Vortical mechanism for collimation and acceleration of jets

A vortical mechanism for the collimation and acceleration of astrophysical jets is proposed on the basis of exact solutions of the hydrodynamic equations in a homogeneous gravitational field taking viscosity into account. Velocity profiles in the form of a jet structure with a uniformly rotating trunk whose pressure decreases in time, and longitudinal and converging radial flows of matter, are examined. Because of the radial flow, the angular velocity of the trunk and the velocity of the longitudinal flow of matter can accelerate exponentially or in the manner of an “explosive” instability. Flows of this type have low energy dissipation and can serve as unique channels for the acceleration and collimation of jet eruptions from young stars, as well as from active galactic nuclei and quasars. __________ Translated from Astrofizika, Vol. 51, No. 3, pp. 431–444 (August 2008).     

Evolution of astrophysical jets generated by a vortex mechanism

The nonlinear dynamics of a rotating jet is examined following its ejection from a compact gravitating object by a vortex mechanism. A scenario is described in which a dense stream expands and is subsequently transformed into a nonstationary vortex consisting of a cylindrical core and a “sheath.” At this stage of development, a converging radial flow of matter in the differentially rotating nonuniform sheath collimates the jet and speeds up the rotation of the core, as well as the flow of matter along the jet, in accordance with a power law or “explosive” instability, until the velocity discontinuity at the surface of the core approaches the sound speed. Flows of this type have low energy dissipation and can serve as unique channels for the acceleration and collimation of jet eruptions from young stars, active galactic nuclei, and quasars. Translated from Astrofizika, Vol. 52, No. 1, pp. 135–145 (February 2009).     

Accelerated vortices in compressible media

A class of exact vortical solutions of the hydrodynamic equations for compressible media (single component or two-phase) is examined, taking viscosity and a gravitational field into account. Velocity profiles that have the structure of a vortex with a uniformly rotating, low-pressure, low-density trunk and a converging radial flow of matter are analyzed. These flows have low energy dissipation and can easily occur under natural conditions. Translated from Astrofizika, Vol. 51, No. 4, pp. 617–632 (November 2008).     

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.     

Restricted four-body problem. The case of a central configuration: Libration points and their stability

We consider the problem of the motion of a zero-mass body in the vicinity of a system of three gravitating bodies forming a central configuration.We study the case where two gravitating bodies of equal mass lie on the same straight line and rotate around the central body with the same angular velocity. Equations for calculating the equilibrium positions in this system have been derived. The stability of the equilibrium points for a system of three gravitating bodies is investigated. We show that, as in the case of libration points for two bodies, the collinear points are unstable; for the triangular points, there exists a ratio of the mass of the central body to the masses of the extreme bodies, 11.720349, at which stability is observed.     

Instability of spherical accretion — I. Shock-free Bondi accretion

We examine the spatial stability of spherical adiabatic Bondi accretion on to a point gravitating mass against external perturbations. Both transonic critical and subsonic subcritical accretion are shown to be stable against purely radial acoustic, vortex or entropy perturbations. In the case of non-radial perturbations the amplitude of the perturbations grows without limit with smaller radii. Instability manifests itself only if the size of the accreting body is much less than the Bondi radius so that the inflow is highly supersonic or highly subsonic at the surface of the accretor in the case of critical or subcritical accretion respectively. These asymptotics hold and consequently the instability may develop for adiabatic index of accreting gas γ < 5/3. We suggest that this instability may lead to an essential thermalization of accreting flow thus, particularly, solving the problem of otherwise inefficient energy release in spherical accretion on to a black hole.     

The effect of long-lived vortical circulation on the dynamics of dust particles in the mid-plane of a protoplanetary disc

We investigate the response of dust particles in the mid-plane of a protoplanetary disc to the turbulent velocity field of long-lived, large-scale vortical circulation. The dynamical problem is studied through numerical integrations of the equations of motion for individual particles (the sizes of which range from centimetres to metres) subject to the solar gravity and the friction drag of the nebular gas. It is found, neglecting the thickness of the disc, that the particles do not drift inwards to the central star as occurs in a standard symmetrical nebula. Vortices tend to capture a large number of the particles. The effectiveness of this size-selective concentration mechanism depends not only on the value of the drag and the distance from the Sun, but also on the elongation of the vortex and its characteristic lifetime. Typical anticyclonic vortices with exponential decay times of 30 orbital periods and semi-axis ratios of 4 can increase the local surface density by a factor of 4 in a lifetime and accumulate 0.03–0.3 Earth masses. If the elongation is significant (>7), the vortex cannot concentrate any significant amount of solid material. Vortices with an elongation of about 2 are the most effective as regards trapping of dust. We have also found analytical expressions for the capture time as well as capture constraints as a function of the friction parameter, the elongation of the vortex and the impact parameter. By increasing the lifetime and the surface density of the solid particles, this confining mechanism can make the agglomeration of the solid material of the nebula (through collisional aggregation or gravitational instabilities) much more efficient than previously believed. This offers new possibilities for the formation of the planetesimals and the giant planet cores, and may explain the rapid formation of extrasolar giant planets.     

