We obtain estimates of Sgr A* accretion flow and black hole parameters by fitting polarized sub-mm observations with spectra computed using three-dimensional (3D) general relativistic (GR) magnetohydrodynamical (MHD) (GRMHD) simulations. Observations are compiled from averages over many epochs from reports in 29 papers for estimating the mean fluxes Fnu, linear polarization (LP) fractions, circular polarization (CP) fractions, and electric vector position angles (EVPAs). GRMHD simulations are computed with dimensionless spins a_*=0,0.5,0.7,0.9,0.98 over a 20,000M time interval. We perform fully self-consistent GR polarized radiative transfer using our new code to explore the effects of spin a_*, inclination angle θ, position angle (PA), accretion rate Mdot, and electron temperature Te (Te is reported for radius 6M). By fitting the mean sub-mm fluxes and LP/CP fractions, we obtain estimates for these model parameters and determine the physical effects that could produce polarization signatures. Our best bet model has a_*=0.5, θ=75deg, PA=115deg, Mdot=4.6*10^{-8}M_Sun/year, and Te=3.1*10^10K at 6M. The sub-mm CP is mainly produced by Faraday conversion as modified by Faraday rotation, and the emission region size at 230GHz is consistent with the VLBI size of 37microas. Across all spins, model parameters are in the ranges θ=42deg-75deg, Mdot=(1.4-7.0)*10^{-8}M_Sun/year, and Te=(3-4)*10^10K. Polarization is found both to help differentiate models and to introduce new observational constraints on the effects of the magnetic field that might not be fit by accretion models so-far considered.
We study model images and polarization maps of Sagittarius A* at 230 GHz. We post-process GRMHD simulations and perform a fully relativistic radiative transfer calculation of the emitted synchrotron radiation to obtain polarized images for a range of mass accretion rates and electron temperatures. At low accretion rates, the polarization map traces the underlying toroidal magnetic field geometry. At high accretion rates, we find that Faraday rotation internal to the emission region can depolarize and scramble the map. We measure the net linear polarization fraction and find that high accretion…
Ongoing millimeter VLBI observations with the Event Horizon Telescope allow unprecedented study of the innermost portion of black hole accretion flows. Interpreting the observations requires relativistic, time-dependent physical modeling. We discuss the comparison of radiative transfer calculations from general relativistic MHD simulations of Sagittarius A* and M87 with current and future mm-VLBI observations. This comparison allows estimates of the viewing geometry and physical conditions of the Sgr A* accretion flow. The viewing geometry for M87 is already constrained from observations of it…
We report on the polarized light curves of the Galactic Center supermassive black hole Sagittarius A*, obtained at millimeter wavelength with the Atacama Large Millimeter/submillimeter Array (ALMA). The observations took place as a part of the Event Horizon Telescope campaign. We compare the observations taken during the low variability source state on 2017 Apr 6 and 7 with those taken immediately after the X-ray flare on 2017 Apr 11. For the latter case, we observe rotation of the electric vector position angle with a timescale of $\sim 70$ min. We interpret this rotation as a signature of th…
Accretion rates and radiative efficiencies of Sagittarius A* and nearby supermassive black holes estimated using empirical relations: Implications for accretion models
We calculate the radiative properties of Sagittarius A* -- spectral energy distribution, variability, and radio-infrared images -- using the first 3D, physically motivated black hole accretion models that directly evolve the electron thermodynamics in general relativistic MHD simulations. These models reproduce the coupled disc-jet structure for the emission favored by previous phenomenological analytic and numerical works. More specifically, we find that the low frequency radio emission is dominated by emission from a polar outflow while the emission above 100 GHz is dominated by the inner re…
