1552326
The cosmic battery revisited
We reinvestigate the generation and accumulation of magnetic flux in optically thin accretion flows around active gravitating objects. The source of the magnetic field is the azimuthal electric current associated with the Poynting-Robertson drag on the electrons of the accreting plasma. This current generates magnetic field loops that open up because of the differential rotation of the flow. We show through simple numerical simulations that what regulates the generation and accumulation of magnetic flux near the center is the value of the plasma conductivity. Although the conductivity is usually considered to be effectively infinite for the fully ionized plasmas expected near the inner edge of accretion disks, the turbulence of those plasmas may actually render them much less conducting due to the presence of anomalous resistivity. We have discovered that if the resistivity is sufficiently high throughout the turbulent disk while it is suppressed inside its inner edge, an interesting steady state process is established: accretion carries and accumulates magnetic flux of one polarity inside the inner edge of the disk, whereas magnetic diffusion releases magnetic flux of the opposite polarity to large distances. In this scenario, magnetic flux of one polarity grows and accumulates at a steady rate in the region inside the inner edge and up to the point of equipartition when it becomes dynamically important. We argue that this inward growth and outward expulsion of oppositely directed magnetic fields that we propose could account for the ~30 minute cyclic variability observed in the Galactic microquasar GRS 1915+105.
119367315
Phase-Transition Theory of Instabilities. IV. Critical Points on the Maclaurin Sequence and Nonlinear Fission Processes
We use a free-energy minimization approach to describe the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems from the Landau-Ginzburg theory of phase transitions. Here we examine higher than 2nd-harmonic disturbances applied to Maclaurin spheroids, the corresponding bifurcating sequences, and their relation to nonlinear fission processes. The triangle and ammonite sequences bifurcate from the two 3rd-harmonic neutral points on the Maclaurin sequence while the square and one-ring sequences bifurcate from two of the three known 4th harmonic neutral points. In the other three cases, secular instability does not set in at the corresponding bifurcation points because the sequences stand and terminate at higher energies relative to the Maclaurin sequence. There is no known bifurcating sequence at the point of 3rd-harmonic dynamical instability. Our nonlinear approach easily identifies resonances between the Maclaurin sequence and various multi-fluid-body sequences that cannot be detected by linear stability analyses. Resonances appear as first-order phase transitions at points where the energies of the two sequences are nearly equal but the lower energy state belongs to one of the multi-fluid-body sequences.
119358963
Phase-Transition Theory of Instabilities. III. The Third-Harmonic Bifurcation on the Jacobi Sequence and the Fission Problem
In Papers I and II, we have used a free-energy minimization approach that stems from the Landau-Ginzburg theory of phase transitions to describe in simple and clear physical terms the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Here we investigate the secular and dynamical 3rd-harmonic instabilities that appear first on the Jacobi sequence of incompressible zero- vorticity ellipsoids. Poincare found a bifurcation point on the Jacobi sequence where a 3rd-harmonic mode becomes neutral. A sequence of pear-shaped equilibria branches off at this point but stands at higher energies. Therefore, the Jacobi ellipsoids remain secularly and dynamically stable. Cartan found that dynamical 3rd-harmonic instability also sets in at the Jacobi-pear bifurcation. We find that Cartan's instability leads to differentially rotating objects and not to uniformly rotating pear-shaped equilibria. We demonstrate that the pear-shaped sequence exists at higher energies and at higher rotation relative to the Jacobi sequence. The Jacobi ellipsoid undergoes fission on a secular time scale and a short-period binary is produced. The classical fission hypothesis of binary-star formation of Poincare and Darwin is thus feasible.
119465098
A new criterion for bar-forming instability in rapidly rotating gaseous and stellar systems. 2. Nonaxisymmetric form
We analyze previous results on the stability of uniformly and differentially rotating, self-gravitating, gaseous and stellar, axisymmetric systems to derive a new stability criterion for the appearance of toroidal, m=2 Intermediate (I) and bar modes. In the process, we demonstrate that the bar modes in stellar systems and the m=2 I-modes in gaseous systems have many common physical characteristics and only one substantial difference: because of the anisotropy of the stress tensor, dynamical instability sets in at lower rotation in stellar systems. This difference is reflected also in the new stability criterion. The new stability parameter "alpha" is formulated first for uniformly rotating systems and is based on the angular momentum content rather than on the energy content of a system. For stability of stellar systems "alpha" = 0.254-0.258, while it is in the range of 0.341-0.354 for gaseous systems. For uniform rotation, one can write "alpha" as a function of the total (rotational) kinetic and gravitational energies, and of a parameter which is characteristic of the topology/connectedness and the geometric shape of a system. "Alpha" can be extended to and calculated for a variety of differentially rotating, gaseous and stellar, axisymmetric disk and spheroidal models whose equilibrium structures and stability characteristics are known. We also estimate "alpha" for gaseous toroidal models and for stellar disk systems embedded in an inert or responsive "halo". We find that the new stability criterion holds equally well for all these previously published axisymmetric models.
