Temporal variation of the zodiacal dust cloud

A Markov chain model is constructed to investigate fluctuations in the mass of the zodiacal cloud. The cloud is specified by a three-dimensional grid, each element of which contains the numbers of dust particles as a function of semimajor axis, eccentricity and mass. The evolutionary pathways of dust particles owing to radiation pressure are described by fixed transition probabilities connecting the grid elements. Other elements are absorbing states representing infall to the Sun or ejection to infinity: particles entering these states are removed from the system. Particles are injected through the breakup of comets entering short-period, high-eccentricity orbits at random times, and are subject to the PoyntingRobertson effect and removal through collisional disintegration and radiation pressure. The main conclusions are that the cometary component of the zodiacal cloud is highly variable, and that in the wake of giant comet entry into a short-period, near-Earth orbit, the dust influx to the Earth's atmosphere may acquire a climatically significant optical depth.     

Dynamical zodiacal cloud models constrained by high resolution spectroscopy of the zodiacal light

The simulated Doppler shifts of the solar Mg I Fraunhofer line produced by scattering on the solar light by asteroidal, cometary, and trans-neptunian dust particles are compared with the shifts obtained by Wisconsin H-Alpha Mapper (WHAM) spectrometer. The simulated spectra are based on the results of integrations of the orbital evolution of particles under the gravitational influence of planets, the Poynting-Robertson drag, radiation pressure, and solar wind drag. Our results demonstrate that the differences in the line centroid position in the solar elongation and in the line width averaged over the elongations for different sizes of particles are usually less than those for different sources of dust. The deviation of the derived spectral parameters for various sources of dust used in the model reached maximum at the elongation (measured eastward from the Sun) between 90° and 120°. For the future zodiacal light Doppler shifts measurements, it is important to pay a particular attention to observing at this elongation range. At the elongations of the fields observed by WHAM, the model-predicted Doppler shifts were close to each other for several scattering functions considered. Therefore the main conclusions of our paper do not depend on a scattering function and mass distribution of particles if they are reasonable. A comparison of the dependencies of the Doppler shifts on solar elongation and the mean width of the Mg I line modeled for different sources of dust with those obtained from the WHAM observations shows that the fraction of cometary particles in zodiacal dust is significant and can be dominant. Cometary particles originating inside Jupiter's orbit and particles originating beyond Jupiter's orbit (including trans-neptunian dust particles) can contribute to zodiacal dust about 1/3 each, with a possible deviation from 1/3 up to 0.1-0.2. The fraction of asteroidal dust is estimated to be ∼0.3-0.5. The mean eccentricities of zodiacal particles located at 1-2 AU from the Sun that better fit the WHAM observations are between 0.2 and 0.5, with a more probable value of about 0.3.     

Out of ecliptic zodiacal cloud profile

In a previous paper, Mujica et al (1980), the optical homogeneity of the medium in the ecliptic plane was established calculating, for the ecliptic, the density and scattering functions ρ(r) and σ(θ) respectively. Starting with these results, we attempt now to find the zodiacal cloud shape out of the ecliptic.     

Mass loss rate of the zodiacal dust cloud

The mass loss rate of the zodiacal dust cloud near the Sun has been estimated on the basis of the orbital behaviour of circumsolar dust grains suffering sublimation. It is found that the solar dust ring located at 4 solar radii from the Sun, which consists of grains whose inward spiraling due to the Poynting-Robertson effect is stopped by the influence of sublimation, loses its mass at a rate of 3.50.35 tons per second.     

Three-dimensional models of the zodiacal dust cloud: A comparative study

Several analytical presentations of the three-dimensional distribution of interplanetary dust have been derived in the literature from measurements of the zodiacal light such as fan, ellipsoid, sombrero, and multilobe models. To provide a basis for comparisons with infrared measurements these classical and some new optical approaches are reviewed and compared with observations of the zodiacal light all over the sky and in selected viewing directions. Strengths and weaknesses of the models are discussed and qualitatively explained. It is shown that multilobe models can be refuted. The remaining models predict in surprising agreement that the interplanetary spatial dust density decreases “above” the Earth's orbit by a factor of 2 within 0.2 to 0.3 AU. Beyond about 3 AU in the ecliptic plane and about 1.5 AU off the ecliptic no reliable density values can be obtained from the zodiacal light.     

