Ideal Magnetohydrodynamic Approximation Research Articles

Hamiltonian formulation of relativistic magnetohydrodynamic accretion on a general spherically symmetric and static black hole: quantum effects on shock states

In this paper, our aim is to extend our earlier work [Ahmed et al. in Eur. Phys. J. C 76:280, 2016], investigating an axisymmetric plasma flow with angular momentum onto a spherical black hole. To accomplish that goal, we focus on the case in which the ideal magnetohydrodynamic approximation is valid, utilizing certain conservation laws which arise from particular symmetries of the system. After formulating a Hamiltonian of the physical system, we solve the Hamilton equations and look for critical solutions of (both in and out) flows. Reflecting the difference from the Schwarzschild spacetime, the positions of sonic points (fast magnetosonic point, slow magnetosonic point, Alfvén point) are altered. We explore several kinds of flows including critical, non-critical, global, magnetically arrested and shock induced. Lastly, we analyze the shock states near a specific quantum corrected Schwarzschild black hole and determine that quantum effects do not favor shock states by pushing the shock location outward.

Investigating the effects of numerical algorithms on global magnetohydrodynamics simulations of solar wind in the inner heliosphere

This paper explores the effects of numerical algorithms on global magnetohydrodynamics simulations of solar wind (SW) in the inner heliosphere. To do so, we use sunRunner3D, a 3-D magnetohydrodynamics model that employs the boundary conditions generated by CORHEL and the PLUTO code to compute the plasma properties of the SW with the ideal magnetohydrodynamics approximation up to 1.1 AU in the inner heliosphere. Mainly, we define three different combinations of numerical algorithms based on their diffusion level. This diffusion level is related to the way of solving the magnetohydrodynamics equations using the finite volume formulation, and, therefore, we set in terms of the divergence-free condition methods, Riemann solvers, variable reconstruction schemes, limiters, and time-steeping algorithms. According to the simulation results, we demonstrate that sunRunner3D reproduces global features of Corotating Interaction Regions observed by Earth-based spacecraft for a set of Carrington rotations that cover a period that lays in the late declining phase of solar cycle 24, independently of the numerical algorithms. Moreover, statistical analyses between models and in-situ measurements show reasonable agreement with the observations, and remarkably, the high diffusive method matches better with in-situ data than low diffusive methods.

The poor man’s magnetohydrodynamic (PMMHD) equations

We present a mathematical derivation of a discrete dynamical system by following a Fourier-Galerkin approximation of the 3-D incompressible magnetohydrodynamic (MHD) equations. In this way, a 6-D map, depending on 12 bifurcation parameters, is derived as a truncated set of nonlinear ordinary differential equations (ODEs) to characterize incompressible plasma dynamical behaviors, also conserving total energy and cross-helicity in the ideal MHD approximation. Moreover, three different subspaces, associated with long-living non-trivial solutions (e.g., fixed point solutions), have been found like the fluid, magnetic, and the Alfvenic fixed points. Our set can be seen as a Lorenz-like model to investigate MHD phenomena.

