Time-dependent Radiative Transfer Research Articles

An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations

The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction between radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this paper, we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme (AP-UGKS) for the gray radiative transfer equations, where the radiation transport equation is coupled with the material thermal energy equation. The current work is based on the UGKS framework for the rarefied gas dynamics [14], and is an extension of a recent work [12] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional gray radiative system. The newly developed scheme has the asymptotic preserving (AP) property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photon's mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture the exact solution in the optical thin regime as well. The current scheme is a finite volume method. Due to the direct modeling for the time evolution solution of the interface radiative intensity, a smooth transition of the transport physics from optical thin to optical thick can be accurately recovered. Many numerical examples are included to validate the current approach.

One-dimensional non-LTE time-dependent radiative transfer of an He-detonation model and the connection to faint and fast-decaying supernovae

We present non-LTE time-dependent radiative transfer simulations for ejecta produced by the detonation of an helium shell at the surface of a low-mass carbon/oxygen white dwarf (WD). This mechanism is one possible origin for supernovae (SNe) with faint and fast-decaying light curves, such as .Ia SNe and Ca-rich transients. Our initial ejecta conditions at 1d are given by the 0.18B explosion model COp45HEp2 of Waldman et al.. The 0.2Msun ejecta initially contains 0.11Msun of He, 0.03Msun of Ca, and 0.03Msun of Ti. We obtain a ~5d rise to a bolometric maximum of 3.59x10^41 erg/s, primarily powered by 48V decay. Multi-band light curves show distinct morphologies, with a rise to maximum magnitude (-14.3 to -16.7mag) that varies between 3 to 9d from the U to the K bands. Near-IR light curves show no secondary maximum. Because of the presence of both HeI and SiII lines at early times we obtain a hybrid Type Ia/Ib classification. During the photospheric phase line blanketing is caused primarily by TiII. At nebular times, the spectra show strong CaII lines in the optical (but no [OI] 6300--6364A emission), and TiII in the near-IR. Overall, these results match qualitatively the very disparate properties of .Ia SNe and Ca-rich transients. Although the strong TiII blanketing and red colors that we predict are rarely observed, they are seen, for example, in OGLE-2013- SN-079. Furthermore, we obtain a faster light-curve evolution than, for example, PTF10iuv, indicating an ejecta mass >0.2Msun. An alternate scenario may be the merger of two WDs, one or both composed of He.

A GLOBAL THREE-DIMENSIONAL RADIATION MAGNETO-HYDRODYNAMIC SIMULATION OF SUPER-EDDINGTON ACCRETION DISKS

We study super-Eddington accretion flows onto black holes using a global three dimensional radiation magneto-hydrodynamical simulation. We solve the time dependent radiative transfer equation for the specific intensities to accurately calculate the angular distribution of the emitted radiation. Turbulence generated by the magneto-rotational instability provides self-consistent angular momentum transfer. The simulation reaches inflow equilibrium with an accretion rate ~220L_edd/c^2 and forms a radiation driven outflow along the rotation axis. The mechanical energy flux carried by the outflow is ~20% of the radiative energy flux. The total mass flux lost in the outflow is about 29% of the net accretion rate. The radiative luminosity of this flow is ~10L_edd. This yields a radiative efficiency ~4.5%, which is comparable to the value in a standard thin disk model. In our simulation, vertical advection of radiation caused by magnetic buoyancy transports energy faster than photon diffusion, allowing a significant fraction of the photons to escape from the surface of the disk before being advected into the black hole. We contrast our results with the lower radiative efficiencies inferred in most models, such as the slim disk model, which neglect vertical advection. Our inferred radiative efficiencies also exceed published results from previous global numerical simulations, which did not attribute a significant role to vertical advection. We briefly discuss the implications for the growth of supermassive black holes in the early universe and describe how these results provided a basis for explaining the spectrum and population statistics of ultraluminous X-ray sources.

