Planar solitonic filaments in solar physics

A new class of analytical solution of the coupled system of Da Rios-diffusion equation in magnetohydrodynamic (MHD) representing solitonic vortex filaments is obtained. One of the solutions is similar to the one found by Rogers and Schief describing a solitary wave propagating along a constant torsion vortex filament. Scalar magnetic diffusion equations are obtained by decomposing the magnetic filament along Frenet frame. The integral invariant of curvature is used to place limits on the diffused 100 eV plasma filament curvature. The resistivity of η=5×10^?5 ohm?cm—close to the stainless steel limit is used to approximate the Frenet curvature. From the scalar diffusion equations the vortex filaments are constrained to move along torsionless (planar) trajectories. Da Rios equations are coupled to diffusion equation to obtain a solitonic vortex diffused filaments. Due to bounds in time and length L we show that the model discussed is particularly useful in solar physics.     

Generation of the magnetic fields of pulsars

The influence of the effect of entrainment of superconducting protons by superfluid neutrons on the distribution of neutron vortices in a rotating neutron star is investigated. It is shown that the proton vortex clusters generated by entrainment currents create the magnetic structure of a neutron vortex. The average magnetic field induction in a neutron vortex is calculated. The presence of the magnetic field of a neutron vortex considerably alters the radius of the vortex zone. The width of the vortex-free zone at the surface of the neutron star’s core increases, reaching macroscopic values on the order of several meters. This result considerably changes earlier concepts of the distribution of neutron vortices in a neutron star. Translated from Astrofizika, Vol. 43, No. 3, pp. 377-386, July–September, 2000.     

Numerical simulations of rotating axisymmetric sunspots

A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the non-linear MHD equations, with density and temperature gradients simulating the upper layer of the Sun's convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotated with a constant angular velocity, the plasma forms a Rankine vortex, with the plasma rotating as a rigid body where the magnetic field is strong, as in the flux tube, while experiencing sheared azimuthal flow in the surrounding convection cells, forming a free vortex. As a result, the azimuthal velocity component has its maximum value close to the outer edge of the flux tube. The azimuthal flow inside the magnetic flux tube and the vortex flow is prograde relative to the rotating cylindrical reference frame. A retrograde flow appears at the outer wall. The most significant convection cell outside the flux tube is the location for the maximum value of the azimuthal magnetic field component. The azimuthal flow and magnetic structure are not generated spontaneously, but decay exponentially in the absence of any imposed rotation of the cylindrical domain.     

An essay on sunspots and solar flares

The presently prevailing theories of sunspots and solar flares rely on the hypothetical presence of magnetic flux tubes beneath the photosphere and the two subsequent hypotheses, their emergence above the photosphere and explosive magnetic reconnection, converting magnetic energy carried by the flux tubes for solar flare energy.In this paper, we pay attention to the fact that there are large-scale magnetic fields which divide the photosphere into positive and negative (line-of-sight) polarity regions and that they are likely to be more fundamental than sunspot fields, as emphasized most recently by McIntosh (1981). A new phenomenological model of the sunspot pair formation is then constructed by considering an amplification process of these largescale fields near their boundaries by shear flows, including localized vortex motions. The amplification results from a dynamo process associated with such vortex flows and the associated convergence flow in the largescale fields.This dynamo process generates also some of the familiar “force-free” fields or the “sheared” magnetic fields in which the magnetic field-aligned currents are essential. Upward field-aligned currents generated by the dynamo process are carried by downward streaming electrons which are expected to be accelerated by an electric potential structure; a similar structure is responsible for accelerating auroral electrons in the magnetosphere. Depending on the magnetic field configuration and the shear flows, the current-carrying electrons precipitate into different geometrical patterns, causing circular flares, umbral flares, two-ribbon flares, etc. Thus, it is suggested that “low temperature flares” are directly driven by the photospheric dynamo process.     

Flux-Vortex Pinning and Neutron Star Evolution

G. Srinivasan et al. (1990) proposed a simple and elegant explanation for the reduction of the neutron star magnetic dipole moment during binary evolution leading to low mass X-ray binaries and eventually to millisecond pulsars: Quantized vortex lines in the neutron star core superfluid will pin against the quantized flux lines of the proton superconductor. As the neutron star spins down in the wind accretion phase of binary evolution, outward motion of vortex lines will reduce the dipole magnetic moment in proportion to the rotation rate. The presence of a toroidal array of flux lines makes this mechanism inevitable and independent of the angle between the rotation and magnetic axes. The incompressibility of the flux-line array (Abrikosov lattice) determines the epoch when the mechanism will be effective throughout the neutron star. Flux vortex pinning will not be effective during the initial young radio pulsar phase. It will, however, be effective and reduce the dipole moment in proportion with the rotation rate during the epoch of spindown by wind accretion as proposed by Srinivasan et al. The mechanism operates also in the presence of vortex creep.     

