Radiation pressure on randomly-oriented nonspherical particles

We describe an efficient method to compute the efficiency factors for radiation pressure for randomly-oriented axially-symmetric nonspherical grains. The method is based on Waterman'sT-matrix approach and may be used in computations for grains with sizes smaller than or of the order of the wavelength. An illustrative numerical example for randomly oriented spheroidal grains is given.     

Scattering by nonspherical particles and optical properties of Martian dust

Ultraviolet spectral reflectance data obtained from the Mariner 9 during the 1971 Mars dust storm were analyzed at two wavelengths to deduce the complex index of refraction of Martian dust. Martian dust particles were considered to be irregularly shaped and randomly oriented nonspherical particles. The analysis shows that the Mariner 9 data are consistent with the scattering by irregular particles with an index of refraction m = 1.59 ? 0.0015i at λ = 0.305 μm and m = 1.55 ? 0.004i at λ = 0.268 μm. Both the real and the imaginary parts of refractive index found are considerably smaller than previously reported results using a spherical shape model for Martian dust particles.     

Radiation forces on small particles in the solar system

We present a new and more accurate expression for the radiation pressure and Poynting-Robertson drag forces; it is more complete than previous ones, which considered only perfectly absorbing particles or artificial scattering laws. Using a simple heuristic derivation, the equation of motion for a particle of mass m and geometrical cross section A, moving with velocity v through a radiation field of energy flux density S, is found to be (to terms of order $\text{v}\text{c}$)

$\text{m}\text{v}\text{?}\text{= (}\text{SA}\text{c}\text{)Q}{}_{\mathrm{<mtext>pr</mtext>}}\text{[(1 ?}\text{r}\text{?}\text{c}\text{)}\text{S}\text{?}\text{?}\text{v}\text{c}\text{]}$

, where ? is a unit vector in the direction of the incident radiation, $\text{r}\text{?}$ is the particle's radial velocity, and c is the speed of light; the radiation pressure efficiency factor Q_pr ≡ Q_abs + Q_sca(1 ? 〈cos α〉), where Q_abs and Q_sca are the efficiency factors for absorption and scattering, and 〈cos α〉 accounts for the asymmetry of the scattered radiation. This result is confirmed by a new formal derivation applying special relativistic transformations for the incoming and outgoing energy and momentum as seen in the particle and solar frames of reference. Q_pr is evaluated from Mie theory for small spherical particles with measured optical properties, irradiated by the actual solar spectrum. Of the eight materials studied, only for iron, magnetite , and graphite grains does the radiation pressure force exceed gravity and then just for sizes around 0.1 μm; very small particles are not easily blown out of the solar system nor are they rapidly dragged into the Sun by the Poynting-Robertson effect. The solar wind counterpart of the Poynting-Robertson drag may be effective, however, for these particles. The orbital consequences of these radiation forces-including ejection from the solar system by relatively small radiation pressures-and of the Poynting-Robertson drag are considered both for heliocentric and planetocentric orbiting particles. We discuss the coupling between the dynamics of particles and their sizes (which diminish due to sputtering and sublimation). A qualitative derivation is given for the differential Doppler effect, which occurs because the light received by an orbiting particle is slightly red-shifted by the solar rotation velocity when coming from the eastern hemisphere of the Sun but blue-shifted when from the western hemisphere; the ratio of this force to the Poynting-Robertson force is $\text{(}\text{R}{}_{\mathrm{\odot }}\text{r}\text{)}{}^2\text{[(}\text{w}{}_{\mathrm{\odot }}\text{n}\text{) ? 1]}$, where R_⊙ and w_⊙ are the solar radius and spin rate, and n is the particle's mean motion. The Yarkovsky effect, caused by the asymmetry in the reradiated thermal emission of a rotating body, is also developed relying on new physical arguments. Throughout the paper, representative calculations use the physical and orbital properties of interplanetary dust, as known from various recent measurements.     

