Time-dependent Radiative Transfer Research Articles

Radiative signatures of plasmoid-dominated reconnection in blazar jets

The multi-wavelength spectral and temporal variability observed in blazars set tight constraints on current theoretical emission models. Here, we investigate the relativistic magnetic reconnection process as a source of blazar emission in which quasi-spherical plasmoids, containing relativistic particles and magnetic fields, are associated with the emission sites in blazar jets. By coupling recent two-dimensional particle-in-cell simulations of relativistic reconnection with a time-dependent radiative transfer code, we compute the non-thermal emission from a chain of plasmoids formed during a reconnection event. The derived photon spectra display characteristic features observed in both BL Lac sources and flat spectrum radio quasars, with the distinction made by varying the strength of the external photon fields, the jet magnetization, and the number of pairs per proton contained within. Light curves produced from reconnection events are composed of many fast and powerful flares that appear on excess of a slower evolving envelope produced by the cumulative emission of medium-sized plasmoids. The observed variability is highly dependent upon the orientation of the reconnection layer with respect to the blazar jet axis and to the observer. Our model provides a physically motivated framework for explaining the multi-timescale blazar variability across the entire electromagnetic spectrum.

Stability analysis of a multilevel quasidiffusion method for thermal radiative transfer problems

In this paper we analyze a multilevel quasidiffusion (QD) method for solving time-dependent multigroup nonlinear radiative transfer problems which describe interaction of photons with matter. The multilevel method is formulated by means of the high-order radiative transfer equation and a set of low-order moment equations. The fully implicit scheme is used to discretize equations in time. The stability analysis is applied to the method in semi-continuous and discretized forms. To perform Fourier analysis, the system of equations of the multilevel method is linearized about an equilibrium solution. The effects of discretization with respect to different independent variables are studied. The multilevel method is shown to be stable and fast converging. We also consider a version of the method in which time evolution in the radiative transfer equation is treated by means of the α-approximation. The Fleck–Cummings test problem is used to demonstrate performance of the multilevel QD method and study its iterative stability.

3D time-dependent hydrodynamical and radiative transfer modeling of Eta Carinae’s innermost fossil colliding wind structures

AbstractEta Carinae is the most massive active binary within 10,000 light-years. While famous for the largest non-terminal stellar explosion ever recorded, observations reveal a supermassive (∼120 M⊙) binary consisting of an LBV and either a WR or extreme O star in a very eccentric orbit (e=0.9) with a 5.54-year period. Dramatic changes across multiple wavelengths are routinely observed as the stars move about in their highly elliptical orbits, especially around periastron when the hot (∼40 kK) companion star delves deep into the denser and much cooler (∼15 kK) extended wind photosphere of the LBV primary. Many of these changes are due to a dynamic wind-wind collision region (WWCR) that forms between the stars, plus expanding radiation-illuminated fossil WWCRs formed one, two, and three 5.54-year orbital cycles ago. These fossil WWCRs have been spatially and spectrally resolved by the Hubble Space Telescope/Space Telescope Imaging Spectrograph (HST/STIS) at multiple epochs, resulting in data cubes that spatially map Eta Carinae’s innermost WWCRs and follow temporal changes in several forbidden emission lines (e.g. [Fe iii] 4659 Å, [Fe ii] 4815 Å) across the 5.54-year cycle. We present initial results of 3D time-dependent hydrodynamical and radiative-transfer simulations of the Eta Carinae binary and its WWCRs with the goal of producing synthetic data cubes of forbidden emission lines for comparison to the available HST/STIS observations. Comparison of the theoretical models to the observations reveals important details about the binary’s orbital motion, photoionization properties, and recent (5–15year) mass loss history. Such an analysis also provides a baseline for following future changes in Eta Carinae, essential for understanding the late-stage evolution of a nearby supernova progenitor. Our modeling methods can also be adapted to a number of other colliding wind binary systems (e.g. WR 140) that are scheduled to be studied with future observatories (e.g. the James Webb Space Telescope).

Enhancing early-time diffusion through beam collimation in pulse propagation in sparse discrete random media.

