The equilibrium and stability of uniformly rotating gaseous systems in hydromagnetics

The theory for investigating the equilibrium and stability of a uniformly rotating gaseous system with a prevalent magnetic field is developed by using the virial tensor approach. Most of the discussion in this paper depends on the assumption that on the surface of the system, the magnetic field is zero. In Appendix A, however, we have considered the case in which the surface magnetic field is non-zero.We have obtained the nine modes of oscillations, grouped into the transverse shear, toroidal and pulsation modes. From this analysis have also found the conditions under which the sequence of a uniformly rotating axially symmetric configuration in the presence of a magnetic field should have a point of bifurcation, that is, a point where objects with genuine triplanar symmetry branch off. This condition is also generalized in the Appendix to include the effects of differential rotation and non-zero surface magnetic field.Applications to the cosmogonic fission problem, the study of the pulsation of rotating magnetic stars and some radio astrophysical problems are briefly discussed.     

The stability of an isothermal,magnetized and causally limited viscosity accretion disk

The stability of an isothermal, magnetized and causally limited viscosity accretion disk is examined in this paper. We find that the viscous modes are always stable throughout the disk, and the magneto-acoustic modes are pulsationally unstable. The results show that the Mach numbers do effect the instabilities of the disk and the magnetic field enhances the instability property of the radial oscillation. Our results are useful for understanding the time variations of AGN.     

Strictly nonlinear waves in an embedded rotating gaseous disk

Nonlinear waves of large amplitude in a gaseous disk, in which perturbations of the gravitational field can be neglected, are considered. Solutions are obtained in the form of a nonlinear, supersonic, periodic density wave, and rules are obtained for the propagation along the disk radius of a nonlinear impulse with a given profile. Translated from Astrofizika, Vol. 40, No. 2, pp. 291–302, April–June, 1997.     

The equilibrium magnetized disks

Analytical solutions are obtained for gravitational and magnetic fields at given distributions of area matter density and surface currents.Numerical solutions ae obtained for a magnetized non-rotating disk, the equilibrium of which is governed by the balance of magnetic and gravitational forces. The models are shown to be unsable against short-wave perturbations. Pressure can make a small contribution (of the order of a few percent) towards stabilizng the disk against short-wave perturbations. Such disks may appear in some galactic nuclei.     

The energy loss of a rotating magnetized neutron star

The analysis of observations of pulsar B1931+24 shows that the mechanism of the spin-down of a rotating magnetized neutron star is due to the plasma generation in its magnetosphere and, consequently, the radio emission generation. The unique observation of the switch on and switch off of this pulsar allows us to distinguish between the energy loss in the absence of radio emission (the magnetodipole radiation) and the current loss due to the rotation energy expenditure to the relativistic plasma generation and acceleration in the pulsar magnetosphere. The inclination angle χ, the angle between the rotation axis and the magnetic dipole axis, can be stationary for this pulsar,  χ=χ_st  . From observations and theory it follows that  χ_st= 59°  .     

Hydrostatic equilibrium in a magnetized, warped Galactic disc

Hydrostatic equilibrium of the multiphase interstellar medium in the solar vicinity is reconsidered, with the regular and turbulent magnetic fields treated separately. The regular magnetic field strength required to support the gas is consistent with independent estimates, provided that energy equipartition is maintained between turbulence and random magnetic fields. Our results indicate that a mid-plane value of B ₀=4 μG for the regular magnetic field near the Sun leads to more attractive models than B ₀=2 μG . The vertical profiles of both the regular and random magnetic fields contain disc and halo components, the parameters of which we have determined. The layer at 1≲| z |≲4 kpc can be overpressured and an outflow at a speed of about 50 km s⁻¹ may occur there, presumably associated with a Galactic fountain flow, if B ₀≃2 μG .
We show that hydrostatic equilibrium in a warped disc must produce asymmetric density distributions in z , in rough agreement with H  i observations in the outer Galaxy. This asymmetry may be a useful diagnostic of the details of the warping mechanism in the Milky Way and other galaxies. We find indications that gas and magnetic field pressures are different above and below the warped midplane in the outer Galaxy, and quantify the difference in terms of turbulent velocity and/or magnetic field strength.     

The configuration of a thin,rotating self-similar disk in general relativity

Einstein's equations for a rotating pressure-free space-time are reduced to a system of four first-order non-linear ordinary differential equations in one self-similar dimensionless variable. Numerical results are given for the vacuum solution. A compatible thin disk can be specified by a surface density and an angular velocity . Self-similarity as a statement of the absence of scales implies that and can be written as=c ²/4Gr, =c/r, and demands that and be pure numbers.     

