Three-dimensional numerical modeling of refraction and reflection scattering from icy galilean satellites

Radar scattering from the icy galilean satellites is marked by unusually high backscatter cross sections and polarization ratios at wavelengths λ₀=3.5-70 cm. The persistence of exotic scattering behavior over this large a wavelength range suggests that the responsible mechanisms remain at least partially effective as the wavelength approaches or exceeds the size of individual scatterers. We examine two models previously analyzed in the geometrical optics limit—radar glory from buried craters (Eshleman, 1986, Science 234, 587-590) and refraction scattering from subsurface lenses (Hagfors et al., 1985, Nature 315, 637-640)—at wavelength scales using three-dimensional finite-difference time-domain (FDTD) numerical simulations. We include craters with rough walls and lenses with random inclusions of heterogeneous material. For hemispherical craters spanning up to 3λ₀ in diameter, we observe none of the exotic backscatter behavior attributed to the geometrical optics models. Nonspherical refraction scatterers can produce circular polarization ratios μ_C>1 and linear polarization ratios μ_L=0.5-0.8 at diameters as small as ∼λ₀, but the density of such inclusions must be high if refraction scattering alone is to account for the measured cross sections.     

Optical reflectance polarimetry of Saturn globe and rings I. Measurements on B ring

The light reflected by the Saturn ring B acquires a polarization which varies with phase angle, wavelength, and position on the rings. This polarization results from the combined effects of two components P₀ and T. The component P₀ keeps its azimuth always parallel to the scattering plane and its amount varies with phase angle and wavelength, as for direct reflection at the surface of solid bodies. The polarization T has its azimuth all around the ring either parallel or perpendicular to the radius vector; unexpectedly its amount varies with time, often significantly in a few days in ways which are not predictable.     

Systematic variations of interstellar linear polarization and growth of dust grains

The observed relation between the interstellar linear polarization curve parameters K and λ _max characterizing the width and the wavelength of the polarization maximum, respectively, is interpreted quantitatively. We have considered 57 stars located in four dark clouds with evidence of star formation: in Taurus, Chamaeleon, around the stars ρ Oph and R CrA. In our modeling we have used the spheroidal dust grain model applied previously to simultaneously interpret the interstellar extinction and polarization curves in a wide wavelength range. The observed trend K ≈ 1.7λ _max is shown to be most likely related to the growth of dust grains due to coagulation rather than accretion. The relationship of the interstellar polarization curve parameters K and λ _max to the mean dust grain size is discussed.     

Radar measurements of Mercury’s north pole at 70 cm wavelength

We present radar imaging of Mercury using the Arecibo Observatory’s 70-cm wavelength radar system during the inferior conjunction of July 1999. At that time the sub-Earth latitude was ∼11°N and the highly reflective region at Mercury’s north pole that was first identified in radar images at the shorter wavelengths of 3.6 cm [Slade, M.A., Butler, B.J., Muhleman, D.O., 1992. Science 258, 635-640] and 13 cm [Harmon, J.K., Slade, M.A., 1992. Science 258, 640-643] was again clearly detected. The reflectivity averaged over a 75,000 km² region including the pole is similar to that measured at the other wavelengths over a comparable area, and the 70 cm circular polarization ratio of μ_C∼0.87 is possibly slightly lower. If this strong backscattering results from volume scattering in low absorption layers, the persistence of this effect over more than an order of magnitude change in wavelength scale has implications for the depth and thickness of the deposits responsible. The resolution of the radar maps at this wavelength is not sufficient to resolve individual craters, nor to discern features at other latitudes, but the planet’s total reflectivity is consistent with previous work and the scattering function suggests a surface roughness at this wavelength similar to the lunar highlands.     

