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Using Multivariate Statistics

We present a series of models for the plasma properties along open magnetic flux tubes rooted in solar coronal holes, streamers, and active regions. These models represent the first self-consistent solutions that combine (1) chromospheric heating driven by an empirically guided acoustic wave spectrum; (2) coronal heating from Alfven waves that have been partially reflected, then damped by anisotropic turbulent cascade; and (3) solar wind acceleration from gradients of gas pressure, acoustic wave pressure, and Alfven wave pressure. The only input parameters are the photospheric lower boundary conditions for the waves and the radial dependence of the background magnetic field along the flux tube. We have not included multifluid or collisionless effects (e.g., preferential ion heating), which are not yet fully understood. For a single choice for the photospheric wave properties, our models produce a realistic range of slow and fast solar wind conditions by varying only the coronal magnetic field. Specifically, a two-dimensional model of coronal holes and streamers at solar minimum reproduces the latitudinal bifurcation of slow and fast streams seen by Ulysses. The radial gradient of the Alfven speed affects where the waves are reflected and damped, and thus whether energy is deposited below or above the Parker critical point. As predicted by earlier studies, a larger coronal "expansion factor" gives rise to a slower and denser wind, higher temperature at the coronal base, less intense Alfven waves at 1 AU, and correlative trends for commonly measured ratios of ion charge states and FIP-sensitive abundances that are in general agreement with observations. These models offer supporting evidence for the idea that coronal heating and solar wind acceleration (in open magnetic flux tubes) can occur as a result of wave dissipation and turbulent cascade.

http://iopscience.iop.org/article/10.1086/518001/pdf

Self-consistent Coronal Heating and Solar Wind Acceleration from Anisotropic Magnetohydrodynamic Turbulence

Presented here is a review of present knowledge of the long-term behavior of solar activity on a multi-millennial timescale, as reconstructed using the indirect proxy method. The concept of solar activity is discussed along with an overview of the special indices used to quantify different aspects of variable solar activity, with special emphasis upon sunspot number. Over long timescales, quantitative information about past solar activity can only be obtained using a method based upon indirect proxies, such as the cosmogenic isotopes 14C and 10Be in natural stratified archives (e.g., tree rings or ice cores). We give an historical overview of the development of the proxy-based method for past solar-activity reconstruction over millennia, as well as a description of the modern state. Special attention is paid to the verification and cross-calibration of reconstructions. It is argued that this method of cosmogenic isotopes makes a solid basis for studies of solar variability in the past on a long timescale (centuries to millennia) during the Holocene. A separate section is devoted to reconstructions of strong solar energetic-particle (SEP) events in the past, that suggest that the present-day average SEP flux is broadly consistent with estimates on longer timescales, and that the occurrence of extra-strong events is unlikely. Finally, the main features of the long-term evolution of solar magnetic activity, including the statistics of grand minima and maxima occurrence, are summarized and their possible implications, especially for solar/stellar dynamo theory, are discussed.

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A History of Solar Activity over Millennia

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.

Small-scale solar magnetic fields: An overview

Electromagnetic radiation from the Sun is Earth’s primary energy source. Space-based radiometric measurements in the past two decades have begun to establish the nature, magnitude and origins of its variability. An 11-year cycle with peak-to-peak amplitude of order 0.1 % is now well established in recent total solar irradiance observations, as are larger variations of order 0.2 % associated with the Sun’s 27-day rotation period. The ultraviolet, visible and infrared spectral regions all participate in these variations, with larger changes at shorter wavelengths. Linkages of solar radiative output variations with solar magnetism are clearly identified. Active regions alter the local radiance, and their wavelength-dependent contrasts relative to the quiet Sun control the relative spectrum of irradiance variability. Solar radiative output also responds to sub-surface convection and to eruptive events on the Sun. On the shortest time scales, total irradiance exhibits five minute fluctuations of amplitude $\approx 0.003$
 %, and can increase to as much as 0.015 % during the very largest solar flares. Unknown is whether multi-decadal changes in solar activity produce longer-term irradiance variations larger than observed thus far in the contemporary epoch. Empirical associations with solar activity proxies suggest reduced total solar irradiance during the anomalously low activity in the seventeenth century Maunder Minimum relative to the present. Uncertainties in understanding the physical relationships between direct magnetic modulation of solar radiative output and heliospheric modulation of cosmogenic proxies preclude definitive historical irradiance estimates, as yet.

Solar radiative output and its variability: evidence and mechanisms

We analyze high-resolution, digital, photoelectric images of solar photospheric magnetic fields. The line-of-sight fields are found to scale in a self-similar way with resolution and thus can be expressed in the form of a signed multifractal measure. The scaling properties of the measure are used to extrapolate field integrals, such as moments of the magnetic field, below resolvable limits. The scaling of the field moments is characteristic of highly intermittent fields. We suggest that the quiet-Sun photospheric fields are generated by local dynamo action based on random convective motions at high magnetic Reynolds number. The properties of active region images are determined by the presence of fields generated by the global, mean field dynamo

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Multifractal measure of the solar magnetic field

The diffusion properties of photospheric bright points associated with magnetic elements (magnetic bright points) in the granulation network are analyzed. We find that the transport is subdiffusive for times less than 20 minutes but normal for times larger than 25 minutes. The subdiffusive transport is caused by the walkers being trapped at stagnation points in the intercellular pattern. We find that the distribution of waiting times at the trap sites obeys a truncated Levy type (power-law) distribution. The fractal dimension of the pattern of sites available to the random walk is less than 2 for the subdiffusive range and tends to 2 in the normal diffusion range. We show how the continuous time random walk formalism can give an analytical explanation of the observations. We simulate this random walk by using a version of a phenomenological model of renewing cells introduced originally for supergranules by Simon, Title, & Weiss. We find that the traps that cause the subdiffusive transport arise when the renewed convection cell pattern is neither fixed nor totally uncorrelated from the old pattern, as required in Leighton's model, but in some intermediate state between these extremes.

/pdf/anomalous-diffusion-of-solar-magnetic-elements-3m2raixmlt.pdf

Anomalous Diffusion of Solar Magnetic Elements

/pdf/turbulent-and-chaotic-dynamics-underlying-solar-magnetic-1x6lwo7jal.pdf

Turbulent and Chaotic Dynamics Underlying Solar Magnetic Variability

Observed solar, interplanetary and geomagnetic time series contain quasi periodicities on scales of 1–2.5 years. The further discovery of 1.3 year fluctuations in helioseismic observations suggests that a variety of signals may be related to the underlying dynamo in the Sun. We use independent component analysis to study the temporal and spatial variations of a few statistically independent global modes of the axisymmetric solar magnetic field over a period of 25 years. Five modes capture the salient properties of the data. Two modes describe the polar and high latitude fields, and present 1–1.5 year quasi periodicities. The other three modes correspond to low and mid-latitude phenomena and show both 1.3 and 1.7-year variations. By comparing the characteristic time scales, dates of occurrence and heliocentric latitudes of these modes, we connect them to their manifestations in heliospheric time series.

John K. Lawrence

Papers

Multifractal measure of the solar magnetic field

Anomalous Diffusion of Solar Magnetic Elements

Anomalous Diffusion of Solar Magnetic Elements

Turbulent and Chaotic Dynamics Underlying Solar Magnetic Variability

Independent Global Modes of Solar Magnetic Field Fluctuations