soc. 35 (1994) 293) based on the interferometric determination of the echo directions and the time delays of echoes from two remote stations to obtain the trajectories and speeds of meteoroids. We describe the hardware and some of the software and present some preliminary results that provide a good indication of present capabilities of the system. Typically, we can measure 1500 individual trajectories, and hence orbits, per day with a mean accuracy of 6° in direction and about 10% in speed. A small subset of these for which it is possible to measure the speeds using Hocking's (Radio. Sci. 35 (2000) 1205) method yield speeds with a precision of about 5%. The purpose of this paper is to show that the radiants and speeds necessary for the computation of orbits are well measured rather than to discuss any orbital surveys.     

The Changes of the Orbital Elements and Estimation of the Initial Velocities of Stream Meteoroids Ejected from Comets and Asteroids

The values of the initial velocity of the meteoroids ejected from the parent bodies are small and as a result, the most of the young meteoroid streams have similar orbits to their parent bodies. Assuming that the members of the observed meteor stream evolved under the influence of gravitational perturbations mostly, Pittich [1991, Proceedings of the Conference on Dynamic of Small Bodies of the Solar System, Polish-Slovak Conference, Warsaw, October 25–28, 1988, pp. 55-61], Williams [1996, Earth, Moon, Planets 72, 321–326; 2001, Proceedings of the Meteoroids 2001 conference, Kiruna, Sweden, August 6–10, 2001, pp. 33–42] estimated the ejection velocities of the stream meteoroids. Equation relating the ejection velocity Δυ and the change Δa of the semi-major axis, Williams (2001), was applied with two slightly different variations. In the first one (M1) as Δa the difference between the mean orbit of the stream and the orbit of the parent body was substituted, in the second one (M2), as Δa the dispersion of semi-major axes around the mean orbit of the stream was used. The results obtained by these two methods are not free from discrepancies, partly explained by the particular orbital structure of the stream. Kresak [1992, Contrib. Astron. Obs. Skalnate Pleso 22, 123–130] strongly criticized the attempts to determine the initial velocities of the stream using the statistics of the meteor orbits. He argued that this is essentially impossible, because the dispersion of the initial velocities are masked by much larger measuring errors and by the accumulated effects of planetary perturbations. In our paper, we study the reliability of M1 and M2 methods. We made a numerical experiment consisting of formation of several meteor streams and their dynamical evolution over 5000 years. We ejected meteoroids particles from the comets: 1P/Halley, 2P/Encke, 55P/Tempel-Tuttle, 109P/Swift-Tuttle and from minor planets (3200) Phaethon and 2002 SY₅₀. During the integration, the ejection velocities were estimated using both M1 and M2 methods. The results show that the velocities obtained by M1 method are unstable: too high or too low, when compared with the known ejection velocities at the time of the stream formation. On the other hand, the velocities obtained using M2 method are too small, mostly. In principle, M2 estimates the dispersion of the distribution of the ejection velocities around the mean value, not the mean value itself. Applying more accurate Equation relating Δυ and Δa we decreased the bias of the results, but not their variation observed during the evolution of the streams and the parent bodies. We have found that the variability of the estimated ejection velocities was caused mainly by the gravitational changes of the semi-major axis and eccentricity of the parent body. In brief, we have found that the reliability of the results obtained by M1 or M2 method are low, and have to be used with great care.     

On the Inclination Distribution of the Jovian Irregular Satellites

Irregular satellites—moons that occupy large orbits of significant eccentricity e and/or inclination I—circle each of the giant planets. The irregulars often extend close to the orbital stability limit, about 1/3-1/2 of the way to the edge of their planet's Hill sphere. The distant, elongated, and inclined orbits suggest capture, which presumably would give a random distribution of inclinations. Yet, no known irregulars have inclinations (relative to the ecliptic) between 47 and 141°.This paper shows that many high-I orbits are unstable due to secular solar perturbations. High-inclination orbits suffer appreciable periodic changes in eccentricity; large eccentricities can either drive particles with ∼70°<I<110° deep into the realm of the regular satellites (where collisions and scatterings are likely to remove them from planetocentric orbits on a timescale of 10⁷-10⁹ years) or expel them from the Hill sphere of the planet.By carrying out long-term (10⁹ years) orbital integrations for a variety of hypothetical satellites, we demonstrate that solar and planetary perturbations, by causing particles to strike (or to escape) their planet, considerably broaden this zone of avoidance. It grows to at least 55°<I<130° for orbits whose pericenters freely oscillate from 0 to 360°, while particles whose pericenters are locked at ±90° (Kozai mechanism) can remain for longer times.We estimate that the stable phase space (over 10 Myr) for satellites trapped in the Kozai resonance contains ∼10% of all stable orbits, suggesting the possible existence of a family of undiscovered objects at higher inclinations than those currently known.     

