Lyman α radiative transfer in a multiphase medium

Hydrogen Lyman α (Lyα) is our primary emission-line window into high-redshift galaxies. Despite an extensive literature, Lyα radiative transfer in the most realistic case of a dusty, multiphase medium has received surprisingly little detailed theoretical attention. We investigate Lyα resonant scattering through an ensemble of dusty, moving, optically thick gas clumps. We treat each clump as a scattering particle and use Monte Carlo simulations of surface scattering to quantify continuum and Lyα surface scattering angles, absorption probabilities, and frequency redistribution, as a function of the gas dust content. This atomistic approach speeds up the simulations by many orders of magnitude, making possible calculations which are otherwise intractable. Our fitting formulae can be readily adapted for fast radiative transfer in numerical simulations. With these surface scattering results, we develop an analytic framework for estimating escape fractions and line widths as a function of gas geometry, motion, and dust content. Our simple analytic model shows good agreement with full Monte Carlo simulations. We show that the key geometric parameter is the average number of surface scatters for escape in the absence of absorption,     , and we provide fitting formulae for several geometries of astrophysical interest. We consider the following two interesting applications. (i) Equivalent widths ( EWs ). Lyα can preferentially escape from a dusty multiphase interstellar medium if most of the dust lies in cold neutral clouds, which Lyα photons cannot penetrate. This might explain the anomalously high EWs sometimes seen in high-redshift/submillimetre sources. (ii) Multiphase galactic outflows . We show the characteristic profile is asymmetric with a broad red tail, and relate the profile features to the outflow speed and gas geometry. Many future applications are envisaged.     

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.     

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.     

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.     

Adiabatic Deceleration of Solar Energetic Particles as Deduced from Monte Carlo Simulations of Interplanetary Transport

Monte Carlo simulations of interplanetary transport are employed to study adiabatic energy losses of solar protons during propagation in the interplanetary medium. We consider four models. The first model is based on the diffusion-convection equation. Three other models employ the focused transport approach. In the focused transport models, we simulate elastic scattering in the local solar wind frame and magnetic focusing. We adopt three methods to treat scattering. In two models, we simulate a pitch-angle diffusion as successive isotropic or anisotropic small-angle scatterings. The third model treats large-angle scatterings as numerous small-chance isotropizations. The deduced intensity–time profiles are compared with each other, with Monte Carlo solutions to the diffusion-convection equation, and with results of the finite-difference scheme by Ruffolo (1995). A numerical agreement of our Monte Carlo simulations with results of the finite-difference scheme is good. For the period shortly after the maximum intensity time, including deceleration can increase the decay rate of the near-Earth intensity essentially more than would be expected based on advection from higher momenta. We, however, find that the excess in the exponential-decay rate is time dependent. Being averaged over a reasonably long period, the decay rate of the near-Earth intensity turns out to be close to that expected based on diffusion, convection, and advection from higher momenta. We highlight a variance of the near-Earth energy which is not small in comparison with the energy lost. It leads to blurring of any fine details in the accelerated particle spectra. We study the impact of realistic spatial dependencies of the mean free path on adiabatic deceleration and on the near-Earth intensity magnitude. We find that this impact is essential whenever adiabatic deceleration itself is important. It is also found that the initial angular distribution of particles near the Sun can markedly affect MeV-proton energy losses and intensities observed at 1 AU. Computations invoked during the study are described in detail.     

The Lateral Trigger Probability function for the Ultra-High Energy Cosmic Ray showers detected by the Pierre Auger Observatory

In this paper we introduce the concept of Lateral Trigger Probability (LTP) function, i.e., the probability for an Extensive Air Shower (EAS) to trigger an individual detector of a ground based array as a function of distance to the shower axis, taking into account energy, mass and direction of the primary cosmic ray. We apply this concept to the surface array of the Pierre Auger Observatory consisting of a 1.5 km spaced grid of about 1600 water Cherenkov stations. Using Monte Carlo simulations of ultra-high energy showers the LTP functions are derived for energies in the range between 10¹⁷ and 10¹⁹ eV and zenith angles up to 65°. A parametrization combining a step function with an exponential is found to reproduce them very well in the considered range of energies and zenith angles. The LTP functions can also be obtained from data using events simultaneously observed by the fluorescence and the surface detector of the Pierre Auger Observatory (hybrid events). We validate the Monte Carlo results showing how LTP functions from data are in good agreement with simulations.     

Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scattering

The effects of various types of topography on the shadow-hiding effect and multiple scattering in particulate surfaces are studied. Two bounding cases were examined: (1) the characteristic scale of the topography is much larger than the surface particle size, and (2) the characteristic scale of the topography is comparable to the surface particle size. A Monte Carlo ray-tracing method (i.e., geometric optics approximation) was used to simulate light scattering. The computer modeling shows that rocky topographies generated by randomly distributed stones over a flat surface reveal much steeper phase curves than surface with random topography generated from Gaussian statistics of heights and slopes. This is because rocks may have surface slopes greater than 90°. Consideration of rocky topography is important for interpreting rover observations. We show the roughness parameter in the Hapke model to be slightly underestimated for bright planetary surfaces, as the model neglects multiple scattering on large-scale topographies. The multiple scattering effect also explains the weak spectral dependences of the roughness parameter in Hapke's model found by some authors. Multiple scattering between different parts of a rough surface suppresses the effect of shadowing, thus the effects produced by increases in albedo on the photometric behavior of a surface can be compensated for with the proper decreases in surface roughness. This defines an effective (photometric) roughness for a surface. The interchangeability of albedo and roughness is shown to be possible with fairly high accuracy for large-scale random topography. For planetary surfaces that have a hierarchically arranged large-scale random topography, predictions made with the Hapke model can significantly differ from real values of roughness. Particulate media with surface borders complicated by Gaussian or clumpy random topographies with characteristic scale comparable to the particle size reveal different photometric behaviors in comparison with particulate surfaces that are flat or the scale of their topographies is much larger than the particle size.     

Monte Carlo Radiative Transfer Modeling of Lightning Observed in Galileo Images of Jupiter

We study lightning on Jupiter and the clouds illuminated by the lightning using images taken by the Galileo orbiter. The Galileo images have a resolution of ∼25 km/pixel and are able to resolve the shape of single lightning spots, which have half widths (radii) at half the maximum intensity in the range 45-80 km. We compare the shape and width of lightning flashes in the images with simulated flashes produced by our 3D Monte Carlo light-scattering model.The model calculates Monte Carlo scattering of photons in a 3D opacity distribution. During each scattering event, light is partially absorbed. The new direction of the photon after scattering is chosen according to a Henyey-Greenstein phase function. An image from each direction is produced by accumulating photons emerging from the cloud in a small range (bins) of emission angles. The light source is modeled either as a point or a vertical line.A plane-parallel cloud layer does not always fit the data. In some cases the cloud over the light source appears to resemble cumulus clouds on Earth. Lightning is estimated to occur at least as deep as the bottom of the expected water cloud. For the six flashes studied, we find that the clouds above the lightning are optically thick (τ>5). Jovian flashes are more regular and circular than the largest terrestrial flashes observed from space. On Jupiter there is nothing equivalent to the 30-40-km horizontal flashes that are seen on Earth.     

