Polarization of the reflected light of asteroid 433 Eros

Linear polarizations measured for asteroid 433 Eros at various wavelengths and at solar phase angles ranging from 9° to 53° are presented. The polarization results are entirely typical of main-belt S asteroids, and indicate a dusty surface with geometric albedo 0.20. The derived effective diameter at photometric maximum is 21 km. Eros is quite uniform polarimetrically; no dependence on aspect is detected, and the polarization is shown to be constant during a single rotation with a precision of one part in forty.     

Polarization Models for Rayleigh Scattering Planetary Atmospheres

We present Monte Carlo simulations for the polarization of light reflected from planetary atmospheres. We investigate dependencies of intensity and polarization on three main parameters: single scattering albedo, optical depth of a scattering layer, and albedo of a Lambert surface underneath. The main scattering process considered is Rayleigh scattering, but isotropic scattering and enhanced forward scattering on haze particles are also investigated. We discuss disk integrated results for all phase angles and radial profiles of the limb polarization at opposition. These results are useful to interpret available limb polarization measurements of solar system planets and to predict the polarization of extra-solar planets as a preparation for VLT/SPHERE. Most favorable for a detection are planets with an optically thick Rayleigh-scattering layer. The limb polarization of Uranus and Neptune is especially sensitive to the vertically stratified methane mixing ratio. From limb polarization measurements constraints on the polarization at large phase angles can be set.     

Spectropolarimetry of comets Austin and Churyumov-Gerasimenko

Spectropolarimetric observations from 5000 to 8000 Å have been obtained for comets P/Austin (1982g) and P/Churyumov-Gerasimenko (1982f). The observations were spaced over phase angles of 50–125° for comet Austin and 10–40° for comet Churyumov-Gerasimenko. The use of spectropolarimetry allowed an evaluation of continuum polarization without molecular line contamination. Especially for comet Churyumov-Gerasimenko, the curve of polarization versus phase angle resembles curves for asteroids, where the polarization is negative (electric vector maximum parallel to the scattering plane) for phase angles less than 20° and the most negative polarization is from ?1 to ?2%. The negative polarization at backscattering angles may be due to multiple scattering in agglomerated grains, as assumed for asteroids, or to Mie scattering by small dielectric particles. If multiple scattering is important in comet dust, polarization measurements may imply a low albedo, less than 0.08. The polarization of comet Austin remained steady during a large change in the dust production rate. Both comets increased continuum flux by a factor of 2 near perihelion. The continuum of comet Churyumov-Gerasimenko had the shape of the solar spectrum with derivations less than 5%. The equivalent width of spectral features of C₂, NH₂, and O varied as r^?2.     

Positive branch of asteroid polarization: Observational data and computer modeling

Observations of near-Earth asteroids at large phase angles made it possible to obtain a more complete (for ground-based observations) phase dependence of the polarization of the E-type asteroids’ radiation including the maximum of the positive branch of the linear polarization degree. It is shown that the position of the polarization maximum of high-albedo asteroids is noticeably shifted to the decrease of phase angles compared with S-type asteroids. Model calculations of polarimetric properties of random Gaussian particles that simulate dust particles on the regolith surface are carried out. Model calculations show a qualitatively similar behavior pattern of parameters of the positive polarization branch. The influence of the refractive index of individual scattering particles on the size and position of the maximum of the positive branch of the linear polarization degree is investigated within the considered model.     

Photometry of Phoebe

Observatios of Phoebe (S9) in the V filter at small solar phase angles (0.2° to 1.2°) with the MIT SNAPSHOT CCD are presented. The value of Phoebe's sideral rotational period is refined to 9.282 ± 0.015hr. Assuming the Voyager-derived 110 km radius, Phoebe's observed mean opposition V magnitude of 16.176 ± 0.033 (extrapolated from small angles) corresponds to a geometric albedo of 0.084 ± 0.003. A strong opposition effect is indicated by the 0.180 ± 0.035 mag/deg solar phase coefficient observed at these small phase angles. The data are shown to be compatible with a phase function for C-type asteroids (K. Lumme and E. Bowell, 1981, Astron. J. 86, 1705–1721; K. Lumme, E. Bowell, and A. W. Harris, 1984, Bull. Amer. Astron. Soc. 16, 684), but give a poorer fit to the average asteroid phase relation of T. Gehrels and E.F. Tedesco (1979, Astron. J. 84, 1079–1087). Phoebe's rotational lightcurve in the V filter is roughly sinusoidal, with a 0.230-mag peak-to-peak amplitude and weaker higher order harmonics indicating primarily bimodal surface feature contrast. In addition to these photometric results, precise positions on 3 nights are given.     

