Numerical General Relativistic MHD with Magnetically Polarized Matter

A new code and methodology are introduced for solving the general relativistic magnetohydrodynamic (GRMHD) equations in fixed background spacetimes using time-explicit, finite-volume discretization. The code has options for solving the GRMHD equations using traditional artificial-viscosity (AV) or non-oscillatory central difference (NOCD) methods, or a new extended AV (eAV) scheme using artificial-viscosity together with a dual energy-flux-conserving formulation. The dual energy approach allows for accurate modeling of highly relativistic flows at boost factors well beyond what has been achieved to date by standard artificial viscosity methods. It provides the benefit of Godunov methods in capturing high Lorentz boosted flows but without complicated Riemann solvers, and the advantages of traditional artificial viscosity methods in their speed and flexibility. Additionally, the GRMHD equations are solved on an unstructured grid that supports local adaptive mesh refinement using a fully threaded oct-tree (in three dimensions) network to traverse the grid hierarchy across levels and immediate neighbors. A number of tests are presented to demonstrate robustness of the numerical algorithms and adaptive mesh framework over a wide spectrum of problems, boosts, and astrophysical applications, including relativistic shock tubes, shock collisions, magnetosonic shocks, Alfven wave propagation, blast waves, magnetized Bondi flow, and the magneto-rotational instability in Kerr black hole spacetimes.

Helios 1 moved from 1 AU on December 10, 1974, to 0.31 AU on March 15, 1975, and the sun rotated beneath the spacecraft nearly 4 times during the interval. Recurrent high‐speed streams with uniform magnetic polarity were observed, and they were associated with coronal holes of the same polarity. Although they were recurrent, the streams and their magnetic field patterns were not stationary, because the coronal holes which produced them changed in shape and latitude from one rotation to the next. We estimated that the magnetic field intensity of open field lines in some of these holes was of the order of 10'20 G. Recurrent slow flows were also observed. The magnetic field polarity and intensity in these flows were irregular, and they changed from one rotation to the next. Cold magnetic enhancements (CME's) characterized by a twofold to threefold enhancement of magnetic field intensity and a fivefold to sevenfold depression of proton temperature relative to conditions ahead of the CME's were observed in some slow flows. Some of these CME's were contiguous with interaction regions of streams. At perihelion, Helios observed a recurrent stream which was associated with a lobe of the south polar coronal hole. The longitudinal width of the stream was three times that of the hole. We estimate that the width of the eastern and western boundaries of the streams at the coronal holes was only 2.5° ± 1.5°, and we infer that the width at the northern boundary of the stream was ≲5°. We conclude that between the sun and 0.3 AU there was a diverging stream surrounded by a thin boundary layer in which there was a large velocity shear. There is evidence for compression of the magnetic field in the western boundary layer (interaction region), presumably due to steepening of the stream within 0.31 AU.

Numerical solutions for field line resonances (FLR) in the magnetosphere are presented for three-dimensional equilibrium magnetic fields represented by two Euler potentials as B = -j Y -a, where j is the poloidal flux and a is a toroidal angle-like variable. The linearized ideal-MHD equations for FLR harmonics of shear Alfvin waves and slow magnetosonic modes are solved for plasmas with the pressure assumed to be isotropic and constant along a field line. The coupling between the shear Alfvin waves and the slow magnetosonic waves is via the combined effects of geodesic magnetic field curvature and plasma pressure. Numerical solutions of the FLR equations are obtained for a quiet time magnetosphere as well as a disturbed time magnetosphere with a thin current sheet in the near-Earth region. The FLR frequency spectra in the equatorial plane as well as in the auroral latitude are presented. The field line length, magnetic field intensity, plasma beta, geodesic curvature and pressure gradient in the poloidal flux surface are important in determining the FLR frequencies. In general, the computed shear Alfvin FLR frequency based on the full MHD model is larger than that based on the commonly adopted cold plasma model in the beq > 1 region. For the quiet time magnetosphere, the shear Alfvin resonance frequency decreases monotonically with the equatorial field line distance, which reasonably explains the harmonically structured continuous spectrum of the azimuthal magnetic field oscillations as a function of L shell in the L is less than or equal to 9RE region. However, the FLR frequency spectrum for the disturbed time magnetosphere with a near-Earth thin current sheet is substantially different from that for the quiet time magnetosphere for R > 6RE, mainly due to shorter field line length due to magnetic field compression by solar wind, reduced magnetic field intensity in the high-beta current sheet region, azimuthal pressure gradient, and geodesic magnetic field curvature .

