Cometary dust properties retrieved from polarization observations: Application to C/1995 O1 Hale-Bopp and 1P/Halley

The analysis of the polarized light scattered by cometary dust particles provides information on the physical properties of the solid component of cometary comae for C/1995 O1 Hale-Bopp and 1P/Halley. A model of light scattering by a size distribution of aggregates of up to 256 submicron-sized grains (spherical or spheroidal) mixed with single spheroidal particles has been developed, with its parameters adjusted to fit the phase angle and wavelength dependence of the polarization observations. The particles are built of two materials: a non-absorbing silicates-type material and a more absorbing organic-type material. The model reproduces accurately the inversion angle and the positive branch of the polarization phase curves from the visible to the near-infrared spectral domains. A negative branch of the polarization phase curves appears in our model, although the negative branch is not deep enough to reproduce accurately the observations. Significant differences are shown between the two comets, with dominance of small grains in the coma of Comet C/1995 O1 Hale-Bopp, well fitted by a distribution of the volume-equivalent diameter, a, following a^−3.0 with a lower cutoff around 0.20 μm and an upper cutoff of at least 40 μm. For 1P/Halley, the size distribution follows a^−2.8 with a lower cutoff around 0.26 μm and an upper cutoff of about 38 μm. The relative amount of organic-type particles is larger for 1P/Halley while the amount of aggregates, significant for both comets, is larger for C/1995 O1 Hale-Bopp.     

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.     

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.     

Polarization of Light Scattered by Solar System Bodies and the Aggregate Model of Dust Particles

The present study considers the dependence of characteristics of light scattering by aggregate particles on the refractive index, size, and number of spherical particles composing the aggregate, as well as on the structure and porosity of the cluster. The parameters were varied in sufficiently wide ranges to let a coherent picture of the polarimetric properties of relatively small aggregate particles emerge (the size parameter of the aggregate is less than 10). It was shown that, in the framework of the aggregate model, the behavior of polarization phase curves observed for both comets and regolith surfaces can be explained. The modeling carried out confirms that the sizes of the cometary dust particles are larger than the wavelength. However, the grains forming the cometary dust particles or the regolith (or details of the particle surface) have a size less than 0.3–0.5 m. This agrees with estimates obtained by other methods. The determining role in the formation of the polarization phase curve is played by the structure of the external layer of the clusters. The appearance of the negative branch of polarization and its shape substantially depend on the effectiveness of the interference of multiply scattered waves and on the interaction in the near field at these phase angles. Interference and interaction in the near field in turn are determined by the sizes of elementary scatterers and the structure of the ensemble. If the number of constituent particles in the aggregate is larger than several tens, its role in the formation of the negative branch of polarization is minor, while the influence on the polarization maximum position is rather substantial. The polarimetric data alone cannot provide a unique estimate of the refractive index: the brightness measurements must be invoked as well. For a more complete quantitative interpretation of the observations, the scattering matrix of aggregates comparable in size to or larger than the wavelength must be calculated in the short- and long-wavelength ranges, which still encounters serious theoretical and technical difficulties. Moreover, in order to obtain unique results, it is obvious that the spectral range of observations must be extended and that other types of measurements, such as spectroscopic ones, must also be used.     

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.     

The formation of Mg,Fe‐silicates by reactions between amorphous magnesiosilica smoke particles and metallic iron nanograins with implications for comet silicate origins

This thermal annealing experiment at 1000 K for up to 167 h used a physical mixture of vapor phase‐condensed magnesiosilica grains and metallic iron nanograins to test the hypothesis that a mixture of magnesiosilica grains and an Fe‐source would lead to the formation of ferromagnesiosilica grains. This exploratory study found that coagulation and thermal annealing of amorphous magnesiosilica and metallic grains yielded ferromagnesiosilica grains with the Fe/(Fe + Mg) ratios in interplanetary dust particles. Furthermore, decomposition of brucite present in the condensed magnesiosilica grains was the source for water and the cause of different iron oxidation states, and the formation of amorphous Fe³⁺‐ferrosilica, amorphous Fe³⁺‐Mg, Fe‐silicates, and magnesioferrite during thermal annealing. Fayalite and ferrosilite that formed from silica/FeO melts reacted with forsterite and enstatite to form Mg, Fe‐silicates. The presence of iron in different oxidation states in extraterrestrial materials almost certainly requires active asteroid‐like parent bodies. If so, the possible presence of trivalent Fe compounds in comet P/Halley suggests that Halley‐type comets are a mixture of preserved presolar and processed solar nebula dust. The results from this thermal annealing experiment further suggest that the Fe‐silicates detected in the impact‐induced ejecta from comet 9P/Temple 1 might be of secondary origin and related to the impact experiment or to processing in a regolith.     

