Two Mechanisms for Extracting Energy and Angular Momentum from a Rotating Black Hole

Two mechanisms of extracting energy and angular momentum from a rotating black hole, the Blandford-Znajek (BZ) process and magnetic coupling (MC) of a rotating black hole (BH) with the surrounding accretion disk, are discussed in detail by using a modified equivalent circuit. We obtain the same value for the BZ power as given by Lee. The strength of the power and torque produced by the rotating BH in the BZ process are compared with those in MC process. In addition, entropy production on the BH horizon due to the BZ process and that due to MC process are compared and discussed also by using the modified equivalent circuit.     

A Toy Model for Magnetic Field Configurations in Black Hole Accretion Discs

We discuss the feature of the magnetic field configuration arising from double counter oriented electric currentrings in the accretion disc around a Kerr black hole （BH）. We discuss the relevant physical quantities corresponding to this configuration： （1） the power and torque transferred by the large-scale magnetic field, （2） the angular momentum and energy fluxes transferred from the BIt to the inner disc, （3） the radiation flux from the disc. In addition, we discuss the possibility that the closed magnetic field anchored at the disc probably evolves to the open magnetic field, which is helpful to produce the jet from the disc.     

黑洞自转角速度的演化特征

在同时考虑吸积和Blandford-Znajek过程的条件下,详细讨论了吸积盘（包括薄盘和厚盘）中心黑洞的自转角速度Ω_h的演化特征.结果表明,当黑洞的无量纲角动量a_*演化到某一临界时,Ω_h对时间的变化率由正变负,从而推断在顺行吸积过程事Ω_h先增后减,演化非单调,因而存在一个极大值.并指出黑洞的无量纲角动理a_*比黑洞的角动量J和自转角速度Ω_h更适合描写吸积盘中心黑洞自转状态的演 关键词：     

Temperature Profile of Black Hole Accretion Disc with Magnetic Coupling

Two new mapping relations between the angular coordinate on the black hole (BH) horizon and radialcoordinate on the disc are given according to the requirement of general relativity and Maxwell‘s equations, and theeffects of magnetic coupling (MC) on temperature of accretion disc are investigated by comparing with pure accretion.It is shown that the MC effects on the temperature profile are related intimately to the BH spin, and the influenceon the peak value of disc temperature based on the modified mapping relations is not as great as that based on thelinear mapping.The peak value and the corresponding radius of peak value ring of disc temperature do not increasemonotonically as the increasing spin of BH, each containing a maximum for the fast-spinning BH. The value ranges ofthe bolometric luminosity and color temperature of the disc are both extended by the MC effects.     

Acoustic rotational manipulation using orbital angular momentum transfer

We report on the first quantitative test of acoustic orbital angular momentum transfer to a sound absorbing object immersed in a viscous liquid. This is done by realizing an original experiment that is to spin a millimeter-size target disk using an ultrasonic vortex beam. We demonstrate the balance between the acoustic radiation torque calculated from the Brillouin stress tensor and the viscous torque evaluated from the steady state spinning frequency. Moreover, we unveil a rotational acoustic streaming phenomenon that results from the acoustic angular momentum transfer to the host fluid. We show that it lowers the viscous torque, thereby restoring the torque balance.     

Fate of an accretion disc around a black hole when both the viscosity and dark energy is in effect

This paper deals with the viscous accretion flow of a modified Chaplygin gas towards a black hole as the central gravitating object. A modified Chaplygin gas is a particular type of dark energy model which mimics of radiation era to phantom era depending on the different values of its parameters. We compare the dark energy accretion with the flow of adiabatic gas. An accretion disc flowing around a black hole is an example of a transonic flow. To construct the model, we consider three components of the Navier–Stokes equation, the equation of continuity and the modified Chaplygin gas equation of state. As a transonic flow passes through the sonic point, the velocity gradient being apparently singular there, it gives rise to two flow branches: one in-falling, the accretion and the other outgoing, the wind. We show that the wind curve is stronger and the wind speed reaches that of light at a finite distance from the black hole when dark energy is considered. Besides, if we increase the viscosity, the accretion disc is shortened in radius. These two processes acting together make the system deviate much from the adiabatic accretion case. It shows a weakening process for the accretion procedure by the work of the viscous system influencing both the angular momentum transport and the repulsive force of the modified Chaplygin gas.     