Visco–Resistive Dissipation in Transient Reconnection Driven by the Orszag–Tang Vortex

Viscous effects are expected to significantly contribute to reconnective energy release mechanisms in solar flares. While simple scaling arguments based on head-on reconnection suggest that viscous dissipation may dominate resistive dissipation, it is not clear whether these findings can be applied in more general merging situations. Here we perform side-by-side planar reconnection simulations driven by the Orszag–Tang vortex, for both classical and Braginskii forms of the viscosity. This formulation has the advantage of providing an autonomous MHD system that develops strong current layers, sustained by large-scale vortical shearing flows. The dissipation rates are shown to follow analytically based scaling laws, which suggest that viscous losses generated from large-scale non-uniform velocity fields are likely to dominate resistive losses in current-sheet reconnection solutions.     

Vortical distribution of sunspots

A remarkable vortical distribution of sunspots, photographed at National Solar Observatory, Tucson, may be an important indication that a vortex flow is essential in the formation of sunspots. It is argued that the concept of vortex flow around a spot is not a heresy, since a generation mechanism of non-trivial force-free fields requires the presence of time varying vorticity in the photosphere.     

Dynamical friction in an isentropic gas

When a gravitating object moves across a given mass distribution, it creates an overdense wake behind it. Here, we performed an analytical study of the structure of the flow far from object when the flow is isentropic and the object moves subsonically within it. We show that the dynamical friction force is the main drag force on the object and by using a perturbation theory, we obtain the density, velocity and pressure of the perturbed flow far from the mass. We derive the expression of the dynamical friction force in an isentropic flow and show its dependence on the Mach number of the flow and on the adiabatic index. We find that the dynamical friction force becomes lower as the adiabatic index increases. We show analytically that the wakes are less dense in our isentropic case in comparison to the isothermal ones.     

A comparison of different cluster mass estimates: consistency or discrepancy?

Rich and massive clusters of galaxies at intermediate redshift are capable of magnifying and distorting the images of background galaxies. A comparison of different mass estimators among these clusters can provide useful information about the distribution and composition of cluster matter and its dynamical evolution. Using the hitherto largest sample of lensing clusters drawn from the literature, we compare the gravitating masses of clusters derived from the strong/weak gravitational lensing phenomena, from the X-ray measurements based on the assumption of hydrostatic equilibrium, and from the conventional isothermal sphere model for the dark matter profile characterized by the velocity dispersion and core radius of galaxy distributions in clusters. While there is excellent agreement between the weak lensing, X-ray and isothermal sphere model-determined cluster masses, these methods are likely to underestimate the gravitating masses enclosed within the central cores of clusters by a factor of 2–4 as compared with the strong lensing results. Such a mass discrepancy has probably arisen from the inappropriate applications of the weak lensing technique and the hydrostatic equilibrium hypothesis to the central regions of clusters, as well as from assuming an unreasonably large core radius for both luminous and dark matter profiles. Nevertheless, it is pointed out that these cluster mass estimators may be safely applied on scales greater than the core sizes. Namely, the overall clusters of galaxies at intermediate redshift can still be regarded as the dynamically relaxed systems, in which the velocity dispersion of galaxies and the temperature of X-ray emitting gas are good indicators of the underlying gravitational potentials of clusters.     

Gravitational collapse and equilibrium conditions of a toroidal vortex with thermal pressure

We found the equilibrium conditions for a self-gravitating toroidal vortex by taking thermal pressure into account. These conditions are shown to significantly differ from those for a disk or a sphere. The evolution of a thin vortex turns it into a compact vortex that loses mechanical stability for low masses at a polytropic index γ<4/3 but retains stability for sufficiently high masses and densities determined by the velocity circulation in the vortex.     

Observations of Photospheric Vortical Motions During the Early Stage of Filament Eruption

Solar filaments/prominences exhibit rotational motion during different phases of their evolution from their formation to eruption. We have observed the rotational/vortical motion in the photosphere near the ends of ten filaments during their initial phase of eruption, at the onset of the fast rise phase. All the filaments were associated with active regions. The photospheric vortical motions we observed lasted for 4?–?20 minutes. In the vicinity of the conjugate ends of the filament the direction of rotation was opposite, except for two cases, where rotational motion was observed at only one end point. The sudden onset of a large photospheric vortex motion could have played a role in destabilizing the filament by transporting axial flux into the activated filament thereby increasing the outward magnetic pressure in it. The outward magnetic pressure may have pushed the filament/flux rope to the height where the torus instability criterion was satisfied, and hence it could have caused the filament instability and eruption.     