The temperature of nonspherical circumstellar dust grains

The temperatures of prolate and oblate spheroidal dust grains in the envelopes of stars of various spectral types are calculated. Homogeneous particles with aspect ratios a/b≤10 composed of amorphous carbon, iron, dirty ice, various silicates, and other materials are considered. The temperatures of spherical and spheroidal particles were found to vary similarly with particle size, distance to the star, and stellar temperature. The temperature ratio T _d(spheroid)/T _d(sphere) depends most strongly on the grain chemical composition and shape. Spheroidal grains are generally colder than spherical particles of the same volume; only iron spheroids can be slightly hotter than iron spheres. At a/b≈2, the temperature differences do not exceed 10%. If a/b≥4, the temperatures can differ by 30–40%. For a fixed dust mass in the medium, the fluxes at wavelengths λ≥100 are higher if the grains are nonspherical, which gives overestimated dust masses from millimeter observations. The effect of grain shape should also be taken into account when modeling Galactic-dust emission properties, which are calculated when searching for fluctuations of the cosmic microwave background radiation in its Wien wing.     

Perihelion motion of small irregular dust particles due to radiation forces

Perihelion motion, i.e. a secular change of longitude of perihelion, of interplanetary dust particles is investigated under the action of solar gravity and solar electromagnetic radiation. As for spherical particle [Kla?ka, J., 2004. Electromagnetic radiation and motion of a particle. Cel. Mech. Dynam. Astron. 89, 1-61]: (i) perihelion motion is of the order ( is heliocentric velocity of the meteoroid and c is the speed of light in vacuum), if a component of electromagnetic radiation acceleration is considered as a part of central acceleration; (ii) perihelion motion is of the first order in if the total electromagnetic radiation force is considered as a disturbing force. The new facts presented in this paper concern irregular dust particles. Detailed numerical calculations were performed for the grains ejected at aphelion of comet Encke. Perihelion motion for irregular interplanetary dust particles exists already in the first order in for both cases of central accelerations. Moreover, perihelion motion of irregular particles exhibits both positive and negative directions during the particle orbital motion. Irregularity of the grains causes not only perihelion motion, but also dispersion of the dust in various directions, also normal to the orbital plane of the parent body.     

Modeling infrared absorption bands with nonspherical particles

We investigated the two deepest absorption bands observed in the spectra of stars and protostars, the water-ice band with the center near 3.1 μm and the silicate band with the center near 9.7 μm, by using a core-mantle confocal spheroid model with various axial ratios and relative volumes of the core material. We considered the effect of grain size, shape, structure, chemical composition, and orientation on the central wavelengths of the two bands, their full widths at half maximum (FWHMs), the ratio of the optical depths at their centers, and the polarization. We found that the observed relationships between the FWHMs of the bands and the ratio of their optical depths at the band centers could be explained if we chose slightly oblate or prolate particles (a/b ? 2) of small sizes (r_v ? 0.35 μm) with a silicate core and a thin ice mantle (V_core/V_total ? 0.7).     

Radiation pressure and dust particle dynamics

The dynamics of small dust grains orbiting a planet are investigated when solar radiation pressure forces are added to the planet's gravitational central field. In the first part a set of differential equations is derived in a reference frame linked to the solar motion. The complete solution of these equations is given for particles lying in the planet's orbital plane, and we show that the orbital eccentricity may undergo considerable variation. At the same time the pericenter longitude librates or circulates according to initial conditions. With this result we establish a criterion for any orbiting particle (because of its highly eccentric orbit) to collide with its planet's atmosphere. The case of inclined orbit is studied through a numerical integration and allows us to draw conclusions related to the stability of the orbital plane. All solutions are periodic, with the period being independent of the initial conditions. This last point permits us to investigate the different time scales involved in that problem. Finally, the Poynting-Robertson drag is included, along with the radial radiation pressure forces, and the secular trend is considered. A coupling effect between the two components is ascertained, yielding a systematic behavior in the eccentricity and thus in the pericenter distance. Our solutions generalize the results of S. J. Peale (1966, J. Geophys. Res.71, 911–933) and J. A. Burns, P. Lamy, and S. Soter (1979, Icarus40, 1–48) by allowing eccentricities to be large (of order 1) and inclinations to be nonzero and by considering Poynting-Robertson drag.     

