Light Scattering by Dust Under Microgravity Conditions

Most of our knowledge on heterogeneous media in the Universe comes from the light they scatter. This light is mainly linearly polarized, and the polarization phase curves contain information about the properties of the scattering dust. In the solar system, the dust seems to be made of irregular aggregates with a size greater than a few microns and a fractal structure. Many constraints appear in the scattering computations, due to the trickiness of the mathematical calculations, and to our ignorance of the precise structure of the dust. This leads to the necessity to perform light scattering measurements on characteristic aggregates, built under low velocity ballistic collisions. Microgravity is a sensible way to achieve such measurements on a cloud of levitating and aggregating dust particles. A first step has been the PROGRA² experiment, which operates during parabolic flights on an aircraft. The instrument is a polar nephelometer measuring successively the light scattered by a dust sample at various angles; it is fully operational, and will provide a data base of polarization phase curves. A second step is the CODAG-SR experiment, which uses the duration of a rocket flight to build up dust aggregates. The instrument measures simultaneously the light scattered at numerous phase angles; it is now space qualified, and should provide in a near future a monitoring of the intensity and polarization phase curves while the aggregation processes are taking place. This revised version was published online in July 2006 with corrections to the Cover Date.     

Optical properties of aerosols in Titan's atmosphere

In the frame of fractal modeling of tholin aggregates we made a systematic analysis of their optical properties. Ballistic particle-cluster aggregation (BPCA) and diffusion-limited aggregation (DLA) of spherical primary particles (monomers) identical in material composition were considered. Aggregates composed of identical particles (monodisperse cluster), as well as of size-distributed particles (polydisperse cluster), were simulated. To calculate the light-scattering models, the code based on the superposition T-matrix method is used. Orientationally averaged properties of light scattering by model particles were extracted, and the normalized phase function and the degree of linear polarization were calculated as functions of scattering angle. We concluded that: (a) aggregation mechanism as well as specific internal structure of the clusters play only a minor role, and for the future it is not necessary to investigate aggregates of different types; (b) the intensity is very sensitive both to the size parameter of forming particles x and to the size parameter of the aggregates X; (c) characterization of the aggregates by the number of monomers is insufficient to retrieve physical properties of aggregates from optical measurement; and (d) it is very desirable to include into the analysis polarization data calculated for the different clusters.     

Light Scattering by Aggregate Particles Comparable in Size to Wavelength: Application to Cometary Dust

Many naturally occurring particles (including, most likely, cometary dust) have an aggregate structure. We study the scattering properties of polydisperse independent aggregate particles (clusters) comparable in size to visible wavelengths. The sizes of the monomers constituting a cluster play a significant role in forming the angular dependences of intensity and linear polarization of the scattered light. Irregularly structured aggregates composed of a moderate number of spheres (<50) with size parameters 1.3–1.65 exhibit properties typical of cometary dust particles: a slight increase in backscattering intensity, a negative polarization at small phase angles, an inversion phase angle close to the observed one, an increase in brightness, and a linear polarization with increasing wavelength. In this case, the imaginary part of the refractive index for particles can increase with decreasing wavelength in the visible spectral range, which is typical of silicates with an admixture of iron or organic material. The spectral dependence of extinction efficiency for aggregates is less steep than that for equivalent spherical particles, and its maximum is shifted to larger size parameters. Therefore, when analyzing extinction measurements, the scatterer shape must be taken into account to avoid underestimation of the scattering-particle sizes.     

Modeling of aggregation of fractal dust clusters in a laminar protoplanetary disk

The evolutionary hydrodynamic model for the formation and growth of loose dust aggregates in the aerodisperse medium of a laminar disk, which was originally comprised of the gas and solid (sub)micrometer particles, is considered as applied to the problem of the formation of planetesimals in the Solar protoplanetary cloud. The model takes into account the fractal properties of dust clusters. It is shown that the clusters partly merge in the process of cluster-cluster coagulation, giving rise to the formation of large fractal aggregates that are the basic structure-forming elements of loose protoplanetesimals arising as a result of physicochemical and hydrodynamic processes similar to the processes of growth of the fractal clusters. Earlier, the modeling was conventionally performed in an “ordinary” continuous medium without considering the multifractional structure of the dust component of the protoplanetary cloud and the fractal nature of the dust clusters being formed during its evolution. Instead, we propose to consider a complex of loose dust aggregates as a special type of continuous medium, namely, the fractal medium for which there exist points and regions that are not filled with its particles. We suggest performing the hydrodynamic modeling of this medium, which has a noninteger mass dimensionality, in a fractional integral model (its differential form) that takes the fractality into account using fractional integrals whose order is determined by a fractal dimensionality of the disk medium.     