End-states of short-period comets and their role in maintaining the zodiacal dust cloud

Physical lifetimes and end-states of short-period comets are analysed in connection with the problem of the maintainance of the zodiacal dust cloud. In particular, the problem of the comet-asteroid relationship is addressed. Recent studies of the physical properties of Apollo-Amor asteroids and short-period comets (e.g., Hartmann et al., 1987) show significant differences between them, suggesting that they are distinct classes of objects. A few percent of the active SP comets might become asteroidal-like bodies in comet-type orbits due to the buildup of dust mantles. The remainder probably disintegrate as they consume their volatile content so their debris can only be observed as fireballs when they meet the Earth. Unobservable faint SP comets — i.e., comets so small (m 10¹⁴ g) that quickly disintegrate before being detected, might be a complementary source of dust material. They might be completely sublimated even at rather large heliocentric distances (r - 3 AU). Yet the released dust grains can reach the vicinity of the Sun by Poynting-Robertson drag. The mass associated with unobservable SP comets with perihelion distances q 3 AU might be comparable to that computed for the sample of observed SP co-mets with q 1.5 AU. It is concluded that SP comets (from the large to the unobservable small ones) may supply an average of several tons/sec of meteoric matter to the zodiacal dust cloud.     

On the gradient of zodiacal light with heliocentric distance

Space density of interplanetary dust grains is directly related to the gradient of zodiacal light observed, at constant elongation ?, by a space photometer moving and aiming in the symmetry plane of the solar system.     

Xenoliths and microxenoliths in H chondrites: Sampling the zodiacal cloud in the asteroid Main Belt

Abstract– Xenoliths are inclusions of a given meteorite group embedded in host meteorites of a different group. Xenoliths with dimensions between a few μm and about 1 mm (microxenoliths) are “meteorite‐trapped” analogues of micrometeorites collected on the Earth. However, they have the unique features of sampling the zodiacal cloud (1) at more ancient times than those sampled by micrometeorites and (2) at larger distances from the Sun (corresponding to the asteroid Main Belt) than that sampled by micrometeorites (1 AU). Herein we describe a systematic search for new xenoliths and microxenoliths in H chondrites, aimed at determining their abundance in these ordinary chondrites, analyzing their mineralogy, and searching for possible correlations with host meteorite properties. Sixty‐six sections from 40 meteorites have been analyzed. Twenty‐four new xenoliths have been discovered. About 87% of them are microxenoliths (i.e., <1 mm), only three are >1 mm in their largest dimension. All the newly discovered xenoliths and microxenoliths are composed of carbonaceous chondritic material. Hence, the zodiacal cloud was dominated by carbonaceous material even in past epochs. All the new xenoliths and microxenoliths have been found in regolith breccias. Hydrous‐phase‐rich xenoliths and microxenoliths in H4 and H5 chondrites attest that their embedding happened after the end of the thermal metamorphism. All these data suggest that xenoliths and microxenoliths were embedded when their host meteorites were part of the parent body regolith. This, combined with the H chondrite impact age distribution, attests that the embedding may have happened as early as 3.5 Gyr ago.     

On the possibility of detecting solar flare effects in the zodiacal light

To evaluate possible effects of solar flares on the brightness of the inner zodiacal light, it is necessary to consider the brightness contribution along the line of sight and as a function of Sun-particle distance. For this purpose, models of the brightness contribution along the line of sight are presented for both dielectric and metallic particles with a spatial distribution of the form r^?ν, ν = 0, 1, 2. These models are discussed in terms of the geometry of shock front interaction. A reported zodiacal light enhancement following a solar flare (Blackwell and Ingham, 1961) is analyzed on the basis of the shock front geometry.     

An Infra-Red model of the zodiacal emission

The Infra-Red Astronomical Satellite (IRAS) observations of the zodiacal dust emission are used to fit the dust grain composition and distribution in the ecliptical plane. We obtain a good fit to the data for a density distribution of black-body grains given by p = pr ^{0.66/log(1.7r/R)} for r < 0.87R and r < 3oR     

On the equivalence of expressions for inverting the 3-dimensional zodiacal light brightness integral

In the research notes of this Journal, both Schuerman (1979, henceforth Paper I) and Buitrago (1979, henceforth Paper II) independently derived expressions for the general¹, mathematical inversion of the zodiacal light brightness integral. In this communication, it is shown that the expressions are equivalent, differing only in the choice of reference systems.     

Inverting the zodiacal light brightness integral

Considerations of the geometry appropriate to observations of the zodiacal light made from out of the ecliptic plane yield the general inversion of the brightness integral. The brightness per unit volume of interplanetary space can thus be determined in the immediate neighborhood of the spacecraft in directions confined to a unique viewing plane which depends upon the spacecraft's trajectory. The implementation of this technique guarantees the maximum information content of optical observations made from future deep-space probes including the “Out-of-Ecliptic” mission scheduled for launch in 1983.     