Modeling the linear polarization of optical emission from red giants

We present the results of solving the radiative transfer equation for the Stokes vector in the case of light scattering by spherical forsterite dust particles in an axisymmetric circumstellar envelope of a red giant. We have assumed that the surfaces of constant scattering-particle density are prolate or oblate spheroids, the particle density decreases with radius as N _d ∝ r ⁻², and the dust particles at the inner boundary of the envelope are in thermal equilibrium with the stellar emission at solid-phase evaporation temperature T _ev = 800 K. In the wavelength range 0.27 μm ≤ λ ≤ 1 μm, particles with radii 0.03 μm ≲ a ≲ 0.2 μm make a major contribution to the linear polarization of the stellar emission. The increase in scattering efficiency factor with decreasing wavelength λ is mainly responsible for the growth of polarization toward the short wavelengths known from observations. However, at a mean number of scatterings 1.2 ≤ N _sca ≤ 1.6, the polarization ceases to grow due to depolarization effects and decreases rapidly as the wavelength decreases further. The wavelength of the polarization maximum is determined mainly by two quantities: the particle radius and the mass loss rate. The upper limits for the degree of linear polarization in the case of light scattering in circumstellar dust envelopes with the geometries of prolate and oblate spheroids are p ≈ 3 and 5%, respectively. The polarization for light scattering by enstatite particles is higher than that for light scattering by forsterite particles approximately by 0.3%. Original Russian Text ? Yu.A. Fadeyev, 2007, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2007, Vol. 33, No. 2, pp. 123–133.     

Long slit spectropolarimetry of Jupiter and Saturn

We present ground-based limb polarization measurements of Jupiter and Saturn consisting of full disk imaging polarimetry for the wavelength 7300 Å and spatially resolved (long-slit) spectropolarimetry covering the wavelength range 5200-9350 Å.For the polar region of Jupiter we find for λ = 6000 Å a very strong radial (perpendicular to the limb) fractional polarization with a seeing corrected maximum of about +11.5% in the South and +10.0% in the North. This indicates that the polarizing haze layer is thicker at the South pole. The polar haze layers extend down to 58° in latitude. The derived polarization values are much higher than reported in previous studies because of the better spatial resolution of our data and an appropriate consideration of the atmospheric seeing. Model calculations demonstrate that the high limb polarization can be explained by strongly polarizing (p ≈ 1.0), high albedo (ω ≈ 0.98) haze particles with a scattering asymmetry parameter of g ≈ 0.6 as expected for aggregate particles of the type described by West and Smith (West, R.A., Smith, P.H. [1991]. Icarus 90, 330-333). The deduced particle parameters are distinctively different when compared to lower latitude regions.The spectropolarimetry of Jupiter shows a decrease in the polar limb polarization towards longer wavelengths and a significantly enhanced polarization in strong methane bands when compared to the adjacent continuum. This is a natural outcome for a highly polarizing haze layer above an atmosphere where multiple scatterings are suppressed in absorption bands. For lower latitudes the fractional polarization is small, negative, and it depends only little on wavelength except for the strong CH₄-band at 8870 Å.The South pole of Saturn shows a lower polarization (p ≈ 1.0-1.5%) than the poles of Jupiter. The spectropolarimetric signal for Saturn decrease rapidly with wavelength and shows no significant enhancements in the fractional polarization in the absorption bands. These properties can be explained by a vertically extended stratospheric haze region composed of small particles <100 nm as suggested previously by Karkoschka and Tomasko (Karkoschka, E., Tomasko, M. [2005]. Icarus 179, 195-221).In addition we find in the V- and R-band a previously not observed strong polarization feature (p = 1.5-2.0%) near the equator of Saturn. The origin of this polarization signal is unclear but it could be related to a seasonal effect.Finally we discuss the potential of ground-based limb polarization measurements for the investigation of the scattering particles in the atmospheres of Jupiter and Saturn.     

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.     

