ALFA: Adaptive Optics for the Calar Alto Observatory Optics, Control Systems, and Performance

The adaptive optics system ALFA differs in some aspects from systems like ADONIS and PUEO which have delivered scientific results since years. Interchangeable lenslet arrays with different numbers of subapertures and a deformable mirror with many more actuators than the number of corrected modesresult in some peculiarities in the calibration of the system and the reconstruction of incident wavefronts.We describe the design of ALFA's optics and its modal control architecture with a focus on a comparative study of the performance of different mode sets used to correct the wavefront aberrations. An outlook on our plans to improve and simplify the use of ALFA is given.The last section is dedicated to issues related to observing with ALFA in its present state. Expected Strehl ratios for different seeing conditions and guide star magnitudes are summarized in a table. AO observations in general, direct imaging and doing spectroscopywith ALFA in particular are discussed.     

A z-invariant Rayleigh beacon wavefront sensor

An innovative concept of wavefront sensing for Rayleigh beacons is introduced along with an example of a possible wavefront sensor. This new approach does not require the gating technique to limit the useful range of the laser source and therefore looks simpler to implement than previous Rayleigh concepts, and may additionally allow more efficient use of the photons emitted by the Rayleigh beacon. Our technique is based upon an optical element in the focal plane area whose section does not change for the conjugation of different ranges from the telescope aperture, hence the name z -invariant. The wavefront sensor shown here is an example of this new class. It is a compact pupil-plane wavefront sensor and as such allows for a layer-oriented configuration. It is shown that its sensitivity, while higher than usual gating approaches, is far from the possible limits leading us to speculate that other z -invariant wavefront sensors can reach much larger efficiencies.     

The optical polarization of spiral galaxies

Scattering of starlight by dust, molecules and electrons in spiral galaxies will produce a modification of the direct intensity and a polarization in the observed light. We treat the case where the distribution of scatterers can be considered to be optically thin, and derive semi-analytic expressions for the resolved intensity and polarized intensity for Thomson, Rayleigh, and more general scattering mechanisms. These expressions are applied to a parametric model for spiral galaxies. It is further shown that in the case of Thomson and Rayleigh scattering, and when scatterers and stars are distributed with rotational symmetry, the total polarized flux depends on the inclination, i , of the galactic axis to the line of sight according to a simple sin²  i law. This generalizes the well-known result for point-like and spherical light sources. By using a method based on spherical harmonics, we generalize this law for more general mechanisms, and show that to good approximation, the sin²  i law still holds for the class of models considered.     

Diffuse reflection and transmission of radiation for Rayleigh phase function

Diffuse reflection and transmission coefficients in a plane parallel medium are calculated for a Rayleigh phase-function averaged over polarization and Rayleigh polarized phase-function. This is calculated by imbedding the finite medium into a semi-infinite scattering and absorbing medium. Numerical calculations for semi-infinite albedo are compared with Pomraning results. The albedos for finite medium are calculated via the imbedding equations which converge for large τ to the value of semi-infinite medium.     

A discrete spherical harmonics method for radiative transfer analysis in inhomogeneous polarized planar atmosphere

A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands both the Stokes vector and the phase matrix in a finite series of generalized spherical functions and the resulting vector radiative transfer equation is expressed in a set of polar directions. Hence, the polarized characteristics of the radiance within the atmosphere at any polar direction and azimuthal angle can be determined without linearization and/or interpolations. The spatial dependent of the problem is solved using the spectral Chebyshev method. The emergent and transmitted radiative intensity and the degree of polarization are predicted for both Rayleigh and Mie scattering. The discrete spherical harmonics method predictions for optical thin atmosphere using 36 streams are found in good agreement with benchmark literature results. The maximum deviation between the proposed method and literature results and for polar directions \(\vert \mu \vert \geq0.1 \) is less than 0.5% and 0.9% for the Rayleigh and Mie scattering, respectively. These deviations for directions close to zero are about 3% and 10% for Rayleigh and Mie scattering, respectively.     