Hybrid model of light propagation in random media based on the time-dependent radiative transfer and diffusion equations

Numerical modeling of light propagation in random media has been an important issue for biomedical imaging, including diffuse optical tomography (DOT). For high resolution DOT, accurate and fast computation of light propagation in biological tissue is desirable. This paper proposes a space–time hybrid model for numerical modeling based on the radiative transfer and diffusion equations (RTE and DE, respectively) in random media under refractive-index mismatching. In the proposed model, the RTE and DE regions are separated into space and time by using a crossover length and the time from the ballistic regime to the diffusive regime, ρDA~10/μt′ and tDA~20/vμt′ where μt′ and v represent a reduced transport coefficient and light velocity, respectively. The present model succeeds in describing light propagation accurately and reduces computational load by a quarter compared with full computation of the RTE.

A Frequency-Domain Approach for the $$\hbox {P}_1$$ P 1 Approximation of Time-Dependent Radiative Transfer

We propose a new frequency-domain method to solve the simplified \(\text {P}_1\) approximation of time-dependent radiative transfer equations. The method employs the Fourier transform and consists of two stages. In the first stage the equations are transformed into an elliptic problem for the frequency variables. The numerical solutions of this problem are approximated using a Galerkin projection method based on the tensor-product B-spline interpolants. In the second stage a Gauss–Hermite quadrature procedure is proposed for the computation of the inverse Fourier transform to recover the numerical solutions of the original simplified \(\text {P}_1\) problem. The method avoids the discretization of the time variable in the considered system and it accurately resolves all time scales in radiative transfer regimes. Several test examples are used to verify high accuracy, effectiveness and good resolution properties for smooth and discontinuous solutions.

Physical layer simulator for undersea free-space laser communications

High bandwidth (10 to 100 Mbps), real-time data networking in the subsea environment using free-space lasers has a potentially high impact as an enabling technology for a variety of future subsea operations in the areas of distributed sensing, real-time wireless data transfer, control of unmanned undersea vehicles, and other submerged assets. However, the development and testing of laser networking equipment in the undersea environment are expensive and time consuming, and there is a clear need for a network simulation framework that will allow researchers to evaluate the performance of alternate optical and electronic configurations under realistic operational and environmental constraints. The overall objective of the work reported in this paper was to develop and validate such a simulation framework, which consists of (1) a time-dependent radiative transfer model to accurately predict the channel impulse characteristics for alternate system designs over a range of geometries and optical properties and (2) digital modulation and demodulation blocks which accurately simulate both laser source and receiver noise characteristics in order to generate time domain bit stream samples that can be digitally demodulated to predict the resulting bit error rate of the simulated link.

TIME-DEPENDENT PHOTOIONIZATION OF GASEOUS NEBULAE: THE PURE HYDROGEN CASE

We study the problem of time-dependent photoionization of low density gaseous nebulae subjected to sudden changes in the intensity of ionizing radiation. To this end, we write a computer code that solves the full time-dependent energy balance, ionization balance, and radiation transfer equations in a self-consistent fashion for a simplified pure hydrogen case. It is shown that changes in the ionizing radiation yield ionization/thermal fronts that propagate through the cloud, but the propagation times and response times to such fronts vary widely and non-linearly from the illuminated face of the cloud to the ionization front (IF). Ionization/thermal fronts are often supersonic, and in slabs initially in pressure equilibrium such fronts yield large pressure imbalances that are likely to produce important dynamical effects in the cloud. Further, we studied the case of periodic variations in the ionizing flux. It is found that the physical conditions of the plasma have complex behaviors that differ from any steady-state solutions. Moreover, even the time average ionization and temperature is different from any steady-state case. This time average is characterized by over-ionization and a broader IF with respect to the steady-state solution for a mean value of the radiation flux. Around the time average of physical conditions there is large dispersion in instantaneous conditions, particularly across the IF, which increases with the period of radiation flux variations. Moreover, the variations in physical conditions are asynchronous along the slab due to the combination of non-linear propagation times for thermal/ionization fronts and equilibration times.

Sensitivity analysis to optical properties of biological tissues subjected to a short-pulsed laser using the time-dependent radiative transfer equation

Visible and near-infrared spectral range of light can be used for estimating the optical properties of a biological tissue in a non-invasive way starting from its response to an external light stimulus. A forward model based on the time-dependent radiative transfer equation, that accurately describes light propagation through such media, is considered and solved with a finite-volume method for the discretization of the spatial domain. Results in terms of fluence and of reflectance at the illuminated transparent or semi-transparent wall for liver and skin tissues subjected to a collimated short-pulsed near-infrared laser are presented and discussed. A sensitivity analysis of the reflectance in the time domain to the four optical parameters of the model shows that only two of them can be estimated: the asymmetry factor of the Henyey–Greenstein phase function as well as either the refractive index or the scattering coefficient of the tissue. The reduced model can be used to invert the experimental reflectance measured assuming the signal over noise ratio of the detector known in the corresponding non-invasive detection technique.

