The amplitude of the coherent backscattering intensity peak for discrete random media: Effect of packing density

The amplitude of the coherent backscattering intensity peak is computed for a medium composed of densely packed, randomly positioned particles. The cyclical component of the Stokes reflection matrix at exactly the backscattering direction is expressed in terms of the ladder component, and the ladder component is rigorously computed by numerically solving the vector radiative transfer equation. The effect of packing density is accounted for by multiplying the single-scattering Mueller matrix by the static structure factor computed in the Percus-Yevick approximation. It is shown that increasing packing density can substantially reduce the amplitude of the copolarized coherent backscattering peak, especially for smaller particles, and can make it significantly lower than 2. The effect of packing density on the amplitude of the cross-polarized peak is significantly weaker.     

The SMART-1 AMIE experiment: implication to the lunar opposition effect

The lunar surface reveals a sharp opposition effect, which is to be explained by the shadowing and coherent backscattering mechanisms. Generalizing the radiative transfer theory via Monte Carlo methods, we are carrying out studies of backscattering in regolith-like scattering media. We have also started systematic laboratory measurements of structural simulators of lunar regolith. The SMART-1 AMIE and D-CIXS/XSM experiments provide us a unique opportunity for a simultaneous multiwavelength study of the lunar regolith close to opposition, since the SMART-1 spacecraft will pass over several different types of lunar surface at zero phase angles. Results of our theoretical and laboratory investigations can be used as a basis to interpret the SMART-1 AMIE and D-CIXS/XSM experiments. In particular, it seems to be possible to estimate regional variations of regolith particle volume fraction and their size. A short review of observational, experimental and theoretical works is also presented here.     

Implications of modified AGN spectra due to absorption by infrared photons

Recent observations of high energy photons from active galactic nuclei (AGN) have lead to a renewed interest in the effect of gamma-ray cascading in background radiation fields. In recent years, numerous authors have explored possible modifications to the observed high energy photon spectra from AGN due to propagation through such fields. This paper will re-examine a number of these issues. The major conclusions of this paper are: (1) The reaction γ + γ → e⁺ + e⁻ provides a highly sensitive probe of background infrared (IR) fields. However little can be inferred about the specific nature of the IR background or the effect on spectra from more distant AGN from a study of nearby sources alone. Currently, only upper limits to the background IR density can be established. (2) The contribution of secondary photons from pair-cascading off of background microwave and infrared radiation is most likely unobservable in the regime of 1 TeV unless the strength of extragalactic magnetic fields are much less than 10⁻¹³ G and the inherent source spectra continue to much higher energies. The possible contribution from this process may be conclusively ruled out through further spectral measurements of AGN in the TeV regime during high and low states. (3) There is little hope of unambiguously extracting the values of either the Hubble constant or Ω from γ-γ attenuation measurements. (4) The sensitivity of the attenuation to the density of the background IR produced prior to the epoch of the observed source suggests a future possibility to probe directly the evolution of the background IR radiation through multiple source observations.     

Polarization characteristics of the coherent backscatter opposition effect

It has been suggested recently that coherent backscattering of photons from discrete disordered media, which has been recently discovered in laboratory-controlled experiments, may play a role in peculiar radar and light scattering from some atmosphereless solar system bodies. In this paper, a rigorous vector theory recently developed by Mishchenko (1991b, 1992a) is used to study polarization characteristics of the coherent backscatter opposition effect. Backscattering enhancement in different polarization components is studied and results of computer calculations for a representative selection of scattering models are presented. It is pointed out that these calculations support recent Hapke's (1990) explanation of unusual radar characteristics of icy outer planet satellites.     

Viking orbiter observations of the Mars opposition effect

The Viking Extended Mission has experienced two major dust storms that have changed the global photometric properties of Mars. Large quantities of atmospheric dust arising from the June 5, 1977, storm have been observed at very low phase angles to measure the opposition effect. These particles yield only a small increase in brightness at 0° phase angle with the least enhancement seen in violet light. The phase function is well modeled by nonspherical particles with a spectrally dependent single scattering albedo. It is doubtful, therefore, that atmospheric dust plays a significant role in the reported blue light brightness surge. Such particles as surface structure combined with a lunar photometric function could, however, produce the wavelength-dependent backscattering observed during the 1967 and 1969 oppositions under clearer conditions.     