Photometric modeling of Asteroid 5535 Annefrank from Stardust observations

In this paper the Stardust disk-integrated phase curve at phase 47.2-134.6° of the Asteroid 5535 Annefrank, combined with groundbased observations (at phase 2.3-18.3°), are fit with Hapke’s photometric model. We confirm Newburn et al.’s (Newburn, R.L. et al. [2003]. J. Geophys. Res. 108 (E11), 5117. doi:10.1029/2003JE002106) observation that Annefrank exhibits a steep phase curve. This manifests itself in an unusually high fit surface roughness parameter of 49°. The single particle scattering albedo is 0.62, also high for an S-asteroid, while the fit phase function is more forward scattering than the typical S-asteroid being nearly isotropic with an asymmetry parameter of −0.09. The fit opposition surge width (h = 0.015) is typical of S-asteroids. However these fits assume a spherical shape to the asteroid. Li et al. (Li, J., A’Hearn, M.F., McFadden, L.A. [2004]. Icarus, 415-431) have shown that this assumption may lead to significant errors particularly at high phase angles leading to higher modeled single particle scattering albedos, macroscopic roughnesses and more forward scattering phase functions than actually exhibited. Our results confirm this finding—fitting only the data below 90° phase yields lower particle albedos (0.41) and roughnesses (20°) and more backscattering particles (−0.19) than the fit including the high phase angle data. Overall Annefrank appears to be on the bright side but otherwise is typical for an S-type asteroid suggesting that it may be a recent collisional fragment with a relatively immature surface which has had relatively little time to be weathered.     

The influence of forward-scattered light in transmission measurements of (exo)planetary atmospheres

The transmission of light through a planetary atmosphere can be studied as a function of altitude and wavelength using stellar or solar occultations, giving often unique constraints on the atmospheric composition. For exoplanets, a transit yields a limb-integrated, wavelength-dependent transmission spectrum of an atmosphere. When scattering haze and/or cloud particles are present in the planetary atmosphere, the amount of transmitted flux not only depends on the total optical thickness of the slant light path that is probed, but also on the amount of forward-scattering by the scattering particles. Here, we present results of calculations with a three-dimensional Monte Carlo code that simulates the transmitted flux during occultations or transits. For isotropically scattering particles, like gas molecules, the transmitted flux appears to be well-described by the total atmospheric optical thickness. Strongly forward-scattering particles, however, such as commonly found in atmospheres of Solar System planets, can increase the transmitted flux significantly. For exoplanets, such added flux can decrease the apparent radius of the planet by several scale heights, which is comparable to predicted and measured features in exoplanet transit spectra. We performed detailed calculations for Titan’s atmosphere between 2.0 and 2.8 μm and show that haze and gas abundances will be underestimated by about 8% if forward-scattering is ignored in the retrievals. At shorter wavelengths, errors in the gas and haze abundances and in the spectral slope of the haze particles can be several tens of percent, also for other Solar System planetary atmospheres. We also find that the contribution of forward-scattering can be fairly well described by modelling the atmosphere as a plane-parallel slab. This potentially reduces the need for a full three-dimensional Monte Carlo code for calculating transmission spectra of atmospheres that contain forward-scattering particles.     

Multidimensional simulations of radiative transfer in Type Ia supernovae

A three-dimensional Monte Carlo code for modelling radiation transport in Type Ia supernovae is described. In addition to tracking Monte Carlo quanta to follow the emission, scattering and deposition of radiative energy, a scheme involving volume-based Monte Carlo estimators is used to allow properties of the emergent radiation field to be extracted for specific viewing angles in a multidimensional structure. This eliminates the need to compute spectra or light curves by angular binning of emergent quanta. The code is applied to two test problems to illustrate consequences of multidimensional structure on the modelling of light curves. First, elliptical models are used to quantify how large-scale asphericity can introduce angular dependence to light curves. Secondly, a model which incorporates complex structural inhomogeneity, as predicted by modern explosion models, is used to investigate how such structure may affect light-curve properties.     

Monte Carlo model of the highly anisotropic solar proton event of 20 April 1971

The anisotropy of the particle distribution and its variation with time at 1 AU early in a solar cosmic ray event can provide information on the pitch-angle scattering of the particles in the interplanetary medium. The proton event of 20 April 1971 is described in which the anisotropy of the 7.6–55 MeV energy channel remained large (? 100%) and field-aligned well into the decay phase of the event. A Monte Carlo technique, which gives the pitch-angle distribution, is employed to investigate two models put forward to explain this sustained anisotropy. It is shown that the observed event is consistent with one model in which the injection of particles at the Sun decayed with ane-folding time of 7 hr. In this model the parallel propagation is determined by small-angle scattering in a diverging field equivalent to a uniform diffusion coefficient of 2.1 × 10²² cm² s^?1 (the corresponding classical mean free path is 0.90 AU). A model with impulsive injection and in whichκ(r) increases strongly with distance from the Sun cannot satisfactorily explain the observations.     