Simulation of lidar waveforms with a time-dependent radiosity algorithm

Our objective was to assess the effect of multiple scattering on lidar radiative transfer. We have developed a time-dependent radiosity-based model (RBL) to simulate the propagation of lidar pulses through forest canopies. This 3-D model enables simulation of lidar waveforms with varied topography and clumping vegetation. The incidence angle can also be specified. This new model has the potential to provide better approximations of return waveforms. The prototype is being tested using data from the Scanning Lidar Imager of Canopies by Echo Recovery (SLICER). Waveforms simulated by RBL resemble SLICER waveforms (R2 > 0.90) over a jack pine canopy and a black spruce canopy. There is also good agreement (R2 > 0.95) when the model results are compared with a time-dependent radiative transfer model. Results to date indicate that multiply scattered photons do increase the intensity of the reflected signal, especially the portion originating from the lower levels of the canopy. A sensitivity analysis enabled assessment of the effects of leaf area index, slope, and canopy height on multiple scattering.

On the heat redistribution of the hot transiting exoplanet WASP-18b

The energy deposition and redistribution in hot Jupiter atmospheres is not well understood currently, but is a major factor for their evolution and survival. We present a time dependent radiative transfer model for the atmosphere of WASP-18b which is a massive (10MJup) hot Jupiter (Teq∼2400K) exoplanet orbiting an F6V star with an orbital period of only 0.94days.Our model includes a simplified parametrisation of the day-to-night energy redistribution by a modulation of the stellar heating mimicking a solid body rotation of the atmosphere. We present the cases with either no rotation at all with respect to the synchronously rotating reference frame or a fast differential rotation.The results of the model are compared to previous observations of secondary eclipses of Nymeyer et al. (Nymeyer, S. et al. [2011]. Astrophys. J. 742, 35) with the Spitzer Space Telescope. Their observed planetary flux suggests that the efficiency of heat distribution from the day-side to the night-side of the planet is extremely inefficient. Our results are consistent with the fact that such large day-side fluxes can be obtained only if there is no rotation of the atmosphere.Additionally, we infer light curves of the planet for a full orbit in the two Warm Spitzer bandpassses for the two cases of rotation and discuss the observational differences.

Hybrid Green’s function of the time-dependent radiative transfer equation for anisotropically scattering semi-infinite media

A semi-infinite space Green's function of the time-dependent radiative transfer equation is derived based upon an exact solution for anisotropic scattering in infinite space and the approximated extrapolated boundary condition. The obtained solution is compared to Monte Carlo simulations and used for retrieving the optical parameters of simulated data in a nonlinear fit. It is shown that the solution performs well for boundaries with mismatched refractive indices. The relative errors in the fitted optical parameters are considerably smaller than by using the diffusion theory.

Time-dependent radiative transfer for multi-level atoms using accelerated Lambda iteration

We present a general formalism for computing self-consistent, numerical solutions to the time-dependent radiative transfer equation in low velocity, multi-level ions undergoing radiative interactions. Recent studies of time-dependent radiative transfer have focused on radiation hydrodynamic and magnetohydrodynamic effects without lines, or have solved time-independent equations for the radiation field simultaneously with time-dependent equations for the state of the medium. In this paper, we provide a fully time-dependent numerical solution to the radiative transfer and atomic rate equations for a medium irradiated by an external source of photons. We use Accelerated Lambda Iteration to achieve convergence of the radiation field and atomic states. We perform calculations for a three-level atomic model that illustrates important time-dependent effects. We demonstrate that our method provides an efficient, accurate solution to the time-dependent radiative transfer problem. Finally, we characterize astrophysical scenarios in which we expect our solutions to be important.