Standing Rankine-Hugoniot Shocks in Black Hole Accretion Discs

We study the problem of standing shocks in viscous disc-like accretion flows around black holes. For the first time we parametrize such a flow with two physical constants, namely the specific angular momentum accreted by the black hole j and the energy quantity K. By providing the global dependence of shock formation in the j- K parameter space, we show that a significant parameter region can ensure solutions with Rankine-Hugoniot shocks; and that the possibilities of shock formation are the largest for inviscid flows, decreasing with increasing viscosity, and ceasing to exist for a strong enough viscosity. Our results support the view that the standing shock is an essential ingredient in black hole accretion discs and is a general phenomenon in astrophysics, and that there should be a continuous change from the properties of inviscid flows to those of viscous ones.     

On the effect of injection of gas in the numerical simulation of accretion flows

We investigate the effects of various ways of injection of gas at the outer boundary in the numerical simulations of non-viscous accretion flows. We study three models. In Model A, we inject material around the equatorial plane. In Models B and C, fullrange θ injection is used (we employ spherical coordinates). In all three models, the injected material has the same density distribution with polar angle θ. From the equatorial region to the polar regions, angular momentum of the injected material of Model B decreases faster than that in Model C. For all of the models, after a transient episode of infall at the beginning of the simulations, the gas piles up in the equatorial regions outside the black hole and forms a thick torus bounded by a centrifugal barrier. We find that the accretion rates of Models B and C are more than ten times higher than that in Model A. In Model A, there is weak accretion only in the torus and outflows are found on the surface of the torus. In Model B, we find strong inflows on the surface of its torus, and the accretion in the torus is weak. In Model C, strong inflows also occur on the surface of its torus, but the accretion regions are narrower and there are strong outflows in its torus. In all of our models, the time-averaged density, pressure and angular momentum in the equatorial region can be described by a radial power law, with P ∝r ^−3/2, P ∝r ⁻² and l∝r ⁰.

     

Accretion of radiation and rotating primordial black holes

We consider rotating primordial black holes (PBHs) and study the effect of accretion of radiation in the radiation-dominated era. The central part of our analysis deals with the role of the angular momentum parameter on the evolution of PBHs. We find that both the accretion and evaporation rates decrease with an increase in the angular momentum parameter, but the rate of evaporation decreases more rapidly than the rate of accretion. This shows that the evaporation time of PBHs is prolonged with an increase in the angular momentum parameter. We also note that the lifetime of rotating PBHs increases with an increase in the accretion efficiency of radiation as in the case of nonrotating PBHs.     

Spin force and torque in non-relativistic Dirac oscillator on a sphere

The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin–orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggests that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.     

Acoustic beams with angular momentum

A family of exact solutions of the Helmholtz equation is used to represent transversely bounded helicoidal sound beams. Simple results are obtained for the energy content per unit length, the momentum content per unit length, and the angular momentum content per unit length. The analysis is restricted to lossless media; scattering and viscous damping are neglected. The energy, momentum, and angular momentum are calculated to second order in the velocity potential. The angular momentum content is always equal to m/omega times the energy content, where m (an integer) is the topological charge and omega is the angular frequency.     

磁场对黑洞吸积盘的能量提取及其天体物理应用

考虑到螺旋不稳定性的影响, 提出了一种黑洞磁层的新磁场位形(NCMF). 其中涉及到磁场提取能量的三种机制: (1) Blandford-Znajek (BZ)过程; (2)磁耦合(MC)过程; (3) 通过开磁力线联系吸积盘和天体物理负载,并提取吸积盘的旋转能量新机制(文中称为DL过程). 利用两类等效电路导出上述三种提能机制的功率和力矩的表达式. 结果表明,在新磁场位形中提能功率和效率比未考虑螺旋不稳定性的磁场位形有所增大,新磁场位形导出的非常陡的发射率指数可以拟合XMM-Newton天文卫星对邻近的明亮的Seyfert 1星系MCG-6-30-15的观测结果.     

Temporal study of GRS 1915+105 with rms-flux relation: The importance of magnetic activities in the corona

The rms-flux relations for some observations of GRS 1915+105 are studied. The rms-flux relations of the light curves in only one state, state C or state A, can be described by the simple non-linear model provided Zhang; we thus interpret that such a linear relation reflects the relative importance of magnetic instability for X-ray emission in the corona of the system, compared to the thermal viscous instability for the X-ray emission in the accretion disk. The rms-flux relations for state B are very scattered, possibly because of the dominance of thermal viscous instability for the X-ray emission in the accretion disk. The complex rms-flux relations for the observations of transitions between two or three states are caused by the combination of the different rms-flux relations of these states. The underlying physical processes are the combination of magnetic topology in the corona and thermal viscous instability in the accretion disk.