Scattering of Light by Composite Particles in a Planetary Surface

It has been proposed that composite particles containing internal scatterers may provide the explanation for the fact that most photometric studies of planetary surfaces based on Hapke's model of bidirectional reflectance have found the planetary particles to exhibit moderately backscattering phase functions. However, an implicit assumption made in this explanation is that the scattering by composite particles containing multiple internal inclusions in a planetary surface can still be adequately computed using standard radiative transfer theory assuming the composite particles to be the fundamental individual scatterers even though such particles are necessarily in close proximity to each other. In this paper, this assumption is explored by examining the effects of close packing on the light scattering by spherical particles containing isotropic internal scatterers using a Monte Carlo routine. As expected, classical radiative transfer (assuming a random distribution of scattering particles) coupled with the assumption that the composite particle is the fundamental scatterer provides a good approximation in the high porosity limit. However, even for porosities as high as 90% the effects of close packing are clearly seen with the radiative transfer calculation underestimating the scattering by ∼10% at high incidence, emission, and phase angles. As the porosity is lowered further, the discrepancy becomes more severe and can reach 50% or more. In contrast, assuming the individual scatterer properties in the radiative transfer calculation leads to a substantial overestimate of the scattering even for porosities as low as 27.5%. This suggests that parameters derived using the classical radiative transfer theory will yield results intermediate between those of the composite as a whole and those of the internal scatterers. Thus, one should exercise caution in interpreting the results of models based on classical radiative transfer theory in terms of the physical properties of the surface particles and, where possible, the bidirectional reflectance of densely packed composite particles should be computed using more accurate methods such as the stochastic radiative transfer theory.     

on the role of nonthermal electrons in EUV and X-ray line emissions from solar flares

The energy and angular distribution of electrons as a function of column densities initially for monoenergetic and monodirectional electron beams and incidence angles of 0‡, 30‡ and 60‡ have been studied by combining small angle scattering using analytical treatment with large angle collisions using Monte Carlo calculations. Using these distributions, X-ray and EUV-line flux have been studied as a function of column density. It is observed that the line flux increases with the increase in column density, becoming significant at intermediate column densities where the electron energies and angular distributions have a non-Maxwellian nature.     

The composition of liquid methane-nitrogen aerosols in Titan’s lower atmosphere from Monte Carlo simulations

Molecular level Monte Carlo simulations have been performed with various model potentials for the CH₄-N₂ vapor-liquid equilibrium at conditions prevalent in the atmosphere of Saturn’s moon Titan. With a single potential parameter adjustment to reproduce the vapor-liquid equilibrium at a higher temperature, Monte Carlo simulations are in excellent agreement with available laboratory measurements. The results demonstrate the ability of simple pair potential models to describe phase equilibria with the requisite accuracy for atmospheric modeling, while keeping the number of adjustable parameters at a minimum. This allows for stable extrapolation beyond the range of available laboratory measurements into the supercooled region of the phase diagram, so that Monte Carlo simulations can serve as a reference to validate phenomenological models commonly used in atmospheric modeling. This is most important when the relevant region of the phase diagram lies outside the range of laboratory measurements as in the case of Titan. The present Monte Carlo simulations confirm the validity of phenomenological thermodynamic equations of state specifically designed for application to Titan. The validity extends well into the supercooled region of the phase diagram. The possible range of saturation levels of Titan’s troposphere above altitudes of 7 km is found to be completely determined by the remaining uncertainty of the most recent revision of the Cassini-Huygens data, yielding a saturation of 100 ± 6% with respect to CH₄-N₂ condensation up to an altitude of about 20 km.     

Introducing PT-REX,the point-to-point TRend EXtractor

Investigating the spatial correlation between different emissions in an extended astrophysical source can provide crucial insights into their physical connection, hence it can be the key to understand the nature of the system. The point-to-point analysis of surface brightness is a reliable method to do such an analysis. In this work we present PT-REX, a software to carry out these studies between radio and X-ray emission in extended sources. We discuss how to reliably carry out this analysis and its limitation and we introduce the Monte Carlo point-to-point analysis, which allows to extend this approach to poorly-resolved sources. Finally we present and discuss the application of our tool to study the diffuse radio emission in a galaxy cluster.     