One-dimensional delayed-detonation models of Type Ia supernovae: confrontation to observations at bolometric maximum

The delayed-detonation explosion mechanism applied to a Chandrasekhar-mass white dwarf offers a very attractive model to explain the inferred characteristics of Type Ia supernovae (SNe Ia). The resulting ejecta are chemically stratified, have the same mass and roughly the same asymptotic kinetic energy, but exhibit a range in 56Ni mass. We investigate the contemporaneous photometric and spectroscopic properties of a sequence of delayed-detonation models, characterized by 56Ni masses between 0.18 and 0.81 Msun. Starting at 1d after explosion, we perform the full non-LTE, time-dependent radiative transfer with the code CMFGEN, with an accurate treatment of line blanketing, and compare our results to SNe Ia at bolometric maximum. Despite the 1D treatment, our approach delivers an excellent agreement to observations. We recover the range of SN Ia luminosities, colours, and spectral characteristics from the near-UV to 1 micron, for standard as well as low-luminosity 91bg-like SNe Ia. Our models predict an increase in rise time to peak with increasing 56Ni mass, from ~15 to ~21d, yield peak bolometric luminosities that match Arnett's rule to within 10%, and reproduce the much smaller scatter in near-IR magnitudes compared to the optical. We reproduce the morphology of individual spectral features, the stiff dependence of the R(Si) spectroscopic ratio on 56Ni mass, and the onset of blanketing from TiII/ScII in low-luminosity SNe Ia with a 56Ni mass <0.3 Msun. We find that ionization effects, which often dominate over abundance variations, can produce high-velocity features in CaII lines, even in 1D. Distinguishing between different SN Ia explosion mechanisms is a considerable challenge but the results presented here provide additional support to the viability of the delayed-detonation model.

Time-dependent radiative transfer with PHOENIX(Corrigendum)

where λ∞/λ = γ (1 + βμ) is the Doppler factor (Baron et al. 2012). In the original work the transformation of the timedependent term from frequency space to wavelength space was neglected. Thus, our discussion of Eqs. (24)–(27) should read: For an implementation of the time dependence in the radiative transfer itself, the spherical symmetric special relativistic radiative transfer equation (SSRTE) for expanding atmospheres (Hauschildt & Baron 1999) is extended so that the additional time-dependent term is given by [ γ (1 + βμ) ]−1 1 c ∂I ∂t (24)

PROSPECT OF STUDYING HARD X- AND GAMMA-RAYS FROM TYPE Ia SUPERNOVAE

We perform multi-dimensional, time-dependent radiation transfer simulations for hard X-ray and gamma-ray emissions, following radioactive decays of 56Ni and 56Co, for two-dimensional delayed detonation models of Type Ia supernovae (SNe Ia). The synthetic spectra and light curves are compared with the sensitivities of current and future observatories for an exposure time of 10^6 seconds. The non-detection of the gamma-ray signal from SN 2011fe at 6.4 Mpc by SPI on board INTEGRAL places an upper limit for the mass of 56Ni of \lesssim 1.0 Msun, independently from observations in any other wavelengths. Signals from the newly formed radioactive species have not been convincingly measured yet from any SN Ia, but the future X-ray and gamma-ray missions are expected to deepen the observable horizon to provide the high energy emission data for a significant SN Ia sample. We predict that the hard X-ray detectors on board NuStar (launched in 2012) or ASTRO-H (scheduled for launch in 2014) will reach to SNe Ia at \sim15 Mpc, i.e., one SN every few years. Furthermore, according to the present results, the soft gamma-ray detector on board ASTRO-H will be able to detect the 158 keV line emission up to \sim25 Mpc, i.e., a few SNe Ia per year. Proposed next generation gamma-ray missions, e.g., GRIPS, could reach to SNe Ia at \sim20 - 35 Mpc by MeV observations. Those would provide new diagnostics and strong constraints on explosion models, detecting rather directly the main energy source of supernova light.

A 3D radiative transfer framework

Context. Time-dependent, 3D radiation transfer calculations are important for the modeling of a variety of objects, from supernovae and novae to simulations of stellar variability and activity. Furthermore, time-dependent calculations can be used to obtain a 3D radiative equilibrium model structure via relaxation in time. Aims. We extend our 3D radiative transfer framework to include direct time dependence of the radiation field; i.e., the $\partial I/ \partial t$ terms are fully considered in the solution of radiative transfer problems. Methods. We build on the framework that we have described in previous papers in this series and develop a subvoxel method for the $\partial I/\partial t$ terms. Results. We test the implementation by comparing the 3D results to our well tested 1D time dependent radiative transfer code in spherical symmetry. A simple 3D test model is also presented. Conclusions. The 3D time dependent radiative transfer method is now included in our 3D RT framework and in PHOENIX/3D.

