Monte Carlo Radiative Transfer Method Research Articles

High Accuracy Photodissociation Rates in VULCAN with MCRT

Photochemical processing is a key influence on the chemical compositions of exoplanet atmospheres. We develop a 1D plane-parallel Monte Carlo radiative-transfer (MCRT) path length method to calculate actinic fluxes for photochemical modeling, which we couple to the VULCAN photochemical model. Due to the flexible nature of MCRT methods, this enables accurate calculation of photodissociation rates for complex multiple scattering scenarios encountered in exoplanet atmospheres such as high altitude haze layers.

Improving Monte Carlo radiative transfer in the regime of high optical depths: The minimum scattering order

Radiative transfer simulations are a powerful tool that enables the calculation of synthetic images of a wide range of astrophysical objects. These simulations are often based on the Monte Carlo method, as it provides the needed versatility that allows the consideration of the diverse and often complex conditions found in those objects. However, this method faces fundamental problems in the regime of high optical depths which may result in overly noisy images and severely underestimated flux values. In this study, we propose an advanced Monte Carlo radiative transfer method, namely, an enforced minimum scattering order that is aimed at providing a minimum quality of determined flux estimates. For that purpose, we extended our investigations of the scattering order problem and derived an analytic expression for the minimum number of interactions that depends on the albedo and optical depth of the system, which needs to be considered during a simulation to achieve a certain coverage of the scattering order distribution. The method is based on the utilization of this estimated minimum scattering order and enforces the consideration of a sufficient number of interactions during a Monte Carlo radiative transfer simulation. Moreover, we identified two notably distinct cases that shape the kind of complexity that arises in such simulations: the albedo-dominated case and the optical depth-dominated case. Based on that, we analyzed the implications related to the best usage of a stretching method as a means to alleviate the scattering order problem. We find that its most suitable application requires taking into account the value of the albedo as well as the optical depth. Furthermore, we argue that the derived minimum scattering order can be used to assess the performance of a stretching method with regard to the scattering orders its usage promotes. Finally, we stress the need for developing advanced pathfinding techniques to fully solve the problem of Monte Carlo radiative transfer simulations in the regime of high optical depths.

The cosmic web in Lyman-alpha emission

ABSTRACT We develop a comprehensive theoretical model for Lyman-alpha (Ly α) emission, from the scale of individual Ly α emitters (LAEs) to Ly α haloes (LAHs), Ly α blobs (LABs), and Ly α filaments (LAFs) of the diffuse cosmic web itself. To do so, we post-process the high-resolution TNG50 cosmological magnetohydrodynamical simulation with a Monte Carlo radiative transfer method to capture the resonant scattering process of Ly α photons. We build an emission model incorporating recombinations and collisions in diffuse gas, including radiative effects from nearby AGN, as well as emission sourced by stellar populations. Our treatment includes a physically motivated dust model, which we empirically calibrate to the observed LAE luminosity function. We then focus on the observability and physical origin of the z = 2 Ly α cosmic web, studying the dominant emission mechanisms and spatial origins. We find that diffuse Ly α filaments are, in fact, illuminated by photons that originate not only from the intergalactic medium itself but also from within galaxies and their gaseous haloes. In our model, this emission is primarily sourced by intermediate mass haloes (1010–1011 M⊙), principally due to collisional excitations in their circumgalactic media as well as central, young stellar populations. Observationally, we make predictions for the abundance, area, linear size, and embedded halo/emitter populations within filaments. Adopting an isophotal surface brightness threshold of 10−20 erg s−1 cm−2 arcsec−2, we predict a volume abundance of Ly α filaments of ∼10−3 cMpc−3 for lengths above 400 pkpc. Given sufficiently large survey footprints, detection of the Ly α cosmic web is within reach of modern integral field spectrographs, including MUSE, VIRUS, and KCWI.

