Monte Carlo Radiative Transfer Simulations Research Articles

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.

Diagnosis of Circumstellar Matter Structure in Interaction-powered Supernovae with Hydrogen Line Features

Some supernovae (SNe) are powered by the collision of the SN ejecta with dense circumstellar matter (CSM). Their emission spectra show characteristic line shapes of combined broad emission and narrow P Cygni lines, which should closely relate to the CSM structure and the mass-loss mechanism that creates the dense CSM. We quantitatively investigate the relationship between the line shape and the CSM structure by Monte Carlo radiative transfer simulations, considering two representative cases of dense CSM formed by steady and eruptive mass loss. Comparing the Hα emission between the two cases, we find that a narrow P Cygni line appears in the eruptive case but does not appear in the steady case due to the difference in the velocity gradient in the dense CSM. We also reproduce the blueshifted photon excess observed in some Type IIn SNe, which is formed by photon transport across the shock wave, and find the relationship between the velocity of the shocked matter and the amount of blueshift of the photon excess. We conclude that the presence or absence of narrow P Cygni lines can distinguish the mass-loss mechanism and suggest high-resolution spectroscopic observations with λ/Δλ ≳ 104 after the light-curve peak for applying this diagnostic method.

Improving Monte Carlo radiative transfer simulations: A shift of framework

Monte Carlo radiative transfer (MCRT) simulations are a powerful tool for determining the appearance of astrophysical objects, analyzing the prevalent physical conditions within them, and inferring their properties on the basis of real observations. Consequently, a broad variety of codes has been implemented and optimized with the goal of solving this task efficiently. To that end, two distinct frameworks have emerged, namely, the extinction and the scattering framework, which form the basis of the path determination procedures of those codes. These procedures affect the step length of simulated photon packages and are used for determining flux estimates. Despite the fact that these simulations play an important role at present and thus require significant computational resources, little attention has been paid to the benefits and the drawbacks of both frameworks so far. In this study, we investigate their differences and assess their performance with regard to the quality of thereby obtained flux estimates, with a particular focus on the required computational demand. To that end, we use a testbed composed of an infinite plane-parallel slab, illuminated from one side, and we determine transmitted intensity using MCRT simulations for both frameworks. We find that there are vast differences between the frameworks with regard to their convergence speed. The scattering framework outperforms the extinction framework across all considered optical depths and albedos when solving this task, particularly in the regime of high optical depths. Its implementation can therefore greatly benefit all modern MCRT codes as it has the potential to significantly reduce required computation times. Thus, we highly recommend its consideration for various tasks that require MCRT simulations.

Monte Carlo radiative transfer peel off mechanism for spatially extended detectors

We present an extension to the well-known peel off optimization for Monte Carlo radiative transfer simulations. The classical method is only applicable when the distance between the detector and the peel off event is much bigger than the size of the detector. We use two alternatives to the classical method and calculate the peel off intensity via a subdivision and an integration method. We compare their performance for a realistic scenario and derive guidelines for a general treatment. This allows for precise peel off calculations at any distance to the detector surface.

A disc wind model for blueshifts in quasar broad emission lines

ABSTRACT Blueshifts – or, more accurately, blue asymmetries – in broad emission lines such as C iv λ1550 are common in luminous quasars and correlate with fundamental properties such as Eddington ratio and broad absorption line (BAL) characteristics. However, the formation of these blueshifts is still not understood, and neither is their physical connection to the BAL phenomenon or accretion disc. In this work, we present Monte Carlo radiative transfer and photoionization simulations using parametrized biconical disc-wind models. We take advantage of the azimuthal symmetry of a quasar and show that we can reproduce C iv blueshifts provided that (i) the disc-mid-plane is optically thick out to radii beyond the line formation region, so that the receding wind bicone is obscured; and (ii) the system is viewed from relatively low (that is, more face-on) inclinations (≲40°). We show that C iv emission-line blueshifts and BALs can form in the same wind structure. The velocity profile of the wind has a significant impact on the location of the line formation region and the resulting line profile, suggesting that the shape of the emission lines can be used as a probe of wind-driving physics. While we are successful at producing blueshifts/blue asymmetries in outflows, we struggle to match the detailed shape or skew of the observed emission-line profiles. In addition, our models produce redshifted emission-line asymmetries for certain viewing angles. We discuss our work in the context of the C iv λ1550 emission blueshift versus equivalent-width space and explore the implications for quasar disc wind physics.

