Anchor depths of flux elements and depths of flux sources in relation to the two rotation profiles of the sun's surface magnetic fields

It is known for over two decades now that the rotation of the photospheric magnetic fields determined by two different methods of correlation analysis leads to two vastly differing rotation laws - one the differential and the other rigid rotation. Snodgrass and Smith (2001) reexamining this puzzle show that the averaging of the correlation amplitudes can tilt the final profile in favour of rigid rotation whenever the contribution of the rigidly rotating large-scale magnetic structures (the plumes) to the correlation dominates over that of the differentially rotating small-scale and mesoscale features. We present arguments to show that the large-scale unipolar structures in latitudes >40 deg, which also show rigid rotation (Stenflo, 1989), are formed mainly from the intranetwork magnetic elements (abbreviated as IN elements). We then estimate the anchor depths of the various surface magnetic elements as locations of the Sun's internal plasma layers that rotate at the same rate as the flux elements, using the rotation rates of the internal plasma layers given by helioseismology. We infer that the anchor depths of the flux broken off from the decay of sunspot active regions (the small-scale and mesoscale features that constitute the plumes) are located in the shallow layers close to the solar surface. From a similar comparison with helioseismic rotation rates we infer that the rigid rotation of the large-scale unipolar regions in high latitudes could only be coming from plasma layers at a radial distance of about 0.66–0.68 R _⊙ from the Sun's centre. Using Stenflo's (1991) ‘balloon man’ analogy, we interpret these layers as the source of the magnetic flux of the IN elements. If so, the IN flux elements seem to constitute a fundamental component of solar magnetism.     

How is the sun working?

I assume that at the solar core finite amplitude flows are generated by some process for which a candidate can be the planetary tides. I assume also that there are some local magnetic flux bundles at the solar core with a strength larger than 10³ G. The aim of this paper is to show that these assumptions involve an electric field generation which then produces local thermonuclear runaways which shoot up convective cells to the outer layers. Within certain conditions these primal convective cells erupt in the subphotospheric layers which phenomenon can produce high-energy particle beams which when injected into magnetic flux tubes appear as flares. I suggest these processes for solving the neutrino problem, and also to interpret the spiky character of the solar neutrino flux and the correlation of the energy production of the Sun with its atmospheric activity.     

Magnetic fields and the structure of the solar corona

Several different mathematical methods are described which use the observed line-of-sight component of the photospheric magnetic field to determine the magnetic field of the solar corona in the current-free (or potential-field) approximation. Discussed are (1) a monopole method, (2) a Legendre polynomial expansion assuming knowledge of the radial photospheric magnetic field, (3) a Legendre polynomial expansion obtained from the line-of-sight photospheric field by a least-meansquare technique, (4) solar wind simulation by zero-potential surfaces in the corona, (5) corrections for the missing flux due to magnetograph saturation. We conclude (1) that the field obtained from the monopole method is not consistent with the given magnetic data because of non-local effects produced by monopoles on a curved surface, (2) that the field given by a Legendre polynomial (which is fitted to the measured line-of-sight magnetic field) is a rigorous and self-consistent solution with respect to the available data, (3) that it is necessary to correct for the saturation of the magnetograph (at about 80 G) because fields exceeding 80 G provide significant flux to the coronal field, and (4) that a zero-potential surface at 2.5 solar radii can simulate the effect of the solar wind on the coronal magnetic field.     

Large-Scale Structure of the Sunspot Activity and the Background Magnetic Field Formation

