We present a new formal solution of the Lagrangian equation of radiative transfer that is useful in solving the equation of radiative transfer in the presence of arbitrary velocity fields. Normally a term due to the inclusion of the wavelength derivative in the Lagrangian equation of radiative transfer is associated with a generalised opacity. In non-monotonic velocity fields, this generalised opacity may become negative. To ensure that the opacity remains positive, this term of the derivative is included in the formal solution of the radiative transfer problem.
The new definition of the generalised opacity allows for a new solution of the equation of radiative transfer in the presence of velocity fields. It is especially useful for arbitrary velocity fields, where it effectively prevents the occurrences of negative generalised opacities and still allows the explicit construction of the Lambda-operator of the system needed for an accelerated Lambda-iteration. We performed test calculations, where the results of old, established solutions were compared with the new solution. The relative deviations never exceeded 1% and so the new solution is indeed suitable for use in radiative-transfer modelling. Non-monotonic velocity fields along photon paths frequently occur in three-dimensional hydrodynamical models of astrophysical atmospheres. Therefore, the formal solution will be of use for multidimensional radiative transfer and has immediate applications in the modelling of pulsating stars and astrophysical shock fronts.
Efficient numerical approximation of the polarized radiative transfer equation is challenging because this system of ordinary differential equations exhibits stiff behavior, which potentially results in numerical instability. This negatively impacts the accuracy of formal solvers, and small step-sizes are often necessary to retrieve physical solutions. This work presents stability analyses of formal solvers for the radiative transfer equation of polarized light, identifies instability issues, and suggests practical remedies. In particular, the assumptions and the limitations of the stability a…
The numerical computation of reliable and accurate Stokes profiles is of great relevance in solar physics. In the synthesis process, many actors play a relevant role: among them the formal solver, the discrete atmospheric model, and the spectral line. This paper tests the performances of different numerical schemes in the synthesis of polarized spectra for different spectral lines and atmospheric models. The hierarchy between formal solvers is enforced, stressing the peculiarities of high-order and low-order formal solvers. The density of grid points necessary for reaching a given accuracy req…
Mass loss from inhomogeneous hot star winds III. An effective-opacity formalism for line radiative transfer in accelerating, clumped two-component media, and first results on theory and diagnostics
A New Diagnostic of Magnetic Field Strengths in Radiatively-Cooled Shocks
我们表明，它是可能的测量阿尔文马赫数，定义为在流中的激波速度除以阿尔文速度，低速（V $_{shock}$ $\lesssim$ 100 km $\,$ s $^{-1}$）辐射激波。该方法结合了明亮的禁线的观测与冷却区的大小的测量，后者通常从巴耳末发射线和禁线之间的空间分离获得。由于磁场在激波后区域的气体冷却时会被压缩，因此即使是相对较弱的震前磁场也可以用这种方法探测到。我们推导出解析公式，解释了空间分离如何与发射线比相关，并计算了一个大网格的辐射冷却激波模型，以开发诊断图，可用于推导流动中的Alfvénic马赫数。将该方法应用于HH 111喷流中亮结的现有数据，我们获得了相对较低的阿尔夫文马赫数$\sim$ 2，这表明磁化喷流内部具有超磁声速度扰动。
The understanding of the evolution of early-type stars is tightly related to that of the effects of rapid rotation. For massive stars, rapid rotation combines with their strong radiation-driven wind. The aim of this paper is to investigate two questions that are prerequisite to the study of the evolution of massive rapidly rotating stars: (i) What is the critical angular velocity of a star when radiative acceleration is significant in its atmosphere? (ii) How do mass and angular momentum loss depend on the rotation rate? To investigate fast rotation, which makes stars oblate, we used the 2D ES…
Hot massive stars present strong stellar winds that are driven by absorption, scattering and re\-emission of photons by the ions of the atmosphere (\textit{line-driven winds}). A better comprehension of this phenomenon, and a more accurate calculation of hydrodynamics and radiative acceleration is required to reduce the number of free parameters in spectral fitting, to determine accurate wind parameters such as mass-loss rates and velocity profiles. We use the non-LTE model-atmosphere code CMFGEN to numerically solve the radiative transfer equation in the stellar atmosphere and to calculate th…
Full non-LTE multi-level radiative transfer I. An atom with three bound infinitely sharp levels
Université de Toulouse, Observatoire Midi-Pyrénées（图卢兹大学，南天观测站）；Cnrs, Institut de Recherche en Astrophysique et Planétologie（法国国家科学研究中心，天体物理学与行星学研究所在）；Indian Institute of Astrophysics（印度天体物理研究所）
We present radiative hydrodynamic simulations of solar flares generated by the RADYN and RH codes to study the perturbations induced in photospheric Fe I lines by electron beam heating. We investigate how variations in the beam parameters result in discernible differences in the induced photospheric velocities. Line synthesis revealed a significant chromospheric contribution to the line profiles resulting in an apparent red asymmetry by as much as 40 m/s close to the time of maximum beam heating which was not reflective of the upflow velocities that arose from the radiative hydrodynamic simula…
Given the low ionization fraction of molecular clouds, ambipolar diffusion is thought to be an integral process in star formation. However, chemical and radiative-transfer effects, observational challenges, and the fact that the ion-neutral drift velocity is inherently very small render a definite detection of ambipolar diffusion extremely non-trivial. Here, we study the ion-neutral drift velocity in a suite of chemodynamical, non-ideal magnetohydrodynamic (MHD), two-dimensional axisymmetric simulations of prestellar cores where we alter the temperature, cosmic-ray ionization rate, visual exti…
Radiative turbulent mixing layers (TMLs) are ubiquitous in astrophysical environments, e.g., the circumgalactic medium (CGM), and are triggered by the shear velocity at interfaces between different gas phases. To understand the shear velocity dependence of TMLs, we perform a set of 3D hydrodynamic simulations with an emphasis on the TML properties at high Mach numbers $\mathcal{M}$. Since the shear velocity in mixing regions is limited by the local sound speed of mixed gas, high-Mach number TMLs develop into a two-zone structure: a Mach number-independent mixing zone traced by significant cool…
Kratos-linerad: GPU-accelerated Monte Carlo radiative transfer of lines with efficient imaging
The Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学柯立夫天文与天体物理研究所）；Department of Astronomy, School of Physics, Peking University（北京大学物理学院天文学系）