Interplanetary dust particles and solar wind

An effect of the solar wind on the motion of interplanetary dust particles is investigated. An equation of motion is derived. It is pointed out that the Pseudo-Poynting-Robertson effect (and its special case — a corpuscular drag) and the corpuscular sputtering represent in reality one and the same effect within the framework of special relativity. In this context perturbation equations of celestial mechanics are also discussed.     

Interplanetary dust particles and impact erosion

Motion of the interplanetary dust particle under the action of collisions with much smaller interplanetary dust particles is investigated. The equation of motion is derived. Perturbation equations of celestial mechanics are also discussed. The results are compared with the Poynting-Robertson effect and the effect of solar wind on the motion of the interplanetary dust particles, from the point of view of observational data.     

Interplanetary dust particles and solar radiation

The problem of the action of the solar radiation on the motion of interplanetary dust particle is discussed. Differences between the action of electromagnetic solar radiation and that of the solar wind are explained not only from the point of view of the physical nature of these phenomena but also from the point of view of dust particle's orbital evolution. As for the electromagnetic solar radiation, general equation of motion for the particle is written and the most important consequences are: (i) the process of inspiralling toward the Sun is not the only possible motion - even spiralling from the Sun is also possible, and, (ii) the orbital plane of the particle (its inclination) may change in time. As for the solar wind, the effect corresponding to the fact that solar wind particles spread out from the Sun in nonradial direction causes that the process of inspiralling toward the Sun is in more than 50% less effective than for radial spread out; in the region of the asteroid belt (long period orbits) the process of inspiralling is changed into offspiralling. Also shift in the perihelion of dust particle's orbit exists.     

Interplanetary dust particles near Jupiter

We calculate the expected counting rate of a flat micrometeoroid detector of finite sensitivity passing in hyperbolic orbit near a planet. We assume that the distribution of particle sizes, s, can be expressed as a power law spectrum of index p, i.e. dN(s) = Cs^?pds, and also that the particles encounter the sphere of influence of the planet with a certain speed v_∞. The results of the calculations are then compared with the results returned by Pioneer 10 in its flyby of Jupiter. The observed increase in impact rate near Jupiter can be completely explained in terms of gravitational “focusing” of particles which are in heliocentric orbits; i.e., they are not in orbit about Jupiter. The absolute concentration of particles near the orbit of Jupiter is of the same order as at 1 AU: the exact ratio being a function of particle speed and spectral index. Data from one flyby are insufficient to determine a unique value for both the spectral index, p, and the particle velocity, v_∞, but limits can be set. For reasonable encounter speeds (corresponding to eccentricities and inclinations of dust particles experienced near the Earth), the particles near Jupiter are characterized by a spectrum of index p ～ 3. The spectral index which best fits the data increases with increasing encounter speeds.     

Interplanetary dust particles and solar electromagnetic radiation

The action of the solar electromagnetic radiation on the motion of interplanetary dust particle of the plane mirror form is investigated. It is shown that for rapidly rotating plane mirror the speed of inspiralling toward the Sun is about a factor of 4 lower than that for spherical mirror of the same cross-sectional area. In principle, it is also possible that the plane mirror can be expelled from the inner part of the Solar System. Presented derivation is a little more general - it is considered that some parts of the incident radiation can be also absorbed or transmitted, not only reflected.Obtained results show that the Poynting-Robertson effect is strongly model-dependent. It is suggested that for real irregular porous particles the speed of inspiralling toward the Sun can be smaller than that for perfectly absorbing sphere. Orbital plane can change in time.     