Interplanetary dust dynamics: III. Dust released from P/Encke: Distribution with respect to the zodiacal cloud

Numerical simulations of the trajectories of over 200 30-μm-radius dust particles released by Comet P/Encke were designed to study the evolution and redistribution of orbital elements as the dust particles spiral in toward the Sun. The dust assumes Jupiter crossing orbits immediately after release due to radiation pressure, while the comet's orbit remains inside Jupiter's orbital path. By the time the dust particles have spiraled past Jupiter, information on their origin from P/Encke is erased from the distribution in orbital elements. The primary objective of this study is to compare the observed spatial distribution of zodiacal/interplanetary dust with that of the model cloud inside Jupiter's orbit. The observed location of the plane of maximum dust density “symmetry plane” of the zodiacal cloud is compared to a least-square-fit plane of the model cloud. A clear correlation between the two planes is found. The variation of the observed inclination and nodes with heliocentric distance agrees also, at least qualitatively, with that found in the model cloud. The hypothesis that short-period comets may have contributed in a major way to the zodiacal cloud is compatible with these results. The study is directly relevant to, and supports, Whipple's suggestion that Comet P/Encke may have been a major source to the zodiacal cloud.     

The properties of large particles in the zodiacal cloud and in the interstellar medium,and their relation to recent IRAS observations

To explain the scattering of sunlight observed from theF-corona and from the zodiac, the scattering particles must have radii of order 15 m, and must have an imaginary component of the refractive index that requires the presence of from 5 to 10% of free carbon. The particles, therefore, have a composition very like the material of C 1 carbonaceous chondrites and like extraterrestrial particles which have been recovered from the high atmosphere.Such particles absorb sunlight, the absorbed solar energy being reradiated in the infrared with a close approximation to black-body emission, even as far into the infrared as 100 m, a deduction in good agreement with recently published observations from the IRAS satellite.The IRAS observations at high ecliptic latitudes require similar particles to be present in large quantity in the interstellar medium, 10⁶ solar masses or more of them. The presence of such a quantity of material with properties very like the material of the C 1 carbonaceous chondrites is a remarkable outcome of the IRAS observations and is likely to have profound implications in many directions.     

Solar flare track densities in interplanetary dust particles: The determination of an asteroidal versus cometary source of the zodiacal dust cloud

Dust particles that are larger than 1 μm, when injected into the Solar System from comets and asteroids, will spiral into the Sun due to the Poynting-Robertson effect. During the process of spiraling in, such dust particles accumulate solar flare tracks in their component minerals. The accumulated track density for a given dust grain is a function of the duration of its space exposure and its distance from the Sun. Using a computer model, it was determined that the expected track density distributions from grains produced by comets are very different from those produced by asteroids. Individual asteroids produce populations of particles that arrive at 1 AU with scaled track density distributions containing “spikes,” while comets supply particles with a flatter and wider distribution of track densities. Particles with track densities above 3 × 10⁷ (sϱA/v) tracks/cm² have probably been exposed to solar flare tracks prior to injection into the interplanetary medium and are therefore likely to be asteroidal. Particles with track densities below 0.7 × 10⁷(sϱA/v) tracks/cm² must be derived from comets or Earth-crossing asteroids. Earth-crossing asteroids are not responsible for all the dust collected at 1 AU since they cannot produce the large track densities observed in some of the interplanetary dust particles collected in the stratosphere. The track densities observed in the stratospheric dust fall within the predicted range, but there is at present an insufficient number of carefully determined densities to make strong statements about the sources of the present dust population.     

Photometric properties of zodiacal light particles

From published ground-base, spacecraft, and rocket photometry and polarimetry of the zodiacal light, a number of optical and physical parameters have been derived. It was assumed that the number density, mean particle size, and albedo vary with heliocentric distance, and shown that average individual interplanetary particles have a small but definite opposition effect, a mean single-scattering albedo in the V band at 1-AU heliocentric distance of 0.09 ± 0.01, and a zero-phase geometric albedo of 0.04. Modeled by a power law, both albedos decrease with increasing heliocentric distance as r^?0.54. The corresponding exponents for changes in mean particle size and number density are related in a simple way. The median orbital inclination of zodiacal light particles with respect to the ecliptic is 12°, close to the observed median value for faint asteroids and short-period comets. Furthermore, the color of dust particles and its variation with solar phase angle closely resemble those of C asteroids. These findings are, at least, consistent with the zodiacal cloud originating primarily from collisions among asteroids. Finally, a value of ?10¹⁸?_ErmE g was derived for the mass of the zodiacal cloud, where ?_E is the mean particle radius (in micrometers) at 1-AU-heliocentric distance. For extinction in the ecliptic, $\text{Δm = 10}{}^{\mathrm{?5}}\text{?}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{mag}$ was obtained, where ? is the solar elongation in degrees.     