Large-scale distribution of the sunspot activity of the Sun has been analyzed by using a technique worked out previously (Erofeev, 1997) to study long-lived, non-axisymmetric magnetic structures with different periods of rotation. Results of the analysis have been compared with those obtained by analyzing both the solar large-scale magnetic field and large-scale magnetic field simulated by means of the well-known flux transport equation using the sunspot groups as a sole source of new magnetic flux in the photosphere. A 21-year period (1964–1985) has been examined.The rotation spectra calculated for the total time interval of two 11-year cycles indicate that sunspot activity consists of a series of discrete components (modes) with different periods of rotation. The largest-scale component of the sunspot activity reveals modes with 27-day and 28-day periods of rotation situated, correspondingly, in the northern and southern hemispheres of the Sun, and two modes with rotation periods of about 29.7 days situated in both hemispheres. Such a modal structure of the sunspot activity agrees well with that of the large-scale solar magnetic field. Moreover, the magnetic field distribution simulated with the flux transport equation also reveals the same modal structure. However, such an agreement between the large-scale solar magnetic field and both the sunspot activity and simulated magnetic field is unstable in time; so, it is absent in the northern hemisphere of the Sun during solar cycle No. 20. Thus the sources of magnetic flux responsible for formation of the large-scale, rigidly rotating magnetic patterns appear to be closely connected, but are not identical with the discrete modes of the sunspot activity.     

An Exploration of Non-kinematic Effects in Flux Transport Dynamos

Recent global magnetohydrodynamical simulations of solar convection producing a large-scale magnetic field undergoing regular, solar-like polarity reversals also present related cyclic modulations of large-scale flows developing in the convecting layers. Examination of these simulations reveal that the meridional flow, a crucial element in flux transport dynamos, is driven at least in part by the Lorentz force associated with the cycling large-scale magnetic field. This suggests that the backreaction of the field onto the flow may have a pronounced influence on the long-term evolution of the dynamo. We explore some of the associated dynamics using a low-order dynamo model that includes this Lorentz force feedback. We identify several characteristic solutions which include single period cycles, period doubling and chaos. To emulate the role of turbulence in the backreaction process we subject the model to stochastic fluctuations in the parameter that controls the Lorentz force amplitude. We find that short term fluctuations produce long-term modulations of the solar cycle and, in some cases, grand minima episodes where the amplitude of the magnetic field decays to near zero. The chain of events that triggers these quiescent phases is identified. A subsequent analysis of the energy transfer between large-scale fields and flows in the global magnetohydrodynamical simulation of solar convection shows that the magnetic field extracts energy from the solar differential rotation and deposits part of that energy into the meridional flow. The potential consequences of this marked departure from the kinematic regime are discussed in the context of current solar cycle modeling efforts based on flux transport dynamos.     

Empirical Modeling of Radiative <Emphasis Type="Italic">versus</Emphasis> Magnetic Flux for the Sun-as-a-Star

We study the relationship between full-disk solar radiative flux at different wavelengths and average solar photospheric magnetic-flux density, using daily measurements from the Kitt Peak magnetograph and other instruments extending over one or more solar cycles. We use two different statistical methods to determine the underlying nature of these flux – flux relationships. First, we use statistical correlation and regression analysis and show that the relationships are not monotonic for total solar irradiance and for continuum radiation from the photosphere, but are approximately linear for chromospheric and coronal radiation. Second, we use signal theory to examine the flux – flux relationships for a temporal component. We find that a well-defined temporal component exists and accounts for some of the variance in the data. This temporal component arises because active regions with high magnetic-field strength evolve, breaking up into small-scale magnetic elements with low field strength, and radiative and magnetic fluxes are sensitive to different active-region components. We generate empirical models that relate radiative flux to magnetic flux, allowing us to predict spectral-irradiance variations from observations of disk-averaged magnetic-flux density. In most cases, the model reconstructions can account for 85 – 90% of the variability of the radiative flux from the chromosphere and corona. Our results are important for understanding the relationship between magnetic and radiative measures of solar and stellar variability.     

A simulation study of the formation of a bipolar magnetic structure

Some recent solar observations show that a bipolar magnetic flux in an active region tends to disappear in situ, in less than one solar rotation, without evidence of spreading. This feature is difficult to explain if it is assumed that magnetic buoyancy is the dominant force in controlling dynamics of a magnetic flux tube, since the assumption implies no other force to submerge the tube. These observations may be explained by assuming that a convective motion is the major cause for the formation of a $\text{Ω}$-shaped geometry of the magnetic flux tube, but that the flux tube thus arisen is submerged by the counteracting Lorentz force as the convective motion decays. A two-dimensional MHD simulation method is used to demonstrate this possibility.     