Five new and three improved mutual orbits of transneptunian binaries

We present three improved and five new mutual orbits of transneptunian binary systems (58534) Logos-Zoe, (66652) Borasisi-Pabu, (88611) Teharonhiawako-Sawiskera, (123509) 2000 WK₁₈₃, (149780) Altjira, 2001 QY₂₉₇, 2003 QW₁₁₁, and 2003 QY₉₀ based on Hubble Space Telescope and Keck II laser guide star adaptive optics observations. Combining the five new orbit solutions with 17 previously known orbits yields a sample of 22 mutual orbits for which the period P, semimajor axis a, and eccentricity e have been determined. These orbits have mutual periods ranging from 5 to over 800 days, semimajor axes ranging from 1600 to 37,000 km, eccentricities ranging from 0 to 0.8, and system masses ranging from 2 × 10¹⁷ to 2 × 10²² kg. Based on the relative brightnesses of primaries and secondaries, most of these systems consist of near equal-sized pairs, although a few of the most massive systems are more lopsided. The observed distribution of orbital properties suggests that the most loosely-bound transneptunian binary systems are only found on dynamically cold heliocentric orbits. Of the 22 known binary mutual orbits, orientation ambiguities are now resolved for 9, of which 7 are prograde and 2 are retrograde, consistent with a random distribution of orbital orientations, but not with models predicting a strong preference for retrograde orbits. To the extent that other perturbations are not dominant, the binary systems undergo Kozai oscillations of their eccentricities and inclinations with periods of the order of tens of thousands to millions of years, some with strikingly high amplitudes.     

Mutual orbits and masses of six transneptunian binaries

We present Hubble Space Telescope observations of six binary transneptunian systems: 2000 QL₂₅₁, 2003 TJ₅₈, 2001 XR₂₅₄, 1999 OJ₄, (134860) 2000 OJ₆₇, and 2004 PB₁₀₈. The mutual orbits of these systems are found to have periods ranging from 22 to 137 days, semimajor axes ranging from 2360 to 10500 km, and eccentricities ranging from 0.09 to 0.55. These orbital parameters enable estimation of system masses ranging from 0.2 to 9.7×¹⁰¹⁸ kg. For reasonable assumptions of bulk density (0.5 to 2.0 g cm⁻³), the masses can be combined with visible photometry to constrain sizes and albedos. The resulting albedos are consistent with an emerging picture of the dynamically “Cold” Classical sub-population having relatively high albedos, compared with comparably-sized objects on more dynamically excited orbits.     

Theoretical meteor radiants for macroscopic Taurid Complex objects

The calculation of theoretical meteor radiants is discussed for comets and asteroids whose orbits pass within, but at present do not necessarily intersect, that of the Earth, in particular from the perspective of developing a suitable method for application to Taurid Complex orbits. The main question addressed here is how to allow for dynamical evolution between epochs when an orbit isnot Earth-intersecting (as at present in most cases for macroscopic bodies) and those when itis (i.e., when meteors can actually be observed). This should be understood in terms of evolution in the past, such that meteoroids released some time ago have evolved differentially from the putative parents, allowing meteors to be detected now. Theoretical radiants for macroscopic Taurid objects are then presented and compared with observations of the nighttime and daytime Taurid meteor showers. These are found to be broadly similar in form, given the sparsity of some of the data, adding weight to the hypothesis that this sub-jovian complex contains kilometre-plus asteroids. A similar conclusion results for the group of objects in similar orbits to (2212) Hephaistos.