Impact erosion of planetary atmospheres

The impact of a large extraterrestrial body onto a planet deposits considerable energy in the atmosphere. If the radius of the impactor is much larger than an atmospheric scale height and its velocity much larger than the planetary escape velocity, some of the planetary atmosphere may be driven off into space. The process is analyzed theoretically in this paper. The amount of gas that escapes is equal to the amount of gas intercepted by the impacting body multiplied by a factor not very different from unity. Escape occurs only if the velocity of the impacting body exceeds the planetary escape velocity. At large impact velocities the enhancement factor, which is the factor multiplying the amount of atmosphere intercepted by the impacting body, approaches a constant value approximately equal to 10¹²/V_e², where V_e is the escape velocity (in cm/sec). The enhancement factor is independent of atmospheric mass or surface pressure. Ablation of the impacting body and the planetary surface adds to the mass of gas that must be accelerated into space if escape is to occur. As a result, impact erosion of the atmosphere does not occur from a planet with an escape velocity in excess of 10 km/sec.     

Effects of the angular momentum of accreting matter on the flow structure in the subsonic settling and Bondi-Hoyle accretion regimes

Previously unexplored accretion regimes associated with the rotation of accreting matter, namely the perturbations of a quasi-spherical subsonic settling flow and Bondi-Hoyle accretion in the presence of axial rotation, are considered within the framework of ideal hydrodynamics. For subsonic settling accretion, the perturbations are shown to grow rapidly as the gravitating center is approached, so that the flow in the inner regions can no longer be considered quasi-spherical. For Bondi-Hoyle accretion, a vacuum cylindrical cavity is shown to be formed at large distances from the gravitating center near the flow axis, with the flow velocity outside this cavity being virtually independent of the distance to the rotation axis.     

Tidal effect of rings on central figures of equilibrium

The effect of a gravitating ring or torus on the central figure of relative equilibrium of a rotating liquid or gaseous mass is studied in the tidal approximation. A formula is derived for the increment in the square of the angular velocity of the central figure. Three models for wide rings are examined and one, for circular tori. The effects of rings on the oblateness of the planet Saturn or on the figure of the sun lie beyond the limits of modern measurements; however, the effect of a gravitating torus is already comparable to the effect of the star’s rotation in the case of the red supergiant WOH G64 in the LMC. The method is modified for galaxies; it then describes the effect of rings both on the stellar subsystem and, separately, on the diffuse subsystem. The well known NGC 4594 “Sombrero” galaxy is introduced as an example. This method may also be useful for estimating the dark mass surrounding giant E-galaxies.     

Lagrangian Solutions of a Plane Restricted Three-Body Problem

We determine the parameters of a passively gravitating body that satisfy the conditions for the existence of Lagrangian solutions in a plane restricted three-body problem. A example is given.     

Evolution of Pulsars with Energy Release in the Superfluid Core of a Neutron Star

The effect of a neutron-proton vortex system on the rotation dynamics of neutron stars is examined. The dynamics of the motion of a two component superfluid system in the core of a neutron star yields an equation for the evolution of the pulsar's rotation period. The spin down of the star owing to energy release at the core boundary, which is associated with a contraction of the length of the neutron vortex as it moves radially and magnetic energy of the vortical cluster is released, is taken into account. Evolutionary curves are constructed for pulsars with different magnetic fields and stellar radii. For certain values of the coefficient of friction between the superfluid and normal components in the core of the neutron star, at the end of its evolution a radio pulsar may become an anomalous x-ray pulsar or a source of soft gamma radiation with a period on the order of 10 seconds.     

Equilibrium structure of magnetized gravitating cylinders

The equilibrium distribution of physical quantities in static and uniformly rotating magnetized gravitating cylinders is investigated on the assumption that the fluid is characterized by a constant Alfvén velocity throughout. The fluid is idealized as a perfect gas obeying a polytropic relation or a degenerate gas at zero temperature.     

Rotation rate and velocity dispersion of planetary ring particles with size distribution II. Numerical simulation for gravitating particles

We examine rotation rates of gravitating particles in low optical depth rings, on the basis of the evolution equation of particle rotational energy derived by Ohtsuki [Ohtsuki, K., 2006. Rotation rate and velocity dispersion of planetary ring particles with size distribution. I. Formulation and analytic calculation. Icarus 183, 373-383]. We obtain the rates of evolution of particle rotation rate and velocity dispersion, using three-body orbital integration that takes into account distribution of random velocities and rotation rates. The obtained stirring and friction rates are used to calculate the evolution of velocity dispersion and rotation rate for particles in one- and two-size component rings as well as those with a narrow size distribution, and agreement with N-body simulation is confirmed. Then, we perform calculations to examine equilibrium rotation rates and velocity dispersion of gravitating ring particles with a broad size distribution, from 1 cm up to 10 m. We find that small particles spin rapidly with 〈ω²〉^1/2/Ω?¹⁰²-¹⁰³, where ω and Ω are the particle rotation rate and its orbital angular frequency, respectively, while the largest particles spin slowly, with 〈ω²〉^1/2/Ω?1. The vertical scale height of rapidly rotating small particles is much larger than that of slowly rotating large particles. Thus, rotational states of ring particles have vertical heterogeneity, which should be taken into account in modeling thermal infrared emission from Saturn's rings.