Solutions of the time-dependent radiative transfer equation (RTE) are used to describe propagation of a pulsed collimated beam through a random medium consisting of discrete scatterers of sizes large compared to the wavelengths-a situation particularly relevant to free-space optical communication through atmospheric obscurants. The RTE is solved in the spherical-harmonics basis with no approximations other than a truncation N in the angular momenta; the results confirm convergence of the solution for a fixed beam width and growing N. The obtained time-resolved radiance includes both the usual "late-time diffusion" (LTD), responsible for the well known reduction of the "coherence bandwidth" and, thus, a serious limitation in the transfer rate, and the more recently identified "early-time diffusion" (ETD) component, attenuated at a rate significantly lower than for the coherent (ballistic) signal and characterized by a very short rise time, allowing a high-rate data transfer. The ratio of the ETD to the LTD signal for the considered collimated beams is much (orders of magnitude) higher than in the previously examined problem of an omnidirectional source, increasing its potential usefulness in communication and related imaging applications.

Theoretical and Numerical Analysis of an Initial-Boundary Value Problem for the Radiative Transfer Equation with Fresnel Matching Conditions

A Cauchy problem for the time-dependent radiative transfer equation in a three-dimensional multicomponent medium with generalized matching conditions describing Fresnel reflection and refraction at the interface of the media is considered. The unique solvability of the problem is proven, a Monte Carlo method for solving the initial-boundary value problem is developed, and computational experiments for different implementations of the algorithm are conducted.

RAPTOR

Context. Observational efforts to image the immediate environment of a black hole at the scale of the event horizon benefit from the development of efficient imaging codes that are capable of producing synthetic data, which may be compared with observational data. Aims. We aim to present RAPTOR, a new public code that produces accurate images, animations, and spectra of relativistic plasmas in strong gravity by numerically integrating the equations of motion of light rays and performing time-dependent radiative transfer calculations along the rays. The code is compatible with any analytical or numerical spacetime. It is hardware-agnostic and may be compiled and run both on GPUs and CPUs. Methods. We describe the algorithms used in RAPTOR and test the code’s performance. We have performed a detailed comparison of RAPTOR output with that of other radiative-transfer codes and demonstrate convergence of the results. We then applied RAPTOR to study accretion models of supermassive black holes, performing time-dependent radiative transfer through general relativistic magneto-hydrodynamical (GRMHD) simulations and investigating the expected observational differences between the so-called fast-light and slow-light paradigms. Results. Using RAPTOR to produce synthetic images and light curves of a GRMHD model of an accreting black hole, we find that the relative difference between fast-light and slow-light light curves is less than 5%. Using two distinct radiative-transfer codes to process the same data, we find integrated flux densities with a relative difference less than 0.01%. Conclusions. For two-dimensional GRMHD models, such as those examined in this paper, the fast-light approximation suffices as long as errors of a few percent are acceptable. The convergence of the results of two different codes demonstrates that they are, at a minimum, consistent.

Dusty Cloud Acceleration by Radiation Pressure in Rapidly Star-forming Galaxies

Abstract We perform two-dimensional and three-dimensional radiation hydrodynamic simulations to study cold clouds accelerated by radiation pressure on dust in the environment of rapidly star-forming galaxies dominated by infrared flux. We utilize the reduced speed of light approximation to solve the frequency-averaged, time-dependent radiative transfer equation. We find that radiation pressure is capable of accelerating the clouds to hundreds of kilometers per second while remaining dense and cold, consistent with observations. We compare these results to simulations where acceleration is provided by entrainment in a hot wind, where the momentum injection of the hot flow is comparable to the momentum in the radiation field. We find that the survival time of the cloud accelerated by the radiation field is significantly longer than that of a cloud entrained in a hot outflow. We show that the dynamics of the irradiated cloud depends on the initial optical depth, temperature of the cloud, and intensity of the flux. Additionally, gas pressure from the background may limit cloud acceleration if the density ratio between the cloud and background is . In general, a 10 pc-scale optically thin cloud forms a pancake structure elongated perpendicular to the direction of motion, while optically thick clouds form a filamentary structure elongated parallel to the direction of motion. The details of accelerated cloud morphology and geometry can also be affected by other factors, such as the cloud lengthscale, reduced speed of light approximation, spatial resolution, initial cloud structure, and dimensionality of the run, but these have relatively little affect on the cloud velocity or survival time.