Laboratory light-scattering measurements with Titan's aerosols analogues produced by a dusty plasma

The chemistry leading to the formation of solid aerosols (tholins) in Titan's atmosphere is simulated by a capacitively coupled plasma in a N₂-CH₄ gas mixture. The solid grains are produced in volume directly in the gas phase and studied ex-situ by SEM imaging and by light scattering on clouds of particles. The scattered light properties depend on the physical properties of the particles (morphologies, size distribution), as well as on the phase angle and the wavelength of the light. The particles may be aggregated or agglomerated grains. The grains size distribution is studied as a function of plasma parameters such as initial methane concentration introduced into the discharge, gas flow, absorbed RF power and plasma duration. The average grain size increases when the amount of CH₄ increases, when the gas flow decreases, and when the plasma duration increases up to a limit for each production condition.For all the samples, the absorption decreases with increasing wavelength in the visible domain. As usually found for irregular particles, the polarization phase curves have a bell-shaped positive branch and a shallow negative branch. The maximum of polarization (P_max) increases when the average grain size decreases (sub-μm-sized grains). To obtain P_max values within the range of those measured in Titan's atmosphere; the average grains diameter has to be smaller than 100 nm, in agreement with the space observations results. In the light-scattering experiment, the size of the agglomerates in the clouds is in the 40-80 μm range in equivalent diameter. As a consequence P_max increases with decreasing wavelength due to the increasing absorption, in agreement with observations of Titan from outside the atmosphere.     

Polarimetric study of levitating dust aggregates with the PROGRA experiment

In order to interpret polarimetric remote observations of solar system dust clouds (e.g. cometary coma dust), laboratory measurements are needed. Three samples composed of aggregates are studied: crystallized enstatite, pyrogenic alumina and titanium oxide. The new version of the PROGRA² instrument allows to obtain polarimetric images of the samples under levitation. The dependence of polarization with phase angle and particle size is studied, as well as the effect of the porosity of the particles. Values of polarization at small phase angles are also discussed. The polarization near 90° decreases when the agglomerate size increases and when the porosity increases.     

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.     

Polarization of Light Scattered by Surfaces with Complex Microstructure at Phase Angles 0.1°–3.5°

We present laboratory measurements of the phase dependences of linear polarization for surfaces with a complex microstructure in the range of phase angles 0.1°–3.5° A sample of freshly fallen snow (with particle sizes of about 50 × 500 m) exhibits a nearly zero polarization. Surfaces with submicron structure show a narrow branch of negative polarization at small phase angles, irrespective of whether the surface is powderlike or solid with microcrystalline structure. This polarization is similar to that exhibited by Jupiter's satellites. The negative polarization branch becomes deeper with decreasing porosity of light dielectric surfaces. At the phase angles between 0.5° and 3.0°, the polarization for quartz powder with 10-m particles is almost constant. The polarization for light dielectric surfaces depends on the geometry of illumination and observation. An inclination of the surface in the scattering plane produces a parallel shift of the negative polarization branch toward large values of the polarization modulus. The same inclination in a perpendicular direction produces the same shift toward positive degrees of polarization.     