A radiatively inefficient accretion flow (RIAF), which is commonly characterized by its sub-Keplerian nature, is a favored accretion model for the supermassive black hole at Galactic center, Sagittarius A$^{*}$. To investigate the observable features of a RIAF, we compare the modeled shadow images, visibilities, and spectra of three flow models with dynamics characterized by (i) a Keplerian shell which is rigidly-rotating outside the innermost stable circular orbit (ISCO) and infalling with a constant angular momentum inside ISCO, (ii) a sub-Keplerian motion, and (iii) a free-falling motion wi…
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 efficie…
Upcoming VLBI observations will resolve nearby supermassive black holes, most notably Sagittarius A* and M87, on event horizon-scales. Recent observations of Sagittarius A* with the Event Horizon Telescope have revealed horizon-scale structure. Accordingly, the detection and measurement of the back hole ``shadow" is expected to enable the existence of astrophysical black holes to be verified directly. Although the theoretical description of the shadow is straightforward, its observational appearance is largely determined by the properties of the surrounding accretion flow, which is highly turb…
We briefly summarize the method of simulating Sgr A* polarized sub-mm spectra from the accretion flow and fitting the observed spectrum. The dynamical flow model is based on three-dimensional general relativistic magneto hydrodynamic simulations. Fully self-consistent radiative transfer of polarized cyclo-synchrotron emission is performed. We compile a mean sub-mm spectrum of Sgr A* and fit it with the mean simulated spectra. We estimate the ranges of inclination angle theta=42-75deg, mass accretion rate Mdot=(1.4-7.0)*10^{-8}Msun/yr, and electron temperature Te=(3-4)*10^{10}K at 6M. We discus…
We present {\tt radpol} - a numerical scheme for integrating multifrequency polarized radiative transfer equations along rays propagating in a curved spacetime. The scheme includes radiative processes such as synchrotron emission, absorption, Faraday rotation and conversion, and, for the first time, relativistic Compton scatterings including effects of light polarization. The scheme is fully covariant and is applicable to model radio-$γ$-ray emission and its polarization from, e.g., relativistic jets and accretion flows onto black holes and other exotic objects described in alternative metric …
We describe ${\tt ipole}$, a new public ray-tracing code for covariant, polarized radiative transport. The code extends the ${\tt ibothros}$ scheme for covariant, unpolarized transport using two representations of the polarized radiation field: in the coordinate frame, it parallel transports the coherency tensor; in the frame of the plasma it evolves the Stokes parameters under emission, absorption, and Faraday conversion. The transport step is implemented to be as spacetime- and coordinate- independent as possible. The emission, absorption, and Faraday conversion step is implemented using an …
Sagittarius A* exhibits regular variability in its multiwavelength emission, including daily X-ray flares and roughly continuous near-infrared (NIR) flickering. The origin of this variability is still ambiguous since both inverse Compton and synchrotron emission are possible radiative mechanisms. The underlying particle distributions are also not well constrained, particularly the non-thermal contribution. In this work, we employ the GPU-accelerated general relativistic magnetohydrodynamics (GRMHD) code H-AMR perform a study of flare flux distributions, including the effect of particle acceler…
We study the flow structure in 3D magnetohydrodynamic (MHD) simulations of accretion onto Sagittarius A* via the magnetized winds of the orbiting Wolf-Rayet stars. These simulations cover over 3 orders of magnitude in radius to reach $\approx$ 300 gravitational radii, with only one poorly constrained parameter (the magnetic field in the stellar winds). Even for winds with relatively weak magnetic fields (e.g., plasma $β$ $\sim$ $10^6$), flux freezing/compression in the inflowing gas amplifies the field to $β$ $\sim$ few well before it reaches the event horizon. Overall, the dynamics, accretion…