Hydromagnetic vortices—II. Further dawnside events

We show that the 11 December 1977 plasma vortex event—the subject of a multi-instrument investigation in Paper I (Saunders et al., 1983)—was neither atypical nor uncommon, by describing the magnetic and plasma characteristics of three further vortices recorded within 3 weeks of, and at similar locations to, the 11 December study. One of the new events has added interest since magnetic pulsations were seen simultaneously on the ground in the vicinity of the satellite magnetic “footprint”.     

Sheared ion flow driven nonlinear coherent structures in inhomogeneous electron-positron-ion quantum magnetoplasmas

Nonlinear equations governing the dynamics of finite amplitude drift-acoustic-waves are derived by taking into account sheared ion flow perpendicular to the ambient magnetic field in a quantum magnetoplasma comprised of electrons, positrons, and ions. It is shown that stationary solution of the nonlinear equations can be represented in the form of a counter-rotating vortex for a particular choice of the equilibrium profile. The counter rotating vortices are, however, observed to form on very short scales i.e., of the order of ion Larmor radius ρ _i in quantum plasmas. It is observed that the scalelengths over which these structures form get modified in the presence of quantum statistical and Bohm potential terms as well as the positron concentration. The relevance of the present investigation with regard to dense astrophysical environments is also pointed out.     

The formation of magnetic channels

The model problem simulating a vortex development is solved numerically. Breakdown of the velocity sheared layer due to the nonlinear evolution of the Kelvin-Helmholtz instability is shown to lead to the wave crest overturning and, eventually, to formation of a large-scale vortex. The magnetic field strength in the vortex core turns out to be lower than that in the ambient plasma, so that vortex core may be called the magnetic channel.The mechanism of the magnetic field generation by a single vortex is studied analytically within the framework of magnetokinematics. It appeared that there is no magnetic field generation in the vortex core where rotation of the plasma is rigid. Therefore, the magnetic field here is reduced, and hence the plasma density is enhanced.These results seem to support the hypothesis of the comet ray origin as magnetically channeled outflow: the magnetic channel might become visible as a comet ray against adjacent plasma of lesser density outside the magnetic channel.     

First order latitude effects in the solar wind

The Weber-Davis model of the solar wind is generalized to include the effects of latitude. The principal assumptions of perfect electrical conductivity, rotational symmetry, a polytropic relation between pressure and density, and a flow aligned magnetic field in a system rotating with the Sun, are retained. A flow aligned magnetic field in the rotating system may be expressed in terms of the flow velocity and density. Rotational symmetry fixes the longitudinal flow velocity V_φ in terms of the flow in the r?θ plane. Thus, the original three dimensional magnetohydrodynamic flow problem is reduced to a two dimensional hydrodynamic flow problem in the r?θ plane.There are three critical surfaces associated with the equations which supply conditions to determine three of six required boundary conditions. The specified boundary conditions at the base of the corona are the temperature, density, and magnitude of the magnetic field. The equations are then expanded about the radial, nonrotating Parker solution and an analytic solution is obtained for the resulting first order equations. The results show that for constant coronal boundary conditions there is a latitudinal flow toward the solar poles, as a result of magnetic stresses, which persists out to large distances for the Sun. Associated with this flow is a latitudinal component of the magnetic field. The radial flow parameters are, to within small first order differences, in agreement with those of the Parker and the Weber-Davis models of the solar wind.The equations are further generalized to permit first order latitudinal variations in the specified coronal boundary conditions. Results at 1 a.u. are presented for 5 per cent latitudinal differences between the equatorial and polar values. These results show that the solution at 1 a.u. is most sensitive to a latitudinal dependence in the boundary temperature and least sensitive to a latitudinal dependence in the magnetic field magnitude.A solution is then obtained for an approximate dipolar variation in the coronal magnetic field magnitude. This solution predicts that the latitudinal flow is initially toward the Equator due to magnetic channeling; however, this effect is rapidly overcome and the latitudinal flow at 1 a.u. is toward the pole and not significantly different from the solution for constant boundary conditions.     

Active region of the nucleus of the blazar 3C 454.3

The superfine structure of the object 3C 454.3 has been investigated at λ = 7 mm in polarized emission. The kinematics of the structure is shown to correspond to a vortex. A spiral structure like an Archimedes spiral has been established in the accretion disk. The orbital velocity of the inflow exceeds considerably the radial velocity. The disk is oriented in the plane of the sky. The bipolar outflow ejection axis is directed toward the observer with a slight inclination to the east. The jet sizes exceed considerably the counterjet sizes. The jet is ejected in a direction opposite to the observer; its apparent separation from the nozzle is determined by the disk shadowing. The counterjet is directed toward the observer; the flow brightness temperature at the exit from the nozzle reaches T _b ≈ 10¹⁵ K. The jet has a spiral shape with an increasing pitch; the counterjet is a mirror reflection of the initial part of the jet. The incoming thermal plasma is accelerated and heated to relativistic temperatures as it is transferred along a spiral to the center. The orientation of the emission polarization plane changes along the flows due to a change in the ratio of the orbital and radial velocities, a change in the magnetic field orientation.     

