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The ground-based astronomic observations of comet cannot provide a proper phase angle coverage that is needed to estimate with a reasonable accuracy all of the attributes of comet polarization phase curve. To find the best approximation to the phase polarization dependences observed for comets, we apply a simple empiric formula that has already shown good results when operating with asteroid and lunar polarimetric curves (Shestopalov, 2004; Shestopalov and Golubeva, 2015). From the set of comets present in DBCP (Kiselev et al., 2006), we selected 20, for which the calculation of regular polarimetric curves (i.e. the phase angle – polarization dependences with a low level of nonsteady activity) was possible. Within the phase angle coverage area for these 20 comets, a potential user can reproduce 82 best-fitting polarimetric phase curves in various spectral domains. Then we analyzed the properties of negative and positive polarization of the comets. The interrelation between the averaged polarimetric slope h at the inversion angle and wavelength was found. In general, the parameters of negative branch vary slightly from one comet to another. We found a close correlation between the maximum polarization degree Pmax and the slope of the segment of polarimetric curve bounded by phase angles of 30° and 50°. This finding allowed to adduce the evidence in support of the idea voiced by Chernova et al. (1993) about two types of comet with high and low Pmax. Moreover, we have found direct correlation between the maximum polarization degree of comets and their dust-to-gas ratio. The latter is actually a visual proof of assumptions voiced many years ago about a mutual effect of gas and dust on observed polarization of comets (see, for instance, a historical review in Kiselev et al., 2015). Thus, the polarimetric effect of resonant fluorescence should be completely eliminated from the phase-dependent polarization curve of comet in order to correctly interpret the physical properties of cometary dust. The simple method that we suggest to deconvolve polarimetric response from comets into “pure dusty” and “gaseous” polarimetric curves meets specific difficulties associated mainly with a shortage of data about the polarized luminescence of molecules and ions commonly present in the gaseous component of cometary atmospheres.

Quite frequently astronomic polarimetric observations of different celestial bodies do not guarantee a proper phase angle coverage that is required for estimating all of the attributes of their polarization phase curves with a high accuracy. To approximate the phase dependences of polarization observed for particulate surfaces, we use a simple empiric formula recently suggested by Shestopalov (2004). The efficiency of the approximating function in a wide range of phase angles is illustrated with the use of the results of polarimetric measurements of lunar areas, lunar samples, and near-Earth asteroids. For asteroids of various types, we can reproduce their negative polarization branches with adequate accuracy and roughly estimate a probable value of the maximum polarization degree at an appropriate phase angle. From the polarimetric database available at NASA PDS [Asteroid Polarimetric Database V7.0 (2012)] we calculated the main parameters of 153 polarimetric curves of asteroids in various spectral bands with the accuracy comparable to the observation errors. One more purpose of our analysis was to find correlations between the polarimetric and photometric properties of asteroids. For C-, M-, S-, E-type asteroids, the characteristics of the negative branch of polarization curves turned out to correlate closely with the phase coefficient of the photometric function of asteroids and the photometric roughness of asteroid surfaces. This implies that the complex geometry of the surface microrelief affects the polarization properties of asteroids. In particular, the data scattering around regression lines on the plots of the albedo versus the depth of negative polarization branch and the slope of the polarimetric function at inversion angle strongly depends on the differences in the photometric roughness of asteroid surfaces.

Analysis of laboratory experiments simulating space weathering optical effects on atmosphereless planetary bodies reveals that the time needed to alter the spectrum of an ordinary chondrite meteorite to resemble the overall spectral shape and slope of an S-type asteroid is about ∼10 5 yr. The time required to reduce the visible albedo of samples to ∼0.05 is ∼10 6 yr. Since both these timescales are much less than the average collisional lifetime of asteroids larger than several kilometers in size, numerous low-albedo asteroids having reddish spectra with subdued absorption bands should be observed instead of an S-type dominated population. This is not the case because asteroid surfaces cannot be considered as undisturbed, unlike laboratory samples. We have estimated the number of collisions occurring in the time of ∼10 5 yr between asteroids and projectiles of various sizes and show that impact-activated motions of regolith particles counteract the progress of optical maturation of asteroid surfaces. We suppose that the maturation level of asteroid surfaces may be a compromise resulting from a competition between impact resurfacing and solar wind darkening, and that after reaching some steady state after a relatively short time (∼7 × 10 5 yr), thereafter depends only slightly on time. Spectroscopic analysis, using relatively invariant spectral parameters, such as band centers and band area ratios, can determine whether the surface of an S asteroid has chondritic composition or not. In this sense, the bodies with the ordinary chondrite composition cannot be masked among S asteroids. Differences in the environment of the main asteroid belt versus that at 1 AU, and the physical difference between the Moon and main belt asteroids (i.e., size) can account for the lack of lunar-type weathering on main belt asteroids.