A Monte Carlo Code to Compute Energy Fluxes in Cometary Nuclei

A Monte Carlo model designed to compute both the input and output radiation fields from spherical-shell cometary atmospheres has been developed. The code is an improved version of that by H. Salo (1988, Icarus76, 253-269); it includes the computation of the full Stokes vector and can compute both the input fluxes impinging on the nucleus surface and the output radiation. This will have specific applications for the near-nucleus photometry, polarimetry, and imaging data collection planned in the near future from space probes. After carrying out some validation tests of the code, we consider here the effects of including the full 4×4 scattering matrix in the calculations of the radiative flux impinging on cometary nuclei. As input to the code we used realistic phase matrices derived by fitting the observed behavior of the linear polarization as a function of phase angle. The observed single scattering linear polarization phase curves of comets are fairly well represented by a mixture of magnesium-rich olivine particles and small carbonaceous particles. The input matrix of the code is thus given by the phase matrix for olivine as obtained in the laboratory plus a variable scattering fraction phase matrix for absorbing carbonaceous particles. These fractions are 3.5% for Comet Halley and 6% for Comet Hale-Bopp, the comet with the highest percentage of all those observed.The errors in the total input flux impinging on the nucleus surface caused by neglecting polarization are found to be within 10% for the full range of solar zenith angles. Additional tests on the resulting linear polarization of the light emerging from cometary nuclei in near-nucleus observation conditions at a variety of coma optical thicknesses show that the polarization phase curves do not experience any significant changes for optical thicknesses τ?0.25 and Halley-like surface albedo, except near 90° phase angle.     

Imaging polarimetry of the dust coma of Comet Tempel 1 before and after Deep Impact at Haute-Provence Observatory

We have observed the coma of Comet 9P/Tempel 1, the target of the Deep Impact mission, by the polarization imaging technique, before and after the impact event (−32, −7, +43 and +65 h). Our observations were conducted in the red wavelength domain from Haute-Provence Observatory (France), with the 80-cm telescope. The overall polarization of 9P/Tempel 1, as obtained near 41° phase angle, is monitored and compared to data from other (active and less active) comets studied by the same technique. The linear polarization of the dust ejected by the impact is compared to previous observations of dust present in jets, ejected during outbursts or released when comets happen to split. At phase angles of about 41°, the difference in polarization between the comets with a low maximum in polarization and the comets with a high maximum in polarization is about 1%; it may thus be difficult to conclude about the classification. Nevertheless, the overall polarization after the impact rapidly reached a value corresponding to the high polarization class of comets, and later progressively decreased to its initial value. The polarization was measured to be slightly lower (about 1%) before the impact than after it in a 26,000-km aperture. The plume formed from dust ejected by the impact was still present 65 h after it. The variations of the intensity and the polarization in the coma provide some clues to variations of the physical properties of the particles; comparison with other techniques corroborates the presence of large particles and of submicron-sized grains in aggregates.     

Theoretical polarimetric responses of fractal aggregates,in relation with experimental studies of dust in the solar system

Dust particles in the solar system (e.g. atmospheric hazes, cometary or interplanetary dust, regolith) are likely to be irregular aggregates whose light scattering properties (phase functions of polarization) are drastically different from those of Mie spheres. However, the observation of the light they scatter may provide informations on their physical properties. If the mechanisms which lead to aggregation are invariant with time, the aggregates are likely to be fractal particles made up from individual monomers. Computations, developped in relation with the CODAG experiment, are performed using a Discrete Dipole Approximation, and each monomer is described by one or more dipoles. When the particles are formed from a few monomers made up of numerous dipoles, the polarimetric response of the aggregate is similar to the one of the constituent monomer. When the particles are formed from many monomers made up of individual dipoles, the phase curves are similar to those observed in the solar system. Our calculations suggest that dust particles have a fractal dimension of the order of 2 (Ballistic Cluster-Cluster Aggregation), and that the values of the real and imaginary part of the complex refractive index of the constituent material are high. Those results are in agreement with laboratory measurements on samples representative of astronomical organics and minerals.     

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.     