Vortex structure of neutron stars with CFL quark cores

The Ginzburg-Landau equations are derived for the magnetic and gluomagnetic gauge fields of nonabelian semi-superfluid vortex filaments in color superconducting cores of neutron stars containing a diquark CFL condensate. The interaction of the diquark CFL condensate with the magnetic and gluomagnetic gauge fields is taken into account. The asymptotic values of the energies of these filaments are determined from the quantization conditions. It is shown that a lattice of semi-superfluid vortex filaments with a minimal quantum of circulation develops in the quark superconducting core during rotation of the star. The magnetic field in the core of this vortex is on the order of 10¹⁸ G. A cluster of proton vortices, which develops in the hadron phase surrounding every superfluid neutron vortex owing to an entrainment effect, creates new semi-superfluid vortex filaments with a minimal quantum of circulation in the quark superconducting core. Translated from Astrofizika, Vol. 51, No. 4, pp. 633–646 (November 2008).     

Diffusion and dispersion in magnetohydrodynamic turbulence: The influence of mean magnetic fields

The properties of magnetohydrodynamic (MHD) turbulence under the influence of a strong mean magnetic field are investigated from the Lagrangian viewpoint by tracking fluid particles in direct numerical simulations. The particle trajectories show characteristic bends near vortex sheets. A strong mean magnetic field leads to preferential diffusion parallel to the mean magnetic field. The two‐particle relative dispersion process shows a dependence on the orientation of the initial separation vector. The relative dispersion is slowed down for initial separation vectors aligned with the mean magnetic field. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structure of the Magnetic Field of a Neutron Star

The magnetic field distribution in the superfluid, spherical, hadronic core of a rotating neutron star, which consists of vortex and vortex-free zones, is investigated. Due to the effect of entrainment of superconducting protons by rotating superfluid neutrons, a nonuniform magnetic field, the average value of which is constant, is formed in the vortex zone of the neutron star, directed parallel to the star's axis of rotation. It is shown that at the stellar surface, near the equatorial plane, there is a vortex-free zone of macroscopic size in which there is no magnetic field. The magnetic field near the boundaries of the vortex-free zone falls off exponentially with depth into the interior of this zone. This result essentially alters earlier concepts about the magnetic field distribution in the superfluid hadronic core of a neutron star. Outside the hadronic core the magnetic field has a dipole character with a magnetic moment on the order of 10³⁰ g×cm³.     

Vortex flow of matter around a singularity and a galactic hypothesis of Jeans

When compact objects or black holes move through a fluid medium, or when turbulent plasma and magnetic fields so conspire, a gas flow is set up which closely resembles the flow of water down a plug-hole (Section 1). A similar hypothesis, but in reverse, was suggested by Jeans in 1928, and would nowadays be referred to as the white hole concept. The dynamics of the flow (Section 2) lead to expressions for the rotational velocity of the fluid far away from (2.1) and near to (2.2) the origin of the vorticity. Rotation curves derived from the model (Section 3) are closely akin to actual galactic rotation curves, but observational data on the latter are not precise enough to permit a delineation to be made between (i) flow around a singularity and (ii) flow around a non-singular sink or source. The other acceptable model, that of (iii) a spreading line vortex, is ruled out by comparison with astrophysical observations (Section 4). The basic analysis for all the models shows that the old problem of the winding-up of spiral arms can be avoided, since the galactic flow system is in a steady state. Section 5 identifies Jeans' speculation as being a hypothesis compatible with singular vortex flow and so with observation, but perhaps not with the usual interpretation of general relativity metrics, even though the requisite dual space does complete the topology in a mathematically satsifying manner. Section 6 concludes that the predictions of the hypothesis of vortex flow agree with the shape, dynamics and structure of galaxies.     

