Astrophysical magnetic fields and nonlinear dynamo theory

The solar dynamo continues to pose a challenge to observers and theoreticians. Observations of the solar surface reveal a magnetic field with a complex, hierarchical structure consisting of widely different scales. Systematic features such as the solar cycle, the butterfly diagram, and Hale's polarity laws point to the existence of a deep-rooted large-scale magnetic field. At the other end of the scale are magnetic elements and small-scale mixed-polarity magnetic fields. In order to explain these phenomena, dynamo theory provides all the necessary ingredients including the \(\alpha\) effect, magnetic field amplification by differential rotation, magnetic pumping, turbulent diffusion, magnetic buoyancy, flux storage, stochastic variations and nonlinear dynamics. Due to advances in helioseismology, observations of stellar magnetic fields and computer capabilities, significant progress has been made in our understanding of these and other aspects such as the role of the tachocline, convective plumes and magnetic helicity conservation. However, remaining uncertainties about the nature of the deep-seated toroidal magnetic field and the \(\alpha\) effect, and the forbidding range of length scales of the magnetic field and the flow have thus far prevented the formulation of a coherent model for the solar dynamo. A preliminary evaluation of the various dynamo models that have been proposed seems to favor a buoyancy-driven or distributed scenario. The viewpoint proposed here is that progress in understanding the solar dynamo and explaining the observations can be achieved only through a combination of approaches including local numerical experiments and global mean-field modeling.

https://amor.cms.hu-berlin.de/~ossendrm/solardynamo.pdf

The solar dynamo

The formation of sunspots from the solar toroidal field. the earth's magnetism and magneto hydrodynamics

This review on coronal mass ejections (CMEs) treats hydromagnetic issues posed by observations, in order to relate CMEs to flares and prominence eruptions and to consider the roles these processes play in the evolution of the solar corona in the course of an 11-year cycle. This global view of the corona, proposed in varying degrees of completeness by the author, physically connects the corona to the photosphere and the dynamo in the solar interior. This view is synthesized afresh starting with CME phenomenology, in order to include some new insights and to arrive at definite statements on the hydromagnetic nature of CMEs. The synthesis shows that each CME culminates a long, coherent physical process involving magnetic-flux emergence; flares and magnetic reconnection; creation of long-lived, large-scale coronal structures; conservation of magnetic helicity; and failure of confinement of magnetic flux ropes in the open atmosphere. Each CME contributes a systematic permanent change to the coronal magnetic field. In this view the cumulative changes brought by all the CMEs in the course of a solar cycle have fundamental implications for the magnetic-flux budgets of the photosphere and the corona.

Coronal mass ejections, magnetic flux ropes, and solar magnetism

The magnetic field of the Sun is the underlying cause of the many diverse phenomena combined under the heading of solar activity. Here we describe the magnetic field as it threads its way from the bottom of the convection zone, where it is built up by the solar dynamo, to the solar surface, where it manifests itself in the form of sunspots and faculae, and beyond into the outer solar atmosphere and, finally, into the heliosphere. On the way it transports energy from the surface and the subsurface layers into the solar corona, where it heats the gas and accelerates the solar wind.

https://iopscience.iop.org/article/10.1088/0034-4885/69/3/R02/pdf

The solar magnetic field

Using a 1988-1997 data set of original photospheric vector magnetograms from the Solar Magnetic Field Telescope (SMFT) of the Huairou Solar Observing Station of Beijing Astronomical Observatory, we computed the local current helicity Bz(∇×B)z for 422 active regions. We found that any given active region contained mixed signs of current helicity, but in most cases current helicity with a particular sign was dominant over a whole region area. In our data set, 84% of the active regions in the northern hemisphere have negative helicity, and 81% in the southern hemisphere have positive helicity. It is estimated that the noise and error in our calculation are at the 2 σ level. In addition, we have studied the evolution of the large-scale surface current helicity during the cycle 22, which is a running mean of absolute current helicity of the active regions observed over a Carrington rotation period. By comparing with monthly mean sunspot number, we found that the average current helicity has a good correlation with solar activity.

