Small-scale Solar Magnetic Fields Research Articles

Cycle-dependent and cycle-independent surface tracers of solar magnetic activity

AbstractWe consider several tracers of magnetic activity that separate cycle-dependent contributions to the background solar magnetic field from those that are independent of the cycle. The main message is that background fields include two relative separate populations. The background fields with a strength up to 100 Mx cm−2 are very poorly correlated with the sunspot numbers and vary little with the phase of the cycle. In contrast, stronger magnetic fields demonstrate pronounced cyclic behaviour. Small-scale solar magnetic fields demonstrate features of fractal intermittent behaviour, which requires quantification. We investigate how the observational estimate of the solar magnetic flux density B depends on resolution D in order to obtain the scaling In BD = −k In D + a in a reasonably wide range. The quantity k demonstrates cyclic variations typical of a solar activity cycle. k depends on the magnetic flux density, i.e. the ratio of the magnetic flux to the area over which the flux is calculated, at a given instant. The quantity a demonstrates some cyclic variation, but it is much weaker than in the case of k. The scaling is typical of fractal structures. The results obtained trace small-scale action in the solar convective zone and its coexistence with the conventional large-scale solar dynamo based on differential rotation and mirror-asymmetric convection. Here we discuss the message for solar dynamo studies hidden in the above results.

Intermittency of the Solar Magnetic Field and Solar Magnetic Activity Cycle

Small-scale solar magnetic fields demonstrate features of fractal intermittent behavior, which requires quantification. For this purpose we investigate how the observational estimate of the solar magnetic flux density \(B\) depends on resolution \(D\) in order to obtain the scaling \(\ln B_{D} = - k \ln D +a\) in a reasonably wide range. The quantity \(k\) demonstrates cyclic variations typical of a solar activity cycle. In addition, \(k\) depends on the magnetic flux density, i.e. the ratio of the magnetic flux to the area over which the flux is calculated, at a given instant. The quantity \(a\) demonstrates some cyclic variation, but it is much weaker than in the case of \(k\). The scaling obtained generalizes previous scalings found for the particular cycle phases. The scaling is typical of fractal structures. In our opinion, the results obtained trace small-scale action in the solar convective zone and its coexistence with the conventional large-scale solar dynamo based on differential rotation and mirror-asymmetric convection.

Changes of solar magnetic asymmetry

The results of an analysis of the north–south asymmetry in solar activity and solar magnetic fields are reported. The analysis is based on solar mean magnetic field and solar polar magnetic field time series, 1975–2015 (http://wso.stanford.edu), and the Greenwich sunspot data, 1875–2015 (http://solarscience.msfc.nasa.gov/greenwch.shtml). A long-term cycle (small-scale magnetic fields, toroidal component) of ~140 years is identified in the north–south asymmetry in solar activity by analyzing the cumulative sum of the time series for the north–south asymmetry in the area of sunspots. A comparative analysis of the variations in the cumulative sums of the time series composed of the daily values of the sun’s global magnetic field and in the asymmetry of the daily sunspot data over the time interval 1975–2015 shows that the photospheric large-scale magnetic fields may also have a similar long-term cycle. The variations in the asymmetry of large-scale and small-scale solar magnetic fields (sunspot area) are in sync until 2005.5 and in antiphase since then.

High-resolution, high-sensitivity, ground-based solar spectropolarimetry with a new fast imaging polarimeter

Context. Remote sensing of weak and small-scale solar magnetic fields is of utmost relevance for a number of important open questions in solar physics. This requires the acquisition of spectropolarimetric data with high spatial resolution (0.1 arcsec) and low noise (1e-3 to 1e-5 of the continuum intensity). The main limitations to obtain these measurements from the ground, are the degradation of the image resolution produced by atmospheric seeing and the seeing-induced crosstalk (SIC). Aims. We introduce the prototype of the Fast Solar Polarimeter (FSP), a new ground-based, high-cadence polarimeter that tackles the above-mentioned limitations by producing data that are optimally suited for the application of post-facto image restoration, and by operating at a modulation frequency of 100 Hz to reduce SIC. Results. The pnCCD camera reaches 400 fps while keeping a high duty cycle (98.6 %) and very low noise (4.94 erms). The modulator is optimized to have high (> 80%) total polarimetric efficiency in the visible spectral range. This allows FSP to acquire 100 photon-noise-limited, full-Stokes measurements per second. We found that the seeing induced signals present in narrow-band, non-modulated, quiet-sun measurements are (a) lower than the noise (7e-5) after integrating 7.66 min, (b) lower than the noise (2.3e-4) after integrating 1.16 min and (c) slightly above the noise (4e-3) after restoring case (b) by means of a multi-object multi-frame blind deconvolution. In addition, we demonstrate that by using only narrow-band images (with low SNR of 13.9) of an active region, we can obtain one complete set of high-quality restored measurements about every 2 s.