UBV lightcurves of asteroid 433 Eros

UBV photometry and lightcurves of Eros were obtained on nine dates between October 1974 and March 1975. The absolute V magnitude at photometric maximum extrapolated to a solar phase angle of zero is 10.75 while the linear phase coefficient is 0.026mag deg^?1. The mean colors at solar phase angles greater than 30° are B?V = 0.92 and U?B = 0.52mag. No significant color variations over the surface were detected.     

A photometric study of Saturn and its rings

Intensity and polarization measures have been made of Saturn in the ultraviolet (0.37 μm) and green (0.57 μm) since 1968, at phase angles which ranged from 0°.0 to 6°.1. During this interval, the tilt of the planet's equatorial plane changed from 11°.2 to 26°.4, with the south pole toward the Earth.The polarization of the disk in the ultraviolet shows a strongly radial pattern at all observed phase angles, with a maximum of about 3.7 × 10^?2 at all limbs and a gradual decrease to nearly zero at the center. Where the rings overlap the disk, the better observations show their polarization to be small and in the direction of the equatorial plane.In green light and close to opposition the relatively small polarization of the disk appeared to be radial in 1968, but by 1973 polarization (still radial ) was detected only in the southern hemisphere. In all years the polarization appears to be strongest near the south pole, particularly when the pole is nearest the limb. When the pole is furthest from the limb (tilt = 26°), there is a suggestion that maximum polarization may occur at the pole itself. At large phase angles the polarization along the E-W diameter shows a prominent phase-dependent component of 1.0 × 10^?2 in a N-S direction.The intensity profiles in the ultraviolet suggest some transmission of light by ring A and less than about 20% by ring B. A limiting value of 39% was obtained from the polarization data.     

利用双行根数计算太阳相位角的精度评估

光度特性测量是获取空间目标的物理特性的重要技术手段之一,无论是光变曲线的事后分析还是建立光度变化的仿真模型,都离不开一个重要的参数——太阳相位角（太阳-空间目标-测站的空间夹角）.目前空间目标的位置通常是通过双行根数（TLE）外推获得,存在一定误差,且随外推时间的延长而变大,因而有必要对其计算所得的太阳相位角的精度进行评估.以典型的不同高度的激光测距卫星LAGEOS1、AJISAI、STELLA为研究对象,以全球激光测距资料解算所得的高精度轨道作为参考轨道,对2012年全年利用双行根数计算所得的太阳相位角数据进行了比对分析,结果表明对于LAGEOS1、AJISAI这样的中高轨卫星,由于轨道较高,表征阻力的B＊恒定,计算所得的太阳相位角偏差较小,角分量级,且随外推时间的延长不会导致偏差明显增大;而对于STELLA这样的低轨卫星,因轨道较低、受变化的大气的影响显著,计算所得的太阳相位角偏差较大,尤其是当B＊比较大、变化较快时,偏差显著变大,且随外推时间的延长显著增大,在最差情况下：外推1d约为13＇,外推3d约为50＇,外推7d约为251＇,已超出目前的精度要求.因此,在事后分析中应尽可能使用1d之内的TLE计算太阳相位角,对于B＊较大且变化较快情况尤其需要注意.另外,针对UTC闰秒的情况,提出了一种处理方法,即在双行根数外推时判断外推时段是否跨越了闰秒时刻,若跨越了则进行修正：增加或减少1s,相应地需要修改结果对应的时间戳计算方法.     

A Statistical Survey of Hard X-ray Spectral Characteristics of Solar Flares with Two Footpoints

The impulsive phase of the 23 July 2002 2B/X4.8 proton flare with a classical two-ribbon structure was observed with the Irkutsk Large Solar Vacuum Telescope (LSVT) in spectropolarimetric mode, with high spatial, spectral, and time resolution. On the basis of 49 spectrograms and 1200 spectral cuts across the flare ribbons, evidence for Hα line impact polarization has been obtained. A systematic change of the Stokes Q and U parameters has been detected across the ribbons for different flare regions measured with a scanning step of 0.85″. In the eastern side of the ribbons, the degree of polarization is 4 – 8%; its plane is oriented toward the solar disk center (radial direction). In the western side, the polarization degree runs up to 25%, and its plane is perpendicular to the disk center direction (tangential direction). A comparison of these results with hard X-ray data (RHESSI) allows us to conclude that high-energy electron beams reached the chromosphere during this flare. The observed changes of the direction of polarization and the vanishing polarization within the ribbons mean that, at the chromospheric level, the energy of electrons remaining in the beam is about 200 eV. A shift of the peak position of polarization relative to the intensity maximum in the ribbons may result from the inclination of the electron beam axis with respect to the solar surface.     