Results from Kodaikanal synoptic observations

The synoptic observations of Kodaikanal form one of the longest unbroken solar data from the beginning of the 20th century to the present day, and consists of the white light and monochromatic images of the sun. In this review, I shall discuss the results of the investigations in two areas using these data: (i) Tilt angles of the magnetic axes of bipolar spot groups, and (ii) structure and dynamics of large scale unipolar magnetic regions on the solar surface. The observed properties and patterns of behaviour of the tilt angles can be used as effective diagnostics to infer the physical conditions in the subsurface layers of the sun, and thus get an insight into the physical effects that act on the rising magnetic flux tubes during their journey through the convection zone to the surface. The second topic of discussion here, namely, the studies of the dynamics of unipolar regions over several solar cycles, show that the global solar activity has a high latitude component which manifests in the form of polar faculae, in addition to the well known sunspot activity at the middle and low latitudes. This raises the question about the origin of this high latitude component.     

中尺度磁绳结构的行星际观测

由磁绳结构主导、平均尺度约二、三十个小时的行星际磁云是日冕物质抛射在行星际膨胀、传播的体现。最近，Moldwin等人报道在太阳风中还观测到一些尺度在几十分钟的小尺度磁绳结构，并认为太阳风中的磁绳结构在尺度分布上可能具有双峰特征，在全面检视了WIND卫星(1995年-2000年)和ACE卫星(1998年-2000年)的观测资料后，发现了在行星际太阳风中一些尺度为几个小时的中尺度磁绳结构，利用初步整理的其中28个中尺度磁绳结构事件，认为太阳风中的磁绳结构在尺度分布上可能是连续的，这对行星际太阳风中磁绳结构物理起源的研究可能提出重要的物理限制。     

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)     

Mechanism of cyclically polarity reversing solar magnetic cycle as a cosmic dynamo

We briefly describe historical development of the concept of solar dynamo mechanism that generates electric current and magnetic field by plasma flows inside the solar convection zone. The dynamo is the driver of the cyclically polarity reversing solar magnetic cycle. The reversal process can easily and visually be understood in terms of magnetic field line stretching and twisting and folding in three-dimensional space by plasma flows of differential rotation and global convection under influence of Coriolis force. This process gives rise to formation of a series of huge magnetic flux tubes that propagate along iso-rotation surfaces inside the convection zone. Each of these flux tubes produces one solar cycle. We discuss general characteristics of any plasma flows that can generate magnetic field and reverse the polarity of the magnetic field in a rotating body in the Universe. We also mention a list of problems which are currently being disputed concerning the solar dynamo mechanism together with observational evidences that are to be constraints as well as verifications of any solar cycle dynamo theories of short and long term behaviors of the Sun, particularly time variations of its magnetic field, plasma flows, and luminosity.     

Sausage MHD Waves in Incompressible Flux Tubes with Twisted Magnetic Fields

Twisted magnetic flux tubes are of considerable interest because of their natural occurrence from the Sun’s interior, throughout the solar atmosphere and interplanetary space up to a wide range of applicabilities to astrophysical plasmas. The aim of the present work is to obtain analytically a dispersion equation of linear wave propagation in twisted incompressible cylindrical magnetic waveguides and find appropriate solutions for surface, body and pseudobody sausage modes (i.e. m = 0) of a twisted magnetic flux tube embedded in an incompressible but also magnetically twisted plasma. Asymptotic solutions are derived in long- and short-wavelength approximations. General solutions of the dispersion equation for intermediate wavelengths are obtained numerically. We found, that in case of a constant, but non-zero azimuthal component of the equilibrium magnetic field outside the flux tube the index ν of Bessel functions in the dispersion relation is not integer any more in general. This gives rise to a rich mode-structure of degenerated magneto-acoustic waves in solar flux tubes. In a particular case of a uniform magnetic twist the total pressure is found to be constant across the boundary of the flux tube. Finally, the effect of magnetic twist on oscillation periods is estimated under solar atmospheric conditions. It was found that a magnetic twist will increase, in general, the periods of waves approximately by a few percent when compared to their untwisted counterparts.     

