On a possible control mechanism for solar wind outflow velocity from coronal holes

In this paper we give an explanation for a control mechanism for velocityV of solar wind (SW) streams for coronal holes (CHs) based on the idea suggested by Rudenko and Fainshtein (1993). In accordance with that idea, the difference of values ofV in high-speed SW streams from different CHs is due to the spread in magnitude of magnetic fieldB _a in the region of acceleration of such streams near the Sun. In this case, with increasing magnitude ofB _a, there is an increase in velocity of the high-speed stream.Through calculations of the coronal magnetic field (potential-field approximation) it is shown that on the source surface the magnetic field B _s, averaged over the cross-section of the magnetic tube from a CH, can vary for different tubes over a wide range and correlates quite well with the area of this tube's base as well as depending on the radial component of the magnetic field at the base of the tube on the source surface B _or.It is found that the value of superradial divergence of the magnetic tube from a CH depends not only on the area of its base (as shown in prior work) but also on B _or. A positive correlation at the Earth's orbit between velocityV of the high-speed SW and the radial component of the magnetic field in the region of this stream is detected, which agrees indirectly with theV-control mechanism under discussion.     

Magnetic diffusion and flare energy buildup

Photospheric motion shears or twists solar magnetic fields to increase magnetic energy in the corona, because this process may change a current-free state of a coronal field to force-free states which carry electric current. This paper analyzes both linear and nonlinear two-dimensional force-free magnetic field models and derives relations of magnetic energy buildup with photospheric velocity field. When realistic data of solar magnetic field (B ₀ 10³ G) and photospheric velocity field (v _max 1 km s^–1) are used, it is found that 3–4 hours are needed to create an amount of free magnetic energy which is of the order of the current-free field energy. Furthermore, the paper studies situations in which finite magnetic diffusivities in photospheric plasma are introduced. The shearing motion increases coronal magnetic energy, while the photospheric diffusion reduces the energy. The variation of magnetic energy in the coronal region, then, depends on which process dominates.     

An extended investigation of Helios 1 and 2 observations: The interplanetary magnetic field between 0.3 and 1 AU

Helios-1 and 2 spacecraft allowed a detailed investigation of the radial dependence of the interplanetary magnetic field components between 0.3 and 1 AU. The behaviour of the radial component B _ris in a very good agreement with Parker's model (B _r r ^-2) and the azimuthal component B also shows a radial dependence which is close to theoretical predictions (B r ^-1). Experimental results for the normal component B and for the field magnitude B are consistent with those from previous investigations. The relative amplitude of the directional fluctuations with periods less than 12 hr is essentially independent of heliocentric distance, while their power decreases approximately as r ^–3 without any appreciable difference between higher and lower velocity regimes.Also at Laboratorio Plasma nello Spazio, CNR, Frascati.     

Towards Calibration of the Mean Magnetic Field of the sun

The 1968–2000 data on the mean magnetic field (MMF, longitudinal component) of the Sun are analysed to study long-time trends of the Sun's magnetic field and to check MMF calibration. It is found that, within the error limits, the mean intensity of photospheric magnetic field (the MMF strength, |H|), did not change over the last 33 years. It clearly shows, however, the presence of an 11-year periodicity caused by the solar activity cycle. Time variations of |H| correlate well with those of the radial component, |B _r|, of the interplanetary magnetic field (IMF). This correlation (r=0.69) appears to be significantly higher than that between |B _r| and the results of a potential source-surface extrapolation, to the Earth's orbit, of synoptic magnetic charts of the photosphere (using the so-called `saturation' factor <sup>–1</sup> for magnetograph measurements performed in the line Fei 525.0 nm; Wang and Sheeley, 1995). It seems therefore that the true source surface of IMF is the `quiet' photosphere – background fields and coronal holes, like those for MMF. The average `effective' magnetic strength of the photospheric field is determined to be about 1.9 G. It is also shown that there is an approximate linear relation between |B <sub>r</sub>| and MMF intensity |H| (in gauss)|B <sub>r</sub>|(H <sub>0</sub>)<sub>min</sub>×(1+C|H|)where =1.5×10<sup>–5</sup> normalizes the photospheric field strength to 1 AU distance from the Sun, (H <sub>0</sub>)<sub>min</sub>=1.2 G is some minimal `effective' intensity of photospheric background fields and C=1.3 G^–1 an empirical constant. It is noted that good correlation between time variations of |H| and |B _r| makes suspicious a correction of the photospheric magnetic fields with the use of saturation factor ^–1.     