Magnetic fields in heavy ion collisions: flow and charge transport

At the earliest times after a heavy-ion collision, the magnetic field created by the spectator nucleons will generate an extremely strong, albeit rapidly decreasing in time, magnetic field. The impact of this magnetic field may have detectable consequences, and is believed to drive anomalous transport effects like the Chiral Magnetic Effect (CME). We detail an exploratory study on the effects of a dynamical magnetic field on the hydrodynamic medium created in the collisions of two ultrarelativistic heavy-ions, using the framework of numerical ideal MagnetoHydroDynamics (MHD) with the ECHO-QGP code. In this study, we consider a magnetic field captured in a conducting medium, where the conductivity can receive contributions from the electromagnetic conductivity sigma and the chiral magnetic conductivity sigma _{chi }. We first study the elliptic flow of pions, which we show is relatively unchanged by the introduction of a magnetic field. However, by increasing the magnitude of the magnetic field, we find evidence for an enhancement of the elliptic flow in peripheral collisions. This effect is stronger at RHIC than the LHC, and it is evident already at intermediate collision centralities. Next, we explore the impact of the chiral magnetic conductivity on electric charges produced at the edges of the fireball. This initial sigma _chi can be understood as a long-wavelength effective description of chiral fermion production. We then demonstrate that this chiral charge, when transported by the MHD medium, produces a charge dipole perpendicular to the reaction plane which extends a few units in rapidity. Assuming charge conservation at the freeze-out surface, we show that the produced charge imbalance can have measurable effects on some experimental observables, like v_1 or langle sin phi rangle . This demonstrates the ability of a MHD fluid to transport the signature of the initial chiral magnetic fields to late times. We also comment on the limitations of the ideal MHD approximation and detail how further development of a dissipative-resistive model can provide a more realistic description of the QGP.

Self-similar structure of resistive ADAFs with outflow and large-scale magnetic field

AbstractThe observations and simulations have revealed that large-scale magnetic field and outflows can exist in the inner regions of an advection-dominated accretion disc where the resistive diffusion may also be important. In the present paper, the roles of large-scale magnetic field and outflows in the structure of resistive advection-dominated accretion discs are explored by assuming that the accretion flow is radially self-similar. In the non-ideal magnetohydrodynamic (MHD) approximation, the results show that the angular velocity is always sub-Keplerian when both the outflow and the large-scale magnetic field are taken into account. A stronger toroidal field component leads to faster rotation, while the disc rotates with faster rate if the vertical field component is weaker. The increase of magnetic diffusivity causes the infall velocity to be close to Keplerian velocity. Although the previous studies in the ideal MHD approximation have shown that the disc temperature decreases due to the vertical field component, we find that the effect of vertical field component on the temperature of a resistive disc depends on the magnetic diffusivity. When the magnetic diffusivity is high, the more efficient mechanism for decreasing the disc temperature can be the outflows, and not the large-scale magnetic field. In such a limit of the magnetic diffusivity, the components of the large-scale magnetic field enhance the gas temperature. The increase of temperature can lead to heating and acceleration of the electrons and help us to explain the origin of phenomena such as the flares in Sgr A*. On the other hand, the infall velocity in such a limit rises as the temperature increases, and therefore the surface density falls to too low values. Any change in the density profile can alter the structure and the emitted spectrum of disc.

A discrete dynamical system: The poor man's magnetohydrodynamic (PMMHD) equations.

A discrete dynamical system is derived, via a Fourier-Galerkin procedure, from three-dimensional equations describing incompressible plasmas in the magnetohydrodynamic (MHD) framework. The obtained six-dimensional (6D) map, consisting of logistic and nonlinear terms, can provide useful insights into incompressible plasmas dynamics when bifurcation parameters, controlling dissipative and coupling terms, are changed. The map preserves the total energy in the ideal MHD approximation (i.e., by neglecting dissipative terms), manifests a sensitive dependence to the initial conditions as well as at least one Lyapunov exponent is positive (as for chaotic systems), and is characterized by a dissipative nature of its phase space. Moreover, all fixed points of the usual MHD equations are recovered, including the fluid fixed point, the Alfvénic point, and the Taylor force-free solution. Finally, also some interesting properties, as the existence of a kinematic dynamo action, are evidenced, suggesting that discrete dynamical systems deserve consideration for the description of incompressible plasmas.

Electrical resistivity and Hall effect in binary neutron star mergers

We examine the range of rest-mass densities, temperatures and magnetic fields involved in simulations of binary neutron-star mergers and identify the conditions under which the ideal-magnetohydrodynamics approximation breaks down and hence the magnetic-field decay should be accounted for. We use recent calculations of the conductivities of warm correlated plasma in envelopes of compact stars and find that the magnetic-field decay timescales are much larger than the characteristic timescales of the merger process for lengthscales down to a meter. Because these are smaller than the currently available resolution in numerical simulations, the ideal-magnetohydrodynamics approximation is effectively valid for all realistic simulations. At the same time, we find that the Hall effect can be important at low densities and low temperatures, where it can induce a non-dissipative rearrangement of the magnetic field. Finally, we mark the region in temperature and density where the hydrodynamic description breaks down.