Numerical solutions for field line resonances (FLRs) in the magnetosphere are presented for three‐dimensional equilibrium magnetic fields represented by two Euler potentials as B = ∇ψ × ∇α, where ψ is the poloidal flux and α is a toroidal angle‐like variable. The linearized ideal MHD equations for FLR harmonics of shear Alfvén waves and slow magnetosonic modes are solved for plasmas with the pressure assumed to be isotropic and constant along a field line. The coupling between the shear Alfvén waves and the slow magnetosonic waves is via the combined effects of geodesic magnetic field curvature and plasma pressure. Numerical solutions of the FLR equations are obtained for a quiet time magnetosphere as well as a disturbed time magnetosphere with a thin current sheet in the near‐Earth region. The FLR frequency spectra in the equatorial plane as well as in the auroral latitude are presented. The field line length, magnetic field intensity, plasma beta, geodesic curvature, and pressure gradient in the poloidal flux surface are important in determining the FLR frequencies. In general, the computed shear Alfvén FLR frequency based on the full MHD model is larger than that based on the commonly adopted cold plasma model in the βeq > 1 region. For the quiet time magnetosphere, the shear Alfvén resonance frequency decreases monotonically with the equatorial field line distance, which reasonably explains the harmonically structured continuous spectrum of the azimuthal magnetic field oscillations as a function of the dipole L shell in the L ≤ 8.8 RE region. However, the FLR frequency spectrum for the disturbed time magnetosphere with a near‐Earth thin current sheet is substantially different from that for the quiet time magnetosphere for R > 6 RE, mainly due to shorter field line length due to magnetic field compression by solar wind, reduced magnetic field intensity in the high β current sheet region, azimuthal pressure gradient and geodesic magnetic field curvature.

Incorporating the radiation reaction force into two-fluid plasma in curved space, we get a set of one-fluid general relativistic magnetohydrodynamics (GRMHD) equations with the Landau-Lifshitz radiation reaction force. We analyze the importance of the radiation reaction acting on plasma around an astrophysical compact object.

We investigate the general relativistic magnetohydrodynamic (GRMHD) equations for cold plasma around the Reissner-Nordström black hole. Applying 3+1 spacetime split we linearize the perturbed equations for non-magnetized/magnetized plasma in both rotating and non-rotating background. By Fourier analyze we then derive dispersion relations and investigate the existence of waves with positive angular frequency in the vicinity of the black hole horizon. The analysis finds propagation of negative phase and group velocities for rotating magnetized surroundings.

Very long baseline interferometry observations reveal that relativistic jets like the one in M87 have a limb-brightened, double-edged structure. Analytic and numerical models struggle to reproduce this limb-brightening. We propose a model in which we invoke anisotropy in the distribution function of synchrotron-emitting nonthermal electrons such that electron velocities are preferentially directed parallel to magnetic field lines, as suggested by recent particle-in-cell simulations of electron acceleration and the effects of synchrotron cooling. We assume that the energy injected into nonthermal electrons is proportional to the jet Poynting flux, and we account for synchrotron cooling via a broken power-law energy distribution. We implement our emission model in both general relativistic magnetohydrodynamic (GRMHD) simulations and axisymmetric force-free electrodynamic (GRFFE) jet models and produce simulated jet images at multiple scales and frequencies using polarized general relativistic radiative transfer. We find that the synchrotron emission is concentrated parallel to the local helical magnetic field and that this feature produces limb-brightened jet images on scales ranging from tens of microarcseconds to hundreds of milliarcseconds in M87. We present theoretical predictions for horizon-scale M87 jet images at 230 and 345 GHz that can be tested with next-generation instruments. Due to the scale-invariance of the GRMHD and GRFFE models, our emission prescription can be applied to other targets and serve as a foundation for a unified description of limb-brightened synchrotron images of extragalactic jets.

