Standing shocks in magnetized dissipative accretion flow around black holes

We explore the global structure of the accretion flow around a Schwarzschild black hole where the accretion disc is threaded by toroidal magnetic fields. The accretion flow is optically thin and advection dominated. The synchrotron radiation is considered to be the active cooling mechanism in the flow. With this, we obtain the global transonic accretion solutions and show that centrifugal barrier in the rotating magnetized accretion flow causes a discontinuous transition of the flow variables in the form of shock waves. The shock properties and the dynamics of the post-shock corona are affected by the flow parameters such as viscosity, cooling rate and strength of the magnetic fields. The shock properties are investigated against these flow parameters. We further show that for a given set of boundary parameters at the outer edge of the disc, accretion flow around a black hole admits shock when the flow parameters are tuned for a considerable range.     

Acceleration and ejection of ring vortices as a mechanism for formation of jet components in AGN

Exact solutions are obtained for the two-dimensional hydrodynamic equations for symmetric configurations of two and four vortices in the presence of an arbitrary flow with a point singularity. These solutions describe the dynamics of a dipole toroidal vortex in accretion and wind flows within the active nuclei of galaxies. It is shown that in a converging (accretion) flow, as they are compressed along their major radius, toroidal vortices are ejected with acceleration along the axis of symmetry of the active nucleus, to form the components of a bilateral jet. For a symmetric flow, the increase in the velocity of the vortices is determined by the monopole component of the flow, and, when there is an asymmetry in the flow, also by the dipole component of the flow, which controls the asymmetry of the ejection.     

Flow behind an attached shock wave in a radiating gas

A simple method is used to determine the curvature of an attached shock wave and the flow variable gradients behind the shock curve at the tip of a straight-edged wedge placed symmetrically in a supersonic flow of a radiating gas near the optically thin limit. The shock curvature and the flow variable gradients along the wedge at the tip are computed for a wide range of upstream flow Mach numbers and wedge angles. Several interesting results are noted; in particular, it is found that the effect of an increase in the upstream flow Mach number or the radiative flux is to enhance the shock wave curvature which, however, decreases with an increase in the specific heat ratio or the wedge angle.     

A time dependent model for spicule flow

A time dependent model for the flow of gas in a spicule is studied. In this model, the flow occurs in a magnetic flux sheath. Starting from hydrostatic equilibrium, the flux sheath is allowed to collapse normal to itself. The collapse induces a flow of gas along the magnetic field and this flow is identified as a spicule. A variety of sheath geometries and velocity patterns for the normal flow have been studied. It is observed that a large curvature in the field geometry and a large initial value for the normal flow are necessary to achieve spicule-like velocities. The duration for which a large velocity of normal flow is required is much shorter than the average lifetime of a spicule. It is proposed that the initial rapid collapse occurs during an impulsive spicule phase and it is the subsequent gradual relaxation of the flow which is observed as a spicule.     

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.     

Dynamical instability of laminar axisymmetric flows of ideal compressible fluid

The instability of axisymmetric flows of inviscid compressible fluid with respect to two-dimensional infinitesimal perturbations with the nonconservation of angular momentum is investigated by numerically integrating the differential equations of hydrodynamics. The compressibility is taken into account for a homentropic flow with an adiabatic index varying over a wide range. The problem has been solved for two angular velocity profiles of an initial axisymmetric flow. In the first case, a power-law rotation profile with a finite enthalpy gradient at the flow edges has been specified. For this angular velocity profile, we show that the instability of sonic and surface gravity modes in a nearly Keplerian flow, when a radially variable vorticity exists in the main flow, can be explained by the combined action of the Landau mechanism and mode coupling. We also show that including a radially variable vorticity makes the limiting exponent in the rotation law at which the unstable surface gravity modes vanish dependent on the fluid compressibility. In the second case, a Keplerian rotation law with a quasi-sinusoidal deviation has been specified in such a way that the enthalpy gradient vanished at the flow edges. We have found than the sonic modes are then stabilized and the flow is unstable only with respect to the perturbations that also exist in an incompressible fluid.     