https://iopscience.iop.org/article/10.1086/311232/pdf

Patterns of current helicity for solar cycle 22

We examine the spatial and temporal rela- tionship between chromospheric H flares and photo- spheric current helicities in active regions. All of the data were obtained by the vector magnetograph system at Huairou Solar Observing Station of Beijing Astronomical Observatory. We focus our analysis on NOAA Active Region 6233, which was observed on 30 August 1990. The result shows that rapid and substantial changes of dis- tribution of current helicity in an area or in its vicinity are most likely to trigger flares, but no compelling cor- relation between peaks of current helicity and flare sites. Furthermore, we study the influence of flares on helicity for several other active regions. We nd that the time vari- ations of current helicity in the active regions with highly productive flares are more signicant than those of the poorly flare-productive active regions, and that the mag- nitude of current helicity does not always decrease after flares. Therefore we conclude that the rate of variation of current helicity may be considered as an indicator of flare activity. In this paper we describe the specication of the in- strumentation and data used, and we describe the meth- ods for computing helicity. The noises and errors in our data are estimated to be at the 2 3 level.

/pdf/a-survey-of-flares-and-current-helicity-in-active-regions-4fl4zo3n2o.pdf

A survey of flares and current helicity in active regions

We compare vector magnetograms of active region NOAA 5747 observed by two very different polarimetric instruments: the imaging vector magnetograph of Huairou Solar Observing Station (HSOS) and the Haleakala Stokes Polarimeter of Mees Solar Observatory (MSO). Unlike previous comparative studies, we concentrate our attention on differences in observations and data reduction techniques that can affect the helicity computation. Overall, we find a qualitative agreement between the HSOS and MSO vector magnetograms. The HSOS data show slightly higher field strength, but the distribution of inclination angles is similar in measurements from the two instruments. There is a systematic difference (up to ∼20°) in the azimuths of transverse fields, which is roughly proportional to the longitudinal field strength. We estimate that Faraday rotation in the HSOS magnetograms contributes ∼12° in the azimuth difference if possible sources of error are taken into account. Next, we apply two independent methods to both data sets to resolve 180° azimuth ambiguity and to compute two helicity measures – the force-free field parameter αbest and the current helicity fractional imbalance ρh. The methods agree reasonably well in sign and value of the helicity measures, but the HSOS magnetograms show systematically smaller values of ρh and αbest in agreement with an expected contribution of Faraday rotation. Finally, we discuss the role of Faraday rotation in computation of αbest and ρh and conclude that it does not affect the strength of the hemispheric helicity rule. The strength of the rule appears to be related to a helicity parameter: αbest shows weaker hemispheric asymmetry than ρh.

Helicity computation using observations from two different polarimetric instruments

In this paper, we describe the distribution of photospheric current helicity of active regions in the solar surface. The sign of helicity is mainly negative in the northern hemisphere of the Sun and positive in the southern hemisphere. We also discuss the relationship between the current helicity parameter B∥ (∇ × B)∥ and the α-factor of the force-free field. Our observations show that active regions with current helicity signs opposite to most others in the same hemispheres occur normally at some heliographic longitudes and persist over long periods.In addition, we analyze a possible mechanism of the sign rule of current helicity that shows opposite signs in both hemispheres.

Distribution of Photospheric Electric Current Helicity and Solar Activities

We compute the signs of two different current helicity parameters (i.e., αbest 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 αbest 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.

Shudong Bao

Papers

Patterns of current helicity for solar cycle 22

A survey of flares and current helicity in active regions

Helicity computation using observations from two different polarimetric instruments

Distribution of Photospheric Electric Current Helicity and Solar Activities

The Hemispheric Sign Rule of Current Helicity During the Rising Phase of Cycle 23