A laboratory study of the bidirectional reflectance from particulate samples

The Hapke (Hapke, B. [1981]. J. Geophys. Res. 86, 3039-3054) photometric model and its modifications are widely used to characterize telescopic, spacecraft, and laboratory observations of the bidirectional reflectance of particulate surfaces. Following work and methods laid out in a companion paper (Helfenstein, P., Shepard, M.K. [2011]. Icarus, in press), we deconstruct the Hapke model and, separating all empirical and ad hoc parameters (opposition surge, particle phase function, surface roughness), combine them into a single parameter called the surface phase function, F(α). We illustrate how to extract this function from scattering data sets acquired with the Bloomsburg University Goniometer (BUG). We show how this method can be used to rapidly and accurately characterize bidirectional reflectance data sets from laboratory and spacecraft measurements, often giving better fits to the data. We examine samples with strong color contrasts in different wavelengths. This allows us to examine the exact same surface, changing only the albedo to investigate how the amplitude and the detailed shape of the surface phase function might systematically depend on wavelength and albedo. We also examine the changes in scattering behavior that result when samples are compacted and find the surface phase function and single scattering albedo to be significantly changed. We suggest that these observations support the hypothesis that much of the scattering behavior attributed to the single particle phase function is instead cause by the surface micro-structure.     

A simulation of the directivity effect to be expected in hard X-ray flares

A Monte Carlo technique has been used to predict the relative visibility of solar hard X-ray flares as a function of solar longitude assuming the model of Takakura and Kai to be realistic. Comparison is made with previous statistical studies of observations. A discernable longitudinal variation in the relative visibility of flares is shown to be expected but the probability of flares being visible towards the limb is shown to be higher than had previously been evident.The effect of the possible downward inclination of the particle beam with respect to the solar surface is considered.     

RHESSI as a Hard X-Ray Polarimeter

Although designed primarily as a hard X-ray imager and spectrometer, the Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) is also capable of measuring the polarization of hard X-rays (20–100 keV) from solar flares. This capability arises from the inclusion of a small unobstructed Be scattering element that is strategically located within the cryostat that houses the array of nine germanium detectors. The Ge detectors are segmented, with both a front and rear active volume. Low-energy photons (below about 100 keV) can reach a rear segment of a Ge detector only indirectly, by scattering. Low-energy photons from the Sun have a direct path to the Be and have a high probability of Compton scattering into a rear segment of a Ge detector. The azimuthal distribution of these scattered photons carries with it a signature of the linear polarization of the incident flux. Sensitivity estimates, based on Monte Carlo simulations and in-flight background measurements, indicate that a 20–100 keV polarization sensitivity of less than a few percent can be achieved for X-class flares.     

Study of photometric phase curve: assuming a cellinoid ellipsoid shape for asteroid(106) Dione

We carried out new photometric observations of asteroid(106) Dione at three apparitions(2004, 2012 and 2015) to understand its basic physical properties. Based on a new brightness model,new photometric observational data and published data of(106) Dione were analyzed to characterize the morphology of Dione's photometric phase curve. In this brightness model, a cellinoid ellipsoid shape and three-parameter(H, G_1, G_2) magnitude phase function system were involved. Such a model can not only solve the phase function system parameters of(106) Dione by considering an asymmetric shape of an asteroid, but also can be applied to more asteroids, especially those without enough photometric data to solve the convex shape. Using a Markov Chain Monte Carlo(MCMC) method, Dione's absolute magnitude of H = 7.66_(-0.03)~(+0.03) mag, and phase function parameters G_1= 0.682_(-0.077)~(+0.077) and G_2= 0.081_(-0.042)~(+0.042) were obtained. Simultaneously, Dione's simplistic shape, orientation of pole and rotation period were also determined preliminarily.