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.     

Origin of the torsional oscillation pattern of solar rotation

A model is presented that explains the `torsional oscillation' pattern of deviations in the solar rotation rate as a geostrophic flow. The flow is driven by temperature variations near the surface due to the enhanced emission of radiation by the small-scale magnetic field. The model explains the sign of the flow, its amplitude and the fact that the maxima occur near the boundaries of the main activity belts. The amplitude of the flow decreases with depth from its maximum at the surface but penetrates over much of the depth of the convection zone, in agreement with the data from helioseismology. It predicts that the flow is axisymmetric only on average, and in reality consists of a superposition of circulations around areas of enhanced magnetic activity. It must be accompanied by a meridional flow component, which declines more rapidly with depth.     

The formation of fluidized ejecta on Mars by granular flows

Abstract— A simple granular flow model is used to investigate some of the conditions under which ejecta may flow as a granular media. The purpose of this investigation is to provide some bounds as to when either volatiles or an atmosphere are required to explain the fluid‐like morphology of many Martian ejecta deposits. We consider the ejecta deposition process from when an ejecta curtain first strikes a target surface via ballistics and possibly flows thereafter. A new finding is that either hard‐smooth surfaces or slightly erodible surfaces allow ejecta to flow readily as a granular medium. Neither volatiles nor an atmosphere are required to initiate flow. A low friction coefficient between ejecta grains can also generate flow and would be analogous to adding volatiles to the ejecta. The presence of either a rough or a densely packed erodible surface does not permit easy ejecta flow. High friction coefficients between ejecta grain also prevent flow, while changes in the coefficient of restitution (a measure of how much energy is retained after collisions between particles) plays a minor role in the flow dynamics of ejecta. A hard smooth or a somewhat erodible surface could be generated by past fluvial activity on Mars, which can either indurate a surface, erode and smooth a surface, or generate sedimentary terrains that are fairly easy to erode. No ramparts or layered ejecta morphologies are generated by our model, but this may be because several simplifying assumptions are used in our model and should not be construed as proof that either volatiles or an atmosphere are required to form fluidized ejecta morphologies.     

Model dependence of transonic properties of accretion flows around black holes

We analytically study how the behaviour of accretion flows changes when the flow model is varied. We study the transonic properties of the conical flow, a flow of constant height and a flow in vertical equilibrium, and show that all these models are basically identical, provided that the polytropic constant is suitably changed from one model to another. We show that this behaviour is extendible even when standing shocks are produced in the flow. The parameter space where shocks are produced remains roughly identical in all these models when the same transformation among the polytropic indices is used. We present applications of these findings.     

Hysteresis effects and diagnostics of the shock formation in low angular momentum axisymmetric accretion in the Kerr metric

The secular evolution of the purely general relativistic low angular momentum accretion flow around a spinning black hole is shown to exhibit hysteresis effects. This confirms that a stationary shock is an integral part of such an accretion disc in the Kerr metric. The equations describing the space gradient of the dynamical flow velocity of the accreting matter have been shown to be equivalent to a first order autonomous dynamical systems. Fixed point analysis ensures that such flow must be multi-transonic for certain astrophysically relevant initial boundary conditions. Contrary to the existing consensus in the literature, the critical points and the sonic points are proved not to be isomorphic in general, they can form in a completely different length scales. Physically acceptable global transonic solutions must produce odd number of critical points. Homoclinic orbits for the flow possessing multiple critical points select the critical point with the higher entropy accretion rate, confirming that the entropy accretion rate is the degeneracy removing agent in the system. However, heteroclinic orbits are also observed for some special situation, where both the saddle type critical points of the flow configuration possesses identical entropy accretion rate. Topologies with heteroclinic orbits are thus the only allowed non-removable degenerate solutions for accretion flow with multiple critical points, and are shown to be structurally unstable. Depending on suitable initial boundary conditions, a homoclinic trajectory can be combined with a standard non-homoclinic orbit through an energy preserving Rankine-Hugoniot type of stationary shock, and multi-critical accretion flow then becomes truly multi-transonic. An effective Lyapunov index has been proposed to analytically confirm why certain class of transonic flow cannot accommodate shock solutions even if it produces multiple critical points.     