Scattering and transmission matrices of partially polarized radiation in a Rayleigh atmosphere bounded by a specular reflector

In a manner similar to that given in a preceding paper (cf. Castiet al., 1970), in this paper we show how to get a Cauchy system for the scattering and transmission matrices of the azimuth-independent term of partially polarized light in accordance with Rayleigh scattering in a homogeneous atmosphere bounded by a specular reflector. This set of integro-differential equations for the scattering and transmission matrices is suitable for numerical computation by high-speed digital computer.     

Compositional mapping of Saturn's satellite Dione with Cassini VIMS and implications of dark material in the Saturn system

Cassini VIMS has obtained spatially resolved imaging spectroscopy data on numerous satellites of Saturn. A very close fly-by of Dione provided key information for solving the riddle of the origin of the dark material in the Saturn system. The Dione VIMS data show a pattern of bombardment of fine, sub-0.5-μm diameter particles impacting the satellite from the trailing side direction. Multiple lines of evidence point to an external origin for the dark material on Dione, including the global spatial pattern of dark material, local patterns including crater and cliff walls shielding implantation on slopes facing away from the trailing side, exposing clean ice, and slopes facing the trailing direction which show higher abundances of dark material. Multiple spectral features of the dark material match those seen on Phoebe, Iapetus, Hyperion, Epimetheus and the F-ring, implying the material has a common composition throughout the Saturn system. However, the exact composition of the dark material remains a mystery, except that bound water and, tentatively, ammonia are detected, and there is evidence both for and against cyanide compounds. Exact identification of composition requires additional laboratory work. A blue scattering peak with a strong UV-visible absorption is observed in spectra of all satellites which contain dark material, and the cause is Rayleigh scattering, again pointing to a common origin. The Rayleigh scattering effect is confirmed with laboratory experiments using ice and 0.2-μm diameter carbon grains when the carbon abundance is less than about 2% by weight. Rayleigh scattering in solids is also confirmed in naturally occurring terrestrial rocks, and in previously published reflectance studies. The spatial pattern, Rayleigh scattering effect, and spectral properties argue that the dark material is only a thin coating on Dione's surface, and by extension is only a thin coating on Phoebe, Hyperion, and Iapetus, although the dark material abundance appears higher on Iapetus, and may be locally thick. As previously concluded for Phoebe, the dark material appears to be external to the Saturn system and may be cometary in origin. We also report a possible detection of material around Dione which may indicate Dione is active and contributes material to the E-ring, but this observation must be confirmed.     

An efficient method to calculate Ambarzumian-Chandrasekhar's and hopf's functions

An efficient method is proposed to calculate scalar Ambarzumian-Chandrasekhar's and Hopf's functions. This method is based on the approximation of Sobolev's resolvent function using exponent series, the coefficients of which are readily found from approximate characteristic equation and from a system of linear algebraic equations.The approximate expressions for the above functions are given. For checking purposes the calculations were carried out in single, double, and quadruple precision. For isotropic, Rocard, and Rayleigh scattering we present a sample of results in 14 significant figures.The Hopf function for isotropic and Rayleigh scattering is presented in 18 significant figures and the well-known Hopf constantq() is found in 59 significant figures.     

Solution of the radiative transfer equation for Rayleigh scattering using the infinite medium Green’s function

The infinite medium Green’s function is used to solve the half-space albedo, slab albedo and Milne problems for the unpolarized Rayleigh scattering case; these problems are the most classical problems of radiative transfer theory. The numerical results are obtained and are compared with previous ones.     

Exact low-energy expansion of the Rayleigh scattering cross-section by atomic hydrogen

We present an exact low-energy expansion redward of Lyα of the Rayleigh scattering cross-section by atomic hydrogen, which is given by the Kramers–Heisenberg formula. The expansion is expressed as a power series of  (ω/ω_l)  , where ω_l and ω are the angular frequencies corresponding to the Lyman limit and the incident radiation, respectively. The expansion coefficients are represented as infinite sums over all the intermediate states and they can also be expressed as the regular particular solutions of inhomogeneous differential equations, which is known as the Dalgarno and Lewis method. In this paper, using a software capable of symbolic calculations, we obtain the exact values of these coefficients. We provide brief discussions on the accuracies of approximate expressions for Rayleigh scattering by a hydrogen atom found in the literature.     