Nanoparticles in the inner solar system

We discuss different scenarios for the formation and dynamics of nanoparticles in the inner solar system. Particles up to a few tens of nanometer size, if formed at a distance larger than several 0.1 AU from the Sun, are picked up by the solar wind and therefore do not reach the regions closer to the sun. At distances ⩽0.1 AU particles of several tens of nanometer in size can stay in bound orbits and, aside from the Lorentz force, the plasma and the photon Poynting–Robertson effect determine their spatial distribution. Local sources of nanometer-sized particles in the inner solar system are collisional fragmentation and sublimation of dust and meteoroids. The most likely materials to survive in the very vicinity of the Sun are MgO particles from the sublimation of cometary and meteoritic silicates, nanodiamonds originating from meteoroid material, and possibly carbon structures formed by thermal alteration of organics. The nanoparticles may produce spectral features in a limited spectral interval, and this spectral interval varies with particle size, composition and temperature. Bearing in mind the wide size distribution of solar system dust and the preponderance of larger particles, it is unlikely that nanoparticles can be detected in thermal emission or scattered light brightness and we are unable to predict observable features for these nanoparticles. If the nanodust produced observable features, they are most likely to appear in the blue or near infrared. We suggest a more promising option is the in situ detection of the particles.     

Porous and fluffy grains in the regions of anomalous extinction

It has long been established that the ratio of total to selective extinction is anomalously large (>- 5) in certain regions of the interstellar medium. In these regions of anomalous extinction the dust grains are likely to be irregular in shape and fluffy in structure. Using discrete dipole approximation (DDA) we calculate the extinction for porous and fluffy grains. We apply DDA first to solid spheroidal particles assumed to be made of a certain (large) number of dipoles. Then we systematically reduce the number of dipoles to model the porous grains. The aggregates of these particles are suggested to form the fluffy grains. We study the extinction for these particles as a function of grain size, porosity and wavelength. We apply these calculations to interpret the observed extincttion data in the regions of star formation (e.g. the Orion complex).     

Physical properties of cometary and interplanetary dust

In the absence of numerous in situ studies, physical properties of cosmic dust may be derived from observations of their light scattering and thermal properties, through numerical simulations making use of realistic assumptions. Estimations about cometary and interplanetary dust composition, structure, size, as well as about their light scattering and thermal properties, are first summarized. We then present and discuss the numerical simulations we have performed with different types of particles: core-mantle submicron-sized elongated grains (having contributed to the formation of cometary dust), fractal aggregates of such grains (found in cometary comae and in the interplanetary dust cloud), and fractal aggregates of large dust grains (found in cometary dust trails).A very satisfactory fit to the numerous polarimetric observations of comet Hale-Bopp is obtained for a mixture with about 33–60% of organics in mass, with a power law size distribution with an index of (−3) and a radius of 20 μm for the upper cut-off. For the less-constrained polarimetric observations of interplanetary dust near 1 AU, a fit is obtained for a mixture with about 40% of organics in mass, with a similar size distribution and a radius of about 50 μm for the upper cut-off. The ensemble of results obtained for the interplanetary dust strongly suggest that its light scattering and thermal properties stem from the presence of compact and fluffy particles, with compositions ranging from silicates to more absorbing materials, whose contribution decreases with decreasing distance to the Sun.     

Dynamics of Dust Particles of Different Structure: Application to the Modeling of Dust Motion in the Vicinity of the Nucleus of Comet 67P/Churyumov–Gerasimenko