Polarimetry of main belt asteroids: Wavelength dependence

New UBVRI polarimetric observations of ten asteroids, including space mission targets 1 Ceres and 21 Lutetia, are presented. These observations were obtained with the 1.25-m telescope of the Crimean Astrophysical Observatory and have been used to study the wavelength dependence of polarization for a sample of asteroids belonging to the M and low albedo classes. A more general analysis including also a larger data set of UBVRI polarimetric observations available in the literature for more than 50 main belt asteroids belonging to different taxonomic classes shows that the variation of the polarization degree Pr as a function of wavelength is generally well described by a linear trend. It typically does not exceed 0.2% in the studied spectral range 0.37-0.83 microns and tends to increase for increasing phase angle. Asteroids belonging to the S and M classes are found to exhibit a deeper negative branch and smaller positive polarization for increasing wavelength (negative sign of the slope of ΔPr/Δλ). Since the objects belonging to these classes are known to exhibit reddish reflectance spectra, the observed wavelength behavior of negative polarization contradicts the well-known inverse correlation of Pmin and albedo. Low albedo asteroids show larger dispersion of spectral slopes, but the overall trend is characterized by a shallower negative branch and a larger positive polarization for increasing wavelength (positive sign of the slope of ΔPr/Δλ). A few exceptions from this general trend are discussed. The observed variety in the wavelength dependence of asteroid polarization seems to be mainly attributed to surface composition.     

Interstellar polarization: New approximation

A new, physically valid, approximation of the wavelength dependences of the degree of linear interstellar polarization P _λ observed in a wavelength range from 0.2 to 4 μm is suggested. The data obtained from the ground-based observations and the HPOL and WUPPE space missions on P _λ of 104 stars located in a galactic latitude range B from ?20° to +20° are used. This approximation provides better agreement with the observational P _λ data than the models by Serkowski (1973) and Whittet et al. (1992) proposed before.     

On the surface composition of Io

The wavelength dependence of the reflectivity of Io indicates the presence of two materials on the surface of this satellite of Jupiter. These materials are sulfur and an unspecified material (R₁) which shows a wavelength dependence of its reflectivity for 0.3 μm < λ < 1.0 μm similar to the non-H₂O frost spectrum of the rings of Saturn. A 60/40 admixture of these two spectra matches the observed reflection spectrum of Io from 0.3μm–3 μm, if the spectrum of R₁ is featureless for λ > 1 μm. Sulfur will give rise to a posteclipse brightening. The variation with wavelength of the temperature dependence of the reflectivity of sulfur will allow an observational confirmation of the presence of sulfur on Io. The material R₁ should show a large geometrical albedo. The translucency of sulfur is consistent with the polarization-phase curve to Io. The material R₁ is also required to be translucent. The thermal conductivity of a cooled sulfur powder under vacuum was measured and found to agree with the value determined for the upper layer of Io from observations at 10 μm. It is shown that this agreement is not necessarily meaningful.     

On Errors in Constructing the Polarization Phase Dependences for Solar System Bodies

In astrophysical studies of Solar System bodies, the measured values of the linear polarization degree P_obs and the position angle of the polarization plane θ are usually considered relative to the plane orthogonal to the scattering plane; and the resulting quantities are designated as P_r and θ_r, respectively. Parameters of the phase curve of polarization P_r = f(α) serve for determining the physical characteristics of grains composing the regolith surfaces of such bodies as, for example, the Moon, Mercury, asteroids, and planetary satellites, or the polydisperse media, such as cometary comae and tails. In this paper it has been shown that the error in the polarization degree grows \({\sigma _{{P_r}}}\) due to the error \({\sigma _{{\theta _{obs}}}}\) in determining the position angle. The interrelations between these errors were obtained, and the conditions, under which the values of the linear polarization degree P_r relative to the orthogonal system can be used to analyze the phase dependences of polarization, were formulated.     

Radar observations of asteroid 1 Ceres

Radar observations of asteroid 1 Ceres were made at a 12.6-cm wavelength from the Arecibo Observatory in March/April 1977. The measurements, made with a received circular polarization orthogonal to that transmitted, yield a radar cross section of (0.04 ± 0.01)πR², for R = 510 km. The corresponding radar reflectivity is less than that measured for any other celestial body. Within the accuracy of measurement, no significant variation of cross section with rotational phase is apparent. The shape of the power spectrum suggests that Ceres is rougher at the scale of the observing wavelength than the Moon and inner planets, but smoother than the outer three Galilean satellites.     