Simultaneous creation of electron-positron pairs and photons due to their interaction in Robertson-Walker universes

The influence of the electromagnetic interaction upon particle creation in expanding Robertson-Walker universes is investigated applying an S-matrix scheme. We discuss all processes contributing to the number density of created particles up to second order in the coupling constant. One process is of particular importance being the only source of photons. It is considered in more detail and evaluated explicitly for a time-symmetrically expanding radiation-dominated Friedman universe as well as statically bounded expansions.     

The angular width of the coherent back-scatter opposition effect: An application to icy outer planet satellites

It has been suggested recently that coherent back-scattering of light from powder-like regolithic surfaces can explain remarkable opposition brightening of some atmosphereless solar system bodies. In this paper, a dense-medium light-scattering theory is used to calculate the half-width at half-maximum (HWHM) of the coherent back-scattering peak for a number of scattering models. We demonstrate that HWHM strongly depends on the optical properties of the scattering medium and can serve as a critical test in comparing alternative models. It is shown that coherent back-scaterring may be a likely explanation of the opposition effect exhibited by icy outer planet satellites.     

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.     

The opposition effect in the outer Solar system: A comparative study of the phase function morphology

In this paper, we characterize the morphology of the disk-integrated phase functions of satellites and rings around the giant planets of our solar system. We find that the shape of the phase function is accurately represented by a logarithmic model [Bobrov, M.S., 1970. Physical properties of Saturn's rings. In: Dollfus, A. (Ed.), Surfaces and Interiors of Planets and Satellites. Academic, New York, pp. 376-461]. For practical purposes, we also parametrize the phase curves by a linear-exponential model [Kaasalainen, S., Muinonen, K., Piironen, J., 2001. Comparative study on opposition effect of icy solar system objects. Journal of Quantitative Spectroscopy and Radiative Transfer 70, 529-543] and a simple linear-by-parts model [Lumme, K., Irvine, W.M., 1976. Photometry of Saturn's rings. Astronomical Journal 81, 865-893], which provides three morphological parameters: the amplitude A and the half-width at half-maximum (HWHM) of the opposition surge, and the slope S of the linear part of the phase function at larger phase angles.Our analysis demonstrates that all of these morphological parameters are correlated with the single-scattering albedos of the surfaces.By taking more accurately into consideration the finite angular size of the Sun, we find that the Galilean, Saturnian, Uranian and Neptunian satellites have similar HWHMs (?0.5^°), whereas they have a wide range of amplitudes A. The Moon has the largest HWHM (∼2^°). We interpret that as a consequence of the “solar size bias”, via the finite angular size of the Sun which varies dramatically from the Earth to Neptune. By applying a new method that attempts to morphologically deconvolve the phase function to the solar angular size, we find that icy and young surfaces, with active resurfacing, have the smallest values of A and HWHM, whereas dark objects (and perhaps older surfaces) such as the Moon, Nereid and Saturn's C ring have the largest A and HWHM.Comparison between multiple objects also shows that solar system objects belonging to the same planet have comparable opposition surges. This can be interpreted as a “planetary environmental effect” that acts to locally modify the regolith and the surface properties of objects which are in the same environment.     

Shadow mechanism and the opposition effect of brightness of atmosphereless celestial bodies

We consider the Irvine-Yanovistkii modification of the shadow model developed by Hapke for the opposition effect of brightness. The relation between the single scattering albedo ω and the transparency coefficient of particles κ is suggested to be used in the form κ = (1 ? ω) ⁿ , which allows the number of unknowns in the model to be reduced to two parameters (the packing density of particles g and ω) and the single-scattering phase function χ(α). The analysis of spectrophotometric measurements of the moon and Mars showed that the data on the observed opposition effect and the changes in the color index with the phase angle α well agree if the values of n = 0.25 and g = 0.4 (the moon) and 0.6 (Mars) are assumed in calculations. When being applied to asteroids of several types, this method also yielded a satisfactory agreement. For the E-type asteroids, the sets of parameters are [g = 0.6, ω = 0.6, A _g = 0.21, and q = 0.83] or [g = 0.3, ω = 0.4, A _g = 0.15, and q = 0.71] under the Martian single-scattering phase function; for the M-type asteroids, it is [g = 0.4, ω ≤ 0.1, A _g ≤ 0.075, and q ≤ 0.42] under the lunar single-scattering phase function; for the S-type asteroids, it is [g = 0.4, ω = 0.4, A _g = 0.28, and q = 0.49] under the lunar single-scattering phase function; and for the C-type asteroids, it is [g = 0.6, ω ≤ 0.1, A _g ≤ 0.075, and q = 0.43] under the modified lunar single-scattering phase function. The polarization measurements fulfilled by Gehrels et al. (1964) for the bright feature on the lunar surface, Copernicus (L = -20°08′, φ = +10°11′), at a phase angle α = 1.6° revealed the deviations in the position of the polarization plane from that typical for the negative branch. They were 22° and 12° in the G and I filters, respectively. At the same time, the deviation was within the error (±3°) in the U filter and for the dark feature Plato (L = -10°32′, φ = +51°25′), which can be caused by the coherent mechanism of the formation of the polarization peak.     