We consider the estimates of the main forces acting on dust particles near a cometary nucleus. On the basis of these estimates, the motion of dust particles of different structure and mass is analyzed. We consider the following forces: (1) the cometary nucleus gravity, (2) the solar radiation pressure, and (3) the drag on dust particles by a flow of gas produced in the sublimation of cometary ice. These forces are important for modeling the motion of dust particles relative to the cometary nucleus and may substantially influence the dust transfer over its surface. In the simulations, solid silicate spheres and homogeneous ballistic aggregates are used as model particles. Moreover, we propose a technique to build hierarchic aggregates—a new model of quasi-spherical porous particles. A hierarchic type of aggregates makes it possible to model rather large dust particles, up to a millimeter in size and larger, while no important requirements for computer resources are imposed. We have shown that the properties of such particles differ from those of classical porous ballistic aggregates, which are usually considered in the cometary physics problems, and considering the microscopic structure of particles is of crucial significance for the analysis of the observational data. With the described models, we study the dust dynamics near the nucleus of comet 67P/Churyumov–Gerasimenko at an early stage of the Rosetta probe observations when the comet was approximately at 3.2 AU from the Sun. The interrelations between the main forces acting on dust aggregates at difference distances from the nucleus have been obtained. The dependence of the velocity of dust aggregates on their mass has been found. The numerical modeling results and the data of spaceborne observations with the Grain Impact Analyzer and Dust Accumulator (GIADA) and the Cometary Secondary Ion Mass Analyzer (COSIMA) onboard the Rosetta probe are compared at a quantitative level.     

High altitude haze: Influence of monomer particles on Titan’s temperature profile

The present study investigates the role of high altitude monomer particles in the energy balance of Titan’s upper atmosphere above an assumed low and high aggregate formation altitude of 385 km and 535 km. A ‘single particle approach’ was applied, where the starting point is the energy balance of an individual aerosol. In our analysis 0.01–0.06 μm radius aerosol particles were chosen for the proposed monomer formation regions. These particles absorb solar radiation, emit in the infrared, and are energetically linked to the surrounding gas by thermal conduction. To compute the monomer particle heating effect, the aerosols are assumed to radiate directly to space. We found that high altitude monomers may affect the profile of Titan’s thermosphere from 2 to 20 K depending on the formation altitude of fluffy non-spherical aggregates, the monomer size and distribution. The actual Titan temperature profile in this altitude range including all heating effects will be measured by the HASI instrument during the descent of the Huygens probe.     

Polarization of Light Scattered by Fluffy Particles (PROGRA Experiment)

This work was carried out with the PROGRA² experiment developed to measure the angular dependence of the polarization of light scattered by dust particles. The dust samples are fluffy aggregates (size range 0.01-1 mm) with constituent grains of about 10 nm. Various setups were used: samples deposited on surfaces, the same samples lifted under the effect of a draft, and particles levitating in microgravity conditions on board the CNES dedicated aircraft. For deposited particles, the maximum value of polarization (P_max) follows the Umov law. For a cloud of particles (P_max) near 100° phase angle decreases when: (i) multiple scattering between the particles—or between the grains inside the particles—increases, or (ii) the real part of the refractive index of the materials increases, or (iii) the size parameter of the constituent grains increases between 0.05 and 0.5. A negative branch in the polarization phase curve is found for deposited samples. For levitating particles made of a single material and a single size distribution, a positive increase of polarization appears at phase angles smaller than 20°; for mixtures of these materials the polarization is negative at the same phase angles. These results are compared to modeling results as well as to polarimetric observations of comets.     

Dust in cometary comae: Present understanding of the structure and composition of dust particles

In situ probing of a very few cometary comae has shown that dust particles present a low albedo and a low density, and that they consist of both rocky material and refractory organics. Remote observations of solar light scattered by cometary dust provide information on the properties of dust particles in the coma of a larger set of comets. The observations of the linear polarization in the coma indicate that the dust particles are irregular, with a size greater (on the average) than about 1 μm. Besides, they suggest, through numerical and experimental simulations, that both compact grains and fluffy aggregates (with a power law of the size distribution in the −2.6 to −3 range), and both rather transparent silicates and absorbing organics are present in the coma. Recent analysis of the cometary dust samples collected by the Stardust mission provide a unique ground truth and confirm, for comet 81P/Wild 2, the results from remote sensing observations. Future space missions to comets should, in the next decade, lead to a more precise characterization of the structure and composition of cometary dust particles.     