We present images of the Sagittarius (Sgr) B giant molecular cloud at 2368 and 1384 MHz obtained using new, multi-configuration Australia Telescope Compact Array (ATCA) observations. We have combined these observations with archival single-dish observations yielding images at resolutions of 47" by 14" and 27" by 8" at 1384 and 2368 MHz respectively. These observations were motivated by our theoretical work (Protheroe et al. 2008) indicating the possibility that synchrotron emission from secondary electrons and positrons created in hadronic cosmic ray (CR) collisions with the ambient matter of …
The accretion flow around the Galactic Center black hole Sagittarius A* (Sgr A*) is expected to have an electron temperature that is distinct from the ion temperature, due to weak Coulomb coupling in the low-density plasma. We present four two-temperature general relativistic radiative magnetohydrodynamic (GRRMHD) simulations of Sgr A* performed with the code KORAL. These simulations use different electron heating prescriptions, motivated by different models of the underlying plasma microphysics. We compare the Landau-damped turbulent cascade model used in previous work with a new prescription…
Millimeter wave Very Long Baseline Interferometry (mm-VLBI) provides access to the emission region surrounding Sagittarius A*, the supermassive black hole at the center of the Milky Way, on sub-horizon scales. Recently, a closure phase of 0+-40 degrees was reported on a triangle of Earth-sized baselines (SMT-CARMA-JCMT) representing a new constraint upon the structure and orientation of the emission region, independent from those provided by the previously measured 1.3mm-VLBI visibility amplitudes alone. Here, we compare this to the closure phases associated with a class of physically motivate…
Ultra-light bosons such as axions or axion-like particles (ALPs), are promising candidates to solve the dark matter problem. A unique way to detect such ALPs is to search for the periodic oscillation feature of the position angles of linearly polarized photons emitted from the regions where ALP dark matter forms a solitonic core. In this work, we use the high-resolution polarimetric measurements of the radiation near the super-massive black hole (SMBH) in the center of the Milky Way, i.e., Sagittarius A$^\star$ (Sgr A$^\star$), by a sub-array of the Event Horizon Telescope to search for the ul…
Millimeter very-long baseline interferometry (mm-VLBI) provides the novel capacity to probe the emission region of a handful of supermassive black holes on sub-horizon scales. For Sagittarius A* (Sgr A*), the supermassive black hole at the center of the Milky Way, this provides access to the region in the immediate vicinity of the horizon. Broderick et al. (2009) have already shown that by leveraging spectral and polarization information as well as accretion theory, it is possible to extract accretion-model parameters (including black hole spin) from mm-VLBI experiments containing only a handf…
We present the combination of dynamical accretion model based on 3D GRMHD simulations and general relativistic (GR) polarized radiative transfer. We write down the formalism of and perform the GR ray-tracing of cyclo-synchrotron radiation through the model of accretion flow in Sagittarius A*. GR polarimetric imaging is presented as well as the results for spectrum for a probable set of spins and orientations. Precise fitting formulae for Faraday rotation and Faraday conversion coefficients are employed for thermal plasma. The axisymmetic flow pattern and the magnetic field geometry correspond …
KPolaris: GPU-accelerated Polarized Radiative Transfer in General Relativity
School of Physical Science and Technology, Ningbo University（宁波大学物理科学与技术学院）；BINGO Center, Ningbo University（宁波大学BINGO中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
We discuss the problem of polarized radiative transfer in general relativity. We present a set of equations suitable for solving the problem numerically for the case of an arbitrary space-time metric, and show numerical solutions to example problems. The solutions are computed with a new ray-tracing code, Arcmancer, developed by the authors.