Protostellar birth with ambipolar and ohmic diffusion

Context. The transport of angular momentum is fundamental during the formation of low-mass stars; too little removal and rotation ensures stellar densities are never reached, too much and the absence of rotation means no protoplanetary disks can form. Magnetic diffusion is seen as a pathway to resolving this long-standing problem. Aims. We aim to investigate the impact of including resistive magnetohydrodynamics (MHD) in simulations of the gravitational collapse of a 1 M⊙ gas sphere, from molecular cloud densities to the formation of the protostellar seed; the second Larson core. Methods. We used the adaptive mesh refinement code RAMSES to perform two 3D simulations of collapsing magnetised gas spheres, including self-gravity, radiative transfer in the form of flux-limited diffusion, and a non-ideal gas equation of state to describe H2 dissociation which leads to the second collapse. The first run was carried out under the ideal MHD approximation, while ambipolar and ohmic diffusion was incorporated in the second calculation using resistivities computed from an equilibrium chemical network. Results. In the ideal MHD simulation, the magnetic field dominates the energy budget everywhere inside and around the first hydrostatic core, fueling interchange instabilities and driving a low-velocity outflow above and below the equatorial plane of the system. High magnetic braking removes essentially all angular momentum from the second core. On the other hand, ambipolar and ohmic diffusion create a barrier which prevents amplification of the magnetic field beyond 0.1 G in the first Larson core which is now fully thermally supported. A significant amount of rotation is preserved and a small Keplerian-like disk forms around the second core. The ambipolar and ohmic diffusions are effective at radii below 10 AU, indicating that a least ~1 AU is necessary to investigate the angular momentum transfer and the formation of rotationally supported disks. Finally, when studying the radiative efficiency of the first and second core accretion shocks, we found that it can vary by several orders of magnitude over the 3D surface of the cores. Conclusions. This proves that magnetic diffusion is a prerequisite to star formation. Not only does it enable the formation of protoplanetary disks in which planets will eventually form, it also plays a determinant role in the formation of the protostar itself.

Relativistic magnetised perturbations: magnetic pressure versus magnetic tension

We study the linear evolution of magnetised cosmological perturbations in the post-recombination epoch. Using full general relativity and adopting the ideal magnetohydrodynamic approximation, we refine and extend the previous treatments. More specifically, this is the first relativistic study that accounts for the effects of the magnetic tension, in addition to those of the field’s pressure. Our solutions show that on sufficiently large scales, larger than the (purely magnetic) Jeans length, the perturbations evolve essentially unaffected by the magnetic presence. The magnetic pressure dominates on small scales, where it forces the perturbations to oscillate and decay. Close to the Jeans length, however, the field’s tension takes over and leads to a weak growth of the inhomogeneities. These solutions clearly demonstrate the opposing action of the aforementioned two magnetic agents, namely of the field’s pressure and tension, on the linear evolution of cosmological density perturbations.

Non-ideal magnetohydrodynamics on a moving mesh

In certain astrophysical systems the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the moving-mesh code AREPO. We include these non-ideal terms for two MHD techniques: the Powell 8-wave formalism and a constrained transport scheme, which evolves the cell-centred magnetic vector potential. We test our implementation against problems of increasing complexity, such as one- and two-dimensional diffusion problems, and the evolution of progressive and stationary Alfv\'en waves. On these test problems, our implementation recovers the analytic solutions to second-order accuracy. As first applications, we investigate the tearing instability in magnetized plasmas and the gravitational collapse of a rotating magnetized gas cloud. In both systems, resistivity plays a key role. In the former case, it allows for the development of the tearing instability through reconnection of the magnetic field lines. In the latter, the adopted (constant) value of ohmic resistivity has an impact on both the gas distribution around the emerging protostar and the mass loading of magnetically driven outflows. Our new non-ideal MHD implementation opens up the possibility to study magneto-hydrodynamical systems on a moving mesh beyond the ideal MHD approximation.