Electrostatic forces and shadow effects in planetary dust rings

The vertical dust distribution of dust clouds around planets, resulting from electrostatic forces, is calculated as a function of dust and plasma parameters. Photoelectric charging is included and differences between clouds on the illuminated side and in the shadow zone are examined. We compute ring structures for conditions which may apply in the spoke-forming regions and study at what dust and plasma conditions the shadow has a significant effect on the vertical dust cloud structure.     

Radiation forces and the formation of planetary systems

We briefly support on some new results about the influence of the rotation and finite size of a stellar radiation source on dust particle orbits, emphasizing the possibility of stable orbits, in the equatorial plane, for dust sizes near the radiation pressure limit.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Reflectance spectroscopy of interplanetary dust particles

Abstract Reflectance spectra were collected from chondritic interplanetary dust particles (IDPs), a polar micrometeorite, Allende (CV3) meteorite matrix, and mineral standards using a microscope spectrophotometer. Data were acquired over the 380–1100 nm wavelength range in darkfield mode using a halogen light source, particle aperturing diaphrams, and photomultiplier tube (PMT) detectors. Spectra collected from titanium oxide (Ti₄O₇), magnetite (Fe₃O₄), and Allende matrix establish that it is possible to measure indigenous reflectivities of micrometer-sized (>5 μm in diameter) particles over the visible (VIS) wavelength range 450–800 nm. Below 450 nm, small particle effects cause a fall-off in signal into the ultraviolet (UV). Near-infrared (IR) spectra collected from olivine and pyroxene standards suggest that the ～1 μm absorption features of Fe-bearing silicates in IDPs can be detected using microscope spectrophotometry. Chondritic IDPs are dark objects (<15% reflectivity) over the VIS 450–800 nm range. Large (>1 μm in diameter) embedded and adhering single mineral grains make IDPs significantly brighter, while surficial magnetite formed by frictional heating during atmospheric entry makes them darker. Most chondritic smooth (CS) IDPs, dominated by hydrated layer silicates, exhibit generally flat spectra with slight fall-off towards 800 nm, which is similar to type CI and CM meteorites and main-belt C-type asteroids. Most chondritic porous (CP) IDPs, dominated by anhydrous silicates (pyroxene and olivine), exhibit generally flat spectra with a slight rise towards 800 nm, which is similar to outer P and D asteroids. The most C-rich CP IDPs rise steeply towards 800 nm with a redness comparable to that of the outer asteroid object Pholus (Binzel, 1992). Chondritic porous IDPs are the first identified class of meteoritic materials exhibiting spectral reflectivities (between 450 and 800 nm) similar to those of P and D asteroids. Although large mineral grains, secondary magnetite, and small particle effects complicate interpretation of IDP reflectance spectra, microscope spectrophotometry appears to offer a rapid, nondestructive technique for probing the mineralogy of IDPs, comparing them with meteorites, investigating their parent body origins, and identifying IDPs that may have been strongly heated during atmospheric entry.     

Temperature-influenced dynamics of small dust particles

The motion of spherical dust particles under the action of gravity, electromagnetic radiation force and Lorentz force (LF) is studied theoretically for materials with temperature-dependent dielectric functions in the visible (VIS) spectral range. Even a weak variation of the optical constants with heliocentric distance may influence predominately a long-term dynamical behaviour of submicron-sized and small micron-sized dust grains. It is shown that the lifetime of carbonaceous or Si particles may change by several tens of per cent because of the temperature dependence of particle refractive indices. The orbital inclination is the most evident difference between the evolution of a dust particle with temperature-dependent optical properties and one without. While carbonaceous 2-μm-sized particles with optical constants independent of temperature may evolve in orbits with inclinations greater than an initial value, grains of the same size with variable refractive indices will be spread along orbits characterized with inclinations lower than the initial one. Here the temperature works as a separation factor for particles having slightly different temperature dependences of the optical constants.     

