Peculiarities of the magnetic flux emerging in the equatorial solar zone

The magnetic flux longitudinal distribution in the equatorial solar zone has been studied. The magnetic synoptic maps of the Wilcox Solar Observatory (WSO) during Carrington rotations (CRs) 2052–2068 in 2007 and early 2008 have been analyzed. The longitudinal distributions of the area of the zones where the photospheric magnetic field locally enhanced have been constructed for each CR. The obtained distributions indicate that the zones are located discretely and that a clearly defined one narrow longitudinal interval with the maximum flux is present. The longitudinal position of this maximum shifted discretely by ≈130° at an interval of 5.5 ± 0.5 CRs. A longitudinal shift of the zones with an increased magnetic flux multiple of 60° was observed between the hemispheres. In addition, a time shift of ≈2.5 CRs existed between the instants when the position of maximum fluxes in different hemispheres shifted. The established peculiarities of the magnetic flux longitudinal distribution and time dynamics are interpreted as an action of supergiant convection cells. These actions result in that magnetic fields are removed from the generation region through the channels that are formed between such cells at a longitudinal interval of 120°. The average synodic rotation velocity of the considered equatorial channels, through which the magnetic flux emerges, is 13.43° day^–1.     

The emergence of braided magnetic fields

We study the emergence of braided magnetic fields from the top of the solar interior through to the corona. It is widely believed that emerging regions smaller than active regions are formed in the upper convection zone near the photosphere. Here, bundles of braided, rather than twisted, magnetic field can be formed, which then rise upward to emerge into the atmosphere. To test this theory, we investigate the behaviour of braided magnetic fields as they emerge into the solar atmosphere. We compare and contrast our models to previous studies of twisted flux tube emergence and discuss results that can be tested observationally. Although this is just an initial study, our results suggest that the underlying magnetic field structure of small emerging regions need not be twisted and that braided field, formed in the convection zone, could suffice.     

Distribution of magnetic energy in αΩ-dynamos,I: The method

Abstract

In this paper a method for solving the equation for the mean magnetic energy <BB> of a solar type dynamo with an axisymmetric convection zone geometry is developed and the main features of the method are described. This method is referred to as the finite magnetic energy method since it is based on the idea that the real magnetic field B of the dynamo remains finite only if <BB> remains finite. Ensemble averaging is used, which implies that fields of all spatial scales are included, small-scale as well as large-scale fields. The method yields an energy balance for the mean energy density ε ≡ B ²/8π of the dynamo, from which the relative energy production rates by the different dynamo processes can be inferred. An estimate for the r.m.s. field strength at the surface and at the base of the convection zone can be found by comparing the magnetic energy density and the outgoing flux at the surface with the observed values. We neglect resistive effects and present arguments indicating that this is a fair assumption for the solar convection zone. The model considerations and examples presented indicate that (1) the energy loss at the solar surface is almost instantaneous; (2) the convection in the convection zone takes place in the form of giant cells; (3) the r.m.s. field strength at the base of the solar convection zone is no more than a few hundred gauss; (4) the turbulent diffusion coefficient within the bulk of the convection zone is about 10¹⁴cm²s^?1, which is an order of magnitude larger than usually adopted in solar mean field models.     

Simulating solar MHD

Two aspects of solar MHD are discussed in relation to the work of the MHD simulation group at KIS. Photospheric magneto-convection, the nonlinear interaction of magnetic field and convection in a strongly stratified, radiating fluid, is a key process of general astrophysical relevance. Comprehensive numerical simulations including radiative transfer have significantly improved our understanding of the processes and have become an important tool for the interpretation of observational data. Examples of field intensification in the solar photosphere (‘convective collapse’) are shown. The second line of research is concerned with the dynamics of flux tubes in the convection zone, which has far-reaching implications for our understanding of the solar dynamo. Simulations indicate that the field strength in the region where the flux is stored before erupting to form sunspot groups is of the order of 10⁵ G, an order of magnitude larger than previous estimates based on equipartition with the kinetic energy of convective flows.     

The kinematics of hexagonal magnetoconvection

Abstract

Calculations are presented for the evolution of a magnetic field which is subject to the effect of three-dimensional motions in a convecting layer of highly conducting fluid with hexagonal symmetry. The back reaction of the field on the motions via the Lorentz force is neglected. We consider cases where the imposed field is either vertical or horizontal. In the former case, flux accumulates at cell centres, with subsidiary concentrations at the vertices of the pattern. In the latter, topological asymmetries between up- and down-moving fluid regions generate positive flux at the base of the layer and negative flux at the top, though the system is actually an amplifier rather than a self-excited dynamo. Spiral field lines form in the interiors of the cells, and the phenomenon of “flux expulsion” found in two-dimensional solutions is somewhat altered when the imposed field is horizontal. Applications for stellar magnetic fields include a possible mechanism for burying flux at the base of a convection zone.     