Spatial variations of Stokes profiles of magnetoactive lines Fe I

Solutions of the polarized radiative transfer problem were obtained within the 3D MHD model of the quiet solar atmosphere. Spatial variations of the Stokes profile parameters caused by the granulation structure and small-scale magnetic fields in the quiet solar photosphere for neutral iron magnetoactive lines are studied. The modulation effect of Stokes V profile parameters (amplitude and area) by the granulation structure of the solar photosphere is revealed. This effect is significant mainly in intergranules, in which the modulation depth reaches 50%. The correlation of Stokes profile parameters with small-scale solar granulation magnetic fields is investigated. It is shown that it is possible to construct calibration relationships that provide the correlation coefficient of 0.98 in diagnostics of small-scale magnetic fields using Stokes profile parameters of Fe I lines λ 525.02 and λ 524.71 nm.

Solar Magnetic Carpet I: Simulation of Synthetic Magnetograms

This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar magnetic fields. In the model, the basic evolution of the magnetic elements is governed by a supergranular flow profile. In addition, magnetic elements may evolve through the processes of emergence, cancellation, coalescence and fragmentation. Model parameters for the emergence of bipoles are based upon the results of observational studies. Using this model, several simulations are considered, where the range of flux with which bipoles may emerge is varied. In all cases the model quickly reaches a steady state where the rates of emergence and cancellation balance. Analysis of the resulting magnetic field shows that we reproduce observed quantities such as the flux distribution, mean field, cancellation rates, photospheric recycle time and a magnetic network. As expected, the simulation matches observations more closely when a larger, and consequently more realistic, range of emerging flux values is allowed (4e16 - 1e19 Mx). The model best reproduces the current observed properties of the magnetic carpet when we take the minimum absolute flux for emerging bipoles to be 4e16 Mx. In future, this 2D model will be used as an evolving photospheric boundary condition for 3D non-potential modeling.

Multiline Stokes Analysis for the Study of Small‐Scale Solar Magnetic Fields

Combining observations of spectral lines with different Zeeman sensitivities, it is possible to infer some properties of the small-scale solar magnetic fields. This paper presents a theoretical analysis of the diagnostics potential of 14 different spectral lines when used for this purpose. These lines span a broad range of wavelengths from the visible to the near-infrared and have been employed in recent studies of the quiet-Sun magnetism. It is shown here that the visible lines analyzed provide only a rough picture of the unresolved field distribution, but their results are more robust. Infrared lines, on the other hand, have the potential of carrying much richer information on the details of the distribution. However, this depends critically on the sensitivity attained and the analysis performed. The best results are obtained when a suitable combination of visible and infrared lines is employed. The analysis of sample visible and infrared quiet-Sun profiles confirms this assessment and suggests the coexistence of weak and strong fields within the resolution element, which would explain the observational discrepancy that surrounds this issue. Finally, I present a table with optimum combinations of spectral lines for three present or upcoming multiline solar spectropolarimeters (THEMIS, SPINOR, and the TIP+POLIS combination).

Why Solar Magnetic Flux Concentrations Are Bright in Molecular Bands

Using realistic ab initio simulations of radiative magnetoconvection, we show that the bright structures in images taken in the G band, a spectral band dominated by lines of the CH molecule, precisely outline small-scale concentrations of strong magnetic fields on the visible solar surface. The brightening is caused by a depletion of CH molecules in the hot and tenuous magnetic structures, thus confirming the model of radiatively heated magnetic flux concentrations. These results provide a firm basis for observational studies of the evolution and dynamics of the small-scale solar magnetic field derived through proxy magnetometry with G-band images.

On the Dynamics of Small-Scale Solar Magnetic Elements

We report on the dynamics of the small-scale solar magnetic field, based on analysis of very high resolution images of the solar photosphere obtained at the Swedish Vacuum Solar Telescope. The data sets are movies from 1 to 4 hr in length, taken in several wavelength bands with a typical time between frames of 20 s. The primary method of tracking small-scale magnetic elements is with very high contrast images of photospheric bright points, taken through a 12 A bandpass filter centered at 4305 A in the Fraunhofer 'G band.' Previous studies have established that such bright points are unambiguously associated with sites of small-scale magnetic flux in the photosphere, although the details of the mechanism responsible for the brightening of the flux elements remain uncertain. The G band bright points move in the intergranular lanes at speeds from 0.5 to 5 km/s. The motions appear to be constrained to the intergranular lanes and are primarily driven by the evolution of the local granular convection flow field. Continual fragmentation and merging of flux is the fundamental evolutionary mode of small-scale magnetic structures in the solar photosphere. Rotation and folding of chains or groups of bright points are also observed. The timescale for magnetic flux evolution in active region plage is on the order of the correlation time of granulation (typically 6-8 minutes), but significant morphological changes can occur on timescales as short as 100 S. Smaller fragments are occasionally seen to fade beyond observable contrast. The concept of a stable, isolated subarcsecond magnetic 'flux tube' in the solar photosphere is inconsistent with the observations presented here.