Surface analysis of stratospheric dust particles

Abstract— A controversially discussed and yet central question in interplanetary dust particle (IDP) research is the degree of alteration of these particles during their residence in the stratosphere. Especially, the typical enrichment of Br in chondritic IDPs (on the average ～21 × CI) has been inferred to be a result of contamination processes, probably invoking aerosol droplets. With time-of-flight secondary ion mass spectrometry (TOF-SIMS), we examined the surfaces of 13 stratospheric particles from the dust collector U2071. Six particles had severe, surface-bound, silicone oil residues preventing a proper analysis of their surfaces. Six other particles—-according to our scanning electron microscopy, energy dispersive x-ray spectrometer (SEM-EDS) studies preclassified as one (Fe,Ni)S-rich IDP, one Ca-rich particle, and four aluminum-oxide spheres—-carry the halogens F, Cl, and Br on the surface. At least for the aluminum-oxide spheres, we provide unequivocal evidence for a surface correlation of halogens. This evidence, taken together with that from previous studies, proves a general stratospheric contamination process which has to be considered in IDP research.     

Characterization of Jovian plasma-embedded dust particles

As the data from space missions and laboratories improve, a research domain combining plasmas and charged dust is gaining in prominence. Our solar system provides many natural laboratories such as planetary rings, comet comae and tails, ejecta clouds around moons and asteroids, and Earth's noctilucent clouds for which to closely study plasma-embedded cosmic dust. One natural laboratory to study electromagnetically controlled cosmic dust has been provided by the Jovian dust streams and the data from the instruments which were on board the Galileo spacecraft. Given the prodigious quantity of dust poured into the Jovian magnetosphere by Io and its volcanoes resulting in the dust streams, the possibility of dusty plasma conditions exist. This paper characterizes the main parameters for those interested in studying dust embedded in a plasma with a focus on the Jupiter environment. I show how to distinguish between dust-in-plasma and dusty-plasma and how the Havnes parameter P can be used to support or negate the possibility of collective behavior of the dusty plasma. The result of applying these tools to the Jovian dust streams reveals mostly dust-in-plasma behavior. In the orbits displaying the highest dust stream fluxes, portions of orbits E4, G7, G8, C21 satisfy the minimum requirements for a dusty plasma. However, the P parameter demonstrates that these mild dusty plasma conditions do not lead to collective behavior of the dust stream particles.     

Composition of jovian dust stream particles

The Cassini spacecraft encountered Jupiter in late 2000. Within more than 1 AU of the gas giant the Cosmic Dust Analyser onboard the spacecraft recorded the first ever mass spectra of jovian stream particles. To determine the chemical composition of particles, a comprehensive statistical analysis of the dataset was performed. Our results imply that the vast majority (>95%) of the observed stream particles originate from the volcanic active jovian satellite Io from where they are sprinkled out far into the Solar System. Sodium chloride (NaCl) was identified as the major particle constituent, accompanied by sulphurous as well as potassium bearing components. This is in contrast to observations of gas in the ionian atmosphere, its co-rotating plasma torus, and the neutral cloud, where sulphur species are dominant while alkali and chlorine species are only minor components. Io has the largest active volcanoes of the Solar System with plumes reaching heights of more than 400 km above the moons surface. Our in situ measurements indicate that alkaline salt condensation of volcanic gases inside those plumes could be the dominant formation process for particles reaching the ionian exosphere.     

Interplanetary dust particles: Disintegration and orbital motion

Abrupt or gradual disintegration of the interplanetary dust particle causes increase of its distance from the Sun due to the solar radiation pressure. The problem of the orbital evolution of the interplanetary dust particles under such disintegration processes is discussed. The process of gradual disintegration due to the solar wind particles is calculated in detail. Obtained results represent corrections to the changes of orbital elements for the Poynting-Robertson effect and effect of the solar wind.