Organics-glued dust aggregates in Halley's coma and some implications of the snow line inward motion for the formation of comets

In view of the solar nebula models, organics-glued dust aggregates (whose disintegration resulted in the two phenomena found in Halley's coma, the dust boundary and small-scale dust structures) originated due to coagulation of iceless dust particles somewhere within the snow line, and then were incorporated into Halley's nucleus as a consequence of the snow line inward motion. This implies that two types of comets exist: outer comets, formed entirely beyond the snow line, and inner comets, similar to Halley, which are bodies intermediate between outer comets and primitive asteroids. The presence of large iceless dust aggregates in nuclei of inner comets constrains the inward drift velocity of meter-sized dust bodies, which in turn implies that the radial transport of water in the solar nebula was predominantly outward. It is shown that in nuclei of inner comets: both the upper mass limit of iceless dust aggregates and the ice mantle thickness increase with decreasing formation heliocentric distance, while the cumulative mass distribution index decreases; the lower limit of the mass index is ∼0.8, and the upper limit of the ice mantle thickness is ∼10⁻³ cm (∼200 times the interstellar value); the lower limit of the latent heat of organics in organic mantles of submicron particles increases toward small heliocentric distances; the recondensation of organics combined with the growth of dust bodies leads to a fractionation of organics within iceless dust aggregates; last accreted sub-units of an aggregate are always glued by organics with the lowest value of the latent heat, which somewhat exceeds 60 kJ/mol. Based on in situ observations at Halley, the parameters characterizing iceless dust aggregates in that comet are calculated. Finally, feasible observational tests of the conclusions drawn are discussed.     

Limits on the size of aerosols from measurements of linear polarization in Titan’s atmosphere

The Descent Imager/Spectral Radiometer (DISR) instrument on the Huygens probe into the atmosphere of Titan yielded information on the size, shape, optical properties, and vertical distribution of haze aerosols in the atmosphere of Titan [Tomasko, M.G., Doose, L., Engel, S., Dafoe, L.E., West, R., Lemmon, M., Karkoschka, E., 2008. Planet. Space Sci. 56, 669-707] from photometric and spectroscopic measurements of sunlight in Titan’s atmosphere. This instrument also made measurements of the degree of linear polarization of sunlight in two spectral bands centered at 491 and 934 nm. Here we present the calibration and reduction of the polarization measurements and compare the polarization observations to models using fractal aggregate particles which have different sizes for the small dimension (monomer size) of which the aggregates are composed. We find that the Titan aerosols produce very large polarizations perpendicular to the scattering plane for scattering near 90° scattering angle. The size of the monomers is tightly constrained by the measurements to a radius of 0.04 ± 0.01 μm at altitudes from 150 km to the surface. The decrease in polarization with decreasing altitude observed in red and blue light is as expected by increasing dilution due to multiple scattering at decreasing altitudes. There is no indication of particles that produce small amounts of linear polarization at low altitudes.     

Light scattering by fluffy Mg-Fe-SiO and C mixtures as cometary analogs (PROGRA experiment)

Cometary particles mainly consist of silicates and carbon compounds; they seem to be fluffy aggregates of tiny grains, as found in some IDPs. The linear polarization of the scattered light is an efficient method to characterize their physical properties. Laboratory simulations of light scattering by cometary analog particles help to disentangle different physical parameters by comparison with observational data. We present here polarization laboratory results with nine samples levitating particles: five samples of vapor-condensed magnesiosilica, one ferrosilica smoke, a mixture of magnesio-ferrosilica smokes, one mixture of ferrosilica with carbon and one mixture of magnesio-ferrosilica with carbon. The phase curves are bell-shaped with a maximum polarization at a phase range of (80°-100°). A shallow negative branch can be present at phase angles smaller than 20°. The different characteristics of the phase curves are discussed considering the size and the structure of the constituent grains and the size of the particles. For the five magnesiosilica samples, the maximum in polarization is in the 40% range (close to cometary values), and no wavelength dependence is detected; the negative branch, whose presence seems to be linked to the presence of large aggregates of fine silica (SiO₂) grains, does not always exist. For the ferrosilica smoke, the maximum in polarization is about 30% in red light (632.8 nm) and 40% in green light (543.5 nm); the negative branch occurs for phase angles smaller than 20°. For the two mixtures with carbon black, the polarization spectral gradient is positive, as expected for cometary analog particles. Finally, the phase curves obtained for agglomerates of magnesio-ferrosilica and carbon (expected to be the main components of cometary particles) are comparable to those obtained by remote observations of dust in cometary comae.     