Hβ Doppler-velocity fields within sites of flares in a solar active region

In this paper, we analyze the relationship between photospheric magnetic fields and chromospheric velocity fields in a solar active region, especially evolving features of the chromospheric velocity field at preflare sites. It seems that flares are related to unusually distributed velocity field structures, and initial bright kernels and ribbons of the flares appear in the red-shifted areas (i.e., downward flow areas) close to the inversion line of H Dopplergrams with steep gradients of the velocity fields, no matter whether the areas have simple magnetic structure or a weak magnetic field, or strong magnetic shear and complex structure of the magnetic fields. The data show that during several hours prior to the flares, while the velocity field evolves, the sites of the flare kernels (or ribbons) with red-shifted features come close to the inversion line of the velocity field. This result holds regardless of whether or not the flare sites are wholly located in blue-shifted areas (i.e., upward flow areas), or are far from the inversion line of the Doppler velocity field (V = 0 line), or are partly within red-shifted areas. There are two cases favourable for the occurrence of flares, one is that the gulf-like neutral lines of the magnetic field (B = 0 line) occur in the H red-shifted areas, the other is that the gulf-like inversion lines of the H Doppler velocity field (V = 0 line) occur in the unipolar magnetic areas. These observational facts indicate that the velocity field and magnetic field have the same effect on the process of flare energy accumulation and release.     

Unsteady MHD flow past a porous plate with step function change in suction at slip flow regime

Unsteady two-dimensional hydromagnetic flow of an electrically conducting viscous incompressible fluid past a semi-infinite porous flat plate with step function change in suction velocity is studied allowing a first order velocity slip at the boundary condition. The solution of the problem is obtained in closed form and the results are discussed with the aid of graphs for various parameters entering in the problem.Notations B intensity of magnetic field - H magnetic field parameter,H=(M+1/4)^1/2–1/2 - h rarefaction parameter - L ₁ slip coefficient; ;I, mean free path of gas molecules;f, Maxwell's reflection coefficient - M magnetic field parameter - r suction parameter - t time - t dimensionless time - u velocity of the fluid - u dimensionless velocity of the fluid - U velocity of the fluid at infinity - v suction velocity - v ₁ suction velocity att<=0 - v ₂ suction velocity att>0 - x distance parallel to the plate - y distance normal to the plate - y nondimensional distance normal to the plate - v kinematic viscosity - electric conductivity of the fluid - density of the fluid - shear stress at the wall - nondimensional shear stress at the wall - erf error function - erfc complementary error function     

A comparison of the optical and microwave emissions of some major solar flares

In the first part of the paper, we study the relations between the frequency of maximum radio flux f _max and the magnetic field strength at the photosphere B _p and between the maximum radio flux F _max and the field and its scale L for two differing flares occurring above very different photospheric conditions. It is shown that the simple relations predicted by the gyro-synchrotron emission mechanism f _max B _p and F _max B ² L ² account for the fact that the flares produced microwave bursts of about the same F _max, but of differing f _max.The spectra of type IV radio bursts associated with three large proton flares with post-flare loops have been analyzed. It is found that the decimetric peak vanishes with the onset of the first optical loops. This is consistent with the model of Kopp and Pneuman (1976) which associates growing systems of loops with gradual fieldline reconnection above flaring regions.     

The azimuthal magnetorotational instability (AMRI)

We consider the flow of an electrically conducting fluid between differentially rotating cylinders, in the presence of an externally imposed current-free toroidal field B₀(R_in/R) ê _ϕ . It is known that the classical, axisymmetric magnetorotational instability does not exist for such a purely toroidal imposed field.We show here that a nonaxisymmetric magnetorotational instability does exist, having properties very similar to the axisymmetric magnetorotational instability in the presence of an axial field. In the nonlinear regime the magnetic energy of the perturbances is shifted (in the sense of an inverse cascade) to the axisymmetric mode rather than to the modes with m > 1. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

MHD flow of an elasto-viscous fluid past a porous flat plate

An analytical study is performed to examine the laminar flow of an electrically-conducting elasto-viscous fluid (Walters's liquidB) past an infinite porous flat plate to a step function change in suction velocity in the presence of a transverse magnetic field. The influence of the various parameters, entering in the problem, on the velocity field and shearing stress is extensively discussed.     