Multifractal models of small-scale solar magnetic fields

Multifractal models of small-scale solar magnetic fields

Small-scale solar magnetic fields: An overview

An overview is given of the observational and the theoretical methods used to investigate solar magnetic fields. It includes an introduction to the Stokes parameters, their radiative transfer in the presence of a magnetic field, and empirical techniques used to measure various properties of solar magnetic features, such as the strength and direction of the magnetic field, magnetic flux, temperature, velocity, size and lifetime. The MHD equations are introduced and some of the most common simplifications used to describe solar magnetic features are outlined. The application of these techniques to small-scale magnetic features is surveyed. The results of empirical and theoretical investigations of small-scale solar magnetic features are reviewed. Current views on their magnetic structure, thermal stratification, velocity field, size, distribution and evolution are presented. Finally, some open questions concerning small-scale solar magnetic fields are listed.

Fractal Flux Tubes of the Solar Magnetic Field

Abstract The small-scale solar magnetic field exceeding a given threshold forms a fractal set. A dimension of this fractal is found from magnetograms with varying linear resolution. The dimension depends on the value of the threshold magnetic field (multifractality). A simple dynamo model explaining the origin of the fractal magnetic structure is considered. The dynamo produces a magnetic field in the form of flux tubes with a fractal distribution of magnetic field across the tube. The observed dimension gives a possibility of estimating a degree of structuredness of the solar velocity field.

IV. Small Scale Magnetic Fields

Considerable progress has been made during the last four years in the theoretical and empirical investigation of the small scale solar magnetic field and associated phenomena. Although the basic outlines established in the 1970s of the structure of the field, namely small fluxtubes or magnetic elements with kllogauss fields embedded in a relatively field free medium have survived, many of the details have changed and some of the large gaps in our knowlegde of these captivating structures have been filled. In the following we briefly outline some of the highlights.

Small scale solar magnetic fields and their relation to various solar activity indices

Correlation studies between various solar activity indices and a long time series of annual sums of the maximum value of solar magnetic field intensity, observed for each group of sunspots during each passage of it over the visible solar hemisphere, have pointed out a couple of interesting points. First, the faculae have a significant contribution to the numerical representation of the small scale solar magnetic coefficients and low standard errors of estimation to the above mentioned maximum values of the solar magnetic field. These properties give to the area index an important physical meaning which is a first approximation to the small scale solar magnetic fields expressed by the above-mentioned maximum values of it. Finally, the main point which comes out is that long term studies of the solar magnetic fields, especially extrapolated studies to the past, could be supported by photospheric indices of the solar activity.

On the size, structure, and strength of the small-scale solar magnetic field

High-resolution magnetograms place an upper limit of 0.33 arcsec on the smallest magnetic-field structures. These magnetograms show that the active-region field is organized into roughly cellular patterns 2-3 arcsec in diameter and that the field structures occur in the centers of 'abnormal' granules. Comparison of these data and other magnetograms with high signal-to-noise ratio indicates that there exists another component of the field that is diffuse on the scale of an arc second and has a maximum strength of less than 500 gauss.

Facular Models, the K-Line, and Magnetic Fields

Photospheric faculae are now believed to be closely associated with the small-scale solar magnetic field. In order to obtain reliable observations of solar magnetic fields, one needs to have a good description of faculae, which is presently lacking. The problem in obtaining good observational data is severe because faculae are usually not spatially resolved, particularly so in the case of spectroscopic observations. Proper use of spectroscopic observations also requires some knowledge of solar velocity fields and atomic physics in the case of a non LTE analysis. Many of these problems can be avoided by making use of the wings of the Ca II K-line. The wing of this line is unaffected by magnetic and velocity effects. The formation of the line has become increasingly well understood and most of the wing (with the exception of the inner 1 - 2 Å) is formed in LTE. The line is so strong that its formation spans the whole depth of the photosphere.

Small-Scale Solar Magnetic Fields

The observed properties of small-scale solar magnetic fields are reviewed. Most of the magnetic flux in the photosphere is in the form of strong fields of about 100–200mT(1–2 kG), which have remarkably similar properties regardless of whether they occur in active or quiet regions. These fields are associated with strong atmospheric heating. Flux concentrations decay at a rate of about 107Wb s-1, independent of the amount of flux in the decaying structure. The decay occurs by smaller flux fragments breaking loose from the larger ones, i.e. a transfer of magnetic flux from smaller to larger Fourier wave numbers, into the wave-number regime where ohmic diffusion becomes significant. This takes place in a time-scale much shorter than the length of the solar cycle.The field amplification occurs mainly below the solar surface, since very little magnetic flux appears in diffuse form in the photosphere, and the life-time of the smallest flux elements is very short. The observations further suggest that most of the magnetic flux in quiet regions is supplied directly from below the solar surface rather than being the result of turbulent diffusion of active-region magnetic fields.

On the Nature of the Small-Scale Solar Magnetic Field

On the Nature of the Small-Scale Solar Magnetic Field

Small-scale solar magnetic fields and ?invisible sunspots?

Small-scale solar magnetic fields and ?invisible sunspots?