Mean-field dynamo in partially ionized plasmas – I

There are several astrophysical situations where one needs to study the dynamics of magnetic flux in partially ionized turbulent plasmas. In a partially ionized plasma, the magnetic induction is subjected to the ambipolar diffusion and the Hall effect in addition to the usual resistive dissipation. In this paper, we initiate the study of the kinematic dynamo in a partially ionized turbulent plasma. The Hall effect arises from the treatment of the electrons and the ions as two separate fluids and the ambipolar diffusion due to the inclusion of neutrals as the third fluid. It is shown that these non-ideal effects modify the so-called α effect and the turbulent diffusion coefficient β in a rather substantial way. The Hall effect may enhance or quench the dynamo action altogether. The ambipolar diffusion brings in an α which depends on the mean magnetic field. The new correlations embodying the coupling of the charged fluids and the neutral fluid appear in a decisive manner. The turbulence is necessarily magnetohydrodynamic with new spatial and time-scales. The nature of the new correlations is demonstrated by taking the Alfvénic turbulence as an example.     

A three-dimensional numerical method for modelling weakly ionized plasmas

Astrophysical fluids under the influence of magnetic fields are often subjected to single- or two-fluid approximations. In the case of weakly ionized plasmas, however, this can be inappropriate due to distinct responses from the multiple constituent species to both collisional and non-collisional forces. As a result, in dense molecular clouds and protostellar accretion discs, for instance, the conductivity of the plasma may be highly anisotropic leading to phenomena such as Hall and ambipolar diffusion strongly influencing the dynamics.
Diffusive processes are known to restrict the stability of conventional numerical schemes which are not implicit in nature. Furthermore, recent work establishes that a large Hall term can impose an additional severe stability limit on standard explicit schemes. Following a previous paper, which presented the one-dimensional case, we describe a fully three-dimensional method which relaxes the normal restrictions on explicit schemes for multifluid processes. This is achieved by applying the little-known Super TimeStepping technique to the symmetric (ambipolar) component of the evolution operator for the magnetic field in the local plasma rest frame, and the new Hall Diffusion Scheme to the skew-symmetric (Hall) component.     

Spatially intermittent fields in photospheric magnetoconvection

Motivated by recent high-resolution observations of the solar surface, we investigate the problem of non-linear magnetoconvection in a three-dimensional compressible layer. We present results from a set of numerical simulations which model the situation in which there is a weak imposed magnetic field. This weak-field regime is characterized by vigorous granular convection and spatially intermittent magnetic field structures. When the imposed field is very weak, magnetic flux tends to accumulate at the edges of the convective cells, where it forms compact, almost 'point-like' structures which are reminiscent of those observed in the quiet Sun. If the imposed field is slightly stronger, there is a tendency for magnetic flux to become concentrated into 'ribbon-like' structures which are comparable to those observed in solar plages. The dependence of these simulations upon the strength of the imposed magnetic field is analysed in detail, and the concept of the fractal dimension is used to make a further, more quantitative comparison between these simulations and photospheric observations.     

Convective intensification of magnetic fields in the quiet Sun

Kilogauss-strength magnetic fields are often observed in intergranular lanes at the photosphere in the quiet Sun. Such fields are stronger than the equipartition field B _e, corresponding to a magnetic energy density that matches the kinetic energy density of photospheric convection, and comparable with the field B _p that exerts a magnetic pressure equal to the ambient gas pressure. We present an idealized numerical model of three-dimensional compressible magnetoconvection at the photosphere, for a range of values of the magnetic Reynolds number. In the absence of a magnetic field, the convection is highly supercritical and characterized by a pattern of vigorous, time-dependent, 'granular' motions. When a weak magnetic field is imposed upon the convection, magnetic flux is swept into the convective downflows where it forms localized concentrations. Unless this process is significantly inhibited by magnetic diffusion, the resulting fields are often much greater than B _e and the high magnetic pressure in these flux elements leads to their being partially evacuated. Some of these flux elements contains ultraintense magnetic fields that are significantly greater than B _p. Such fields are contained by a combination of the thermal pressure of the gas and the dynamic pressure of the convective motion, and they are constantly evolving. These ultraintense fields develop owing to non-linear interactions between magnetic fields and convection; they cannot be explained in terms of 'convective collapse' within a thin flux tube that remains in overall pressure equilibrium with its surroundings.     