The reflectivity spectrum and opposition effect of Titan's surface observed by Huygens' DISR spectrometers

We determined Titan's reflectivity spectrum near the Huygens' landing site from observations taken with the Descent Imager/Spectral Radiometer below 500 m altitude, in particular the downward-looking photometer and spectrometers. We distinguish signal coming from illumination by sunlight and the lamp onboard Huygens based on their different spectral signatures. For the sunlight data before landing, we find that spatial variations of Titan's reflectivity were only ～0.8%, aside from the phase angle dependence, indicating that the probed area within ～100 m of the landing site was very homogeneous. Only the very last spectrum taken before landing gave a 3% brighter reflectivity, which probably was caused by one bright cobble inside its footprint. The contrast of the cobble was higher at 900 nm wavelength than at 600 nm.For the data from lamp illumination, we confirm that the phase function of Titan's surface displays a strong opposition effect as found by Schröder and Keller (2009. Planetary and Space Science 57, 1963–1974). We extend the phase function to even smaller phase angles (0.02°), which are among the smallest phase angles observed in the solar system. We also confirm the reflectivity spectrum of the dark terrain near the Huygens' landing site between 900 and 1600 nm wavelength by Schröder and Keller (2008. Planetary and Space Science 56, 753–769), but extend the spectrum down to 435 nm wavelength. The reflectivity at zero phase angle peaks at 0.45±0.06 around 750 nm wavelength and drops down to roughly 0.2 at both spectral ends. Our reflectivity of 0.45 is much higher than all previously reported values because our observations probe lower phase angles than others. The spectrum is very smooth except for a known absorption feature longward of 1350 nm. We did not detect any significant variation of the spectral shape along the slit for exposures after landing, probing a 25×4 cm² area. However, the recorded spectral shape was slightly different for exposures before and after landing. This difference is similar to the spectral differences seen on scales of kilometers (Keller et al., 2008. Planetary and Space Science 56, 728–752), indicating that most observations may probe spatially variable contributions from two basic materials, such as a dark soil partially covered by bright cobbles.We used the methane absorption features to constrain the methane mixing ratio near the surface to 5.0±0.3%, in agreement with the 4.92±0.24% value measured in situ by Niemann et al. (2005. Nature 438, 779–784), but smaller than their revised value of 5.65±0.18% (Niemann et al., 2010. Journal of Geophysical Research 115, E12006). Our results were made possible by an in depth review of the calibration of the spectroscopic and photometric data.     

The effect of weak lensing on the angular correlation function of faint galaxies

The angular correlation function ο(θ) of faint galaxies is affected both by non-linear gravitational evolution and by magnification bias resulting from gravitational lensing. We compute the resulting ο(θ) for different cosmological models and show how its shape and redshift evolution depend on Ω and Λ. For galaxies at redshift greater than 1 ( R magnitude fainter than about 24), magnification bias can significantly enhance or suppress ο(θ), depending on the slope of the number–magnitude relation. We show, for example, how it changes the ratio of ο(θ) for two galaxy samples with different number count slopes.     

The effect of finite electrical conductivity on the angular-momentum loss of the sun due to the solar wind

In general the solutions to the azimuthal equations of motion of the solar wind possess a singularity at the radial Alfvénic critical point if the fluid is non-viscous and has an infinite electrical conductivity. This singularity can only be removed by a proper choice of boundary conditions. If a plasma with a large but finite conductivity is considered, the singularity is removed in the mathematical sense. However, it is shown that for this latter case the actual solution does not differ significantly from the former model and that the boundary condition is still determined from the behavior of the solution at or near the Alfvénic critical point.Kitt Peak National Observatory Contribution No. 411.Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Cooling of quark stars in the colour superconductive phase: effect of photons from glueball decay