Exploring the polarization of axially symmetric supernovae with unsupervised deep learning

ABSTRACT The measurement of non-zero polarization can be used to infer the presence of departures from spherical symmetry in supernovae (SNe). The origin of the majority of the intrinsic polarization observed in SNe is in electron scattering, which induces a wavelength-independent continuum polarization that is generally observed to be low ($\lesssim\!\! 1{{\ \rm per\, cent}}$) for all SN types. The key indicator of asymmetry in SNe is the polarization observed across spectral lines, in particular the characteristic ‘inverse P Cygni’ profile. The results of a suite of 900 Monte Carlo radiative transfer simulations are presented here. These simulations cover a range of possible axisymmetric structures (including unipolar, bipolar, and equatorial enhancements) for the line-forming region of the Ca ii infrared triplet. Using a variational auto-encoder, seven key latent parameters are learned that describe the relationship between Stokes I and q, under the assumption of an axially symmetric line-forming region and resonant scattering. Likelihood-free inference techniques are used to invert the Stokes I and q line profiles, in the latent space, to derive the underlying geometries. For axially symmetric structures that yield an observable ‘dominant axis’ on the Stokes q–u plane, we propose the existence of a geometry ‘conjugate’ (which is indistinguishable under a rotation of π/2). Using this machine learning infrastructure, we attempt to identify possible geometries associated with spectropolarimetric observations of the Type Ib SN 2017gax.

Impact of jets on kilonova photometric and polarimetric emission from binary neutron star mergers

ABSTRACT A merger of binary neutron stars creates heavy unstable elements whose radioactive decay produces a thermal emission known as a kilonova. In this paper, we predict the photometric and polarimetric behaviour of this emission by performing 3D Monte Carlo radiative transfer simulations. In particular, we choose three hydrodynamical models for merger ejecta, two including jets with different luminosities and one without a jet structure, to help decipher the impact of jets on the light curve and polarimetric behaviour. In terms of photometry, we find distinct colour evolutions across the three models. Models without a jet show the highest variation in light curves for different viewing angles. In contrast to previous studies, we find models with a jet to produce fainter kilonovae when viewed from orientations close to the jet axis, compared to a model without a jet. In terms of polarimetry, we predict relatively low levels (≲0.3–0.4 per cent) at all orientations that, however, remain non-negligible until a few days after the merger and longer than previously found. Despite the low levels, we find that the presence of a jet enhances the degree of polarization at wavelengths ranging from 0.25 to $2.5\rm{\mu m}$, an effect that is found to increase with the jet luminosity. Thus, future photometric and polarimetric campaigns should observe kilonovae in blue and red filters for a few days after the merger to help constrain the properties of the ejecta (e.g. composition) and jet.

Investigation of three-dimensional radiative transfer effects for UV–Vis satellite and ground-based observations of volcanic plumes

Abstract. We investigate effects of the three-dimensional (3D) structure of volcanic plumes on the retrieval results of satellite and ground-based UV–Vis observations. For the analysis of such measurements, 1D scenarios are usually assumed (the atmospheric properties only depend on altitude). While 1D assumptions are well suited for the analysis of many atmospheric phenomena, they are usually less appropriate for narrow trace gas plumes. For UV–Vis satellite instruments with large ground pixel sizes like the Global Ozone Monitoring Experiment-2 (GOME-2), the SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) or the Ozone Monitoring Instrument (OMI), 3D effects are of minor importance, but usually these observations are not sensitive to small volcanic plumes. In contrast, observations of the TROPOspheric Monitoring Instrument (TROPOMI) on board Sentinel-5P have a much smaller ground pixel size (3.5 × 5.5 km2). Thus, on the one hand, TROPOMI can detect much smaller plumes than previous instruments. On the other hand, 3D effects become more important, because the TROPOMI ground pixel size is smaller than the height of the troposphere and also smaller than horizontal atmospheric photon path lengths in the UV–Vis spectral range. In this study we investigate the following 3D effects using Monte Carlo radiative transfer simulations: (1) the light-mixing effect caused by horizontal photon paths, (2) the saturation effect for strong SO2 absorption, (3) geometric effects related to slant illumination and viewing angles and (4) plume side-effects related to slant illumination angles and photons reaching the sensor from the sides of volcanic plumes. The first two effects especially can lead to a strong and systematic underestimation of the true trace gas content if 1D retrievals are applied (more than 50 % for the light-mixing effect and up to 100 % for the saturation effect). Besides the atmospheric radiative transfer, the saturation effect also affects the spectral retrievals. Geometric effects have a weaker influence on the quantitative analyses but can lead to a spatial smearing of elevated plumes or even to virtual double plumes. Plume side-effects are small for short wavelengths but can become large for longer wavelengths (up to 100 % for slant viewing and illumination angles). For ground-based observations, most of the above-mentioned 3D effects are not important because of the narrow field of view (FOV) and the closer distance between the instrument and the volcanic plume. However, the light-mixing effect shows a similar strong dependence on the horizontal plume extension as for satellite observations and should be taken into account for the analysis of ground-based observations.