Polarization of comets at small phase angles

Comets Kopff (1982k) and Tempel 2 (1982d) were observed with a photopolarimeter. The observations spanned phase angles of 10-30° for Comet Kopff and of 45° for Comet Tempel 2. The Comet Kopff observations were near the phase angle where the position angle of the polarization switches from parallel to perpendicular to the scattering plane. The polarization showed no color dependence in the V, R, and I filters. The polarization of Comet Kopff as sa function of phase angle resembles polarization curves of asteroids. The minimum polarization was -1.5±0.1%. The data from Comet Kopff and four other comets were combined in a polarization versus phase-angle diagram. The coincidence of the data was remarkable. The collection of comet data determined a crossover phase angle of 22 ± 0° and a polarimetric slope of 0.34 ± 0.01% per degree. Mie models were unable to represent the group polarization curve, even though five parameters were varied over wide ranges. Assuming that multiple scattering provides the basis for the correlations between asteroid polarization and albedo, and that the multiple scattering process dominates the scattering from comet dust, the comet polarization implies an albedo. The two parameters of the comet polarization curve imply the same low albedo.     

Two Practical Methods for Coronal Intensity Determination

Determining the relative brightness of the solar corona is one of the most critical stages in solar eclipse studies. For this purpose, images taken with different exposures and polarization angles in white-light observations are used. The composite image of each polarization angle is produced by combining the images of different exposures. With the help of the intensity calibration function of these images, the relative intensity of the corona can be calculated. The total brightness of the solar corona is calculated using Stokes parameters obtained from intensity values of three polarization angles. In this study, two methods are presented: the first is used to obtain the intensity calibration function of the photographic material using calibration images, and the second is used to calculate the combined intensity values of images taken with different polarization angles.     

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.     

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.     

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.     

Venus: On the phase variation of CO2 line profiles

The shapes of Venus' CO₂ profiles are found to vary with solar phase angle. High-resolution spectra of the P16 and P14 lines in the 8689- and 7820-Å bands, respectively, are presented for phase angles ranging from 6 to 158°. The scattering mean free path at 80 mbar, approximately the effective pressure, is 1.7 km. Use of the van de Hulst similarity relations with simple, parametric scattering models is inadequare to separate effects due to the scattering phase function from those due to inhomogeneities in depth when one attempts to determine the atmospheric structure by fitting a family of such models over a wide range of phase angles.     

Possible application of circular polarization for remote sensing of cosmic bodies

Phase dependences of circular polarization were obtained with a precision Stokes polarimeter designed and constructed at the Main Astronomical Observatory of AS Ukraine. A study was made of dielectric and metallic powders with grains of diameter 10–100 m. Metallic powders were found to produce an essential circular polarization - up to 3%, just as dielectric powders did not show circular polarization values more than 0.05% Change of circular polarization with phase angle V is greatly depended on surface structure. Loose powders give phase curves with the same sign of circular polarization everywhere and with maximum at large phase angles V > 120 . Measurements of compacted powders show curves which change the sign repeatedly and have additional maxima, including a maximum at small phase angles V < 40 . A theory was created which considers a circular polarization as a result of multiple reflections of light from particulate surface. The theory provides reasonable good fit to the experimental data. It was concluded that measurements of circular polarization can be used to find metals in surface material of cosmic bodies (especially asteroids) and to determine characteristics of surface structure, in particular, to establish presence of regolith on metal-rich bodies.     

554 Peraga—an asteroid with unusual polarization properties?

This paper presents the results of polarization observations of asteroid 554 Peraga obtained with the UBVRI polarimeter using the 1.25 m telescope of the Crimean Astrophysical Observatory down to phase angles of 3.1°–16.6° from October to November 2006. The asteroid’s polarization phase curve is shown to have a negative branch with the parameters P _min = −1.7% and α_min = 8.4°, which is typical of C-type asteroids. However, these data contradict the results of Zellner and Gradie (1976) obtained in March 1975 that the reflected light from the asteroid’s surface is positively polarized, ≈1% at phase angles of 8°–10°. Since the asteroid’s ecliptic longitudes differ by 160°-145° for the two observation periods, we discuss the possibility that the two sets of observations refer to the asteroid’s two hemispheres with different polarimetric properties.     

On the cause of the discrepancy between groundbased and spaceborne lightcurves of Ganymede and Callisto in the <Emphasis Type="Italic">V</Emphasis> band

Properties of the surfaces of Jupiter’s satellites—Ganymede and Callisto—are shortly described. Their images acquired in space missions are shown. Causes of the discrepancy between orbital lightcurves of the satellites obtained from the earth and spaceborne maps of the satellites are considered. The groundbased observations were carried out under phase angles of solar illumination ranging from 0° to 12°, and the maps were built from images acquired from spacecraft in a wide interval of solar phase angles. We suggest that the main cause of the discrepancies between the lightcurves is the coherent backscattering effect observed only at small phase angles of the sun.