Linking the Monte Carlo radiative transfer algorithm to the radiative transfer equation

Abstract This manuscript presents a short route to justify the widely used Monte Carlo Radiative Transfer (MCRT) algorithm straight from the Radiative Transfer Equation (RTE). In this regard, this paper starts deriving a probability measure obtained from the integral formulation of the RTE under a unidirectional point source in an infinite domain. This derivation only requires the analytical integration of the first two terms of a perturbation expansion. Although derivations have been devised to clarify the relationship between the MCRT and the RTE, they tend to be rather long and elaborate. Considering how simple it is to justify the MCRT from a loose probabilistic interpretation of the photon’s physical propagation process, the decay in popularity of former approaches relating MCRT to the RTE is entirely understandable. Unfortunately, all of this has given the false impression that MCRT and the RTE are not that closely related, to the point that recent works have explicitly stated that no direct link exists between them. This work presents a simpler route demonstrating how the MCRT algorithm emerges to statistically sample the RTE explicitly through Markov chains, further clarifying the method’s foundations. Although compact, the derivation proposed in this work does not skip any fundamental step, preserving mathematical rigor while giving specific expressions and functions. Thus, this derivation can help devise efficient ways to statistically sample the RTE for different scenarios or when coupling the MCRT method with other methods traditionally grounded in the RTE, such as the Spherical Harmonics and Discrete Ordinates methods.

Modeling Thermal Emission under Lunar Surface Environmental Conditions

Thermal emission spectra can provide key insights into the composition and thermophysical properties of the regolith on the Moon and other airless bodies. However, under lunar surface environmental conditions, the uppermost millimeters of the regolith (from which thermal emission originates) cannot be characterized by a single temperature, leading to changes in spectral characteristics that should be accounted for in interpreting thermal emission measurements. Here, we develop and apply a Monte Carlo radiative transfer method to model thermal emission from particulate media with varying, nonisothermal subsurface temperature profiles. We model emission spectra for three major lunar mineral phases (pyroxene, olivine, and plagioclase), and investigate the effects of particle size and packing density. Modeled spectra are compared to lab measurements acquired under both ambient and simulated lunar conditions. We find that in some cases, the model provides useful constraints on the magnitude of the temperature profile established in a lab sample under lunar-like conditions, whereas in other cases, lab spectra are not well represented by the linear temperature profiles considered in this work. The model is generally successful at predicting changes in spectral contrast under lunar-like conditions, but less successful in accurately predicting shifts in the position of the Christiansen feature emissivity maximum; we illustrate and discuss the validity of the modeling approach for a range of different cases. Model results can also be used to quantify the depth within which observed thermal emission originates; this depth depends on composition and grain size, and ranges from ∼100 to 1000 μm for representative packing densities.

DART-Lux: An unbiased and rapid Monte Carlo radiative transfer method for simulating remote sensing images

Accurate and efficient simulation of remote sensing images is increasingly needed in order to better exploit remote sensing observations and to better design remote sensing missions. DART (Discrete Anisotropic Radiative Transfer), developed since 1992 based on the discrete ordinates method (i.e., standard mode DART-FT), is one of the most accurate and comprehensive 3D radiative transfer models to simulate the radiative budget and remote sensing observations of urban and natural landscapes. Recently, a new method, called DART-Lux, was integrated into DART model to address the requirements of massive remote sensing data simulation for large-scale and complex landscapes. It is developed based on efficient Monte Carlo light transport algorithms (i.e., bidirectional path tracing) and on DART model framework. DART-Lux can accurately and rapidly simulate the bidirectional reflectance factor (BRF) and spectral images of arbitrary landscapes. This paper presents its theory, implementation, and evaluation. Its accuracy, efficiency and advantages are also discussed. The comparison with standard DART-FT in a variety of scenarios shows that DART-Lux is consistent with DART-FT (relative differences <1%) with simulation time and memory reduced by a hundredfold. DART-Lux is already part of the DART version freely available for scientists (https://dart.omp.eu).