In the present paper we seek to understand the geologic diversity of units in the northern hemisphere of Vesta using HST observations ( Binzel et al., 1997 ). First, we compare colors R (0.673 μm)/ R (0.953 μm) and R (0.673 μm)/ R (1.042 μm) of Vesta’s units with those of V-type asteroids (vestoids) as well as howardite, eucrite, and diogenite meteorites (HEDs). This comparative analysis showed that: (i) on the color–color plot, regions on Vesta are clustered whereas vestoids and HEDs cover a wide range in color; (ii) very few vestoids or HEDs fall into Vesta’s color region. This implies that Vesta’s units are more homogenous than most vestoids and HEDs examined here and material of the units are slightly different from that of vestoids and HEDs. Assuming reasonable choice of end-member materials, an optical model ( Shkuratov et al., 1999 ) was used to simulate intimate mixtures of particles at the surface of Vesta’s units. Simulation of albedo, colors, and four-point spectra of Vesta’s units reveals that the rock-forming material is nearly equal for all units and has HED-like composition. Diversity of the units depends on the minor constituents such as chromite and a neutral phase. The western units contain more chromite and neutral phase than the eastern, consequently albedo of the western units is lower and their four-point spectra are flatter. Olivine and feldspar are also needed to give the best fit for the calculated and observed albedos and colors of Vesta’s units, but being in minor amount in Vesta’s rocks they play a secondary role in contributing to the optical properties of the units. Questions about the proportions of HED-like rock and the constituent called neutral phase remain open. Spectrophotometric studies of Vesta with both higher spatial and spectral resolution as expected from NASA’s Dawn mission are needed for resolving these problems.

High-resolution (0.34 nm) reflectance spectra of a suite of terrestrial ortho- and clinopyroxenes were characterized in the 506-nm region. This region exhibits absorption bands attributed to spin-forbidden transitions in Fe2+ located in the M2, and possibly M1, crystallographic site(s). The most intense absorption bands (up to 3.8% deep in

Faint absorption bands in the visible range of the smoothed vestoid spectra have been found. The bands centered near 505, 530, and 550 nm are attributed to ferrous iron in low-calcium pyroxene and are typical for pyroxene-bearing vestoid surfaces. In accordance with characteristics of the faint absorption bands around 600 and 650 nm the studied vestoid spectra can be sorted into five types. Since the same absorptions are also seen in the laboratory spectra of the minerals and meteorites, which appear to be similar to vestoid material, spectral types of the vestoids can be related to their surface compositions. Regolith of the Type-I vestoids consists of pure low-calcium pyroxenes. Minor amount of olivine along with pyroxene appear to be on the Type-II vestoids whereas the mixtures of low-calcium pyroxene with minor chromite define the Type-III and -IV. The causes for the fifth spectral type in terms of minor mineral phases are unclear now. Simulation of the spectra of vestoids was employed to estimate content of olivine ( ∼ 6 – 12 vol% ) and chromite ( ∼ 12 – 30 vol% ) on their surfaces.

Faint absorption bands detected in the visible range of the reflectance spectra of A-type asteroids suggest a various mineralogical composition of their surface. From the analysis of these bands, we conclude that, on some asteroids of this optical type, both olivine and pyroxene are present, while mostly clinopyroxene with minor admixtures of Cr-containing minerals, presumably chromites, is on the surface of others. A new esti- mate of the forsterite content in the olivine of the asteroids 289 Nenetta and 446 Aeternitas (Fo ∼ 50-60%) made by the absorption band near 500 nm in their spectra agrees with the estimate we obtained previously from the modeling of the reflectance spectra of the asteroid Aeternitas.

An optimization method of smoothing noisy spectra was developed to investigate faint absorption bands in the visual spectral region of reflectance spectra of asteroids and the compositional information derived from their analysis. The smoothing algorithm is called “optimal” because the algorithm determines the best running box size to separate weak absorption bands from the noise. The method is tested for its sensitivity to identifying false features in the smoothed spectrum, and its correctness of forecasting real absorption bands was tested with artificial spectra simulating asteroid reflectance spectra. After validating the method we optimally smoothed 22 vestoid spectra from SMASS1 [Xu, Sh., Binzel, R.P., Burbine, T.H., Bus, S.J., 1995. Icarus 115, 1–35]. We show that the resulting bands are not telluric features. Interpretation of the absorption bands in the asteroid spectra was based on the spectral properties of both terrestrial and meteorite pyroxenes. The bands located near 480, 505, 530, and 550 nm we assigned to spin-forbidden crystal field bands of ferrous iron, whereas the bands near 570, 600, and 650 nm are attributed to the crystal field bands of trivalent chromium and/or ferric iron in low-calcium pyroxenes on the asteroids' surface. While not measured by microprobe analysis, Fe 3+ site occupancy can be measured with Mossbauer spectroscopy, and is seen in trace amounts in pyroxenes. We believe that trace amounts of Fe 3+ on vestoid surfaces may be due to oxidation from impacts by icy bodies. If that is the case, they should be ubiquitous in the asteroid belt wherever pyroxene absorptions are found. Pyroxene composition of four asteroids of our set is determined from the band position of absorptions at 505 and 1000 nm, implying that there can be orthopyroxenes in all range of ferruginosity on the vestoid surfaces. For the present we cannot unambiguously interpret of the faint absorption bands that are seen in the spectra of 4005 Dyagilev, 4038 Kristina, 4147 Lennon, and 5143 Heracles. Probably there are other spectrally active materials along with pyroxenes on the surfaces of these asteroids.

