Sun's Magnetic Flux Research Articles

THE SUN'S SMALL-SCALE MAGNETIC ELEMENTS IN SOLAR CYCLE 23

With the unique database from Michelson Doppler Imager aboard the Solar and Heliospheric Observatory in an interval embodying solar cycle 23, the cyclic behavior of solar small-scale magnetic elements is studied. More than 13 million small-scale magnetic elements are selected, and the following results are unclosed. (1) The quiet regions dominated the Sun's magnetic flux for about 8 years in the 12.25 year duration of Cycle 23. They contributed (0.94 - 1.44) $\times 10^{23}$ Mx flux to the Sun from the solar minimum to maximum. The monthly average magnetic flux of the quiet regions is 1.12 times that of active regions in the cycle. (2) The ratio of quiet region flux to that of the total Sun equally characterizes the course of a solar cycle. The 6-month running-average flux ratio of quiet region had been larger than 90.0% for 28 continuous months from July 2007 to October 2009, which characterizes very well the grand solar minima of Cycles 23-24. (3) From the small to large end of the flux spectrum, the variations of numbers and total flux of the network elements show no-correlation, anti-correlation, and correlation with sunspots, respectively. The anti-correlated elements, covering the flux of (2.9 - 32.0)$\times 10^{18}$ Mx, occupies 77.2% of total element number and 37.4% of quiet Sun flux. These results provide insight into reason for anti-correlated variations of small-scale magnetic activity during the solar cycle.

Distribution functions for magnetic fields on the quiet Sun

The statistical properties of the highly structured magnetic field of the quiet Sun are best described in terms of distribution functions, in particular the probability density functions (PDF) for the flux densities and the angular distribution for the orientations of the field vector. They are needed to test the validity of various MHD simulations, but past determinations have led to contradictory results. A main reason for these difficulties lies in the circumstance that the magnetic structuring continues on scales that are much smaller than the telescope resolution, and that this structuring strongly affects the quantities averaged over each pixel due to the non-linear relation between polarization and magnetic field. Here we use a Hinode SOT/SP data set for the disk center of the quiet Sun to explore the complex behavior of the polarized 6301-6302 A line system and identify the observables that allow the most robust determinations of inclination angles and flux densities. These observables are then used to derive the empirical distribution functions. Our Stokes V line ratio analysis leads us to an unexpected discovery: a magnetic dichotomy with two distinct populations, representing strong (kG) and weak fields. This can be understood in terms of the convective collapse mechanism, which makes the Sun's magnetic flux end up in two states: collapsed and uncollapsed. With the linear-to-circular polarization ratio as a robust observable for the inclination angles, we find that the angular distribution is extremely peaked around the vertical direction for the largest flux densities, but gradually broadens as we go to smaller flux densities, to become asymptotically isotropic at zero flux density. The PDF for the vertical flux density, after accounting for the smearing effect of measurement noise, is found to have an extremely narrow core peak centered at zero flux density, which can be analytically represented by a stretched exponential. The PDF wings are extended and decline quadratically. The PDFs for the horizontal and total flux densities have a similar behavior. In particular we demonstrate that earlier claims that the PDF for the total flux density increases from small values at zero flux density to have a maximum significantly shifted from zero is an artefact of measurement noise.

The quiet Sun's magnetic flux estimated from Ca II H bright inter-granular G-band structures

We determine the number density and area contribution of small-scale inter-granular calcium-II bright G-band structures in images of the quiet Sun as tracers of kilo-Gauss magnetic flux-concentrations. In a 149" x 117" G-band image of the disk center at the activity minimum, 7593 small inter-granular structures ['IGS']were segmented with the `multiple-level tracking' pattern recognition algorithm ['MLT_4']. The scatter-plot of the continuum versus the G-band brightness shows the known magnetic and non-magnetic branches. These branches are largely disentangled by applying an intrinsic Ca-II excess criterion. The thus obtained 2995 structures contain 1152 G-band bright points ['BP'] and 1843 G-band faint points ['FP']. They show a tendency of increasing size with decreasing G-band excess, as expected from the `hot wall' picture. Their Ca-H and G-band brightness are slightly related, resembling the known relation of Ca-II and magnetic field strength. The magnetic flux density of each individual BP and FP is estimated from their G-band brightness according to MHD-model calculations. The entity of BP and FP covers the total field-of-view ['FOV'] with a number density of 0.32/Mm^2 and a total area contribution of 2.0%. Their individual calibrations yield a mean flux density of 20 Mx/cm^2 in the entire FOV and 13 Mx/cm^2 for inter-network regions.

Effect of spatial resolution on estimating the Sun's magnetic flux

A critical question related to a possible secular trend in the Sun's total magnetic flux and consequently in solar irradiance is the total amount of magnetic flux present on the Sun and how it is distributed between active regions and the quiet Sun. NSO/Kitt Peak synoptic charts have in the past been used to estimate the total flux and the fraction of the flux in active regions and in the quiet Sun. Since a single pixel of these synoptic charts is much bigger than individual small-scale magnetic elements and opposite polarities may be present within the same pixel, some magnetic flux escaped notice. Here we estimate the fraction of the magnetic flux escaping detection in Kitt Peak synoptic charts. By artificially reducing the spatial resolution of MDI full-disc and high-resolution magnetograms we study the influence of the resolution on the measured total magnetic flux. Noise in the data poses the main difficulty to this approach and is carefully studied. It is concluded that at least half of the magnetic flux in the quiet Sun remains undetected in Kitt Peak synoptic charts and that the total flux present on the solar surface at maxima of activity is around twice the flux present at activity minima.

Secular variation of the Sun's magnetic flux

We present an extension of the model of Solanki et al. (2000) that allows us to reconstruct the time evolution of both the total and the open magnetic flux at the solar surface since 1700. The flux emerging in large active regions is determined using the sunspot number as a proxy, while the flux emergence in small ephemeral regions is described by an extended cycle whose amplitude and length are related to the corresponding sunspot cycle. Both types of regions contribute to the open flux, which is the source of the heliospheric field. The overlap of the activity cycles of ephemeral regions leads to a secular variation of the total cycle-related magnetic flux (active region flux + ephemeral region flux + open flux). The model results indicate that the total surface flux has doubled in the first half of the last century. The evolution of the open flux is in good agreement with the reconstruction by Lockwood et al. (1999).