Opposition Effects in Brightness,Color, and Polarization of Comet 1P/Halley: Comparison with Atmosphereless Solar System Bodies

Systematic and uniform sets of photometric and polarimetric observations of comet 1P/Halley have been analyzed. The phase dependence of brightness for comet Halley was obtained at phase angles α ranging from 1.4° ≤ α ≤ 65°. The following parameters were determined: the amplitude of the opposition effect Δm = 0.75^m ± 0.06^m; the half-width at a half-maximum of intensity HWHM = 6.4° ± 1.6°; the linear phase coefficient β = 0.0045 ± 0.0001 mag/deg for α from 30° ≤ α ≤ 65°; and the phase angle at which a nonlinear increase in brightness starts, α _opp ≈ 31°. For the first time, the phase-angle dependence was obtained for the color of the dust of comet Halley: the color index BC-RC systematically decreases with increasing phase angle. Such a phase behavior of the dust color can be caused by the decrease in the mean size of dust particles that occurs when the comet approaches the Sun. For comet Halley, the negative polarization branch is almost symmetric; the minimal value of polarization is P _min = −1.54% at a phase angle α_min = 10.5°, and the inversion angle is α_inv = 21.7°. A comparative analysis of the phase functions of brightness and polarization has been performed for the cometary dust and atmosphereless bodies. Among the latter are low-albedo asteroids of the P and C types (102 Miriam and 47 Aglaja, respectively), as well as Deimos; high-albedo objects, such as the E-type asteroid 64 Angelina and the icy satellite of Jupiter Europa; and the Moon with its intermediate albedo. The possibility of a weak depression in the negative polarization branch of comets Halley and 47P/Ashbrook-Jackson at phase angles smaller than 2° is discussed.__________Translated from Astronomicheskii Vestnik, Vol. 39, No. 4, 2005, pp. 353–363.Original Russian Text Copyright © 2005 by Rosenbush.     

Observations Of Scattered Light From Cometary Dust And Their Interpretation

This review begins with a discussion of the techniques needed for observations of scattered light from cometary dust. After an introduction into the basic concepts of the scattering process, observations of the phase curves of brightness, colour and polarization are covered. Images of colour and polarization are presented and the observed relation of colour and polarization in jets and shells is discussed. The interpretation of the measurements is based on the power law size distributions of dust grains observed from space. The power index must lie between 2 and 4 to provide the mass budget and visibility of the dust coma in accordance with the basic facts of cometary physics. Application of mechanical (radiation pressure) theory to cometary images allows us to derive related power law distributions for comets not explored by spacecraft. Grain scattering models are presented and compared with observations. A prediction is made of the spatial distribution of Stokes parameters U and V in the presence of aligned particles. Up to now such patterns have not been observed. Future work should include the exploration of comets at small and possibly very small phase angles and a detailed comparison of polarization and colour images of comets with thermal images and with models based on mechanical theory. This revised version was published online in July 2006 with corrections to the Cover Date.     

The F-type asteroids with small inversion angles of polarization

UBVRI polarimetric observations carried out in 1997-2004 for the F-type Asteroids 302 Clarissa, 419 Aurelia, 704 Interamnia, and 762 Pulcova (V band only) are presented. Asteroid 419 Aurelia is characterized by a negative polarization branch which is unusual for low-albedo asteroids. Its depth is about 1%, while the inversion angle, close to 14°, reaches the smallest value ever observed for asteroids. This is the first definite example of a minor body exhibiting a considerable decrease of both the depth and width of the negative polarization branch in comparison with polarization properties of other low-albedo bodies, mimicking a behavior previously found in laboratory measurements of extremely dark surfaces. The F-type Asteroids 302 Clarissa and 704 Interamnia are also characterized by unusually small inversion angles compared to other asteroid types, while Asteroid 762 Pulcova seems to have an ordinary negative polarization branch. Laboratory measurements of low-albedo samples and computer simulations of light scattering by particles of irregular shapes were made to interpret observational data. We find that an optical homogeneity of regolith microstructure at scales of the order of visible light wavelengths may be responsible for relatively small values of the depth of the negative polarization branch and of the inversion angle. Peculiar features of the F-type asteroids compared to other taxonomic classes are discussed.     