The rapid dissipation of magnetic fields in highly conducting fluids

Abstract

This paper treats the dynamical conditions that obtain when long straight parallel twisted flux tubes in a highly conducting fluid are packed together in a broad array. It is shown that there is generally no hydrostatic equilibrium. In place of equilibrium there is a dynamical nonequilibrium, leading to neutral point reconnection and progressive coalescence of neighboring tubes (with the same sense of twisting), forming tubes of larger diameter and reduced twist. The magnetic energy in the twisting of each tube declines toward zero, dissipated into small-scale motions of the fluid and thence into heat.

The physical implications are numerous. For instance, it has been suggested that the subsurface magnetic field of the sun is composed of close-packed twisted flux tubes. Any such structures are short lived, at best.

The footpoints of the filamentary magnetic fields above bipolar magnetic regions on the sun are continually shuffled and rotated by the convection, so that the fields are composed of twisted rubes. The twisting and mutual wrapping is converted directly into fluid motion and heat by the dynamical nonequilibrium, so that the work done by the convection of the footpoints goes directly into heating the corona above. This theoretical result is the final step, then, in understanding the assertion by Rosner, Tucker, and Valana, and others, that the observed structure of the visible corona implies that it is heated principally by direct dissipation of the supporting magnetic field. It is the dynamical nonequilibrium that causes the dissipation, in spite of the high electrical conductivity. It would appear that any bipolar magnetic field extending upward from a dense convective layer into a tenuous atmosphere automatically produces heating, and a corona of some sort, in the sun or any other convective star.     

The flux ejection dynamo effect

Abstract

The mean-field effects of cyclonic convection become increasingly complex when the cyclonic rotation exceeds ½-π. Net helicity is not required, with negative turbulent diffusion, for instance, appearing in mirror symmetric turbulence. This paper points out a new dynamo effect arising in convective cells with strong asymmetry in the rotation of updrafts as against downdrafts. The creation of new magnetic flux arises from the ejection of reserve flux through the open boundary of the dynamo region. It is unlike the familiar α-effect in that individual components of the field may be amplified independently. Several formal examples are provided to illustrate the effect. Occurrence in nature depends upon the existence of fluid rotations of the order of π in the convective updrafts. The flux ejection dynamo may possibly contribute to the generation of field in the convective core of Earth and in the convective zone of the sun and other stars.     

Penetrative convection in rotating fluids: A model for the base of stellar convection zones

Abstract

To model penetrative convection at the base of a stellar convection zone we consider two plane parallel, co-rotating Boussinesq layers coupled at their fluid interface. The system is such that the upper layer is unstable to convection while the lower is stable. Following the method of Kondo and Unno (1982, 1983) we calculate critical Rayleigh numbers R_c for a wide class of parameters. Here, R_c is typically much less than in the case of a single layer, although the scaling R_c～T^2/3 as T → ∞ still holds, where T is the usual Taylor number. With parameters relevant to the Sun the helicity profile is discontinuous at the interface, and dominated by a large peak in a thin boundary layer beneath the convecting region. In reality the distribution is continuous, but the sharp transition associated with a rapid decline in the effective viscosity in the overshoot region is approximated by a discontinuity here. This source of helicity and its relation to an alpha effect in a mean-field dynamo is especially relevant since it is a generally held view that the overshoot region is the location of magnetic field generation in the Sun.     

Topological semi-dynamos

Abstract

Magnetic field generation in a continuous medium in processes without self-excitation—the so-called semi-dynamo, involving as essential elements both magnetohydrodynamic processes and the presence of an impressed e.m.f.—has been studied for the case of the topological pumping effect on the magnetic field generation by an impressed e.m.f. operating in a three-dimensional Bénard convection layer.

Under conditions of interest for astrophysical applications the magnetic flux produced can exceed substantially that excited by the e.m.f. in the absence of motion.

The results obtained permitted an evaluation of the general quasi-steady magnetic field of the Sun generated by an azimuthal Coriolis e.m.f. which is active in the outermost layers of the convective envelope, taking into account small-scale convective and turbulent motions. In the polar regions of the Sun this field can reach ～10^?1 G.     