The cooling history of a quark star in the colour superconductive phase is investigated. Here we specifically focus on the two-flavour colour (2SC) phase where the novel process of photon generation via glueball (GLB) decay has already been investigated. The picture we present here can, in principle, be generalized to quark stars entering a superconductive phase where similar photon generation mechanisms are at play. As much as 10⁴⁵–10⁴⁷ erg of energy is provided by the GLB decay in the 2SC phase. The generated photons slowly diffuse out of the quark star, keeping it hot and radiating as a blackbody (with possibly a Wien spectrum in gamma-rays) for millions of years. We discuss hot radio-quiet isolated neutron stars in our picture (such as RX J185635–3754 and RX J0720.4–3125) and argue that their nearly blackbody spectra (with a few broad features) and their remarkably tiny hydrogen atmosphere are indications that these might be quark stars in the colour superconductive phase where some sort of photon generation mechanism (reminiscent of the GLB decay) has taken place. Fits to observed data of cooling compact stars favour models with superconductive gaps of  Δ_2SC∼ 15–35 MeV  and densities  ρ_2SC= (2.5–3.0) ×ρ_N  (ρ_N being the nuclear matter saturation density) for quark matter in the 2SC phase. If correct, our model combined with more observations of isolated compact stars could provide vital information to studies of quark matter and its exotic phases.     

Photometry of Saturn's satellites: The opposition effect of Iapetus at maximum light and the variability of Titan

We present photometry, V and (B - V), of Iapetus at six western elongations (the phase of maximum brightness) that span a range in solar phase, α, from ≈6° to <0°.4, and we find that a substantial opposition effect, >0.12 mag (V), is present. We make a few cautious remarks about the possible relevance of the use of this result to interpret the phase curve of Saturn's ring. We also give a few measures of Rhea and Hyperion, at $\text{α ? 0.3°}$, and more of Titan, which indicate that the latter has been anomalously bright during much of 1973 and 1974, sometimes by nearly 0.1 mag (V).     

The effect of damping on geomagnetic pulsation amplitude and phase at ground observatories

We present some results from a model of forced oscillations of the magnetosphere. The purpose of this work is to examine the effects and consequences of damping on geomagnetic pulsations as observed on the ground. The aim of the current work is to quantify the amount of damping applicable to geomagnetic pulsation waveforms. Ionospheric conductivities vary with latitude and time of day and this variation will effect the damping of geomagnetic pulsations. The variations in ionospheric conductivities are taken into account to predict the changes in amplitude and phase of geomagnetic pulsations over an extended latitudinal array of ground observatories. Three situations are modelled where the damping factor γ/ω_n, which is related to the amplitude loss per cycle, is different: (i) γ/ω_n approximately equal to 0.01, this corresponds to the ionospheric Joule damping of Newton et al. (1978); (ii) λ/ω_n equal to 0.1, this value is consistent with the empirically determined day-time damping factors from the observed latitude-dependent transient decays of the pulsation single effect events discussed by Siebert (1964). The value of 0.1 as the damping factor is taken as typical of day-time conditions and its effect on amplitude and phase for continuous pulsations is considered; and (iii) λ/ω_n is latitude-dependent; three different levels of damping are used appropriate for the night-time conditions associated with the auroral electrojet, plasmatrough and plasmasphere.The results from the model suggest that observationally determined damping factors are greater than those computed from ionospheric Joule damping alone. The model also illustrates the broadening of the latitudinal resonance width with increasing damping and the reducing of the phase change across resonance to less than 180°. The model also successfully reproduces features of pulsation single effect events and Pi2 pulsations.     

Influence of cosmological expansion on the threshold effects in the annihilation reaction of hard photons with CMB photons

The redshift (z) dependence of the dispersion relations for free particles is analyzed by taking into account the Lorentz invariance violation. A nonlinear algebraic equation is derived for the momenta of the particles involved in the annihilation reaction of a hard photon from a γ-ray source with a soft cosmic microwave background (CMB) photon near the threshold of this reaction. The solutions of this threshold equation are constructed and analyzed as a function of the redshift. We show that the threshold of the reaction under consideration tends to decrease with increasing z; the energy spectra of γ-ray sources at energies of ～10 TeV must be cut off in accordance with the calculated z dependence. We also calculate the time delay of the light signals from γ-ray sources that corresponds to the Lorentz invariance violation for photons. We discuss the possibility of improving the standard constraints on the Lorentz invariance violation parameters for fields of various physical natures.