Colour dependence of zodiacal light models

Colour models of the zodiacal light in the ecliptic have been calculated for both dielectric and metallic particles in the sub-micron and micron size range. Two colour ratios were computed, a blue ratio C_b (0.40 μm, 0.53 μm) and a red ratio, either C_r (0.82 μm, 0.53 μm) or C_r' (0.71 μm, 0.53 μm). The models with a size distribution ∝s^−2.5ds generally show a colour close to the solar colour and almost independent of elongation. Especially in the blue colour ratio there is generally no significant dependence on the lower cutoff size (0.1–1 μm). The main feature of absorbing particles is a reddening at small elongations. The models for size distributions ∝s⁻⁴ds show larger departures from solar colour and more variation with model parameters. Colour measurements, including red and near infra-red, therefore are useful to distinguish between flat and steep size spectra and to verify the presence of slightly absorbing particles.     

The mid-infrared spectrum of the zodiacal and exozodiacal light

The zodiacal light is the dominant source of the mid-infrared sky brightness seen from Earth, and exozodiacal light is the dominant emission from planetary and debris systems around other stars. We observed the zodiacal light spectrum with the mid-infrared camera ISOCAM over the wavelength range 5-16 μm and a wide range of orientations relative to the Sun (solar elongations 68°-113°) and the ecliptic (plane to pole). The temperature in the ecliptic ranged from 269 K at solar elongation 68° to 244 K at 113°, and the polar temperature, characteristic of dust 1 AU from the Sun, is 274 K. The observed temperature is exactly as expected for large (>10 μm radius), low-albedo (<0.08), rapidly-rotating, gray particles 1 AU from the Sun. Smaller particles (<10 μm radius) radiate inefficiently in the infrared and are warmer than observed. We present theoretical models for a wide range of particle size distributions and compositions; it is evident that the zodiacal light is produced by particles in the 10-100 μm radius range. In addition to the continuum, we detect a weak excess in the 9-11 μm range, with an amplitude of 6% of the continuum. The shape of the feature can be matched by a mixture of silicates: amorphous forsterite/olivine provides most of the continuum and some of the 9-11 μm silicate feature, dirty crystalline olivine provides the red wing of the silicate feature (and a bump at 11.35 μm), and a hydrous silicate (montmorillonite) provides the blue wing of the silicate feature. The presence of hydrous silicate suggests the parent bodies of those particles were formed in the inner solar nebula. Large particles dominate the size distribution, but at least some small particles (radii ∼1 μm) are required to produce the silicate emission feature. The strength of the feature may vary spatially, with the strongest features being at the lowest solar elongations as well as at high ecliptic latitudes; if confirmed, this would imply that the dust properties change such that dust further from the Sun has a weaker silicate feature. To compare the properties of zodiacal dust to dust around other main sequence stars, we reanalyzed the exozodiacal light spectrum for β Pic to derive the shape of its silicate feature. The zodiacal and exozodiacal spectra are very different. The exozodiacal spectra are dominated by cold dust, with emission peaking in the far-infrared, while the zodiacal spectrum peaks around 20 μm. We removed the debris disk continuum from the spectra by fitting a blackbody with a different temperature for each aperture (ranging from 3.7″ to 27″); the resulting silicate spectra for β Pic are identical for all apertures, indicating that the silicate feature arises close to the star. The shape of the silicate feature from β Pic is nearly identical to that derived from the ISO spectrum of 51 Oph; both exozodiacal features are very different from that of the zodiacal light. The exozodiacal features are roughly triangular, peaking at 10.3 μm, while the zodiacal feature is more boxy, indicating a different mineralogy.     

Optical properties of single-component zodiacal light models

To provide material for interpretations of forthcoming zodiacal light measurements the characteristics of 468 single-component, in-ecliptic models are summarized in two survey diagrams. The models are based on Mie theory and on a power law dn ∞ r^?γα^?kdα for the dependence of the particle number density n on solar distance r and on the size parameter α (circumference/wavelength). The size range involves particles with α_min ≤ α ≤ 120; (α_min = 1,2,4,10,60), flat (k = 2·5) and steep (k = 4) size spectra, and complex refractive indices m = m₁ ? m₂i with m₁ = 1·33; 1·5; 1·7 and m₂ = 0; 0·01; 0·05; 0·1.The models suggest that the spatial variation of dust particle number densities should be less than about ∞ r^?0·5 in the ecliptic plane. Either dielectric particles of tenth-micron size or absorbing particles of half-micron size or very slightly absorbing particles of some tens of microns in size are able to produce polarization that agrees in sign and location of the maximum with the observations. Ambiguities can only be removed by considering intensity and polarization over a wide range of wavelengths.