Spatial field reconstruction with INLA

Aims. Monte Carlo radiative transfer (MCRT) simulations are a powerful tool for understanding the role of dust in astrophysical systems and its influence on observations. However, due to the strong coupling of the radiation field and medium across the whole computational domain, the problem is non-local and non-linear, and such simulations are computationally expensive in the case of realistic 3D inhomogeneous dust distributions. We explore a novel technique for post-processing MCRT output to reduce the total computational run time by enhancing the output of computationally less expensive simulations of lower-quality. Methods. We combined principal component analysis (PCA) and non-negative matrix factorisation (NMF) as dimensionality reduction techniques together with Gaussian Markov random fields and the integrated nested Laplace approximation (INLA), an approximate method for Bayesian inference, to detect and reconstruct the non-random spatial structure in the images of lower signal-to-noise ratios or with missing data. Results. We tested our methodology using synthetic observations of a galaxy from the SKIRT Auriga project - a suite of high-resolution magnetohydrodynamic Milky Way-sized galaxies simulated in cosmological environment using a ‘zoom-in' technique. With this approach, we are able to reproduce high-photon-number reference images ~5 times faster with median residuals below ~20%.

Dynamical Unification of Tidal Disruption Events

The ∼100 tidal disruption events (TDEs) observed so far exhibit a wide range of emission properties both at peak and over their lifetimes. Some TDEs radiate predominantly at X-ray energies, while others radiate chiefly at UV and optical wavelengths. While the peak luminosities across TDEs show distinct properties, the evolutionary behavior can also vary between TDEs with similar peak emission properties. In particular, for optical TDEs, while their UV and optical emissions decline somewhat following the fallback pattern, some events can greatly rebrighten in X-rays at late time. In this Letter, we conduct three-dimensional general relativistic radiation magnetohydrodynamics simulations of TDE accretion disks at varying accretion rates in the regime of super-Eddington accretion. We make use of Monte Carlo radiative transfer simulations to calculate the reprocessed spectra at various inclinations and at different evolutionary stages. We confirm the unified model proposed by Dai et al., which predicts that the observed emission largely depends on the viewing angle of the observer with respect to the disk orientation. Furthermore, we find that disks with higher accretion rates have elevated wind and disk densities, which increases the reprocessing of the high-energy radiation and thus generally augments the optical-to-X-ray flux ratio along a particular viewing angle. This implies that at later times, as the accretion level declines, we expect that more X-rays will leak out along intermediate viewing angles. Such dynamical model for TDEs can provide a natural explanation for the diversity in the emission properties observed in TDEs at peak and along their temporal evolution.

Investigating the X-ray polarization of lamp-post coronae in BHXRBs

ABSTRACT High-sensitivity X-ray polarimetric observations of black hole X-ray binaries, which will soon become available with the launches of space-borne X-ray observatories with sensitive X-ray polarimeters, will be able to put independent constraints on the black hole as well as the accretion flow, and possibly break degeneracies that cannot be resolved by spectral/timing observations alone. In this work, we perform a series of general relativistic Monte Carlo radiative transfer simulations to study the expected polarization properties of X-ray radiation emerging from lamp-post coronae in black hole X-ray binaries. We find that the polarization degree of the coronal emission of black hole X-ray binaries is sensitive to the spin of the black hole, the height of the corona, and the dynamics of the corona.

A new Monte Carlo radiative transfer simulation of cyclotron resonant scattering features

ABSTRACT We present a new Monte Carlo radiative transfer code, which we have used to model the cyclotron line features in the environment of a variable magnetic field and plasma density. The code accepts an input continuum and performs only the line transfer by including the three cyclotron resonant processes (cyclotron absorption, cyclotron emission, cyclotron scattering). Subsequently, the effects of gravitational redshift and light bending on the emergent spectra are computed. We have applied our code to predict the observable spectra from three different emission geometries; (1) an optically thin slab near the stellar surface, (2) an accretion mound formed by the accumulation of the accreted matter, (3) an accretion column representing the zone of a settling flow on to the star. Our results show that the locally emergent spectra from the emission volume are significantly anisotropic. However, in the presence of strong light bending the anisotropy reduces considerably. This averaging also drastically reduces the strength of harmonics higher than second in the observable cyclotron spectra. We find that uniform field slabs produce line features that are too narrow, and mounds with large magnetic distortions produce features that are too wide compared to the average widths of the spectral features observed from various sources. The column with a gently varying (dipole) field produces widths in the intermediate range, similar to those observed.