Radiative transfer across a magnetic flux tube

In the coming years, some solar telescopes will be able to yield the Stokes' parameters of polarized light with a resolution better than 1 arc sec (0.3 arc sec for THEMIS). We have simulated the Stokes' parameters of a solar magnetic flux tube as seen with such a resolution. We have shown that, observing with a line-of-sight not parallel to the axis of the flux tube (assumed vertical and axisymmetric), it is possible to see differences between different configurations of the magnetic field inside the flux tube (presence, and in what direction, of an azimuthal component of the field). Furthermore, along such a line-of-sight, the polarization profiles of any atomic line are strongly absorbed at the line center. We then suggest a strategy to infer the structure of the magnetic field from observations at high spatial resolution.     

Photospheric Injection of Magnetic Helicity: Connectivity-Based Flux Density Method

Magnetic helicity quantifies the degree to which the magnetic field in a volume is globally sheared and/or twisted. This quantity is believed to play a key role in solar activity due to its conservation property. Helicity is continuously injected into the corona during the evolution of active regions (ARs). To better understand and quantify the role of magnetic helicity in solar activity, the distribution of magnetic helicity flux in ARs needs to be studied. The helicity distribution can be computed from the temporal evolution of photospheric magnetograms of ARs such as the ones provided by SDO/HMI and Hinode/SOT. Most recent analyses of photospheric helicity flux derived a proxy to the helicity-flux density based on the relative rotation rate of photospheric magnetic footpoints. Although this proxy allows a good estimate of the photospheric helicity flux, it is still not a true helicity flux density because it does not take into account the connectivity of the magnetic field lines. For the first time, we implement a helicity density that takes this connectivity into account. To use it for future observational studies, we tested the method and its precision on several types of models involving different patterns of helicity injection. We also tested it on more complex configurations – from magnetohydrodynamics (MHD) simulations – containing quasi-separatrix layers. We demonstrate that this connectivity-based proxy is best-suited to map the true distribution of photospheric helicity injection.     

The Evolution of the Sun's Open Magnetic Flux – II. Full Solar Cycle Simulations

In this paper the origin and evolution of the Sun's open magnetic flux is considered by conducting magnetic flux transport simulations over many solar cycles. The simulations include the effects of differential rotation, meridional flow and supergranular diffusion on the radial magnetic field at the surface of the Sun as new magnetic bipoles emerge and are transported poleward. In each cycle the emergence of roughly 2100 bipoles is considered. The net open flux produced by the surface distribution is calculated by constructing potential coronal fields with a source surface from the surface distribution at regular intervals. In the simulations the net open magnetic flux closely follows the total dipole component at the source surface and evolves independently from the surface flux. The behaviour of the open flux is highly dependent on meridional flow and many observed features are reproduced by the model. However, when meridional flow is present at observed values the maximum value of the open flux occurs at cycle minimum when the polar caps it helps produce are the strongest. This is inconsistent with observations by Lockwood, Stamper and Wild (1999) and Wang, Sheeley, and Lean (2000) who find the open flux peaking 1–2 years after cycle maximum. Only in unrealistic simulations where meridional flow is much smaller than diffusion does a maximum in open flux consistent with observations occur. It is therefore deduced that there is no realistic parameter range of the flux transport variables that can produce the correct magnitude variation in open flux under the present approximations. As a result the present standard model does not contain the correct physics to describe the evolution of the Sun's open magnetic flux over an entire solar cycle. Future possible improvements in modeling are suggested.     

Solar Cycle Variation of Magnetic Flux Ropes in a Quasi-Static Coronal Evolution Model

The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free “potential-field” extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this model – in particular the flux ropes – varies over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, non-potential, magnetic structure at all latitudes.     