Relationships between field-aligned currents and convection observed by EISCAT and implications concerning the mechanism that produces region-2 currents: Statistical study

Fluid theories explain the origin of region-2 field-aligned currents as the closure of the ring current, driven itself by the azimuthal pressure gradients generated in the magnetospheric ring plasma by the sunward convection. Although the structure of pressure gradients appears experimentally complex, observations confirm that a close connection exists between the region-2 field-aligned currents and the ring current. The fluid linear theory of the adiabatic transport by convection of the ring plasma gives a first estimate of this process, and leads ultimately to phase quadrature (in terms of magnetic local time) between the region-2 field-aligned currents and the convection potential. When significant non-adiabatic processes are taken into account, such as precipitations at auroral latitudes, the theoretical phase difference rotates toward opposition. We determine experimentally the phase relationship between the region-2 field-aligned currents and the convection potential from recent statistics, depending on the magnetic activity index K_p, and performed from the EISCAT data base. For geometrical reasons of sufficient probing of region 2, it is only computed in the case of a moderate magnetic activity corresponding to 2\leqK_p<4. Region-2 field-aligned currents are found to be in phase opposition with the convection electrostatic potential at auroral latitudes. This confirms the importance of non adiabatic processes, especially ion losses, in the generation of region-2 field-aligned currents, as theoretically suggested.     

Magnetic tracers,a probe of the solar convective layers

Abstract

A meridional circulation of sunspots has been measured through the digital analysis of the Meudon spectroheliograms from 1978 to 1983. Old and young sunspots follow a zonal meridional circulation, in several bands of latitude, in which two adjacent bands have opposite motions. This meridional circulation pattern is time-dependent. Using the H _α filaments as magnetic field tracers, a large-scale magnetic pattern has been found that was also obtained independently by direct measurement of the magnetic field (Hoeksema, 1988).

The coincidence of a large-scale magnetic pattern with a zonal meridional circulation suggests the existence of azimuthal rolls below the surface, and these azimuthal rolls can explain a number of properties of the solar cycle. New rolls occur with increasing proximity to the Equator, thereby indicating the direction of propagation of the dynamo wave. The occurrence of rolls is very favorable to the emergence of the magnetic regions. The rolls also influence the magnetic complexity of the active regions. They modulate the surface rotation through the Coriolis force, which accelerates or decelerates the fluid particles. They therefore offer a plausible explanation of the torsional oscillation pattern.

There are a number of problems raised by such an unexpected circulation pattern: for example, the coexistence of axisymmeric rolls with hypothetical giant cells, the location of the dynamo source below or within the convective zone, and the coupling of the radiative interior and the convective layers. To resolve these important issues, continuous observational studies are needed of the manifestation of solar activity, as well as of radius and luminosity variations. So, we have aimed our paper at an audience of theoreticians in the hope that they take up the challenges we describe.     

Two-dimensional electric field measurements in the ionospheric footprint of a flux transfer event

Line-of-sight Doppler velocities from the SuperDARN CUTLASS HF radar pair have been combined to produce the first two-dimensional vector measurements of the convection pattern throughout the ionospheric footprint of a flux transfer event (a pulsed ionospheric flow, or PIF). Very stable and moderate interplanetary magnetic field conditions, along with a preceding prolonged period of northward interplanetary magnetic field, allow a detailed study of the spatial and the temporal evolution of the ionospheric response to magnetic reconnection. The flux tube footprint is tracked for half an hour across six hours of local time in the auroral zone, from magnetic local noon to dusk. The motion of the footprint of the newly reconnected flux tube is compared with the ionospheric convection velocity. Two primary intervals in the PIFs evolution have been determined. For the first half of its lifetime in the radar field of view the phase speed of the PIF is highly variable and the mean speed is nearly twice the ionospheric convection speed. For the final half of its lifetime the phase velocity becomes much less variable and slows down to the ionospheric convection velocity. The evolution of the flux tube in the magnetosphere has been studied using magnetic field, magnetopause and magnetosheath models. The data are consistent with an interval of azimuthally propagating magnetopause reconnection, in a manner consonant with a peeling of magnetic flux from the magnetopause, followed by an interval of anti-sunward convection of reconnected flux tubes.     