Modeling correctly the transport of neutrinos is crucial in some astrophysical scenarios such as core-collapse supernovae and binary neutron star mergers. In this paper, we focus on the truncated-moment formalism, considering only the first two moments (M1 scheme) within the grey approximation, which reduces Boltzmann seven-dimensional equation to a system of 3+1 equations closely resembling the hydrodynamic ones. Solving the M1 scheme is still mathematically challenging, since it is necessary to model the radiation-matter interaction in regimes where the evolution equations become stiff and behave as an advection-diffusion problem. Here, we present different global, high-order time integration schemes based on Implicit-Explicit Runge-Kutta methods designed to overcome the time-step restriction caused by such behavior while allowing us to use the explicit Runge-Kutta commonly employed for the magneto-hydrodynamics and Einstein equations. Finally, we analyze their performance in several numerical tests.

Based on electro-magneto-rheological (EMR) effect, this paper presents a novel micro machining method to form an instantaneous tiny-grinding wheel to polish the surface of optical glass, ceramic and other rigid-fragile materials under both electric and magnetic field. Experiments were conducted to reveal the synergistic effect of electrorheological and magnethorheological effect, and the effects of process parameters, such as intensity of electric field, intensity of magnetic field, working time, machining gap between the workpiece and the needle-like tool, on material removal rate of glass surface. Experimental results confirm the effectiveness of the micro machining technique with EMR effect-based tiny-grinding wheel and the machining efficiency under the combination of electric and magnetic field is much greater than the one under applied external electric or magnetic field. The material removal rate of workpiece is directly proportional to the intensity of external electric field and will maintain stable when the voltage of external electric field reaches 2000v, while the material removal rate is directly proportional to the intensity of external magnetic field. The material removal rate markedly descends with the increase of the machining gap. In addition, the working time is directly proportional to the amount of material removal of workpiece, but inversely proportional to material removal rate.

The global magnetic-field resonances previously found in a modal analysis of a 25 yr Mt Wilson-Kitt Peak data set of synoptic magnetic maps are also revealed when only the magnetic polarities are used, disregarding the magnitude of the flux. Thus the topological organization of the magnetic polarities alone suffices to bring out the correct modal structure, although the results are noisier as compared with the case when the magnetic fluxes are included. This result suggests that magnetic polarities indirectly inferred from Hα data may be used to study the resonances. Whereas synoptic magnetograph observations are not available before 1959, Hα observations date back to the last century, and could in principle be used to enhance the frequency resolution in the power spectra. Using zonal distributions of magnetic polarities inferred from Hα data by Makarov for the period 1941–1983, we have performed a power spectrum analysis of the rotationally symmetric spherical harmonic modes (m = 0), and compared the results with the corresponding analysis for the magnetic fields and polarities determined from real magnetograph data. The same parity selection rule that governs the 22 yr magnetic cycle in the magnetograph data is also revealed by the Hα data. The Hα results are however much noisier and do not show the pattern of resonant frequencies discovered in the magnetograph data for the modes of even parity. It is concluded that only real magnetograph data should be used to investigate the global resonances in the magnetic-field pattern.

It is shown that a hot neutron star with an intense dipole magnetic field (1012 G) appears as an X-ray pulsar. The mean free path of X-ray photons depends on the direction of the propagation vector with respect to the magnetic field. When the neutron star is viewed from varying directions according to its rotation, pluses of X-rays are observed. Profiles of the pulses are computed for different geometries, energies of photons and intensities of the magnetic field. Fitting the computed pulses with the observed profiles of Her X-1 and Cen X-3, values of those parameters such as the intensity of the surface magnetic field, the inclination of the spin axis and the obliquity of the magnetic dipole relative to the spin axis are determined. The validity of this model will be checked, when we observe the polarization profile of the pulse and/or the energy dependence of the pulsed component relative to the steady component.