Fine Structure of the Core of the Blazar OJ 287. II. Wavelength 2 cm

We have continued our studies of the fine structure of the active region in the blazar OJ 287 at wavelength λ = 2cm with a resolution of 20 μas, the epochs of 1995–2017. We have identified fragments of two arms along which the surrounding plasma comes to the nozzle. The brightness temperature of the flows rises as the nozzle is approached to T_b ? 10¹² K. The high-velocity bipolar outflow surrounded by lowvelocity components carries away an excess angular momentum as it is accumulated. The high collimation and helicity of the flows are determined by rotation and precession, respectively. Ring currents responsible for the longitudinal magnetic fields are excited in the flows. The jet and counterjet are a mirror reflection of each other; the difference in sizes is determined by the acceleration/deceleration of the flows along/opposite to the magnetic field. The velocity of the high-velocity outflow is v ? 0.06 c. The brightness temperature of the nozzle reaches T_b ? 10¹⁴ K. The spectral index of the southern and northern nozzles is α ≈ 0.66 and ≈0.4, respectively; the difference is determined by absorption in the bulge. The separation between the nozzles is 12 μas or 0.05 pc. The central region of reduced brightness with a diameter ? ≈ 3.6 pc corresponds to the bulge inclined toward the jet at an angle of 65° to the plane of the sky. The counterjet is ejected toward the observer; the jet is ejected in the opposite direction and is visible outside the bulge from a distance of 1.5 pc. The structure and kinematics of the bulge correspond to a vortex nature. An enhanced supply of matter from the northern arm in the middle of 2000 increased the activity of the low-velocity nozzle. A secondary vortex located at a distance of 0.28 mas (1.3 pc) was formed. The high-velocity flow is ejected in a direction of ?110°.     

Effects of mass transfer on the hydromagnetic flow past a vertical limiting surface

An analysis of a two-dimensional steady free convective flow of a conducting fluid, in the presence of a magnetic field and a foreign mass past an infinite, vertical porous and unmoving surface is carried out, when we have constant heat flux at the limiting surface and the magnetic Reynolds number of the flow is not small. If we assume constant suction at the surface, approximate solutions of coupled nonlinear equations are derived for the velocity field, temperature field, magnetic field and for their related quantities. During the course of discussion, the effectsM (magnetic parameter),Gr (Grashof number), andGm (modified Grashof number) have been presented.     

Tripolar vortex in plasma flow

Strongly nonlinear processes in a two-component plasma with sheared flow, in the low-frequency limit, in comparison with the ion gyro frequency Ω_i, and for perturbations propagating perpendicularly to the ambient magnetic field are studied. In the linear domain such a system is prone to the development of instability of the Kelvin–Helmholtz type. In the nonlinear regime this instability can saturate into stationary travelling solutions of the form of vortex chains and tripolar vortices, which are found in this paper.     

On solar wind interaction with the earth's magnetosphere

Hydrodynamic and electrodynamic problems of solar wind interaction with the Earth's magnetosphere on the day-side are investigated.The initial fact, well established, is that the density of the magnetic field energy in the solar wind is rather small. Magnetic field intensity and orientation are shown to determine the character of the solar wind flow around the magnetosphere. For mean parameters of the wind, if the tangential component of the magnetic field is more or equal 5γ, the flow in the magneto-sheath will be laminar. For other cases the flow is of a turbulent type.For turbulent flow, typical plasma parameters are estimated: mean free path, internal scale of inhomogeneities and dissipated energy. The results obtained are compared with experimental data.For the case of laminar flow, special attention is paid to the situation when magnetic fields of the solar wind and Earth are antiparallel. It is suggested, on the basis of solid arguments, that the southward interplanetary field diffuses from the magnetosheath into the Earth's magnetosphere. These ideas are used for the estimation of the distance to the magnetopause subsolar point. A detailed comparison with results of observation is made. The coincidence is satisfactory. Theoretical investigation has been made to a great extent for thin magnetopause with thickness δ ～ R_He-gyroradius of an electron.It is shown that during magnetospheric substorms relaxation oscillations with the period τ = 100–300 sec must appear. A theorem is proved about the appearance of a westward electrical field during the substorm development, when the magnetosphere's day-side boundary moves Earthward and about the recovery phase, when the magnetopause motion is away from the Earth, when there is an eastward electrical field.In the Appendix, plasma wave exitation in the magnetopause is considered and conductivity magnitudes are calculated, including the reduction due to the scattering by plasma turbulence.     

Vortex–interface interactions and generation of glitches in pulsars

We show that the crust–core interface in neutron stars acts as a potential barrier to the peripheral neutron vortices approaching the interface in the model in which these are coupled to the proton vortex clusters. This elementary barrier arises because of the interaction of vortex magnetic flux with the Meissner currents set up by the crustal magnetic field at the interface. The dominant part of the force is derived from the cluster–interface interaction. As a result of the stopping of the continuous neutron vortex current through the interface, angular momentum is stored in the superfluid layers in the vicinity of the crust–core interface during the interglitch period. Discontinuous annihilation of proton vortices at the boundary restores the neutron vortex current and spins up the observable crust on short time-scales, leading to a glitch in the spin characteristics of a pulsar.