Scattering, absorption, and thermal emission by large cometary dust particles: Synoptic numerical solution

Context.Remote light scattering and thermal infrared observations provide clues about the physical properties of cometary and interplanetary dust particles. Identifying these properties will lead to a better understanding of the formation and evolution of the Solar System.Aims.We present a numerical solution for the radiative and conductive heat transport in a random particulate medium enclosed by an arbitrarily shaped surface. The method will be applied to study thermal properties of cometary dust particles.Methods.The recently introduced incoherent Monte Carlo radiative transfer method developed for scattering, absorption, and propagation of electromagnetic waves in dense discrete random media is extended for radiative heat transfer and thermal emission. The solution is coupled with the conductive Fourier transport equation that is solved with the finite-element method.Results.The proposed method allows the synoptic analysis of light scattering and thermal emission by large cometary dust particles consisting of submicrometer-sized grains. In particular, we show that these particles can sustain significant temperature gradients resulting in the superheating factor phase function observed for the coma of comet 67P/Churyumov–Gerasimenko.

Exoplanetary Monte Carlo radiative transfer with correlated-k – I. Benchmarking transit and emission observables

Abstract Current observational data of exoplanets are providing increasing detail of their 3D atmospheric structures. As characterization efforts expand in scope, the need to develop consistent 3D radiative-transfer methods becomes more pertinent as the complex atmospheric properties of exoplanets are required to be modelled together consistently. We aim to compare the transmission and emission spectra results of a 3D Monte Carlo radiative transfer (MCRT) model to contemporary radiative-transfer suites. We perform several benchmarking tests of an MCRT code, Cloudy Monte Carlo Radiative Transfer (cmcrt), to transmission and emission spectra model output. We add flexibility to the model through the use of k-distribution tables as input opacities. We present a hybrid MCRT and ray tracing methodology for the calculation of transmission spectra with a multiple scattering component. cmcrt compares well to the transmission spectra benchmarks at the 10s of ppm level. Emission spectra benchmarks are consistent to within 10 per cent of the 1D models. We suggest that differences in the benchmark results are likely caused by geometric effects between plane-parallel and spherical models. In a practical application, we post-process a cloudy 3D HD 189733b GCM model and compare to available observational data. Our results suggest the core methodology and algorithms of cmcrt produce consistent results to contemporary radiative transfer suites. 3D MCRT methods are highly suitable for detailed post-processing of cloudy and non-cloudy 1D and 3D exoplanet atmosphere simulations in instances where atmospheric inhomogeneities, significant limb effects/geometry or multiple scattering components are important considerations.

Fast and slow winds from supergiants and luminous blue variables

We predict quantitative mass-loss rates and terminal wind velocities for early-type supergiants and luminous blue variables (LBVs) using a dynamical version of the Monte Carlo radiative transfer method. First, the observed drop in terminal wind velocity around spectral type B1 is confirmed by the Monte Carlo method at the correct effective temperature of about 21 000 K. This drop in wind velocity is much steeper than would be expected from the drop in escape speed for cooler stars. The results may be particularly relevant for slow winds inferred for some high-mass X-ray binaries. Second, the strength of the mass-loss bi-stability jump is found to be significantly greater than previously assumed. This could this make bi-stability braking more efficient in massive star evolution; in addition, a rotationally induced version of the bi-stability mechanism may now be capable of producing the correct density of outflowing disks around B[e] supergiants, although multi-dimensional modelling including the disk velocity structure is still needed. For LBVs we find that the bi-stability jump becomes larger at higher metallicities, but perhaps surprisingly also larger at lower Eddington parameters. This may have consequences for the role of LBVs in the evolution of massive stars at different metallicities and cosmic epochs. Finally, our predicted low wind velocities may be important for explaining the slow outflow speeds of supernova type IIb/IIn progenitors, for which the direct LBV-SN link was first introduced.