Magnetoconvection in an inclined magnetic field: linear and weakly non-linear models

Recent observations of sunspots have revealed a rich range of behaviour and a complicated magnetic field structure; magnetoconvection is the key physical process underlying these phenomena. Traditional studies of magnetoconvection have considered vertical, or sometimes horizontal, imposed fields. Tilted fields have received less attention, and yet these are crucial to sunspot dynamics, particularly in the penumbra where field lines are inclined at a variety of angles to the vertical. Tilting the field is also interesting from a purely theoretical viewpoint since it breaks many of the symmetries usually associated with convection problems. In this paper we study the linear stability of a layer permeated by an inclined magnetic field and go on to set up model equations in order to study the patterns formed in the weakly non-linear regime. Possible applications of the results to sunspots are discussed.     

The Solar Optical Telescope for the Hinode Mission: An Overview

The Solar Optical Telescope (SOT) aboard the Hinode satellite (formerly called Solar-B) consists of the Optical Telescope Assembly (OTA) and the Focal Plane Package (FPP). The OTA is a 50-cm diffraction-limited Gregorian telescope, and the FPP includes the narrowband filtergraph (NFI) and the broadband filtergraph (BFI), plus the Stokes Spectro-Polarimeter (SP). The SOT provides unprecedented high-resolution photometric and vector magnetic images of the photosphere and chromosphere with a very stable point spread function and is equipped with an image-stabilization system with performance better than 0.01 arcsec rms. Together with the other two instruments on Hinode (the X-Ray Telescope (XRT) and the EUV Imaging Spectrometer (EIS)), the SOT is poised to address many fundamental questions about solar magnetohydrodynamics. This paper provides an overview; the details of the instrument are presented in a series of companion papers. M. Otsubo is a former NAOJ staff scientist.     

The Balbus–Hawley instability in weakly ionized discs

MHD in protostellar discs is modified by the Hall current when the ambipolar diffusion approximation breaks down. Here I examine the Balbus–Hawley (magnetorotational) instability of a weak, vertical magnetic field within a weakly ionized disc. Vertical stratification is neglected, and a linear analysis is undertaken for the case in which the wavevector of the perturbation is parallel to the magnetic field.
The growth rate depends on whether the initial magnetic field is parallel or antiparallel to the angular momentum of the disc. The parallel case is less (more) unstable than the antiparallel case if the Hall current is dominated by negative (positive) species. The less-unstable orientation is stable for χ ≲0.5, where χ is the ratio of a generalized neutral–ion collision frequency to the Keplerian frequency. The other orientation has a formal growth rate of the order of the Keplerian angular frequency even in the limit χ →0! In this limit the wavelength of the fastest-growing mode tends to infinity, so the minimum level of ionization for instability is determined by the requirement that a wavelength fit within a disc scaleheight. In the ambipolar diffusion case, this requires χ > v _A c _s; in the Hall case this imposes a potentially much weaker limit,         

An interpretation of rapid changes in the magnetic field associated with solar flares

The energy source of a flare is the magnetic field in the corona. A topological model of the magnetic field is used here for interpreting the recently discovered drastic changes in magnetic field associated with solar flares. The following observational results are self‐consistently explained: (1) the transverse field strength decreases at outer part of active regions and increases significantly in their centers; (2) the center‐of‐mass positions of opposite magnetic polarities converge towards the magnetic neutral line just after flares onset; (3) the magnetic flux of active regions decreases steadily during the course of flares. For X‐class flares, almost 50% events show such changes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Center to limb variation of penumbral Stokes V profiles