Errata: Applying a new computational method for biological tissue optics based on the time-dependent two-dimensional radiative transfer equation

Errata: Applying a new computational method for biological tissue optics based on the time-dependent two-dimensional radiative transfer equation

Applying a new computational method for biological tissue optics based on the time-dependent two-dimensional radiative transfer equation

Optical tomography is a medical imaging technique based on light propagation in the near infrared (NIR) part of the spectrum. We present a new way of predicting the short-pulsed NIR light propagation using a time-dependent two-dimensional-global radiative transfer equation in an absorbing and strongly anisotropically scattering medium. A cell-vertex finite-volume method is proposed for the discretization of the spatial domain. The closure relation based on the exponential scheme and linear interpolations was applied for the first time in the context of time-dependent radiative heat transfer problems. Details are given about the application of the original method on unstructured triangular meshes. The angular space (4πSr) is uniformly subdivided into discrete directions and a finite-differences discretization of the time domain is used. Numerical simulations for media with physical properties analogous to healthy and metastatic human liver subjected to a collimated short-pulsed NIR light are presented and discussed. As expected, discrepancies between the two kinds of tissues were found. In particular, the level of light flux was found to be weaker (inside the medium and at boundaries) in the healthy medium than in the metastatic one.

Time-dependent radiative transfer calculations for supernovae

In previous papers we discussed results from fully time-dependent radiative transfer models for core-collapse supernova (SN) ejecta, including the Type II-peculiar SN 1987A, the more "generic" SN II-Plateau, and more recently Type IIb/Ib/Ic SNe. Here we describe the modifications to our radiative modeling code, CMFGEN, which allowed those studies to be undertaken. The changes allow for time-dependent radiative transfer of SN ejecta in homologous expansion. In the modeling we treat the entire SN ejecta, from the innermost layer that does not fall back on the compact remnant out to the progenitor surface layers. From our non-LTE time-dependent line-blanketed synthetic spectra, we compute the bolometric and multi-band light curves: light curves and spectra are thus calculated simultaneously using the same physical processes and numerics. These upgrades, in conjunction with our previous modifications which allow the solution of the time dependent rate equations, will improve the modeling of SN spectra and light curves, and hence facilitate new insights into SN ejecta properties, the SN progenitors and the explosion mechanism(s). CMFGEN can now be applied to the modeling of all SN types

Radiative transfer effects during primordial helium recombination

In this paper we refine the calculation of primordial helium recombination, accounting for several additional effects that were neglected or treated more approximately in previous studies. These include consideration of the following: (i) time-dependent radiative transfer interaction between the 21P1–11S0 and 23P1–11S0 resonances; (ii) time-dependent radiative transfer for the partially overlapping n1P1–11S0, n1D2–11S0 and n3P1–11S0 series with 3 ≤n≤ 10; (iii) electron scattering within a kernel approach. We also briefly discuss the effect of electron scattering and H i quadrupole lines on the recombination of hydrogen. Although the physics of all considered processes is interesting and subtle, for the standard cosmology, with helium abundance Yp≃ 0.24, the overall correction to the ionization history during helium recombination with respect to the previous implementation of CosmoRec remains smaller than |ΔNe/Ne| ≃ 0.05 per cent. The dominant improvement is caused by consistent inclusion of resonance scattering for the 21P1–11S0 resonance. For cosmologies with a large helium fraction, Yp≃ 0.4, the difference reaches |ΔNe/Ne| ≃ 0.22 per cent at z≃ 1800; however, the overall correction to the cosmic microwave background power spectra is small, exceeding |ΔCl/Cl| ≃ 0.05 per cent only at l≳ 3000. In comparison to the current version of Recfast the difference reaches |ΔCl/Cl| ≃ 0.4 per cent at l≃ 3000 for Yp≃ 0.4, and also for the standard value Yp≃ 0.24 we find differences of |ΔCl/Cl| ≳ 0.1 per cent at l≃ 2500. The new processes are now included by the cosmological recombination code CosmoRec and can be activated as needed for most settings without affecting its runtime significantly.