The Failure of Monte Carlo Radiative Transfer at Medium to High Optical Depths

Abstract Computer simulations of photon transport through an absorbing and/or scattering medium form an important research tool in astrophysics. Nearly all software codes performing such simulations for three-dimensional geometries employ the Monte Carlo (MC) radiative transfer (RT) method, including various forms of biasing to accelerate the calculations. Because of the probabilistic nature of the MC technique, the outputs are inherently noisy, but it is often assumed that the average values provide the physically correct result. We show that this assumption is not always justified. Specifically, we study the intensity of radiation penetrating an infinite, uniform slab of material that absorbs and scatters the radiation with equal probability. The basic MCRT method, without any biasing mechanisms, starts to break down for transverse optical depths τ ≳ 20 because so few of the simulated photon packets reach the other side of the slab. When including biasing techniques such as absorption/scattering splitting and path length stretching, the simulated photon packets do reach the other side of the slab but the biased weights do not necessarily add up to the correct solution. While the noise levels seem to be acceptable, the average values sometimes severely underestimate the correct solution. Detecting these anomalies requires the judicious application of statistical tests, similar to those used in the field of nuclear particle transport, possibly in combination with convergence tests employing consecutively larger numbers of photon packets. In any case, for transverse optical depths τ ≳ 75 the MC methods used in our study fail to solve the one-dimensional slab problem, implying the need for approximations such as a modified random walk.

Spamcart: a code for smoothed particle Monte Carlo radiative transfer

We present a code for generating synthetic SEDs and intensity maps from Smoothed Particle Hydrodynamics simulation snapshots. The code is based on the Lucy (1999) Monte Carlo Radiative Transfer method, i.e. it follows discrete luminosity packets, emitted from external and/or embedded sources, as they propagate through a density field, and then uses their trajectories to compute the radiative equilibrium temperature of the ambient dust. The density is not mapped onto a grid, and therefore the calculation is performed at exactly the same resolution as the hydrodynamics. We present two example calculations using this method. First, we demonstrate that the code strictly adheres to Kirchhoff's law of radiation. Second, we present synthetic intensity maps and spectra of an embedded protostellar multiple system. The algorithm uses data structures that are already constructed for other purposes in modern particle codes. It is therefore relatively simple to implement.

Monte Carlo radiative transfer in embedded prestellar cores

We implement a Monte Carlo radiative transfer method, that uses a large number of monochromatic luminosity packets to represent the radiation transported through a system. These packets are injected into the system and interact stochastically with it. We test our code against various benchmark calculations and determine the number of packets required to obtain accurate results under different circumstances. We then use this method to study cores that are directly exposed to the interstellar radiation field (non-embedded cores). Our code predicts temperature and intensity profiles inside these cores which are in good agreement with previous studies using different radiative transfer methods. We also explore a large number of models of cores that are embedded in the centre of a molecular cloud. We study cores with different density profiles embedded in molecular clouds with various optical extinctions and we calculate temperature profiles, SEDs and intensity profiles. Our study indicates that the temperature profiles in embedded cores are less steep than those in non-embedded cores. Deeply embedded cores (ambient cloud with visual extinction larger than 15-25) are almost isothermal at around 7-8 K. The temperature inside cores surrounded by an ambient cloud of even moderate thickness ( $A_{\rm V}\sim 5$) is less than 12 K, which is lower than previous studies have assumed. Thus, previous mass calculations of embedded cores (for example in the $\rho$ Ophiuchi protocluster), based on mm continuum observations, may underestimate core masses by up to a factor of 2. Our study shows that the best wavelength region to observe embedded cores is between 400 and 500 $\mu {\rm m}$, where the core is quite distinct from the background. We also predict that very sensitive observations (~ 1-3 MJy ${\rm\, sr^{-1}}$) at 170-200 $\mu {\rm m}$ can be used to estimate how deeply a core is embedded in its parent molecular cloud. The upcoming Herschel mission (ESA, 2007) will, in principle, be able to detect these features and test our models.

Cosmological reionization around the first stars: Monte Carlo radiative transfer

We study the evolution of ionization fronts around the first protogalaxies by using high-resolution numerical cosmological (Λ+ cold dark matter, CDM, model) simulations and Monte Carlo radiative transfer methods. We present the numerical scheme in detail and show the results of test runs from which we conclude that the scheme is both fast and accurate. As an example of interesting cosmological application, we study the reionization produced by a stellar source of total mass M=2×108 M⊙ turning on at z≈12, located at a node of the cosmic web. The study includes a spectral energy distribution of a zero-metallicity stellar population, and two initial mass functions (IMFs; Salpeter/Larson). The expansion of the ionization front (I-front) is followed as it breaks out from the galaxy and is channelled by the filaments into the voids, assuming (in a 2D representation) a characteristic butterfly shape. The ionization evolution is very well tracked by our scheme, as realized by the correct treatment of the channelling and shadowing effects resulting from overdensities. We confirm previous claims that both the shape of the IMF and the ionizing power metallicity dependence are important to correctly determine the reionization of the Universe.