Thermochemical stability of low‐iron,manganese‐enriched olivine in astrophysical environments

Abstract– Low‐iron, manganese‐enriched (LIME) olivine grains are found in cometary samples returned by the Stardust mission from comet 81P/Wild 2. Similar grains are found in primitive meteoritic clasts and unequilibrated meteorite matrix. LIME olivine is thermodynamically stable in a vapor of solar composition at high temperature at total pressures of a millibar to a microbar, but enrichment of solar composition vapor in a dust of chondritic composition causes the FeO/MnO ratio of olivine to increase. The compositions of LIME olivines in primitive materials indicate oxygen fugacities close to those of a very reducing vapor of solar composition. The compositional zoning of LIME olivines in amoeboid olivine aggregates is consistent with equilibration with nebular vapor in the stability field of olivine, without re‐equilibration at lower temperatures. A similar history is likely for LIME olivines found in comet samples and in interplanetary dust particles. LIME olivine is not likely to persist in nebular conditions in which silicate liquids are stable.     

Gravitational instability in the dust layer of a protoplanetary disk: Interaction of solid particles with turbulent gas in the layer

Gravitational instability of the dust layer formed after the aggregates of dust particles settle toward the midplane of a protoplanetary disk under turbulence is considered. A linearized system of hydrodynamic equations for perturbations of dust (monodisperse) and gas phases in the incompressible gas approximation is solved. Turbulent diffusion and the velocity dispersion of solid particles and the perturbation of gas azimuthal velocity in the layer upon the transfer of angular momentum from the dust phase due to gas drag are taken into account. Such an interaction of the particles and the gas establishes upper and lower bounds on the perturbation wavelength that renders the instability possible. The dispersion equation for the layer in the case when the ratio of surface densities of the dust phase and the gas in the layer is well above unity is obtained and solved. An approximate gravitational instability criterion, which takes the size-dependent stopping time of a particle (aggregate) in the gas into account, is derived. The following parameters of the layer instability are calculated: the wavelength range of its subsistence and the dependence of the perturbation growth rate on the perturbation wavelength in the circumsolar disk at a radial distance of 1 and 10 AU. It is demonstrated that at a distance of 1 AU, the gas–dust disk should be enriched with solids by a factor of 5–10 relative to the initial abundance as well as the particle aggregates should grow to the sizes higher than about 0.3 m in order for the instability to emerge in the layer in the available turbulence models. Such high disk enrichment and aggregate growth is not needed at a distance of 10 AU. The conditions under which this gravitational instability in the layer may be examined with no allowance made for the transfer of angular momentum from the gas in the layer to the gas in a protoplanetary disk outside the layer are discussed.     

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.     

Light scattering by Gaussian random particles

We introduce multivariate lognormal statistics to describe the shapes of small particles, and compute scattering phase matrices in the ray optics approximation. The results help us understand light scattering by solar system dust particles, and thereby constrain the physical properties of, for example, asteroid regoliths and cometary comae. The present stochastic geometry could turn useful in modeling the shapes of asteroids.     

Light scattering by Gaussian random particles

We introduce multivariate lognormal statistics to describe the shapes of small particles, and compute scattering phase matrices in the ray optics approximation. The results help us understand light scattering by solar system dust particles, and thereby constrain the physical properties of, for example, asteroid regoliths and cometary comae. The present stochastic geometry could turn useful in modeling the shapes of asteroids.     

A Negative Branch of Polarization for Comets and Atmosphereless Celestial Bodies and the Light Scattering by Aggregate Particles

Optical observations of comets and atmosphereless celestial bodies show that a change of sign of the linear polarization of scattered light from negative to positive at phase angles less than 20° is typical of the cometary coma, as well as of the regolith of Mercury, the Moon, planetary satellites, and asteroids. To explain a negative branch of polarization, this research suggests a unified approach to the treatment of cometary-dust particles and regolith grains as aggregate forms. A composite structure of aggregate particles resulting in the interaction of composing structural elements (monomers) in the light-scattering process is responsible for the negative polarization at small phase angles, if the monomer sizes are comparable to the wavelength. The characteristics of single scattering of light calculated for aggregates of this kind turned out to be close to the properties observed for cometary dust. Unlike the cometary coma, the regolith is an optically semi-infinite medium, where the interaction between particles is significant. To find the reflectance characteristics of regolith, the radiative-transfer equation should be solved for a regolith layer. In this case, the interaction between scatterers can be modeled to a certain extent by representing the regolith grains as aggregate structures consisting of several or many elements. Although real regolith grains are much larger than the particles considered here, laboratory measurements have shown that it is precisely the surface irregularities comparable to the wavelength that cause a negative branch of polarization. The main observed features of the phase and spectral dependence of the linear polarization of light scattered from comets and atmosphereless celestial bodies, which are due to the difference of the elementary scatterers in composition, size, and structure, can be successfully explained using the aggregate model of particles.