The chemo-dynamical evolution of a disk galaxy

I present a model for the formation and evolution of a massive disk galaxy, within a growing dark halo whose mass evolves according to cosmological simulations of structure formation. The galactic evolution is simulated with a new three-dimensional chemo-dynamical code, including dark matter, stars and a multi-phase ISM. We follow the evolution from redshift z= 4.85 until the present epoch. The energy release by massive stars and supernovae prevents a rapid collapse of the baryonic matter and delays the maximum star formation until redshift z ≈ 1. The galaxy forms radially from inside-out and vertically from top-to-bottom. Correspondingly, the inner halo is the oldest component, followed by the outer halo, the bar/bulge, the thick and the thin disk. The bulge in the model consists of at least two stellar subpopulations, an early collapse population and a population that formed later in the bar. This revised version was published online in August 2006 with corrections to the Cover Date.     

Simulations of jet formation from a magnetized accretion disk

Axisymmetric magnetohydrodynamic (MHD) simulations have been made of the formation of jets from a Keplerian disk threaded by a magnetic field. The disk is treated as a boundary condition, where matter with high specific entropy is ejected with a Keplerian azimuthal speed and a poloidal speed less than the slow magnetosonic velocity, and where boundary conditions on the magnetic fields correspond to a highly conducting disk. Initially, the space above the disk, the corona, is filled with high specific entropy plasma in the thermal equilibrium in the gravitational field of the central object. The initial magnetic field is poloidal and is represented by the superposition of the fields of monopoles located below the plane of the disk.The rotation of the disk twists the initial poloidal magnetic field lines, and this twist propagates into the corona pushing matter into jet-like outflow in a cylindrical region. After the first switch-on wave, which originates during the first rotation period of the inner radius of the disk, the matter outflowing from the disk starts to flow and accelerate in thez-direction owing to both the magnetic and pressure gradient forces. The flow accelerates through the slow magnetosonic and Alfvén surfaces and at larger distances through the fast magnetosonic surface. The flow velocity of the jet is approximately parallel to thez-axis, with the collimation mainly a result of the pinching force of the toroidal magnetic field. The energy flux of the flow increases with increasing magnetic field strength on the disk. Some of the cases studied have been run for long times, 60 rotation periods of the inner radius of the disk, and show indications of approaching a stationary state.     

The equilibrium of a rotating body of arbitrary density

This paper extends Clairaut's theory of rotational equilibrium to third order terms in a small parameter and is meant to be a sequel to a 1962 publication by the author bearing on the same topic. It has been feasible to obtain the Clairaut equation, which governs the deformation of the equipotential surfaces within a rapidly rotating mass in hydrostatic equilibrium, as an ordinary differential equation. This has been achieved by eliminating the two integral terms which appeared in the original formulation. It is expected that the numerical integration of this newly obtained equation will contribute toward a more precise solution of certain geophysical problems — e.g., the determination of the geoid to an accuracy of ±1 m, and the correction to the travel-time of seismic waves; it should also assist in some planetary questions like the determination of the exterior shape for the rapidly rotating planets Jupiter and Saturn.     

The Eulerian equations of differentially rotating gaseous polytropes

In this paper, we present in detail the whole process by which the Eulerian general equation is obtained, holding in case of a differentially rotating gaseous polytrope. The explicit form of this equation is derived on the basis of a model developed in a previous investigation.     

Unipolar induction of a magnetized accretion disk around a black hole

The structure and magnitude of the electromagnetic field produced by a rotating accretion disk around a black hole were determined. The disk matter is assumed to be a magnetized plasma with a frozenin poloidal magnetic field. The vacuum approximation is used outside the disk.     

Nonlinear convective motion in a rotating magnetized electron-positron plasma

A set of coupled nonlinear equations is derived which describes the coupling of the vorticity and the external-field aligned flow of a strongly magnetized rotating electron-positron plasma. The possibility of dipole vortex formation is discussed.     

Obliquity and magnetic dipole radiation from collapsing,rotating, magnetized stars

We consider in this paper the evolution of a collapsing (or exploding), uniformly rotating, uniformly magnetized spheroidal star with non-aligned rotational and magnetic axes. Analytical expressions were obtained for the change in angle (obliquity) between the two axes (based on the frozen field condition), and the energy loss via magnetic, dipole radiation. Numerical estimates with typical data show that the obliquity increases (asymptotically to /2) with the collapse from white dwarf to neutron star, and the energy loss could be as much as 4×10³⁹ ergs, about twice the amount emitted when the two axes are aligned.