Reflections on Scattered Light: Monte Carlo Simulations of the Flux and Polarization Curves of β Lyrae

AbstractPolarimetry has proven to be a useful observational tool in the study of Be stars. In recent years, Monte Carlo radiative transfer methods have often been used in modeling polarimetric measurements, since they allow accurate predictions of flux and polarization via numerical simulation of the interaction of light with matter, even in systems with complex configurations. We have extended these two complementary techniques to the investigation of binary Be stars by developing a Monte Carlo code that models the flux and polarization phase curves of a binary-disk system. We here present the latest results matching geometrical model configurations with our own spectropolarimetric observations of the Algol binary β Lyrae.

Independent Pixel and Monte Carlo Estimates of Stratocumulus Albedo

Monte Carlo radiative transfer methods are employed here to estimate the plane-parallel albedo bias for marine stratocumulus clouds. This is the bias in estimates of the mesoscale-average albedo, which arises from the assumption that cloud liquid water is uniformly distributed. The authors compare such estimates with those based on a more realistic distribution generated from a fractal model of marine stratocumulus clouds belonging to the class of 'bounded cascade' models. In this model the cloud top and base are fixed, so that all variations in cloud shape are ignored. The model generates random variations in liquid water along a single horizontal direction, forming fractal cloud streets while conserving the total liquid water in the cloud field. The model reproduces the mean, variance, and skewness of the vertically integrated cloud liquid water, as well as its observed wavenumber spectrum, which is approximately a power law. The Monte Carlo method keeps track of the three-dimensional paths solar photons take through the cloud field, using a vectorized implementation of a direct technique. The simplifications in the cloud field studied here allow the computations to be accelerated. The Monte Carlo results are compared to those of the independent pixel approximation, which neglects net horizontal photon transport. Differences between the Monte Carlo and independent pixel estimates of the mesoscale-average albedo are on the order of 1% for conservative scattering, while the plane-parallel bias itself is an order of magnitude larger. As cloud absorption increases, the independent pixel approximation agrees even more closely with the Monte Carlo estimates. This result holds for a wide range of sun angles and aspect ratios. Thus, horizontal photon transport can be safely neglected in estimates of the area-average flux for such cloud models. This result relies on the rapid falloff of the wavenumber spectrum of stratocumulus, which ensures that the smaller-scale variability, where the radiative transfer is more three-dimensional, contributes less to the plane-parallel albedo bias than the larger scales, which are more variable. The lack of significant three-dimensional effects also relies on the assumption of a relatively simple geometry. Even with these assumptions, the independent pixel approximation is accurate only for fluxes averaged over large horizontal areas, many photon mean free paths in diameter, and not for local radiance values, which depend strongly on the interaction between neighboring cloud elements.

Radiation transfer computation in cylindrical arc columns using a Monte Carlo method

A one-dimensional, axisymmetric, Monte Carlo radiative transfer method has been developed to calculate the energy transfer and temperature profiles of moderate to high pressure cylindrical electric arc columns. The model includes the energy transfer due to the emission and absorption of a non-gray gas and thermal conduction but neglects convection. The thermal and electrical conductivities and the wavelength dependent spectral absorptivities are calculated based on assumption of local thermodynamical equilibrium (LTE). To verify the method, calculations were performed for the case of an electric arc in air at 30 atm pressure. The results were compared to those obtained from an earlier calculation which used the diffusion approximation for the radiative transfer. This case is representative of conditions that are typical of constrictors in arc heaters. The method was then applied to an arc in NH 3 at 1 atm for conditions that are typical of the constrictor in arcjet thrusters. The geometrical part of the method was then extended to enable a fully two-dimensional, axisymmetric simulation of radiative transfer for generic geometrical shapes.