Monte Carlo Radiative Transfer Simulation to Analyze the Spectral Index for Remote Detection of Oil Dispersed in the Southern Baltic Sea Seawater Column: The Role of Water Surface State

The article presents the results of simulations that take into account the optical parameters of the selected sea region (from literature data on the southern Baltic Sea) and two optically extreme types of crude oil (from historical data) which exist in the form of a highly watered-down oil-in-water emulsion (10 ppm). The spectral index was analyzed based on the results of modeling the radiance reflectance distribution for almost an entire hemisphere of the sky (zenith angle from 0 to 80°). The spectral index was selected and is universal for all optically different types of oil (wavelengths of 650 and 412 nm). The possibility of detecting pollution in the conditions of the wavy sea surface (as a result of wind of up to 10 m/s) was studied. It was also shown that if the viewing direction is close to a direction perpendicular to the sea surface, observations aimed at determining the spectral index are less effective than observations under the zenith angle of incidence of sunlight for all azimuths excluding the direction of sunlight’s specular reflection.

Self-scattering on large, porous grains in protoplanetary disks with dust settling

Context. Observations of protoplanetary disks in the sub-millimetre wavelength range suggest that polarisation is caused by scattering of thermal re-emission radiation. Most of the dust models that are used to explain these observations have major drawbacks: they either use much smaller grain sizes than expected from dust evolution models, or result in polarisation degrees that are lower than observed. Aims. We investigate the effect of dust grain porosity on the observable polarisation due to scattering at sub-millimetre wavelengths arising from grain size distributions up to millimetre sizes, as they are expected to be present close to the midplane of protoplanetary disks. Methods. Using the effective medium theory, we calculated the optical properties of porous dust and used them to predict the behaviour of the observable polarisation degree due to scattering. Subsequently, Monte Carlo radiative transfer simulations for protoplanetary disks with porous dust grains were performed to analyse the additional effect of the optical depth structure, and thus the effect of multiple scattering events and inhomogeneous temperature distributions on the net observable polarisation degree. Results. We find that porous dust grains with moderate filling factors of about 10% increase the degree of polarisation compared to compact grains. For higher grain porosities, that is, grains with a filling factor of 1% or lower, the extinction opacity decreases, as does the optical depth of a disk with constant mass. Consequently, the unpolarised direct radiation dominates the scattered flux, and the degree of polarisation drops rapidly. Even though the simulated polarisation degree is higher than in the case of compact grains, it is still below the typical observed values for face-on disks. However, the polarisation degree can be increased when crucial model assumptions derived from disk and dust evolution theories, for instance, dust settling and millimetre-sized dust grains, are dropped. In the case of inclined disks, however, our reference model is able to achieve polarisation degrees of about 1%, and using higher disk masses, even higher than this.

Transmission across the water-air interface: resolving the impact of multiple interactions at the sea surface.

A series of Monte Carlo and HydroLight radiative transfer simulations are used to demonstrate that the traditional form of the Fresnel transmission across the water-air interface is accurate. This contradicts assertions to the contrary in a recent paper [Opt. Express25, 27086 (2017)10.1364/OE.25.027086] that suggested that the impact of multiple surface interactions had previously been ignored and that the transmission factor was dependent upon the turbidity of the water.

The scattering order problem in Monte Carlo radiative transfer

Radiative transfer simulation is an important tool that allows us to generate synthetic images of various astrophysical objects. In the case of complex three-dimensional geometries, a Monte Carlo-based method that simulates photon packages as they move through and interact with their environment is often used. Previous studies have shown, in the regime of high optical depths, that the required number of simulated photon packages strongly rises and estimated fluxes may be severely underestimated. In this paper we identify two problems that arise for Monte Carlo radiative transfer simulations that hinder a proper determination of flux: first, a mismatch between the probability and weight of the path of a photon package and second, the necessity of simulating a wide range of high scattering orders. Furthermore, we argue that the peel-off method partly solves these problems, and we additionally propose an extended peel-off method. Our proposed method improves several shortcomings of its basic variant and relies on the utilization of precalculated sphere spectra. We then combine both peel-off methods with the Split method and the Stretch method and numerically evaluate their capabilities as opposed to the pure Split & Stretch method in an infinite plane-parallel slab setup. We find that the peel-off method greatly enhances the performance of these simulations; in particular, at a transverse optical depth of τmax = 75 our method achieved a significantly lower error than previous methods while simultaneously saving > 95% computation time. Finally, we discuss the inclusion of polarization and Mie-scattering in the extended peel-off method, and argue that it may be necessary to equip future Monte Carlo radiative transfer simulations with additional advanced pathfinding techniques.