The Umov effect for single irregularly shaped particles with sizes comparable with wavelength

The Umov effect manifests itself as an inverse correlation between the linear polarization maximum of an object’s scattered light P_max and its geometric albedo A. This effect is observed for the Moon, Mercury and Mars, and there are data suggesting this effect is valid for asteroids. The Umov effect is due to the contribution of interparticle multiple scattering that increases albedo and decreases polarization. We here study if the Umov effect can be extended to the case of single irregularly shaped particles with sizes comparable with the wavelength. This, in particular, is important for cometary dust polarimetry. We show the Umov effect being valid for weakly absorbing irregular particles (Im(m) ? 0.02) almost through the entire range of size parameters x considered. Highly absorbing particles (Im(m) > 0.02) follow the Umov effect only if x exceeds 14. In the case of weakly absorbing particles, the inverse correlation is essentially non-linear, which is caused by the contribution of particles with small x. However, averaging over many different types of irregularly shaped particles could make it significantly more linear. The size averaging does not change qualitatively the diagram log(P_max)-log(A) for weakly absorbing particles. For single irregular particles whose sizes are comparable with wavelength, there is no reliable correlation between the slope of the polarization curve h near the inversion phase angle and geometric albedo A. Using the extended Umov Law, we estimate the geometric albedo of dust particles forming cometary circumnuclear haloes A = 0.1 − 0.2, which is a few times larger than the average geometric albedo over the entire comae. Note that, using the obtained values for A of cometary particles, one can derive their number density in circumnuclear haloes from photometric observations.     

The optical properties of Venus and the Jovian planets I. The atmosphere of Jupiter according to polarimetric observations

Results are given for polarization measurements of both the entire Jupiter disk and its centre for seven wavelength regions in the 0.373–0.800 μm range. Interpretation of these observations is based on two model atmospheres: (A) The cloud layer particles and molecules are mixed with a constant ratio. (B) A gas layer with small optical thickness, τ₀, is situated above the cloud layer which consists of aerosol particles. The aerosol particles are considered to be non-absorbing spheres, their size distribution being normal Gaussian. The index of refraction for the particles is considered to be independent of wavelength in the above spectral range. An approximate method is used for the determination of parameters of the Jovian atmosphere. This method was tested by evaluation of the parameters for the Venus cloud layer: The refractive index was found to be n = 1.435 ± 0.015, the square of the logarithmic dispersion of the radius of particles σ² = 0.12 and the mean geometrical radius of particles r₀ = 0.74 μm which agree well with exact values given by Hansen and Arking (1971). For the atmosphere of Jupiter it was found: n = 1.36 ± 0.01, σ² ? 0.3, r₀ ? 0.2 μm. This refractive index for the particles agrees well with the ammonia cloud layer hypothesis.     

Transmission of light by slit designed for astronomical spectrograph

The paper discusses an investigation of linear polarization produced by the transmission of light through an astronomical spectrograph slit. An experimental apparatus was designed and set up to carry out this work. The parallel beam of plane polarized light was rotated in the measuring system, by optically active of half-wave plate. The intensity of normally incident of polarized light of wavelength 0.436 μm transmitted by various slit was measured as a function of slit width. The results indicate:

1. That the degree of polarization increased as thedepth of the narrow slit was increased.
2. That the degree of polarization increased as thewidth of the narrow slit was decreased.
3. That when the width of slit was widened the degree of polarization tended to approach a constant value asymptotically.
4. That the theoretical calculation of Slater (1942) predicts the measured experimental values more accurately than Thiessen (1947) and Jones and Richards (1954).

It is shown that the existence and order of magnitude of all these effects may be predicted from the propagation losses of the electromagnetic theory of light in metallic wave guide. The paper brings out the salient points related to the degree of polarization of light by a dielectric slit of finite depth. The polarization effects from one such slit have been investigated and the results were compared with those for metallic slits.     

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.     