Polarization opposition effect for the Galilean satellites of Jupiter

We present results of polarimetric observations of the Galilean satellites Io, Europa, Ganymede, and Callisto at phase angles ranging from 0.19° to 2.22°. The observations in the UBVR filters were performed using a one-channel photoelectric polarimeter attached to 70-cm telescope of the Chuguev Observation Station (Ukraine) on November 19-December 7, 2000. We have observed the polarization opposition effect for Io, Europa, and Ganymede to be a sharp secondary spike of negative polarization with an amplitude of about −0.4% centered at phase angles of 0.2°-0.7° and superimposed on the regular negative polarization branch. Although these minima for Io, Europa, and Ganymede show many similarities, they also exhibit a number of distinctions. The polarization opposition effect appears to be wavelength-dependent, at least for Europa and Ganymede. No polarization opposition effect was found for Callisto. The results obtained are discussed within the framework of different mechanisms of light scattering.     

Polarization and brightness opposition effects for the E-type Asteroid 44 Nysa

We present new polarimetric and photometric observations of high-albedo E-type Asteroid 44 Nysa in the BVRI wavebands at phase angles ranging from 0.41° to 7.49° during the 2005 opposition. A bimodal phase-angle dependence of polarization was found for Nysa in the V band. The polarization opposition effect was revealed in the form of a secondary minimum of negative polarization with amplitude ∼0.3% centered at a phase angle ∼0.8°. It is superimposed on the regular negative polarization branch with minimal polarization −0.30% at a phase angle 5.8°. We analyzed all available polarimetric data for E-type Asteroids 44 Nysa, 64 Angelina, and 214 Ashera and confirmed the presence of the polarization opposition effect for high-albedo asteroids at phase angle ∼1° with an amplitude ∼0.35%. The magnitude-phase curves reveal the presence of spike-like opposition effect of brightness for 44 Nysa in the BVRI spectral bands. 44 Nysa is the second high-albedo asteroid after 64 Angelina for which both the polarization opposition effect and the brightness opposition effect are detected. The differences between the parameters of the opposition effects for silicate surfaces (44 Nysa, 64 Angelina, Io) and icy surfaces (Europa, Ganymede, Iapetus, Saturn's rings) are discussed. The specific morphological parameters of opposition effects, in particular the angular width of the polarization opposition effect is comparable to that of the brightness opposition effect, provide almost unequivocal evidence that they are caused by coherent backscattering. One of unexpected results of our investigation is that 44 Nysa becomes bluer with increasing phase angle, while 64 Angelina shows phase reddening.     

The Opposition Effect and Negative Polarization of Structural Analogs for Planetary Regoliths

To better understand the negative polarization and brightness opposition effects observed on airless celestial bodies, we carried out simultaneous photometric and polarimetric measurements of laboratory samples that simulate the structure of planetary regoliths. Computer modeling of shadow-hiding and coherent backscatter in regolith-like media are also presented. The laboratory investigations were carried out with a photometer/polarimeter at phase angles covering 0.2°-4° and wavelengths of 0.63 and 0.45 μm. We studied samples that characterize a variety of microscopic structures and albedos. A particle-size dependence of the negative branch of polarization for powdered dielectric surfaces was found. Colored samples such as a powder Fe₂O₃ exhibit a very prominent wavelength dependence of the photometric and polarimetric opposition phenomena. Metallic powders usually exhibit a wide branch of the negative polarization independent of the size of particles. For fine dielectric powders, both opposition phenomena become more prominent when the samples were compressed. Our computer modeling based on ray tracing in particulate media shows that shadow-hiding affects the negative polarization only in combination with the coherent backscatter enhancement. Modeling reveals that scattering orders higher than second contribute to negative polarization even in dark particulate surfaces. Our model qualitatively reproduces the effects of varying sample-compression that we observed in the laboratory. Our experimental and computer modeling studies mutually confirm that the degree of polarization for highly reflective dielectric surfaces depends not only on phase angle but also on surface tilt. Even at exactly zero phase the degree of polarization for tilted surfaces can be nonzero. A tilt of the surface normal to the scattering plane gives a parallel shift of the negative polarization branch to large values of |P|. The tilt in the perpendicular plane gives the same shift in the direction of positive polarization. At exactly zero phase angle, a celestial body of irregular shape can exhibit nonzero polarization even in integral polarimetric observations.