Coronal magnetic-field model with non-spherical source surface

Previous global models of coronal magnetic fields have used a geometrical construction based on a spherical source surface because of requirements for computational speed. As a result they have had difficulty accounting for (a) the tendency of full magnetohydrodynamic (MHD) models to predict non-radial plasma flow out to r 10r and (b) the appreciable magnitude, 3, of B _r , (the radial component of B) consistently observed at r 1 AU. We present a new modelling technique based on a non-spherical source surface, which is taken to be an isogauss of the underlying potential field generated by currents in or below the photosphere. This modification of the source surface significantly improves the agreement between the geometrical construction and the MHD solution while retaining most of the computational ease provided by a spherical source surface. A detailed comparison between the present source-surface model and the MHD solution is made for the internal dipole case. The resulting B field agrees well in magnitude and direction with the coronal B field derived from the full MHD equations. It shows evidence of the slightly equatorward meridional plasma flow that is characteristic of the MHD solution. Moreover, the B field obtained by using our non-spherical source surface agrees well with that observed by spacecraft in the vicinity of the Earth's orbit. Applied to a solar dipole field with a moment of 1 G-r ³ , the present model predicts that B _r at r 1 AU lies in the range of 1–2 and is remarkably insensitive to heliomagnetic latitude. Our method should be applicable also to more general (i.e., more realistic) configurations of the solar magnetic field. Isogauss surfaces for two representative solar rotations, as calculated from expansions of observed photospheric magnetic-field data, are found to show large and significant deviations from sphericity.     

Bipolar outflows from stars and galaxies as a tornado phenomenon

At an early stage in the lives of stars and galaxies when they are surrounded by discs, vorticity in the disc concentrates into a central vortex, thus converting a Keplerian velocity fieldu _ø r ^–1/2 into an irrotational velocity fieldu _ør ^–1, which implies inward transfer of angular momentum. Centrifugal forces due to spin-up of the inner region and gravity dominant in the outer region then squeeze gas at intermediate layers, increasing pressure gradient in the axial direction sufficiently to drive a wide-angle low-velocity bipolar outflow from the disc. A logarithmic singularity of vorticity at the axis implies strong centrifugal forces which expand plasma to radiusR where pressure gradient balances centrifugal force density of ions; the much weaker centrifugal force density of electrons cannot balance pressure gradient, so that electrons are driven inwards relative to ions until charge separation limits the relative displacement. Now the radial gradient ofu _øcauses ions to rotate at a different rate to electrons, generating an azimuthal current densityj _øwhich is the source of an axial magnetic fieldB _zin the core of the central vortex. Centrifuging carries lines of B to the core wall, where they are wound into helical force-free configuration with B j. An annular channel of radiusR and thickness R into which parallel helical lines ofj andB are compressed constitutes a magnetic vortex tube (MVT). An MVT separates an inner high-velocity highly collimated outflow from the outer low-velocity wide-angle outflow, and is responsible for jets. Magnetic pinches in the MVT may constrict the core flow at HH objects.     

A model of the magnetized solar wind

A steady state, inviscid, single fluid model of the solar win d in the equatorial plane is developed using magneto-hydrodynamics and including the heat equation wit h thermal conduction but no non-thermal heating (i.e. a conduction model). The effects of solar rotation and magnetic field are included enabling both radial and azimuthal components of the velocity and magnetic fields to be found in a conduction model for the first time.The magnetic field cuts off the thermal conduction far from the sun and leads to an increased temperature at 1 AU and relatively small changes to the radial velocity and density. Models have been found which fit the experimental electron densities in 2 R < r < 16 R . These models predict at 1 AU a radial velocity of 300–380 km·sec^-1 and a density of 8 protons·cm^-3. The latter velocity corresponds to a density profile obtained by Blackwell and Petford (1966) during the last sunspot minimum, and is about 100 km·sec^-1 above that found in previous conduction models which fit the coronal electron densities. The radial velocities are now consistent with the mean quiet solar wind, as are the densities when the experimental values are averaged over a magnetic sector. However, the azimuthal velocity at 1 AU is only 1–2 km·sec^-1 which is low compared to the experimental values, as found by previous authors.     