The polarization of optical radiation from the magnetic white dwarfs

It is pointed out that, because of the large Faraday rotation an outlet of linear polarization from the photosphere of a white dwarf is hampered. In accordance with this fact it is proposed to distinguish two types of magnetic white dwarfs. The first type (its representative is Grw 70°8247) has a linear polarization which is comparable in magnitude with the circular one. Polarization of radiation from the white dwarfs of the first type cannot arise in the photosphere. It arises in the corona of the star either as a result of cyclotron emission of hot electrons (T～10⁶ K) or as a result of scattering of slightly polarized emission from the photosphere in the corona. For the first type dwarfs such magnetic fields are required thatω _B ω_opt, i.e.B(1?3)×10⁸G. The white dwarfs of the second type (its representative is G 99-37) have their linear polarization much smaller than the circular one. Polarization of these white dwarfs can arise as a result of the transfer of radiation in the nonisothermal photosphere. Magnetic fields required for the second type can be much smaller:B cos γ=(1?10)×10⁶ G. It is shown that the photospheric model allows to obtain the quantitative accordance of the theory with all the observational data for G 99-37 and is not in accordance with the data for Grw 70°8247, at the same time the model with cyclotron emission from the corona explains the magnitude of both linear and circular polarization and their wavelength dependence for Grw 70°8247.     

More evidence for an oscillation superimposed on the Hubble flow

In a recent investigation evidence was presented for a low-level sinusoidal oscillation superimposed on top of the Hubble flow. This oscillation was in V _CMB , in a sample of type Ia Supernovae sources with accurate distances, and it was found to have a wavelength close to 40 Mpc. It became easily visible after the removal of several previously identified discrete velocity components. Its amplitude like that of the Hubble velocity showed an increase with distance, as would be expected for a constant-amplitude space oscillation. Here we report that this oscillation is also present in distance clumping in these sources, with the same wavelength, but in phase quadrature. The discrete velocity components do not play a role in detecting the distance clumping wavelength. Assuming that time proceeds from high cosmological redshift to low, the blue-shifted velocity peaks, which represent the contraction stage of the velocity oscillation, then lead the density peaks. With the discrete velocity components removed we also find evidence for at least one other, weaker velocity oscillation. It is found to have a wavelength similar to one reported in density clumping by previous investigators. In those cases the source samples were much larger.     

The circular polarization of sources of synchrotron radiation

The degree of circular polarizationp _c is calculated for two models of a source of synchrotron radiation:

1. A source with an inhomogeneous magnetic field and isotropic angular distribution of the electrons with respect to the magnetic field;
2. A source with a homogeneous magnetic field and anisotropic angular distribution of the electrons in which the anisotropy of angular distribution substantially increases with the electron energy.

The first model can be used to describe extended radio-sources; and the second, to describe compact radio-sources. For those sources, whose observed polarization properties correspond to the first model, we obtain an integral equation which connects the observed distribution of the sources with the extent of their linear and circular polarization (p _l andp _c ) and the unknown distribution of the sources over the strengthB and the degree of homogeneity ?=(B ₀/B)² of the magnetic field;B ₀ is a homogenous field,B ₀?B. A solution of the integral equation obtained is found for a particular case. This solution makes it possible to determine the distribution of different types of sources over ? if the distribution of these sources in the extent of linear polarization is known. The formulae obtained make it possible to indicate which sources with a known degree of linear polarization should be expected to exhibit highest circular polarization. In the discussion of the first model the question is raised as to the information one can get about the magnetic field by using observations of both linear and circular polarization for a separate source, and for a number of sources. It is shown that the determination of the most probable values ofB and ? in a separate source based on the known values ofp _l andp _c for the source, is possible only if one knows the distribution overB and ? of the sources of the type to which the source in question belongs. The observational data now available make it possible to find the distribution of the sources only over ?. Since the distribution overB and ? is at present unknown, even a very strong upper limit forp _c in the case of a separate source does not enable us to give an exact upper limit for the strength of the magnetic field in this source. In the first model the upper limit for the magnetic field can be obtained only if the upper limit ofp _c is known for a certain number of sourcesN, withN?1. This limit allows for much stronger fields than are usually admitted. This last fact should be taken into consideration when one deals with the results of observations of circular polarization in sources with strong magnetic fields. The first model presents some difficulties when we compare it with observations of some compact sources. The second model can explain why one observes in these sources a violation of the lawp _c ～v ^?1/2 and a change of sign inp _c when the frequency of the observationsv changes.