The chromospheric Evershed flow

High-resolution filtergrams of a sunspot region observed at seven wavelengths in Hα with a resolution of 1/8 Å have been used to investigate the three-dimensional structure of the chromospheric Evershed flow and its time variation. The flow channels have the form of loops whose cross-section alters with height and distance from the spot. The loops probably reach a height of 5000 km. The presence of a compression shock is suggested by the observations. Many velocity channels appear to alter their direction with position in the line, giving the impression of a screw-like motion resembling a Beltrami flow. The flow channel alters with a characteristic time of 8±2 min. It is suggested that this relatively short time constant represents the characteristic time of perturbations of the flow channels and the superpenumbra fibrils. The lifetime of the flow channel istelf is estimated to be 70 min. The observations are discussed in terms of material moving inwards towards the spot along curved flux loops.     

The concentration of the large-scale solar magnetic field by a meridional surface flow

We calculate analytical and numerical solutions to the magnetic flux transport equation in the absence of new bipolar sources of flux, for several meridional flow profiles and a range of peak flow speeds. We find that a poleward flow with a broad profile and a nominal 10 m s^–1 maximum speed concentrates the large-scale field into very small caps of less than 15° half-angle, with average field strengths of several tens of gauss, contrary to observations. A flow which reaches its peak speed at a relatively low latitude and then decreases rapidly to zero at higher latitudes leads to a large-scale field pattern which is consistent with observations. For such a flow, only lower latitude sunspot groups can contribute to interhemispheric flux annihilation and the resulting decay and reversal of the polar magnetic fields.     

The structure of the hydrodynamic plasma flow near the heliopause stagnation point

The plasma flow in the vicinity of the heliopause stagnation point in the presence of the H atom flow is studied. The plasma at both sides of the heliopause is considered to be a single fluid. The back reaction of the plasma flow on the H atom flow is neglected, and the density, temperature and velocity of the H atom flow are taken to be constant. The solution describing the plasma flow is obtained in the form of power series expansions with respect to the radial distance from the symmetry axis. The main conclusion made on the basis of the obtained solution is that the heliopause is not the surface of discontinuity anymore. Rather, it is the surface separating the flows of the solar wind and interstellar medium with all plasma parameters continuous at this surface.     

Hybrid Simulation of Collisionless Shock Formation in Support of Laboratory Experiments at Unr

The problem of producing collisionless shocks in the laboratory is of great interest for space and astrophysical plasmas. One approach is based on the idea of combining strong magnetic field (up to 100 Tesla) created during a Z-pinch discharge with a plasma flow produced in the process of the interaction of a laser pulse with a solid target. In support of laboratory experiments we present hybrid simulations of the interaction of the plasma flow with frozen in it magnetic field, with the spherical obstacle. Parameters of the flow correspond to a laser plasma ablation produced in the laboratory during irradiation of the target by a 3 J laser. Magnetic fields in the plasma flow and around the obstacle are created by the currents produced by the pulse power ZEBRA voltage generator. With the appropriate set of initial conditions imposed on the flow collisionless shocks can be created in such a system. Using independent generators for plasma flow and magnetic field allows for the exploration of a wide range of shock parameters. We present simulations of the formation of supercritical collisionless shock relevant to the experiment, performed with the 2D version of the hybrid code based on the CAM-CL algorithm [Planet. Space Sci. 51, 649, 2003].     