Confinement of pulsar wind nebulae by their supernova remnants and magnetic dissipation

The standard model of the pulsar wind nebula states that the pulsar wind should be low-magnetization just upstream the termination shock, called the ‘sigma-problem’. Low-magnetization is required in order to confine the pulsar wind nebula inside the slowly expanding supernova remnant whose expansion velocity is much smaller than the speed of light. Although the standard model is based on the ideal magnetohydrodynamic approximation, the recent studies indicate that the non-ideal magnetohydrodynamic effects would be important to resolve the sigma-problem. In this study, we extend the standard model including the turbulent magnetic field and the magnetic dissipation. The conversion of the toroidal magnetic field to the turbulent magnetic field and the magnetic dissipation terms are treated phenomenologically. We find that the conversion of the toroidal magnetic field to the turbulent magnetic field decelerates the nebular flow to fit the observed value of the expansion velocity. On the other hand, the magnetic dissipation hardly contributes the flow deceleration, although the magnetic dissipation is important to reproduce the observed emission properties of the PWNe.

General-relativistic resistive-magnetohydrodynamic simulations of binary neutron stars

We have studied the dynamics of an equal-mass magnetized neutron-star binary within a resistive magnetohydrodynamic (RMHD) approach in which the highly conducting stellar interior is matched to an electrovacuum exterior. Because our analysis is aimed at assessing the modifications introduced by resistive effects on the dynamics of the binary after the merger and through to collapse, we have carried out a close comparison with an equivalent simulation performed within the traditional ideal magnetohydrodynamic approximation. We have found that there are many similarities between the two evolutions but also one important difference: the survival time of the hyper massive neutron star increases in a RMHD simulation. This difference is due to a less efficient magnetic-braking mechanism in the resistive regime, in which matter can move across magnetic-field lines, thus reducing the outward transport of angular momentum. Both the RMHD and the ideal magnetohydrodynamic simulations carried here have been performed at higher resolutions and with a different grid structure than those in previous work of ours [L. Rezzolla, B. Giacomazzo, L. Baiotti, J. Granot, C. Kouveliotou, and M. A. Aloy, Astrophys. J. Letters 732, L6 (2011)], but confirm the formation of a low-density funnel with an ordered magnetic field produced by the black hole--torus system. In both regimes the magnetic field is predominantly toroidal in the highly conducting torus and predominantly poloidal in the nearly evacuated funnel. Reconnection processes or neutrino annihilation occurring in the funnel, none of which we model, could potentially increase the internal energy in the funnel and launch a relativistic outflow, which, however, is not produced in these simulations.

Outgoing electromagnetic power induced from pair plasma falling into a rotating black hole

We examine energy conversion from accreting pair plasma to outgoing Poynting flux by black hole rotation. Our approach is based on a two-fluid model consisting of collisionless pair plasma. The electric potential is not constant along magnetic field lines, unlike an ideal magnetohydrodynamics approximation. We show how and where longitudinal electric fields and toroidal magnetic fields are generated by the rotation, whereas they vanish everywhere for radial flow in a split monopole magnetic field in a Schwarzschild black hole. Outgoing electromagnetic power in a steady state is calculated by applying the WKB method to the perturbation equations for a small spin parameter. In our model, the luminosity has a peak in the vicinity of the black hole, but is damped toward the event horizon and infinity. The power at the peak is of the same order as that in the Blandford--Znajek process, although the physical mechanism is different.