We investigated the horizontal and the vertical component of the Evershed flow (EF). To this end, we computed average Stokes V profiles for various velocity classes in penumbrae at different heliocentric angles. Our results show that for blueshifted profiles an additional lobe with the same polarity as the spot is present in the blue side of the average Stokes V profile. The amplitude of the additional lobe grows with increasing blueshift and with increasing heliocentric angle. For small redshifts, the profiles show an additional lobe with the opposite polarity as the spot on the red side of the average Stokes V profile. Even at disk center, the original polarity of the average Stokes V profile is reversed for strong redshifts. The transition between the different types of Stokes V profiles is continuous and indicates that not only the vertical, but also the horizontal EF is a magnetized stream of plasma in a magnetic background field (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Alleviation of catastrophic quenching in solar dynamo model with nonlocal alpha‐effect

The nonlocal alpha‐effect of Babcock‐Leighton type is not prone to the catastrophic quenching due to conservation of magnetic helicity. This is shown with a dynamo model, which jointly applies the nonlocal alpha‐effect, the diamagnetic pumping, and dynamical equation for the magnetic alpha‐effect. The same model shows catastrophic quenching when the alpha‐effect is changed to its local formulation. The nonlocal model shows a preferred excitation of magnetic fields of dipolar symmetry, which oscillate with a period of about ten years and have a toroidal‐to‐polar fields ratio of about a thousand (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Projection Effects on Physical Parameters Obtained from Solar Vector Magnetograms

1 INTRODUCTION Magnetic field plays an important role in solar activity. The stressing and subsequent partialrelaxation of magnetic fields in the active regions are generally accepted to be the energy sourceof solar flares. To quantitatively study the extent of stressed magnetic field as distinct from itspotential field, Hagyard et al. (1984) defined a magnetic shear angle膖he azimuth differencebetween the observed transverse magnetic field vector and the computed potential field vectorth…     

Modeling a Maunder minimum

We introduce on/off intermittency into a mean field dynamo model by imposing stochastic fluctuations in either the alpha effect or through the inclusion of a fluctuating electromotive force. Sufficiently strong small scale fluctuations with time scales of the order of 0.3–3 years can produce long term variations in the system on time scales of the order of hundreds of years. However, global suppression of magnetic activity in both hemispheres at once was not observed. The variation of the magnetic field does not resemble that of the sunspot number, but is more reminiscent of the ¹⁰Be record. The interpretation of our results focuses attention on the connection between the level of magnetic activity and the sunspot number, an issue that must be elucidated if long term solar effects are to be well understood. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The hemispheric sign rule of current helicity during the rising phase of cycle 23

We compute the signs of two different current helicity parameters (i.e., α_best andH _c) for 87 active regions during the rise of cycle 23 The results indicate that 59% of the active regions in the northern hemisphere have negative α_best and 65% in the southern hemisphere have positive. This is consistent with that of the cycle 22. However, the helicity parameterH _cshows a weaker opposite hemispheric preference in the new solar cycle. Possible reasons are discussed.     

Magnetic flux participation in solar surface magnetism during solar cycle 24

This study aims at investigating surface magnetic flux participation among different types of magnetic features during solar cycle 24. State-of-the-art observations from SDO/HMI and Hinode/SOT are combined to form a unique database in the interval from April 2010 to October 2015. Unlike previous studies, the statistics presented in this paper are feature-detection-based. More than 20 million magnetic features with relatively large scale, such as sunspot/pore, enhanced and quiet networks, are automatically detected and categorized from HMI observations, and the internetwork features are identified from SOT/SP observations. The total flux from these magnetic features reaches 5.9×10²² Mx during solar minimum and2.4 × 10²³ Mx in solar maximum. Flux occupation from the sunspot/pore region is 29% in solar maximum.Enhanced and quiet networks contribute 18% and 21% flux during the solar minimum, and 50% and 9% flux in the solar maximum respectively. The internetwork field contributes over 55% of flux in the solar minimum, and its flux contribution exceeds that of sunspot/pore features in the solar maximum. During the solar active condition, the sunspot field increases its area but keeps constant flux density of about 150 G,while the enhanced network follows the sunspot number variation showing increasing flux density and area,but the quiet network displays decreasing area and somewhat increasing flux density of about 6%. The origin of the quiet network is not known exactly, but is suggestive of representing the interplay between mean-field and local dynamos. The source, magnitude and possible importance of ‘hidden flux' are discussed in some detail.     