A magnetar model for the hydrogen-rich super-luminous supernova iPTF14hls

Transient surveys have recently revealed the existence of H-rich super-luminous supernovae (SLSN; e.g., iPTF14hls, OGLE-SN14-073) that are characterized by an exceptionally high time-integrated bolometric luminosity, a sustained blue optical color, and Doppler-broadened HIlines at all times. Here, I investigate the effect that a magnetar (with an initial rotational energy of 4 × 1050erg and field strength of 7 × 1013G) would have on the properties of a typical Type II supernova (SN) ejecta (mass of 13.35M⊙, kinetic energy of 1.32 × 1051erg, 0.077M⊙of56Ni) produced by the terminal explosion of an H-rich blue supergiant star. I present a non-local thermodynamic equilibrium time-dependent radiative transfer simulation of the resulting photometric and spectroscopic evolution from 1 d until 600 d after explosion. With the magnetar power, the model luminosity and brightness are enhanced, the ejecta is hotter and more ionized everywhere, and the spectrum formation region is much more extended. This magnetar-powered SN ejecta reproduces most of the observed properties of SLSN iPTF14hls, including the sustained brightness of −18 mag in theRband, the blue optical color, and the broad HIlines for 600 d. The non-extreme magnetar properties, combined with the standard Type II SN ejecta properties, offer an interesting alternative to the pair-unstable super-massive star model recently proposed, which involves a highly energetic and super-massive ejecta. Hence, such Type II SLSNe may differ from standard Type II SNe exclusively through the influence of a magnetar.

Ejecta mass diagnostics of Type Ia supernovae

We present one-dimensional non-local thermodynamic equilibrium time-dependent radiative transfer simulations (using CMFGEN) of two sub-Chandrasekhar (sub-$M_{\rm Ch}$), one $M_{\rm Ch}$ and one super-$M_{\rm Ch}$ Type Ia SN ejecta models. Three originate from $M_{\rm Ch}$ delayed detonation models, and the fourth is a sub-$M_{\rm Ch}$ detonation model. Ejecta masses are 1.02, 1.04, 1.40, and 1.70 M$_\odot$, and all models have 0.62 M$_\odot$ of $^{56}{\rm Ni}$. Sub-$M_{\rm Ch}$ model light curves evolve faster, reaching bolometric maximum 2--3 days earlier and having 3--4 days shorter bolometric half light widths. The models vary by $\sim$12 per cent at maximum bolometric luminosity and by 0.17 mag in $B_{\rm max}$. While $\Delta M_{15}(B)$ increases with ejecta mass it only varies by $\sim$5 per cent around 1 mag. Sub-$M_{\rm Ch}$ models are 0.25 mag bluer in $B-R$ at $B_{\rm max}$. Optical spectra share many similarities, but lower mass models exhibit less UV line blanketing during the photospheric phase. At nebular times, significant NIR spectroscopic differences are seen. In particular, emission lines of the Ca II NIR triplet; [S III] $\lambda\lambda$9068,9530; [Ca II] $\lambda\lambda$7291,7324; [Ar III] $\lambda\lambda$7135,7751; and [Ni II] 1.939 $\mu$m are stronger in higher mass models. The [Ni II] 1.939 $\mu$m line is absent in the sub-$M_{\rm Ch}$ detonation model, and provides a valuable potential tool to distinguish sub-$M_{\rm Ch}$ explosions from $M_{\rm Ch}$ explosions. In general, the nebular phase models are too highly ionized. We attribute this to the neglect of clumping and/or the distribution of intermediate mass and iron group elements. The two sub-$M_{\rm Ch}$ models, while exploded by different mechanisms, can be distinguished in the $J$ and $H$ bands at late times (e.g., $+200$ days).