     

Experimental observation and characterization of the magnetorotational instability

Differential rotation occurs in conducting flows in accretion disks and planetary cores. In such systems, the magnetorotational instability can arise from coupling Lorentz and centrifugal forces to cause large radial angular momentum fluxes. We present the first experimental observation of the magnetorotational instability. Our system consists of liquid sodium between differentially rotating spheres, with an imposed coaxial magnetic field. We characterize the observed patterns, dynamics, and torque increases, and establish that this instability can occur from a hydrodynamic turbulent background.     

Constant curvature f(R) gravity minimally coupled with Yang–Mills field

In this work, we have studied accretion of the dark energies in new variable modified Chaplygin gas (NVMCG) and generalized cosmic Chaplygin gas (GCCG) models onto Schwarzschild and Kerr?CNewman black holes. We find the expression of the critical four velocity component which gradually decreases for the fluid flow towards the Schwarzschild as well as the Kerr?CNewman black hole. We also find the expression for the change of mass of the black hole in both cases. For the Kerr?CNewman black hole, which is rotating and charged, we calculate the specific angular momentum and total angular momentum. We showed that in both cases, due to accretion of dark energy, the mass of the black hole increases and angular momentum increases in the case of a Kerr?CNewman black hole.     

Stokes Flows under Random Boundary Velocity Excitations

A viscous Stokes flow over a disc under random fluctuations of the velocity on the boundary is studied. We give exact Karhunen-Loève (K-L) expansions for the velocity components, pressure, stress, and vorticity, and the series representations for the corresponding correlation tensors. Both the white noise fluctuations, and general homogeneous random excitations of the velocities prescribed on the boundary are studied. We analyze the decay of correlation functions in angular and radial directions, both for exterior and interior Stokes problems. Numerical experiments show the fast convergence of the K-L expansions. The results indicate that ignoring the stochastic fluctuations in boundary conditions dramatically underestimates the variance of the velocity and pressure in the interior/exterior of the domain. The support of the RFBR Grant N 06-01-00498 is kindly acknowledged.     

Ferrofluids as thermal ratchets

Colloidal suspensions of ferromagnetic nanoparticles, so-called ferrofluids, are shown to be suitable systems to demonstrate and investigate thermal ratchet behavior: By rectifying thermal fluctuations, angular momentum is transferred to a resting ferrofluid from an oscillating magnetic field without net rotating component. Via viscous coupling the noise driven rotation of the microscopic ferromagnetic grains is transmitted to the carrier liquid to yield a macroscopic torque. For a simple setup we analyze the rotation of the ferrofluid theoretically and show that the results are compatible with the outcome of a simple demonstration experiment.     

Accretion onto a Kerr black hole in the presence of a dipole magnetic field

We analyze the accretion of charged matter onto a rotating black hole immersed in an aligned dipolar magnetic field. We specialize to motion in the equatorial plane and calculate the ‘Keplerian’ angular momentum distribution, the marginally stable and marginally bound orbits, and the efficiency of mass-to-energy conversion as functions of the angular momentum of the black hole and of the product of the dipole moment and the charge of the infalling matter. Although the detailed results are quite different from those previously obtained in the case of an uniform magnetic field, the astrophysically relevant results are very similar; when hydrodynamical accretion is considered, these effects of the magnetic field are always very small. But for test particles the efficiency can be significantly increased for limited ranges of the parameters.     

Torque equations for spin and orbital angular momenta of radiation fields and Faraday effect

The spin angular momentum S of light has never been linked to the Faraday rotation of light traveling in an optically active medium possessing a rotational invariance of a crystal, because there was no helicity term associated with the phase shift in the previous torque equation for S. In order to relate the change in S with time to the Faraday rotation, therefore, we derived an exact torque equation for S. As a result, a magnetic helicity term appeared in a new torque equation for S, so that one-half of the phase shift derived from the helicity term was equivalent to the Faraday rotation angle. However, the orbital angular momentum L had no relation to the Faraday rotation. It was thus clarified that the change in S with time is related to the Faraday rotation angle of light traveling in an optically active medium, owing to the appearance of the helicity term without a rotational invariance around the optical axis. It was also demonstrated theoretically that the Faraday rotation is accompanied by a torque acting on the crystal so that the total angular momentum of light and matter is conserved.     

Evolution of Dimensionless Angular Momentum of Central Black Holes of Accretion Disks

The effects of the Blandford-Znajek (BZ) process on the evolution of the central black holes of accretion disks are investigated. It is proved that the dimensionless angular momentum a_* of the central black hole will evolve to a stable value in the case of thin disks, while it will evolve to a stable value in the case of thick disks. These results imply that the central black holes of accretion disks will never evolve to extreme Kerr black holes.