118829636
Phase-Transition Theory of Instabilities. I. Second-Harmonic Instability and Bifurcation Points
A free-energy minimization approach is used to address the secular & dynamical instabilities & the bifurcations along sequences of rotating, self-gravitating fluid and stellar systems. Our approach stems from the Landau-Ginzburg theory of phase transitions. We focus on the Maclaurin sequence of oblate spheroids & on the effects of second-harmonic disturbances. Second-order phase transitions appear on the Maclaurin sequence also at the points of dynamical instability & of bifurcation of the Dedekind sequence. Distinguishing characteristic of each second-order phase transition is the (non)conservation of an integral of motion (e.g. circulation) which determines the appearance of the transition. Circulation is not conserved in stellar systems because the stress-tensor gradient terms that appear in the Jeans equations of motion include viscosity-like off-diagonal terms of the same order of magnitude as the conventional pressure gradient terms. This explains why the Jacobi bifurcation is a point of dynamical instability in stellar systems but only a point of secular instability in viscous fluids. The second-order phase transitions are discussed in relation to the dynamical instability of stellar systems, the lambda-transition of liquid He-4, the second-order phase transition in superconductivity & the mechanism of spontaneous symmetry breaking.
14867269
Exact Solutions of the Isothermal Lane--Emden Equation with Rotation and Implications for the Formation of Planets and Satellites
We have derived exact solutions of the isothermal Lane--Emden equation with and without rotation in a cylindrical geometry. The corresponding hydrostatic equilibria are most relevant to the dynamics of the protosolar nebula before and during the stages of planet and satellite formation. The nonrotating solution for the mass density is analytic, nonsingular, monotonically decreasing with radius, and it satisfies easily the usual physical boundary conditions at the center. When differential rotation is added to the Lane--Emden equation, an entire class of exact solutions for the mass density appears. We have determined all of these solutions analytically as well. Within this class, solutions that are power laws or combinations of power laws are not capable of satisfying the associated boundary--value problem, but they are nonetheless of profound importance because they constitute "baselines" to which the actual solutions approach when the central boundary conditions are imposed. Numerical integrations that enforce such physical boundary conditions show that the actual radial equilibrium density profiles emerge from the center close to the nonrotating solution, but once they cross below the corresponding baselines, they cease to be monotonic. The actual solutions are forced to oscillate permanently about the baseline solutions without ever settling onto them because the central boundary conditions strictly prohibit such settling, even in the asymptotic regime of large radii. Based on our results, we expect that quasistatically--evolving protoplanetary disks should develop oscillatory density profiles in their midplanes during their isothermal phase. The peaks in these profiles correspond to local potential minima and their locations are ideal sites for the formation of protoplanets ...
1552326
The cosmic battery revisited
We reinvestigate the generation and accumulation of magnetic flux in optically thin accretion flows around active gravitating objects. The source of the magnetic field is the azimuthal electric current associated with the Poynting-Robertson drag on the electrons of the accreting plasma. This current generates magnetic field loops that open up because of the differential rotation of the flow. We show through simple numerical simulations that what regulates the generation and accumulation of magnetic flux near the center is the value of the plasma conductivity. Although the conductivity is usually considered to be effectively infinite for the fully ionized plasmas expected near the inner edge of accretion disks, the turbulence of those plasmas may actually render them much less conducting due to the presence of anomalous resistivity. We have discovered that if the resistivity is sufficiently high throughout the turbulent disk while it is suppressed inside its inner edge, an interesting steady state process is established: accretion carries and accumulates magnetic flux of one polarity inside the inner edge of the disk, whereas magnetic diffusion releases magnetic flux of the opposite polarity to large distances. In this scenario, magnetic flux of one polarity grows and accumulates at a steady rate in the region inside the inner edge and up to the point of equipartition when it becomes dynamically important. We argue that this inward growth and outward expulsion of oppositely directed magnetic fields that we propose could account for the ~30 minute cyclic variability observed in the Galactic microquasar GRS 1915+105.