The role of emerging bipoles in the formation of a sunspot penumbra

The generation of magnetic flux in the solar interior and its transport from the convection zone into the photosphere, the chromosphere, and the corona will be in the focus of solar physics research for the next decades. With 4 m class telescopes, one plans to measure essential processes of radiative magneto‐hydrodynamics that are needed to understand the nature of solar magnetic fields. One key‐ingredient to understand the behavior of solar magnetic field is the process of flux emergence into the solar photosphere, and how the magnetic flux reorganizes to form the magnetic phenomena of active regions like sunspots and pores. Here, we present a spectropolarimetric and imaging data set from a region of emerging magnetic flux, in which a proto‐spot without penumbra forms a penumbra. During the formation of the penumbra the area and the magnetic flux of the spot increases. First results of our data analysis demonstrate that the additional magnetic flux, which contributes to the increasing area of the penumbra, is supplied by the region of emerging magnetic flux. We observe emerging bipoles that are aligned such that the spot polarity is closer to the spot. As an emerging bipole separates, the pole of the spot polarity migrates towards the spot, and finally merges with it. We speculate that this is a fundamental process, which makes the sunspot accumulate magnetic flux. As more and more flux is accumulated a penumbra forms and transforms the proto‐spot into a full‐fledged sunspot (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dimensionless measures of turbulent magnetohydrodynamic dissipation rates

The magnetic Reynolds number, R _M, is defined as the product of a characteristic scale and associated flow speed divided by the microphysical magnetic diffusivity. For laminar flows, R _M also approximates the ratio of advective to dissipative terms in the total magnetic energy equation, but for turbulent flows this latter ratio depends on the energy spectra and approaches unity in a steady state. To generalize for flows of arbitrary spectra we define an effective magnetic dissipation number,   R _M,e  , as the ratio of the advection to microphysical dissipation terms in the total magnetic energy equation, incorporating the full spectrum of scales, arbitrary magnetic Prandtl numbers, and distinct pairs of inner and outer scales for magnetic and kinetic spectra. As expected, for a substantial parameter range   R _M,e∼ O (1) ≪ R _M  . We also distinguish   R _M,e  from     where the latter is an effective magnetic Reynolds number for the mean magnetic field equation when a turbulent diffusivity is explicitly imposed as a closure. That   R _M,e  and     approach unity even if   R _M≫ 1  highlights that, just as in hydrodynamic turbulence, energy dissipation of large-scale structures in turbulent flows via a cascade can be much faster than the dissipation of large-scale structures in laminar flows. This illustrates that the rate of energy dissipation by magnetic reconnection is much faster in turbulent flows, and much less sensitive to microphysical reconnection rates compared to laminar flows.     

Detection of opposite polarities in a sunspot light bridge: evidence of low-altitude magnetic reconnection

A multiwavelength photometric analysis was performed in order to study the sub-structure of a sunspot light bridge in the photosphere and the chromosphere. Active region NOAA 8350 was observed on 1998 October 8. The data consist of a 100 min time series of 2D spectral scans of the lines Fe  i 5576 Å, Hα 6563 Å, Fe  i 6302.5 Å, and continuum images at 5571 Å. We recorded line-of-sight magnetograms in 6302.5 Å. The observations were taken at the Dunn Solar Telescope at US National Solar Observatory, Sacramento Peak. We find evidence for plasma ejection from a light bridge followed by Ellerman bombs. Magnetograms of the same region reveal opposite polarity in light bridge with respect to the umbra. These facts support the notion that low-altitude magnetic reconnection can result in the magnetic cancellation as observed in the photosphere.