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.     

X‐ray spectra and polarization from accreting black holes: polarization from an orbiting spot

The polarization from a spot orbiting around Schwarzschild and extreme Kerr black holes is studied. We assume different models of local polarization. Firstly, as a toy model we set the local polarization vector either normal to the disc plane, or perpendicular to the toroidal magnetic field. Then we examine the more realistic situation with a spot arising due to the emission from the primary source above the disc. We employ either Rayleigh single scattering or Compton multiple scattering approximations. The time dependence of the degree and angle of polarization during the spot revolution is examined as a function of the observer's inclination angle and black hole angular momentum. The gravitational and Doppler shifts, lensing effect as well as time delays are taken into account. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The complete solution for the scattering of polarized light in a Rayleigh and isotropically scattering atmosphere

TheF _N method is used to solve, in a concise manner, the complete problem concerning the diffusion of polarized light in a plane-parallel Rayleigh and isotropically scattering atmosphere.     

High resolution observations of linear polarization of the 6818.8 Å feature of methane for Uranus and Saturn

Observations of the linear polarization in the fully resolved 6818.8 Å feature of CH₄ in Saturn and Uranus show dramatic changes of linear polarization across the line profile. The change in position angle of polarization across the line core, especially for Saturn, indicates a likely Rayleigh scattering origin for the observed polarization.     

The polarization of radiation reflected diffusely by an inhomogeneous plane medium

The problem of determining the intensity and the degree of polarization of radiation emerging from an inhomogeneous finite plane medium for the case of Rayleigh scattering with internal energy source is considered. A system of coupled integral equations are obtained and solved by the Galerkin method. The degree of polarization for homogeneous and inhomogeneous media are calculated for uniform and nonuniform sources.     

Impact of atmospheric parameters on the atmospheric Cherenkov technique

Atmospheric density profiles as well as several light absorption and scattering processes depend on geographic position and are generally time-variable. Their impact on the atmospheric Cherenkov technique in general (imaging or non-imaging) is investigated. Different density profiles lead to differences in Cherenkov light density of up to 60%. Seasonal variations at mid-latitude sites are of the order of 15–20%. The quest for improved energy calibration of Cherenkov experiments also shows the need for improved transmission calculations, taking all relevant processes into account and using realistic profiles of absorbers. Simulations including the scattering mechanisms also reveal the relevance of Rayleigh and Mie scattering for atmospheric Cherenkov experiments. Refraction and the differences between treating the atmosphere in plane-parallel or spherical geometry are also investigated.     

Polarization in spectral lines

The general formalism, presented in a previous paper of this series (Landi Degl'Innocenti, 1983a), is particularized to deduce the radiative transfer equations for polarized radiation and the statistical equilibrium equations for a multi-level atom in the zero-magnetic field, collisionless regime. The formulae are developed both in the standard representation and in the representation of the statistical tensors. For resonance scattering in a two-level atom, in the limiting case of complete depolarization of the ground level, we recover the classical results for Rayleigh scattering and we derive the expression of the phase matrix in terms of ordinary rotation matrices. The law of scattering is then generalized to take properly into account the influence of the anisotropy of the radiation field on the atomic polarization of the ground level (depopulation pumping).     

Rayleigh scattering in planetary atmospheres

The vector equation of radiative transfer is solved both for conservative and non-conservative planetary atmospheres using the method of discrete ordinates. The atmosphere, bounded by a Lambert bottom, is considered plane-parallel and homogeneous. The scattering in the atmosphere obeys the Rayleigh or Rayleigh-Cabannes law. The compiled package of FORTRAN codes allows us to find the Stokes parameters for such an atmosphere at arbitrary optical depth.     

An analysis of spectra in the Red Rectangle nebula

This paper presents an analysis of a series of spectra in the Red Rectangle nebula. Only the reddest part of the spectra can safely be attributed to light from the nebula, and indicates Rayleigh scattering by the gas, in conformity with the large angles of scattering involved and the proximity of the star. In the blue, light from HD 44179, refracted or scattered in the atmosphere, dominates the spectra. This paper questions the reliability of ground-based broad-band spectra of extended objects in the blue.