Spatial-Scale Characteristics of a Three-Dimensional Cloud-Resolving Solar Radiation Budget Based on Monte Carlo Radiative Transfer Simulations

Spatial-Scale Characteristics of a Three-Dimensional Cloud-Resolving Solar Radiation Budget Based on Monte Carlo Radiative Transfer Simulations

Polarized kilonovae from black hole–neutron star mergers

ABSTRACT We predict linear polarization for a radioactively powered kilonova following the merger of a black hole and a neutron star. Specifically, we perform 3D Monte Carlo radiative transfer simulations for two different models, both featuring a lanthanide-rich dynamical ejecta component from numerical-relativity simulations while only one including an additional lanthanide-free disc-wind component. We calculate polarization spectra for nine different orientations at 1.5, 2.5, and 3.5 d after the merger and in the $0.1\!-\!2\, \mu$m wavelength range. We find that both models are polarized at a detectable level 1.5 d after the merger while show negligible levels thereafter. The polarization spectra of the two models are significantly different. The model lacking a disc wind shows no polarization in the optical, while a signal increasing at longer wavelengths and reaching $\sim 1\!-\!6{{\ \rm per\ cent}}$ at $2\, \mu$m depending on the orientation. The model with a disc-wind component, instead, features a characteristic ‘double-peak’ polarization spectrum with one peak in the optical and the other in the infrared. Polarimetric observations of future events will shed light on the debated neutron richness of the disc-wind component. The detection of optical polarization would unambiguously reveal the presence of a lanthanide-free disc-wind component, while polarization increasing from zero in the optical to a peak in the infrared would suggest a lanthanide-rich composition for the whole ejecta. Future polarimetric campaigns should prioritize observations in the first ∼48 h and in the $0.5\!-\!2\, \mu$m range, where polarization is strongest, but also explore shorter wavelengths/later times where no signal is expected from the kilonova and the interstellar polarization can be safely estimated.

Modeling the Transmission of Optical Lightning Signals Through Complex 3‐D Cloud Scenes

AbstractSpace‐based lightning imagers have shown that complex cloud scenes consisting of multiple tall convective features, anvil clouds, and warm boundary cloud layers are illuminated by lightning in many different ways depending on where the lightning occurs and how energetic it is. Modifications to the optical lightning signals from radiative transfer in the cloud medium can lead to reductions in detection efficiency and location accuracy for these instruments and can also cause some of the optical signals that are detected to have unexpected spatial energy distributions. In this study, we perform Monte Carlo radiative transfer simulations of optical lightning emissions in clouds with complex 3‐D geometries to shed some light on the origins of certain irregular radiance patterns that have been recorded from orbit. We show that diffuse reflections off nearby cloud faces can explain lightning signals in nonelectrified clouds, tall clouds can result in poor optical transmission and suppressed radiances that could lead to missed events and that particularly favorable viewing conditions can cause otherwise normal lightning to produce a superbolt that is orders of magnitude brighter than the same flash seen from a different angle.

CMACIONIZE 2.0: a novel task-based approach to Monte Carlo radiation transfer

Context. Monte Carlo radiative transfer (MCRT) is a widely used technique to model the interaction between radiation and a medium. It plays an important role in astrophysical modelling and when these models are compared with observations. Aims. We present a novel approach to MCRT that addresses the challenging memory-access patterns of traditional MCRT algorithms, which prevent an optimal performance of MCRT simulations on modern hardware with a complex memory architecture. Methods. We reformulated the MCRT photon-packet life cycle as a task-based algorithm, whereby the computation is broken down into small tasks that are executed concurrently. Photon packets are stored in intermediate buffers, and tasks propagate photon packets through small parts of the computational domain, moving them from one buffer to another in the process. Results. Using the implementation of the new algorithm in the photoionization MCRT code CMACIONIZE 2.0, we show that the decomposition of the MCRT grid into small parts leads to a significant performance gain during the photon-packet propagation phase, which constitutes the bulk of an MCRT algorithm because memory caches are used more efficiently. Our new algorithm is faster by a factor 2 to 4 than an equivalent traditional algorithm and shows good strong scaling up to 30 threads. We briefly discuss adjustments to our new algorithm and extensions to other astrophysical MCRT applications. Conclusions. We show that optimising the memory access patterns of a memory-bound algorithm such as MCRT can yield significant performance gains.