We present a new numerical code, X-ECHO, for general relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes. This is aimed at studying astrophysical situations where strong gravity and magnetic fields are both supposed to play an important role, such as for the evolution of magnetized neutron stars or for the gravitational collapse of the magnetized rotating cores of massive stars, which is the astrophysical scenario believed to eventually lead to (long) GRB events. The code is based on the extension of the Eulerian conservative high-order (ECHO) scheme [Del Zanna et al., A&A 473, 11 (2007)] for GRMHD, here coupled to a novel solver for the Einstein equations in the extended conformally flat condition (XCFC). We fully exploit the 3+1 Eulerian formalism, so that all the equations are written in terms of familiar 3D vectors and tensors alone, we adopt spherical coordinates for the conformal background metric, and we consider axisymmetric spacetimes and fluid configurations. The GRMHD conservation laws are solved by means of shock-capturing methods within a finite-difference discretization, whereas, on the same numerical grid, the Einstein elliptic equations are treated by resorting to spherical harmonics decomposition and solved, for each harmonic, by inverting band diagonal matrices. As a side product, we build and make available to the community a code to produce GRMHD axisymmetric equilibria for polytropic relativistic stars in the presence of differential rotation and a purely toroidal magnetic field. This uses the same XCFC metric solver of the main code and has been named XNS. Both XNS and the full X-ECHO codes are validated through several tests of astrophysical interest.

X-ray reflection spectroscopy is currently one of the leading techniques for studying the inner part of accretion disks around black holes, measuring black hole spins, and even testing fundamental physics in strong gravitational fields. However, the accuracy of these measurements depends on the reflection models employed for the spectral analysis, which are sometimes questioned. In this work, we use a general relativistic magnetohydrodynamic (GRMHD) code to generate a thin accretion disk in Kerr spacetime and ray-tracing techniques to calculate its relativistically broadened reflection spectrum. We simulate NuSTAR observations and we test the capability of current reflection models based on Novikov-Thorne disks to recover the correct input parameters. Our study shows that we can measure the correct input parameters in the case of high inclination angle sources, while we find some minor discrepancy when the inclination angle of the disk is low.

Event Horizon Telescope (EHT) observations at 230 GHz have now imaged polarized emission around the supermassive black hole in M87 on event-horizon scales. This polarized synchrotron radiation probes the structure of magnetic fields and the plasma properties near the black hole. Here we compare the resolved polarization structure observed by the EHT, along with simultaneous unresolved observations with the Atacama Large Millimeter/submillimeter Array, to expectations from theoretical models. The low fractional linear polarization in the resolved image suggests that the polarization is scrambled on scales smaller than the EHT beam, which we attribute to Faraday rotation internal to the emission region. We estimate the average density n e ∼ 104–7 cm−3, magnetic field strength B ∼ 1–30 G, and electron temperature T e ∼ (1–12) × 1010 K of the radiating plasma in a simple one-zone emission model. We show that the net azimuthal linear polarization pattern may result from organized, poloidal magnetic fields in the emission region. In a quantitative comparison with a large library of simulated polarimetric images from general relativistic magnetohydrodynamic (GRMHD) simulations, we identify a subset of physical models that can explain critical features of the polarimetric EHT observations while producing a relativistic jet of sufficient power. The consistent GRMHD models are all of magnetically arrested accretion disks, where near-horizon magnetic fields are dynamically important. We use the models to infer a mass accretion rate onto the black hole in M87 of (3–20) × 10−4 M ⊙ yr−1.

Alignment behavior of the primary Al 3Ni phase in Al–Ni alloy under a high magnetic field