Stability of siphon flow in coronal magnetic loops

Plasma siphon flow with velocities up to 100 km/s have been observed in coronal magnetic loops. We discuss the stability of this siphon flow using slab and cylinder models. We calculate numerically the dispersion relation and obtain the rate of growth of instability and the frequency of perturbing waves. Our main conclusions are that magnetic field is a stabilizing factor and that flow velocity is a de-stabilizing factor. We discuss the question whether stationary, high-velocity siphon flow can exist in coronal magnetic loops.     

Hall effects on the oscillatory MHD flow in the stokes problem past an infinite vertical porous plate,II

In this work we present the effects of Hall current on the hydromagnetic free-convection flow of a viscous, incompressible and electrically conducting fluid past an infinite vertical porous plate for the Stokes problem when the fluid is subject to a constant suction velocity. The flow is normal to the porous plate and the free-stream oscillates about a mean value. As the mean steady flow has been presented in part I, only the solution for the transient primary velocity profiles, transient secondary velocity profiles, transient temperature profiles; the amplitude and phase of skin-friction components and the rate of heat transfer are presented in this work. As in the case of mean steady flow, the influence of the various parameters on the unsteady flow field is discussed with the help of graphs and tables for both the cases cooling and heating of the porous plate.     

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.     

Evidence for ice flow prior to trough formation in the martian north polar layered deposits

The relative importance of surface mass fluxes and ice flow in shaping the north polar layered deposits (NPLD), now or in the past, remains a fundamental and open question. Motivated by observation of an apparent ice divide on Gemina Lingula (also known as Titania Lobe), we propose a two-stage evolution leading to the present-day topography on that lobe of the NPLD. Ice flow approximately balances surface mass fluxes in the first stage, but in the second stage ice flow has minimal influence and topography is modified predominantly by the formation of troughs. We focus here on evidence for the first stage, by testing the fit of topography between troughs to an ice-flow model. We find that independent model fits on distinct flow paths closely match inter-trough topography, uniformly over a broad region on Gemina Lingula, with mutually consistent and physically reasonable fitting parameters. However, our model requires ice to occupy and flow in spaces where troughs currently incise the ice. We therefore infer that the troughs (and the distribution of mass balance that caused them) post-date deposition of the inter-trough material and its modification by flow. Because trough formation has apparently altered inter-trough topography very little, we infer that trough formation must have been rapid in comparison to the (still unknown) time-scale of flow since troughs began to form. We view the evidence for past flow as strong, but we do not think that topographic evidence alone can be conclusive. Observations of englacial stratigraphy using orbital sounding radars will yield conclusive tests of our inferred mechanism for the formation of inter-trough topography.     

Sediment transport by liquid surficial flow: Application to Titan

Sediment transport by surficial flow likely occurs on Titan. Titan is thought to have a volatile cycle, such as on Earth and likely in the past on Mars, which would entail surficial liquid flow. And surficial flow is implied in interpretations of Cassini-Hyugens data as showing fluvial channels, which would require sediment transport by surficial flow to form the observable features. We present calculations from basic hydraulic formulae of sediment entrainment and transport by surficial flow. First, we describe the conditions for (non-cohesive) sediment entrainment by grain size through use of the Shields' threshold curve. We then calculate settling velocities by grain size to describe the type of sediment transport—washload, suspended load, or bedload—that would follow entrainment. These calculations allow derivation of required flow depths for sediment transport by grain size over a given slope. A technique to estimate required flow velocities and unit discharges is also presented. We show the results of these calculations for organic and water ice sediment movement by liquid methane flow under Titan gravity. For comparative purposes, plots for movement of quartz sediment by water on Earth and basalt sediment by water on Mars are also included. These results indicate that (non-cohesive) material would move more easily on Titan than on Earth or Mars. Terrestrial field observations suggest that coarse grain transport is enhanced by hyperconcentration of fine-grained sediment; and the apparent availability of organic (fine grained) sediment on Titan, in conjunction with the possibility of convection-driven rainstorms, may lead to hyperconcentrated flows. Thus, significant sediment transport may occur on Titan during individual overland flow events.