Improving the thin-disk models of circumstellar disk evolution. The 2+1-dimensional model

Circumstellar disks of gas and dust are naturally formed from contracting pre-stellar molecular cores during the star formation process. To study various dynamical and chemical processes that take place in circumstellar disks prior to their dissipation and transition to debris disks, the appropriate numerical models capable of studying the long-term disk chemodynamical evolution are required. We present a new 2+1-dimensional numerical hydrodynamics model of circumstellar disk evolution, in which the thin-disk model is complemented with the procedure for calculating the vertical distributions of gas volume density and temperature in the disk. The reconstruction of the disk vertical structure is performed at every time step via the solution of the time-dependent radiative transfer equations coupled to the equation of the vertical hydrostatic equilibrium. We perform a detailed comparison between circumstellar disks produced with our previous 2D model and with the improved 2+1D approach. The structure and evolution of resulting disks, including the differences in temperatures, densities, disk masses and protostellar accretion rates, are discussed in detail. The new 2+1D model yields systematically colder disks, while the in-falling parental clouds are warmer. Both effects act to increase the strength of disk gravitational instability and, as a result, the number of gravitationally bound fragments that form in the disk via gravitational fragmentation as compared to the purely 2D thin-disk simulations with a simplified thermal balance calculation.

Evidence for sub-Chandrasekhar-mass progenitors of Type Ia supernovae at the faint end of the width–luminosity relation

The faster light-curve evolution of low-luminosity Type Ia supernovae (SNe Ia) suggests that they could result from the explosion of white dwarf (WD) progenitors below the Chandrasekhar mass ($M_{\rm Ch}$). Here we present 1D non-LTE time-dependent radiative transfer simulations of pure central detonations of carbon-oxygen WDs with a mass ($M_\rm{tot}$) between 0.88 M$_{\odot}$ and 1.15 M$_{\odot}$, and a $^{56}\rm{Ni}$ yield between 0.08 M$_{\odot}$ and 0.84 M$_{\odot}$. Their lower ejecta density compared to $M_{\rm Ch}$ models results in a more rapid increase of the luminosity at early times and an enhanced $\gamma$-ray escape fraction past maximum light. Consequently, their bolometric light curves display shorter rise times and larger post-maximum decline rates. Moreover, the higher $M(^{56}\rm{Ni})/M_\rm{tot}$ ratio at a given $^{56}\rm{Ni}$ mass enhances the temperature and ionization level in the spectrum-formation region for the less luminous models, giving rise to bluer colours at maximum light and a faster post-maximum evolution of the $B-V$ colour. For sub-$M_{\rm Ch}$ models fainter than $M_B\approx -18.5$ mag at peak, the greater bolometric decline and faster colour evolution lead to a larger $B$-band post-maximum decline rate, $\Delta M_{15}(B)$. In particular, all of our previously-published $M_{\rm Ch}$ models (standard and pulsational delayed detonations) are confined to $\Delta M_{15}(B) < 1.4$ mag, while the sub-$M_{\rm Ch}$ models with $M_\rm{tot}\lesssim 1$ M$_{\odot}$ extend beyond this limit to $\Delta M_{15}(B)\approx 1.65$ mag for a peak $M_B\approx -17$ mag, in better agreement with the observed width-luminosity relation (WLR). Regardless of the precise ignition mechanism, these simulations suggest that fast-declining SNe Ia at the faint end of the WLR could result from the explosion of WDs whose mass is significantly below the Chandrasekhar limit.

Transient polarized radiative transfer analysis in a scattering medium by a discontinuous finite element method.

Transient (time-dependent) polarized radiative transfer in a scattering medium exposed to an external collimated beam illumination is conducted based on the time-dependent polarized radiative transfer theory. The transient term, which persists the nanosecond order time and cannot be ignored for the time-dependent radiative transfer problems induced by a short-pulsed beam, is considered as well as the polarization effect of the radiation. A discontinuous finite element method (DFEM) is developed for the transient vector radiative transfer problem and the derivation of the discrete form of the governing equation is presented. The correctness of the developed DFEM is first verified by comparing the DFEM solutions with the results from the literature. The DFEM is then applied to study the transient polarized radiative transfer induced by a pulsed beam. The time-dependent Stokes vector components are calculated, plotted and analyzed as functions of the axis coordinate and discrete direction. Effects of the diffuse/specular boundary and the incident beam polarization state with respect to the Stokes vector components are further analyzed for cases of different boundary reflection modes and incident beam illuminations.