Free-convection effects on MHD flow past a porous plate with step function change in suction velocity

Free convection effects on MHD flow past a semi infinite porous flat plate is studied when the time dependent suction velocity changes in step function form. The solution of the problem is obtained in closed form for the fluid with unit Prandtl number. It is observed that for both cooling and heating of the plate the suction velocity enhances the velocity field. The heat transfer is higher with increase in suction velocity.Notations B intensity of magnetic field - G Grashof number - H magnetic field parameter,H=(M+1/4) ^1/2–1/2 - M magnetic field parameter - N _u Nusselt number - P Prandtl number of the fluid - r suction parameter - T temperature of the fluid - T _w temperature of the plate - T temperature of the fluid at infinity - t time - t non-dimensional time - u velocity of the fluid parallel to the plate - u non-dimensional velocity - U velocity of the free stream - suction velocity - ₁ suction velocity att0 - ₂ suction velocity att>0 - x,y coordinate axes parallel and normal to the plate, respectively - y non-dimensional distance normal to the plate - coefficient of volume expansion - thermal diffusivity - kinematic viscosity - electric conductivity of the fluid - density of the fluid - non-dimensional temperature of the fluid - shear stress at the plate - non dimensional shear stress - erf error function - erfc complementary error function     

Restrictions on radial magnetic field and flow solutions for the solar wind

In Parker's original model, the solar wind is represented as a spherically symmetric hydrodynamic flow. The velocity is radially directed and decoupled from the magnetic field. The simple extension of this model to include a dependence on the polar angle, , is shown to be invalid for radial flow and radial magnetic field. This work demonstrates how ad hoc symmetry conditions imposed to simplify a non-linear problem can be incompatible with the basic hydromagnetic equations.     

A numerical study of the unsteady MHD free convection with hall current

Effect of Hall current on the hydromagnetic free-convection flow of an electrically-conducting viscous incompressible fluid past an impulsively accelerated vertical porous plate in the presence of a uniform transverse magnetic field subjected to a constant transpiration velocity is analyzed for the case of small magnetic Reynolds number. Numberical solutions are obtained for the axial and transverse components of the velocity as well as the skin-friction by employing the Crank-Nicolson implicit finite-difference method for all probable values of the Prandtl number. The results are discussed with the effects of the Grashof number Gr, the transpiration velocity parameter , the Hall current parameterm, and the magnetic field parameterM for the Prandtl number Pr=0.71 which represents air at 20° C.     

The relationship between the longitudinal magnetic field and the line-of-sight velocity at different angular positions of sunspots

Using observational data on 14 sunspots from the Sayan Observatory vector magnetograph, a study was made of the relationship between the sunspot magnetic field and the Evershed motions. It is shown that the central area of the solar disk is dominated by an anti-correlation of the longitudinal magnetic field B and the line-of-sight velocity V when a maximum of V corresponds to the neutral line of the longitudinal field. Near the limb there usually is a coincidence of the field and velocity neutral lines. There is evidence for the possible asymmetric character of the effect with respect to the central meridian.     

On a Babcock-Leighton dynamo model with a deep-seated generating layer for the toroidal magnetic field

A dynamo model of the Babcock-Leighton type having the following features is studied. The toroidal fieldB is generated in a thin layer (the GL), located at the lower solar convection zone, by a shear in the angular velocity acting on the poloidal fieldB _p (= × [0, 0,A ].) If, in this layer, and for a certain value of the polar angle,, |B _Ø | exceeds a critical field,B _cr , then the eruption of a flux tube occurs. This flux tube, which is assumed to rise radially, generates, when reaching the surface, a bipolar magnetic region (BMR) with fluxes _p and _f for the preceding and following spot respectively. For the purpose of the numerical calculations this BMR is replaced by its equivalent axisymmetrical magnetic ring doublet. The ensemble of these eruptions acts as the source term for the poloidal field. This field, generated in the surface layers, reaches the lower solar convection by transport due to meridional motions and by diffusion. The meridional motions are the superpositions of a one-cell velocity field that rises at the equator and sinks at the poles and of a two-cell circulation that rises at the equator and poles and sinks at mid latitudes. The toroidal field andA _Ø were expanded in Legendre polynomials, and the coupled partial differential equations (int andr; time and radial coordinate) satisfied by the coefficients in these expansions were solved by a finite difference method. In the expansions, Legendre polynomials up to order thirty were included.In spite of an exhaustive search no solutions were found with _p = – _f . The solutions presented in this paper were obtained with _p = –0.5 _f . In this case, the northern and southern hemisphere are not entirely decoupled since lines of force join both hemispheres. Most of the solutions found were periodic. For the one-cell meridional flow described above and for a purely radial shear in the GL (the angular velocity increasing inwards) the dynamo wave propagates from the pole towards the equator. The new cycle starts at the poles while the old cycle is still present in the equatorial regions.     