To compare the spectra of main-belt S-type asteroids and ordinary chondrites, we investigated the correlation between the reflectance peak position near 750 nm, the bend of the spectral curves in the 359-701 nm region, the linear gradient in the 359-853 nm range, and the absorption band position near 950 nm. In the dia- grams of spectral parameters, the regions occupied by S-type asteroids and ordinary chondrites are separated. The modeling of the optical effect of maturation of ordinary-chondrite samples, which leads to variations in the meteorite spectral parameters, was carried out under the following conditions: (1) the increase of the concen- tration of reduced-iron grains (SMFe) in particles without any change in their size; (2) the increase/decrease of the size of particles at a constant concentration of SMFe in them; (3) we also examined different relations between the concentration and the size of SMFe in particles. But, under no conditions did we manage to bring into coincidence the asteroid and meteorite regions simultaneously in all spectral-parameter diagrams. Hence, the conclusion was made that the difference between the reflectance spectra of ordinary chondrites and those of large main-belt S-type asteroids is determined not only by space weathering of asteroidal surfaces but also by systematic differences in the material composition.

The existence of gaps in the perihelion distribution of the orbits of multikilometer-sized asteroids that approach the orbits of terrestrial-group planets is confirmed. This property of the orbits of “large” asteroids suggests the existence among them of a family of last meteorite parent bodies. Astrophysical data were considered for S-asteroids of the Main Belt and those that approach terrestrial planets. The u–x color index, which is related to the position of the absorption band at 950 nm in the asteroid spectra, was chosen for a qualitative comparison of the surface composition of these asteroids (identical or differing composition). The u – x color-index distributions were analyzed statistically according to the perihelion (q) and mean heliocentric distances (a) of the S-asteroids. It is shown that these distributions are Λ-shaped, peaking at q ≈ 1.8 AU and a ≈ 2.2 AU. The wings of the distributions can be approximated by linear regressions. A comparison of the u – x color-index mean values for S-asteroids in the regions of the Earth and Mars and of the Main Belt prompts the conclusion that the last meteorite parent bodies in the vicinity of the orbits of the Earth and Mars come primarily from various regions of the asteroid Main Belt.

We model the reflectance spectra of SI–SVII-subtype asteroids. The spectra of minor planets contain little information as regards the abundance of free metal and the form of its existence on the asteroid surfaces. We investigate the properties of a set of probable spectra for the surface pyroxene and olivine of minor planets. Clinopyroxene with high calcium and iron contents and orthopyroxene with a ferrosilite molecular content of about 40% are typical of the S-type asteroids. The subtype number of S-type asteroids can be correlated with the bulk pyroxene composition. The forsterite molecular content in asteroid olivine lies within the probable range 40–74%. The prevalence of pyroxene over olivine and feldspar in the computed compositions of S-type asteroids suggests the probable presence of basalts on their surfaces.

A reflectance spectrum of A-asteroid 446 Aeternitas was numerically simulated. Probable mineral composition of the asteroid surface (Px > Ol ∼ Met) and probable spectra of these minerals were obtained. Since the grain size of asteroid regolith is unknown, a method for estimating the range of the chemical composition of olivine is proposed. According to the modeled spectra of the asteroid olivine, the probable range for the concentration of the forsterite molecule is from 40 to 56 mol %. No analogues of the material of A-asteroids were found among differentiated meteorites.

International audience; In this paper, we present arguments for the presence of optically active Ti 3+ in the structure of low iron pyroxenes to explain the strong 0.49-mum absorption band in spectra of E[II] asteroids. Such an interpretation supports the idea that E asteroid material is formed at high temperature in a strongly reducing medium. We also discuss the possibility of high temperature and hydrated rocks coexisting on some E asteroids. Our discussion is based on the idea of collisional evolution of aubrite parent bodies that was presented by Keil (1989).

The values of radio fluxes from some emitting areas were employed at wavelengths λ = 3.2cm and 8cm for 1969–1970 (Solar Activity Charts). 18 groups of spots were selected which were responsible for the longest series of radio observations. Flux differences ΔF i = F i( λ1) − F i(λ2) were composed for each spot group where F i( λ1) and F i( λ2) are radio fluxes at a wavelength of 3.2cm and 8cm respectively for the i-th spot group. Next, another set of differences Δ2Fi j = ΔF i ( t j + 1) − ΔFi(t j) was constructed where t j is the j - th moment of observation.. All subsequent calculations were carried out with Δ2Fi j values.