Counter effects of meridional flows and magnetic fields in stationary axisymmetric self-gravitating barotropes under the ideal MHD approximation: clear examples – toroidal configurations

We obtain the general forms for the current density and the vorticity from the integrability conditions of the basic equations which govern the stationary states of axisymmetric magnetized self-gravitating barotropic objects with meridional flows under the ideal magnetohydrodynamics (MHD) approximation. As seen from the stationary condition equations for such bodies, the presence of the meridional flows and that of the poloidal magnetic fields act oppositely on the internal structures. The different actions of these two physical quantities, the meridional flows and the poloidal magnetic fields, could be clearly seen through stationary structures of the toroidal gaseous configurations around central point masses in the framework of Newtonian gravity because the effects of the two physical quantities can be seen in an amplified way for toroidal systems compared to those for spheroidal stars. The meridional flows make the structures more compact, i.e. the widths of toroids thinner, while the poloidal magnetic fields are apt to elongate the density contours in a certain direction depending on the situation. Therefore, the simultaneous presence of the internal flows and the magnetic fields would work as if there were no such different actions within and around the stationary gaseous objects such as axisymmetric magnetized toroids with internal motions around central compact objects under the ideal MHD approximation, although these two quantities might exist in real systems.

Vorticity production and survival in viscous and magnetized cosmologies

We study the role of viscosity and the effects of a magnetic field on a rotating, self-gravitating fluid, using Newtonian theory and adopting the ideal magnetohydrodynamic approximation. Our results confirm that viscosity can generate vorticity in inhomogeneous environments, while the magnetic tension can produce vorticity even in the absence of fluid pressure and density gradients. Linearizing our equations around an Einstein-de Sitter cosmology, we find that viscosity adds to the diluting effect of the universal expansion. Typically, however, the dissipative viscous effects are confined to relatively small scales. We also identify the characteristic length bellow which the viscous dissipation is strong and beyond which viscosity is essentially negligible. In contrast, magnetism seems to favor cosmic rotation. The magnetic presence is found to slow down the standard decay-rate of linear vortices, thus leading to universes with more residual rotation than generally anticipated.

The Kelvin-Helmholtz instability in weakly ionized plasmas - II. Multifluid effects in molecular clouds

We present a study of the Kelvin-Helmholtz instability in a weakly ionised, multifluid MHD plasma with parameters matching those of a typical molecular cloud. The instability is capable of transforming well-ordered flows into disordered flows. As a result, it may be able to convert the energy found in, for example, bowshocks from stellar jets into the turbulent energy found in molecular clouds. As these clouds are weakly ionised, the ideal magnetohydrodynamic approximation does not apply at scales of around a tenth of a parsec or less. This paper extends the work of Jones & Downes (2011) on the evolution of the Kelvin-Helmholtz instability in the presence of multifluid magnetohydrodynamic effects. These effects of ambipolar diffusion and the Hall effect are here studied together under physical parameters applicable to molecular clouds. We restrict our attention to the case of a single shear layer with a transonic, but super-Alfvenic, velocity jump and the computational domain is chosen to match the wavelength of the linearly fastest growing mode of the instability. We find that while the introduction of multifluid effects does not affect the linear growth rates of the instability, the non-linear behaviour undergoes considerable change. The magnetic field is decoupled from the bulk flow as a result of the ambipolar diffusion, which leads to a significant difference in the evolution of the field. The Hall effect would be expected to lead to a noticeable re-orientation of the magnetic field lines perpendicular to the plane. However, the results reveal that the combination with ambipolar diffusion leads to a surprisingly effective suppression of this effect.