Civ plasma flow near active region filaments

Selected Civ V ₀ lines (lines separating adjacent regions of strong blue shift and strong red shift) located near the solar limb and oriented parallel to the radius vector from disk center are shown to be closely aligned with H dark filaments in active regions. The filaments, in turn, are known to lie in the vicinity of magnetic neutral lines. The radial orientation of the V ₀ lines minimizes uncertainties in image registration and their location near the limb ensures that the observed fluid motion has major components paralleling V ₀. It follows that the filaments are located at sites of velocity shear, and, by inference, of magnetic shear. For a case in which a given V ₀ line is observed near both east and west limbs, the gradient of Doppler velocity across the V ₀ line reverses sign from one limb to the other as is expected for horizontal steady flow. Thus, the velocity vectors remain fixed with respect to the filament.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Plasma flow in a curved magnetic field

A beam of collisionless plasma is injected along a longitudinal magnetic field into a region of curved magnetic field. Two unpredicted phenomena are observed: The beam becomes deflected in the directionopposite to that in which the field is curved, and itcontracts to a flat slab in the plane of curvature of the magnetic field.The plasma is produced by a conical theta-pinch gun and studied by means of high speed photography, electric and magnetic probes, ion analyser, and spectroscopy.The plasma beam is collisionless and its behaviour is, in principle, understood on the basis of gyro-centre drift theory. A fraction of the transverse electric fieldE=–v×B, which is induced when the beam enters the curved magnetic field, is propagated upstream and causes the reverse deflection byE×B drift. The upstream propagation of the transverse electric field is due to electron currents.The circuit aspect on the plasma is important. The transverse polarization current in the region with the curved field connects to a loop of depolarization currents upstream. The loop has limited ability to carry current because of the collisionless character of the plasma; curlE is almost zero and electric field components arise parallel to the magnetic field. These play an essential role, producing runaway electrons, which have been detected. An increased electron temperature is observed when the plasma is shot into the curved field. Runaway electrons alone might propagate the electric field upstream in case the electron thermal velocity is insufficient.The phenomenon is of a general character and can be expected to occur in a very wide range of ensities. The lower density limit is set by the condition for self-polarization,nm _i / ₀ B ² 1 or, which is equivalent,c ²/v _A ² ;1, wherec is the velocity of light, andv _A the Alfvén velocity. The upper limit is presumably set by the requirement _{e e} 1.The phenomenon is likely to be of importance, for example, for the injection of plasma into magnetic bottles and in space and solar physics. The paper illustrates the complexity of plasma flow phenomena and the importance of close contact between experimental and theoretical work.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978     

Generation of waves by the solar magnetic field polarity reversal

In this paper an excitation of waves is considered during the time interval in which the undisturbed magnetic field changes its direction. If this interval is taken to be 2 years, which is shorter than the 11-year cycle, then the undisturbed components of the magnetic field may be linearly dependent on time and independent of the coordinates. The excitation of waves is due to the undisturbed stationaryV ₀ flow with divV ₀ = 0 and with (V ₀ rot₀) = constant.We use the local Cartesian coordinate system, which is immovable towards the solar centre, and consider the case when the toroidal component of the undisturbed magnetic field changes its sign simultaneously with one of the axial components. The third component does not change its direction.The efficiency of the enhancement of the magnetic field and velocity disturbances depends on the Alfvén wave frequency, _A. When _A = 0, the component of the disturbed velocity, which is directed along the constant component of the undisturbed magnetic field, increases. In this case the shear waves excite the carrier (high) frequency (KV ₀), whereK is the wave vector. Due to the shear instability the amplitude of the velocity increases during 1 year before the moment of reversal of the global magnetic field polarity (RGMFP) for an arbitrary latitude. It reaches a maximum at RGMFP and decreases in the next year. When _A > 0, then the amplitudes of the disturbed values reach maxima before the moment of RGMFP, and when _A < 0, they reach maxima after it.We argue that the shear waves propagate from middle latitudes to the pole and equator. Using the results of the analytical solutions and leaning on the evidence of the observational data (Gigolashvili and Japaridze, 1992), we derive the result that the component of the undisturbed magnetic field, which is perpendicular to the solar surface, changes its sign simultaneously with the toroidal component.