Modification of “Pressed” Atmospheres in Active Regions of Ultracool Stars

Ultracool stars usually have active regions, which is confirmed by their high-power radiofrequency emission modulated by the star axial rotation. The interpretation of this emission is commonly based on the electron cyclotron maser mechanism realized in the active regions. A plasma mechanism of radiofrequency emission is not considered, because ultracool star atmospheres are tightly “pressed” against the star surface, and the plasma frequency is much lower than the electron gyrofrequency (f_L ? f_B) at the coronal levels. This paper explores active regions of ultracool stars for the possible existence of a system of coronal magnetic loops carrying electric current generated by photospheric convection. It is shown that current dissipation induces a temperature increase inside the loops to about 10⁷ K, which causes an increase in the scale of height of the inhomogeneous atmosphere and, at the coronal levels, effectuates condition f_L ? f_B, at which the plasma mechanism of radiofrequency emission prevails over the electron cyclotron maser mechanism. The magnetic loop parameters, intensity of electric currents generated by the photospheric convection, and efficiency of plasma heating inside the magnetic loops are evaluated on the example of the brown dwarf TVLM513-46546. The scale of the height of the modified atmosphere, which appears to be comparable to the star radius, is calculated; it is shown that the soft X-ray flow created by the hot modified atmosphere inside a coronal magnetic loop is about equal to that observed for brown dwarf TVLM513-46546.     

Diagnostics of Turbulent Dynamo from the Flux Emergence Rate in Solar Active Regions

Line-of-sight magnetograms acquired by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamic Observatory (SDO) and by the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO) for 14 emerging ARs were used to study the derivative of the total unsigned flux–the flux emergence rate, R(t). We found that the emergence regime is not universal: each AR displays a unique emergence process. Nevertheless, two types of the emergence process can be identified. First type is a “regular” emergence with quasi-constant behavior of R(t) during a 1–3 day emergence interval with a rather low magnitude of the flux derivative, R_max = (0.57 ± 0.22) × 10²² Mx day^–1. The second type can be described as “accelerated” emergence with a long interval (>1 day) of the rapidly increasing flux derivative R(t) that result in a rather high magnitude of R_max= (0.92 ± 0.29) × 10²² Mx day^–1, which later changes to a very short (about a one third of day) interval of R(t) = const followed by a monotonous decrease of R(t). The first type events might be associated with emergence of a flux tube with a constant amount of flux that rises through the photosphere with a quasi-constant speed. Such events can be explained by the traditional largescale solar dynamo generating the toroidal flux deep in the convective zone. The second-type events can be interpreted as a signature of sub-surface turbulent dynamo action that generates additional magnetic flux (via turbulent motions) as the magnetic structure makes its way up to the solar surface.     

The correlation between geomagnetic disturbances and topology of quasi-open structures in the solar magnetic field

Results of photospheric magnetic field extrapolation in a potential approximation and of the technique for separating the open part of magnetic flux have revealed that changes in the relationship between the open part of the south polarity magnetic flux obtained in the chromosphere and corona from July to November 2006 correlate with variations in the Akasofu parameter calculated from data on the solar wind parameters and interplanetary magnetic field at Lagrange point L1, and with the K _p index.     

Magnetic field generation by convective flows in a plane layer: the dependence on the Prandtl numbers

Investigation of magnetic field generation by convective flows is carried out for three values of kinematic Prandtl number: P = 0.3, 1 and 6.8. We consider Rayleigh–Bénard convection in Boussinesq approximation assuming stress-free boundary conditions on horizontal boundaries and periodicity with the same period in the x and y directions. Convective attractors are modelled for increasing Rayleigh numbers for each value of the kinematic Prandtl number. Linear and non-linear dynamo action of these attractors is studied for magnetic Prandtl numbers P _m ≤ 100. Flows, which can act as magnetic dynamos, have been found for all the three considered values of P, if the Rayleigh number R is large enough. The minimal R, for which of magnetic field generation occurs, increases with P. The minimum (over R) of critical P_m for magnetic field generation in the kinematic regime is admitted for P = 0.3. Thus, our study indicates that smaller values of P are beneficial for magnetic field generation.     

On the formation mechanism of the sporadic solar wind

In this paper, we examine the nature of the main source of the sporadic solar wind on the Sun: coronal mass ejections (CMEs). Analysis of data from Mark 3 and Mark 4, the Digital Prominence Monitor (MLSO), and STEREO (EUVI) spacecraft has revealed the existence of two types of CMEs: gradual and impulse. They differ in the place, velocity, and angular size at the instant of their emergence. The source of gradual CMEs is located in the corona, at a distance of 1.1 R ₀ < R ≤ 1.7 R ₀ from the center of the Sun. They start moving from a state of rest, having an angular size ≈15–65° (in the heliographic coordinate system). Impulse CMEs are probably formed under the Sun’s photosphere. This may be due to the supersonic emergence of magnetic tubes (ropes) from the convective zone. The possibility of this phenomenon has been demonstrated earlier in theory. The radial velocity of such tubes at the photospheric level may be 100 km/s or higher; the minimum angular size is ∼1°.