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Register a new userRAPTOR II: Polarized radiative transfer in curved spacetime
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Accreting supermassive black holes are sources of polarized radiation that propagates through highly curved spacetime before reaching the observer. In order to help interpret observations of such polarized emission, accurate and efficient numerical schemes for polarized radiative transfer in curved spacetime are needed. In this manuscript we extend our publicly available radiative transfer code RAPTOR to include polarization. We provide a brief review of different codes and methods for covariant polarized radiative transfer available in the literature and existing codes, and present an efficient new scheme. For the spacetime-propagation aspect of the computation, we develop a compact, Lorentz-invariant representation of a polarized ray. For the plasma-propagation aspect of the computation, we perform a formal analysis of the stiffness of the polarized radiative-transfer equation with respect to our explicit integrator, and develop a hybrid integration scheme that switches to an implicit integrator in case of stiffness, in order to solve the equation with optimal speed and accuracy for all possible values of the local optical/Faraday thickness of the plasma. We perform a comprehensive code verification by solving a number of well-known test problems using RAPTOR and comparing its output to exact solutions. We also demonstrate convergence with existing polarized radiative-transfer codes in the context of complex astrophysical problems. RAPTOR is capable of performing polarized radiative transfer in arbitrary, highly curved spacetimes. This capability is crucial for interpreting polarized observations of accreting black holes, which can yield information about the magnetic-field configuration in such accretion flows. The efficient formalism implemented in RAPTOR is computationally light and conceptually simple. The code is publicly available.
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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. 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. We describe the algorithms used in RAPTOR and test the codes 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. 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%. 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.
We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is generated by o
ne-parameter subgroups which have either self-adjoint or unitary quantizations. We analytically continue the self-adjoint semigroups to one-parameter unitary groups, and thus construct a unitary representation of the isometry group of the associated Lorentzian manifold. The method is illustrated for the example of hyperbolic space, whose Lorentzian continuation is Anti-de Sitter space.
The underlying plasma composition of relativistic extragalactic jets remains largely unknown. Relativistic magnetohydrodynamic (RMHD) models are able to reproduce many of the observed macroscopic features of these outflows. The nonthermal synchrotron emission detected by very long baseline interferometric (VLBI) arrays, however, is a by-product of the kinetic-scale physics occurring within the jet, physics that is not modeled directly in most RMHD codes. This paper attempts to discern the radiative differences between distinct plasma compositions within relativistic jets using small-scale 3D relativistic particle-in-cell (PIC) simulations. We generate full Stokes imaging of two PIC jet simulations, one in which the jet is composed of an electron-proton ($e^{-}$-$p^{+}$) plasma (i.e., a normal plasma jet), and the other in which the jet is composed of an electron-positron ($e^{-}$-$e^{+}$) plasma (i.e., a pair plasma jet). We examined the differences in the morphology and intensity of the linear polarization (LP) and circular polarization (CP) emanating from these two jet simulations. We find that the fractional level of CP emanating from the $e^{-}$-$p^{+}$ plasma jet is orders of magnitude larger than the level emanating from an $e^{-}$-$e^{+}$ plasma jet of a similar speed and magnetic field strength. In addition, we find that the morphology of both the linearly and circularly polarized synchrotron emission is distinct between the two jet compositions. We also demonstrate the importance of slow-light interpolation and we highlight the effect that a finite light-crossing time has on the resultant polarization when ray-tracing through relativistic plasma.
Context. Magnetic fields are important to the dynamics of many astrophysical processes and can typically be studied through polarization observations. Polarimetric interferometry capabilities of modern (sub)millimeter telescope facilities have made it possible to obtain detailed velocity resolved maps of molecular line polarization. To properly analyze these for the information they carry regarding the magnetic field, the development of adaptive three-dimensional polarized line radiative transfer models is necessary. Aims. We aim to develop an easy-to-use program to simulate the polarization maps of molecular and atomic (sub)millimeter lines in magnetized astrophysical regions, such as protostellar disks, circumstellar envelopes, or molecular clouds. Methods. By considering the local anisotropy of the radiation field as the only alignment mechanism, we can model the alignment of molecular or atomic species inside a regular line radiative transfer simulation by only making use of the converged output of this simulation. Calculations of the aligned molecular or atomic states can subsequently be used to ray trace the polarized maps of the three-dimensional simulation. Results. We present a three-dimensional radiative transfer code, POlarized Radiative Transfer Adapted to Lines (PORTAL), that can simulate the emergence of polarization in line emission through a magnetic field of arbitrary morphology. Our model can be used in stand-alone mode, assuming LTE excitation, but it is best used when processing the output of regular three-dimensional (nonpolarized) line radiative transfer modeling codes. We present the spectral polarization map of test cases of a collapsing sphere and protoplanetary disk for multiple three-dimensional magnetic field morphologies.
We describe the incorporation of polarized radiative transfer into the atmospheric radiative transfer modelling code VSTAR (Versatile Software for Transfer of Atmospheric Radiation). Using a vector discrete-ordinate radiative transfer code we are able to generate maps of radiance and polarization across the disc of a planet, and integrate over these to get the full-disc polarization. In this way we are able to obtain disc-resolved, phase-resolved and spectrally-resolved intensity and polarization for any of the wide range of atmopsheres that can be modelled with VSTAR. We have tested the code by reproducing a standard benchmark problem, as well as by comparing with classic calculations of the polarization phase curves of Venus. We apply the code to modelling the polarization phase curves of the hot Jupiter system HD 189733b. We find that the highest polarization amplitudes are produced with optically thick Rayleigh scattering clouds and these would result in a polarization amplitude of 27 ppm for the planetary signal seen in the combined light of the star and planet. A more realistic cloud model consistent with the observed transmission spectrum results is an amplitude of ~20 ppm. Decreasing the optical depth of the cloud, or making the cloud particles more absorbing, both have the effect of increasing the polarization of the reflected light but reducing the amount of reflected light and hence the observed polarization amplitude.
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