A new scheme of the time-domain fluorescence tomography for a semi-infinite turbid medium

A new scheme for reconstruction of a fluorophore target embedded in a semi-infinite medium was proposed and evaluated. In this scheme, we neglected the presence of the fluorophore target for the excitation light and used an analytical solution of the time-dependent radiative transfer equation (RTE) for the excitation light in a homogeneous semi-infinite media instead of solving the RTE numerically in the forward calculation. The inverse problem for imaging the fluorophore target was solved using the Landweber–Kaczmarz method with the concept of the adjoint fields. Numerical experiments show that the proposed scheme provides acceptable results of the reconstructed shape and location of the target. The computation times of the solution of the forward problem and the whole reconstruction process were reduced by about 40 and 15%, respectively.

A study of the low-luminosity Type II-Plateau supernova 2008bk

Supernova (SN) 2008bk is a well observed low-luminosity Type II event visually associated with a low-mass red-supergiant progenitor. To model SN 2008bk, we evolve a 12Msun star from the main sequence until core collapse, when it has a total mass of 9.88Msun, a He-core mass of 3.22Msun, and a radius of 502Rsun. We then artificially trigger an explosion that produces 8.29Msun of ejecta with a total energy of 2.5x10^50erg and ~0.009Msun of 56Ni. We model the subsequent evolution of the ejecta with non-Local-Thermodynamic-Equilibrium time-dependent radiative transfer. Although somewhat too luminous and energetic, this model reproduces satisfactorily the multi-band light curves and multi-epoch spectra of SN 2008bk, confirming the suitability of a low-mass massive star progenitor. As in other low-luminosity SNe II, the structured Halpha profile at the end of the plateau phase is probably caused by BaII 6496.9A rather than asphericity. We discuss the sensitivity of our results to changes in progenitor radius and mass, as well as chemical mixing. A 15% increase in progenitor radius causes a 15% increase in luminosity and a 0.2mag V-band brightening of the plateau but leaves its length unaffected. An increase in ejecta mass by 10% lengthens the plateau by ~10d. Chemical mixing introduces slight changes to the bolometric light curve, limited to the end of the plateau, but has a large impact on colours and spectra at nebular times.

Modeling of light propagation in the human neck for diagnoses of thyroid cancers by diffuse optical tomography.

Diffuse optical tomography using near-infrared light in a wavelength range from 700 to 1000nm has the potential to enable non-invasive diagnoses of thyroid cancers; some of which are difficult to detect by conventional methods such as ultrasound tomography. Diffuse optical tomography needs to be based on a physically accurate model of light propagation in the neck, because it reconstructs tomographic images of the optical properties in the human neck by inverse analysis. Our objective here was to investigate the effects of three factors on light propagation in the neck using the 2D time-dependent radiative transfer equation: (1) the presence of the trachea, (2) the refractive-index mismatch at the trachea-tissue interface, and (3) the effect of neck organs other than the trachea (spine, spinal cord, and blood vessels). There was a significant influence of reflection and refraction at the trachea-tissue interface on the light intensities in the region between the trachea and the front of the neck surface. Organs other than the trachea showed little effect on the light intensities measured at the front of the neck surface although these organs affected the light intensities locally. These results indicated the necessity of modeling the refractive-index mismatch at the trachea-tissue interface and the possibility of modeling other neck organs simply as a homogeneous medium when the source and detectors were far from large blood vessels.