A model of the cosmic ray induced atmospheric neutron environment

In order to optimise the design of space instruments making use of detection materials with low atomic numbers, an understanding of the atmospheric neutron environment and its dependencies on time and position is needed. To produce a simple equation based model, Monte Carlo simulations were performed to obtain the atmospheric neutron fluxes produced by charged galactic cosmic ray interactions with the atmosphere. Based on the simulation results the omnidirectional neutron environment was parametrized including dependencies on altitude, magnetic latitude and solar activity. The upward- and downward-moving component of the atmospheric neutron flux are considered separately. The energy spectra calculated using these equations were found to be in good agreement with data from a purpose built balloon-borne neutron detector, high altitude aircraft data and previously published simulation based spectra.     

Comparison study of magnetic flux ropes in the ionospheres of Venus, Mars and Titan

Magnetic flux ropes are created in the ionosphere of Venus and Mars during the interaction of the solar wind with their ionospheres and also at Titan during the interaction of the Saturnian magnetospheric plasma flow with Titan’s ionosphere. The flux ropes at Venus and Mars were extensively studied from Pioneer Venus Orbiter and Mars Global Surveyor observations respectively during solar maximum. Based on the statistical properties of the observed flux ropes at Venus and Mars, the formation of a flux rope in the ionosphere is thought first to arise near the boundary between the magnetic barrier and the ionosphere and later to sink into the lower ionosphere. Venus flux ropes are also observed during solar minimum by Venus Express and the observations of developing and mature flux ropes are consistent with the proposed mechanism. With the knowledge of flux rope structure in the Venus ionosphere, the twisted fields in the lower ionosphere of Titan from Cassini observations are studied and are found to resemble the Venus flux ropes.     

Rotation of Plasma in Sunspots

In this paper we present the results of a sunspot rotation study using Abastumani Astrophysical Observatory photoheliogram data for 324 sunspots. The rotation amplitudes vary in theinebreak 2–64° range (with maximum at 12–14°), and the periods around 0–20 days (with maximum atinebreak 4–6 days). It could be concluded that sunspot rotations are rather inhomogeneous and asymmetric, but several types of sunspots are distinguished by their rotational parameters.During solar activity maximum, sunspot average rotation periods and amplitudes slightly increase. This can be affected by the increase of sunspot magnetic flux tube depth. So we can suppose that sunspot formation during solar activity is connected to a rise of magnetic tubes from deeper layers of the solar photosphere, strengthening the processes within the tube and causing variations in rotation.There is a linear relation between tilt-angle oscillation periods and amplitudes, showing higher amplitudes for large periods. The variations of those periods and especially amplitudes have a periodical shape for all types of sunspots and correlate well with the solar activity maxima with a phase delay of about 1–2 years.     

Magnetic Fields and Solar Activities

We discuss the study of solar magnetic fields based on the photospheric vector magnetograms of solar active regions which were obtained at Huairou Solar Observing Station near Beijing in the period of 22nd and 23th solar cycles. The measurements of the chromospheric magnetic field and the spatial configuration of the field at the lower solar atmosphere inferred by the distribution of the solar photospheric and chromospheric magnetic field. After the analysis on the formation process of delta configuration in some super active regions based on the photospheric vector magnetogram observations, some results are obtained: (1) The analysis of magnetic writhe of whole active regions cannot be limited in the strong field of sunspots, because the contribution of the fraction of decayed magnetic field is non-negligible. (2) The magnetic model of kink magnetic ropes, proposed to be generated in the subatmosphere, is not consistent with the evolution of large-scale twisted photospheric transverse magnetic field and the relationship with magnetic shear in some delta active regions completely. (3) The proposition is that the large-scale delta active regions are formed from contribution by highly sheared non-potential magnetic flux bundles generated in the subatmosphere. We present some results of a study of the magnetic helicity. We also compare these results with other data sets obtained by magnetographs (or Stokes polarimeters) at different observatories, and analyze the basic chirality of the magnetic field in the solar atmosphere.