Equilibrium states of magnetized toroid-central compact object systems

Equilibrium configurations of self-gravitating magnetized toroid–central compact object systems have been constructed in the framework of the Newtonian gravity. We have succeeded in including not only poloidal but also toroidal magnetic fields under the ideal magnetohydrodynamic approximation. We find two new and interesting results about the critical equilibrium states of such systems beyond which no equilibrium states are allowed to exist. First, there appear critical distances from the central compact objects to the inner surfaces of the magnetized toroids. Furthermore, these critical distances are much larger than the distances of the innermost stable circular orbits. It implies that even if these systems would be treated in the framework of general relativity, there would appear cusp structures of the effective total potential of the gravitational and magnetic forces for strongly magnetized toroids which are different from the general relativistic cusp structures. Secondly, since the strength of the magnetic field for the critical equilibrium configurations is roughly 10 15 G if the mass of the c

Inhomogeneous magnetic seed fields and gravitational waves within the magnetohydrodynamic limit

In this paper we apply second-order gauge-invariant perturbation theory to investigate the possibility that the non-linear coupling between gravitational waves (GW) and a large scale inhomogeneous magnetic field acts as an amplification mechanism in an `almost' Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe. The spatial inhomogeneities in the magnetic field are consistently implemented using the magnetohydrodynamic (MHD) approximation, which yields an additional source term due to the interaction of the magnetic field with velocity perturbations in the plasma. Comparing the solutions with the corresponding results in our previous work indicates that, on super-horizon scales, the interaction with the spatially inhomogeneous field in the dust regime induces the same boost as the case of a homogeneous field, at least in the ideal MHD approximation. This is attributed to the observation that the MHD induced part of the generated field effectively only contributes on scales where the coherence length of the initial field is less than the Hubble scale. At sub-horizon scales, the GW induced magnetic field is completely negligible in relation to the MHD induced field. Moreover, there is no amplification found in the long-wavelength limit.

Absolute and Convective Instabilities of Circularly Polarized Alfvén Waves

We discuss the recent progress in studying the absolute and convective instabilities of circularly polarized Alfven waves (pump waves) propagating along an ambient magnetic field in the approximation of ideal magnetohydrodynamics (MHD). We present analytical results obtained for pump waves with small dimensionless amplitude a, and compare them with numerical results valid for arbitrary a. The type of instability, absolute or convective, depends on the velocity U of the reference frame where the pump wave is observed with respect to the rest plasma. One of the main results of our analysis is that the instability is absolute when Ul Ur) we consider the signalling problem, and show that spatially amplifying waves exist only when the signalling frequency is in two symmetric frequency bands. Then, we write down the analytical expressions determining the boundaries of these frequency bands and discuss how they agree with numerically calculated values. We also present the dependences of the maximum spatial amplification rate on U calculated both analytically and numerically. The implication of the obtained results on the interpretation of observational data from space missions is discussed. In particular, it is shown that circularly polarized Alfven waves propagating in the solar wind are convectively unstable in a reference frame of any realistic spacecraft.

Absolute and convective instabilities of parallel propagating circularly polarized Alfvén waves: Decay instability

The absolute and convective instabilities of circularly polarized Alfvén waves propagating along an ambient magnetic field are studied. The approximation of ideal magnetohydrodynamics is used. The analysis is restricted to the decay instability that occurs when the sound speed is smaller than the Alfvén speed. In addition, it is assumed that the amplitude a of an unstable Alfvén wave (pump wave) is small. This assumption allows us to study the problem analytically using expansions in power series with respect to a. It is shown that there are quantities, Ul<0 and Ur>0, such that the pump wave is absolutely unstable in a reference frame moving with velocity U with respect to the rest plasma if Ul<U<Ur. If either U<Ul or U>Ur, then the pump wave is convectively unstable. The expressions for Ul and Ur are found. The signaling problem is studied in a reference frame where the pump wave is convectively unstable. It is shown that spatially amplifying waves exist only when the signaling frequency is in two narrow symmetric frequency bands with the widths of the order of a. The implication of the obtained results on the interpretation of observational data obtained in space missions is discussed. It is shown that circularly polarized Alfvén waves propagating in the solar wind are convectively unstable in a reference frame of any spacecraft moving with the velocity not exceeding a few tens of km/s in the solar reference frame. The spatial amplification scale of these waves is very large, of the order of 1/6 a.u. In view of these results it is not surprising at all that evidence of the decay instability of Alfvén waves in the solar wind is sparse.