A Stable 1D Multigroup High-Order Low-Order Method

ABSTRACTThe high-order low-order (HOLO) method is a recently developed moment-based acceleration scheme for solving time-dependent thermal radiative transfer problems, and has been shown to exhibit orders of magnitude speedups over traditional time-stepping schemes. However, a linear stability analysis by Haut et al. (2015) revealed that the current formulation of the multigroup HOLO method was unstable in certain parameter regions. Since then, we have replaced the intensity-weighted opacity in the first angular moment equation of the low-order (LO) system with the Rosseland opacity. This results in a modified HOLO method (HOLO-R) that is significantly more stable.This paper has two primary components. First, we present results from a linear stability analysis of the HOLO-R method for a 2-group problem. These results show that HOLO-R is stable in all regions of the parameter space we considered, and strongly suggest that HOLO-R is unconditionally stable. The predicted decay factors from the stability analysis are verified with numerically computed decay factors from a spectral HOLO-R code. Second, we describe a preliminary (unoptimized) implementation of HOLO-R in Capsaicin – a deterministic, discrete-ordinates radiation transport code at Los Alamos National Laboratory. The results from this implementation further verify the stability of the HOLO-R method. Moreover, in the simulation of a 50-group, nonlinear Marshak wave problem, away from the 2-group, linearized stability analysis, we assess HOLO-R’s accuracy, efficiency, and robustness as compared to current methods in Capsaicin. To our knowledge, this is the first implementation of HOLO that uses a mass-lumped discontinuous Galerkin spatial discretization for both the high-order (HO) and LO systems, and details of this discretization are provided in the Appendix.

A NUMERICAL SCHEME FOR SPECIAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT RADIATIVE TRANSFER EQUATION

ABSTRACT We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitly solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.

A class of Galerkin Schemes for Time-Dependent Radiative Transfer

The numerical solution of time-dependent radiative transfer problems is challenging, due to the high dimension and to the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a general framework for designing numerical methods for time-dependent radiative transfer based on a Galerkin discretization in space and angle combined with appropriate time stepping schemes. This allows us to systematically incorporate boundary conditions and also to preserve basic properties such as exponential stability and decay to equilibrium on the discrete level. We present the basic a priori error analysis and provide abstract error estimates that cover a wide class of methods. The starting point for our considerations is to rewrite the radiative transfer problem as a system of evolution equations which has a similar structure to first order hyperbolic systems in acoustics or electrodynamics. This analogy allows us to generalize the main arguments of the numerical analysis f...

TIME-DEPENDENT MULTI-GROUP MULTI-DIMENSIONAL RELATIVISTIC RADIATIVE TRANSFER CODE BASED ON SPHERICAL HARMONIC DISCRETE ORDINATE METHOD

We develop a time-dependent multi-group multidimensional relativistic radiative transfer code, which is required to numerically investigate radiation from relativistic fluids involved in, e.g., gamma-ray bursts and active galactic nuclei. The code is based on the spherical harmonic discrete ordinate method (SHDOM) that evaluates a source function including anisotropic scattering in spherical harmonics and implicitly solves the static radiative transfer equation with a ray tracing in discrete ordinates. We implement treatments of time dependence, multi-frequency bins, Lorentz transformation, and elastic Thomson and inelastic Compton scattering to the publicly available SHDOM code. Our code adopts a mixed frame approach; the source function is evaluated in the comoving frame whereas the radiative transfer equation is solved in the laboratory frame. This implementation is validated with various test problems and comparisons with results of a relativistic Monte Carlo code. These validations confirm that the code correctly calculates intensity and its evolution in the computational domain. The code enables us to obtain an Eddington tensor that relates first and third moments of intensity (energy density and radiation pressure) and is frequently used as a closure relation in radiation hydrodynamics calculations.

Detection of tumor-like inclusions embedded within human liver tissue using a short-pulsed near-infrared laser beam: Parallel simulations with radiative transfer equation

An efficient solution to detect tumor-like inclusions embedded within a human liver tissue model is presented, using illumination by a short-pulsed laser beam. Light propagation was accurately solved using the time-dependent radiative transfer equation, with multithreaded parallel computing. A modified finite volume method based on unstructured grids and the fourth-order Runge–Kutta approach was employed to solve the equation in the (2-D/3-D) spatial and time domains. The normalization technique applied to the Henyey–Greenstein phase function was adopted to ensure numerical stability for values of the anisotropy factor that were close to unity. The presence of one or two circular/spherical inclusions was analyzed from the time and spatially resolved reflectance on the medium bounding surface. The results allowed a minimal size and a maximum distance for the detection of the inclusion to be highlighted.