The rising amount of polarized observations of relativistic sources requires the correct theory for proper model fitting. The equations for general relativistic (GR) polarized radiative transfer are derived starting from the Boltzmann equation and basic ideas of general relativity. The derivation is aimed at providing a practical guide to reproducing the synchrotron part of radio & sub-mm emission from low luminosity active galactic nuclei (LLAGNs), in particular Sgr A*, and jets. The recipe for fast exact calculation of cyclo-synchrotron emissivities, absorptivities, Faraday rotation and conv…
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 r…
The advent of the Event Horizon Telescope (EHT), a millimeter-wave very-long baseline interferometric array, has enabled spatially-resolved studies of the sub-horizon-scale structure for a handful of supermassive black holes. Among these, the supermassive black hole at the center of the Milky Way, Sagittarius A* (Sgr A*), presents the largest angular cross section. Thus far, these studies have focused upon measurements of the black hole spin and the validation of low-luminosity accretion models. However, a critical input into the analysis of EHT data is the structure of the black hole spacetim…
Context: Active galactic nuclei (AGN) are anisotropic objects surrounded by an optically thick equatorial medium whose true geometry still defy observers. Aims: In this paper, we aim to explore the optical, scattering-induced, polarization emerging from clumpy and warped dusty tori to check whether they can fit with the unified model predictions. Methods: We run polarized radiative transfer simulations in a set of warped and non warped clumpy tori to explore the differences induced by distorted dust distributions. We then include warped tori in a more complex model representative of an AGN to …
Near a black hole, differential rotation of a magnetized accretion disk is thought to produce an instability that amplifies weak magnetic fields, driving accretion and outflow. These magnetic fields would naturally give rise to the observed synchrotron emission in galaxy cores and to the formation of relativistic jets, but no observations to date have been able to resolve the expected horizon-scale magnetic-field structure. We report interferometric observations at 1.3-millimeter wavelength that spatially resolve the linearly polarized emission from the Galactic Center supermassive black hole,…
Magnetic fields are believed to drive accretion and relativistic jets in black hole accretion systems, but the magnetic-field structure that controls these phenomena remains uncertain. We perform general relativistic (GR) polarized radiative transfer of time-dependent three-dimensional GR magnetohydrodynamical (MHD) simulations to model thermal synchrotron emission from the Galactic Center source Sagittarius A$^\ast$ (Sgr A*). We compare our results to new polarimetry measurements by the Event Horizon Telescope (EHT) and show how polarization in the visibility (Fourier) domain distinguishes an…
Validation and Calibration of Semi-Analytical Models for the Event Horizon Telescope Observations of Sagittarius A*
Perimeter Institute for Theoretical Physics（理论物理研究所）；University of Waterloo（多伦多大学）；University of Toronto（多伦多大学）；Waterloo Centre for Astrophysics（滑铁卢天体物理中心）
We report the first detections of circularly polarized emission at submillimeter wavelengths from the compact radio source and supermassive black hole candidate Sgr A* at a level of 1.2\pm0.3% at 1.3 mm wavelength (230 GHz) and 1.6\pm0.3% at 860 microns (345 GHz) with the same handedness as observed at lower frequencies (1.4-15 GHz). The observations, taken with the Submillimeter Array in multiple epochs, also show simultaneous linear polarization (LP) at both wavelengths of about 6%. These properties differ sharply from those at wavelengths longer than 1 cm (frequencies below 30 GHz), where w…
We present the first spectral energy distributions produced self-consistently by 2.5D general relativistic magneto-hydrodynamical (GRMHD) numerical simulations, where radiative cooling is included in the dynamical calculation. As a case study, we focus on the accretion flow around the supermassive black hole in the Galactic Centre, Sagittarius A* (Sgr A*), which has the best constrained physical parameters. We compare the simulated spectra to the observational data of Sgr A* and explore the parameter space of our model to determine the effect of changing the initial magnetic field configuratio…
Ray-tracing is a central tool for constructing mock observations of compact object emission and for comparing physical emission models with observations. We present Arcmancer, a publicly available general ray-tracing and tensor algebra library, written in C++ and providing a Python interface. Arcmancer supports Riemannian and semi-Riemannian spaces of any dimension and metric, and has novel features such as support for multiple simultaneous coordinate charts, embedded geometric shapes, local coordinate systems and automatic parallel propagation. The Arcmancer interface is extensively documente…
The $230$ GHz Variability of Numerical Models of Sagittarius~A* I. Parameter Surveys on Varying Ion-electron Temperature Ratios Under Strongly Magnetized Conditions
