Small-scale Magnetic Elements Research Articles

Turbulent convective flows in the solar photospheric plasma

The origin of the 22-year solar magnetic cycle lies below the photosphere where multiscale plasma motions, due to turbulent convection, produce magnetic fields. The most powerful intensity and velocity signals are associated with convection cells, called granules, with a scale of typically 1 Mm and a lifetime of a few minutes. Small-scale magnetic elements (SMEs), ubiquitous on the solar photosphere, are passively transported by associated plasma flows. This advection makes their traces very suitable for defining the convective regime of the photosphere. Therefore the solar photosphere offers an exceptional opportunity to investigate convective motions, associated with compressible, stratified, magnetic, rotating and large Rayleigh number stellar plasmas. The magnetograms used here come from a Hinode/SOT uninterrupted 25-hour sequence of spectropolarimetric images. The mean-square displacement of SMEs has been modelled with a power law with spectral index ${\it\gamma}$. We found ${\it\gamma}=1.34\pm 0.02$ for times up to ${\sim}2000~\text{s}$ and ${\it\gamma}=1.20\pm 0.05$ for times up to ${\sim}10\,000~\text{s}$. An alternative way to investigate the advective–diffusive motion of SMEs is to look at the evolution of the two-dimensional probability distribution function (PDF) for the displacements. Although at very short time scales the PDFs are affected by pixel resolution, for times shorter than ${\sim}2000~\text{s}$ the PDFs seem to broaden symmetrically with time. In contrast, at longer times a multi-peaked feature of the PDFs emerges, which suggests the non-trivial nature of the diffusion–advection process of magnetic elements. A Voronoi distribution analysis shows that the observed small-scale distribution of SMEs involves the complex details of highly nonlinear small-scale interactions of turbulent convective flows detected in solar photospheric plasma.

Evolution of Small-Scale Magnetic Elements in the Vicinity of Granular-Sized Swirl Convective Motions

Advances in solar instrumentation have led to a widespread usage of time series to study the dynamics of solar features, specially at small spatial scales and at very fast cadences. Physical processes at such scales are determinant as building blocks for many others occurring from the lower to the upper layers of the solar atmosphere and beyond, ultimately for understanding the bigger picture of solar activity. Ground-based (SST) and space-borne (Hinode) high-resolution solar data are analyzed in a quiet Sun region displaying negative polarity small-scale magnetic concentrations and a cluster of bright points observed in G-band and Ca II H images. The studied region is characterized by the presence of two small-scale convective vortex-type plasma motions, one of which appears to be affecting the dynamics of both, magnetic features and bright points in its vicinity and therefore the main target of our investigations. We followed the evolution of bright points, intensity variations at different atmospheric heights and magnetic evolution for a set of interesting selected regions. A description of the evolution of the photospheric plasma motions in the region nearby the convective vortex is shown, as well as some plausible cases for convective collapse detected in Stokes profiles.

THE BUILDUP OF A SCALE-FREE PHOTOSPHERIC MAGNETIC NETWORK

We use a global Monte Carlo simulation of the formation of the solar photospheric magnetic network to investigate the origin of the scale invariance characterizing magnetic flux concentrations visible on high-resolution magnetograms. The simulations include spatially and temporally homogeneous injection of small-scale magnetic elements over the whole photosphere, as well as localized episodic injection associated with the emergence and decay of active regions. Network elements form in response to cumulative pairwise aggregation or cancellation of magnetic elements, undergoing a random walk on the sphere and advected on large spatial scales by differential rotation and a poleward meridional flow. The resulting size distribution of simulated network elements is in very good agreement with observational inferences. We find that the fractal index and size distribution of network elements are determined primarily by these post-emergence surface mechanisms, and carry little or no memory of the scales at which magnetic flux is injected in the simulation. Implications for models of dynamo action in the Sun are briefly discussed.

The Evolution of the Solar Magnetic Field

AbstractThe almost stately evolution of the global heliospheric magnetic field pattern during most of the solar cycle belies the intense dynamic interplay of photospheric and coronal flux concentrations on scales both large and small. The statistical characteristics of emerging bipoles and active regions lead to development of systematic magnetic patterns. Diffusion and flows impel features to interact constructively and destructively, and on longer time scales they may help drive the creation of new flux. Peculiar properties of the components in each solar cycle determine the specific details and provide additional clues about their sources. The interactions of complex developing features with the existing global magnetic environment drive impulsive events on all scales. Predominantly new-polarity surges originating in active regions at low latitudes can reach the poles in a year or two. Coronal holes and polar caps composed of short-lived, small-scale magnetic elements can persist for months and years. Advanced models coupled with comprehensive measurements of the visible solar surface, as well as the interior, corona, and heliosphere promise to revolutionize our understanding of the hierarchy we call the solar magnetic field.

Sun’s small-scale magnetic field : from quiet region to polar region

In this contribution, we present our recent effort in understanding the solar small-scale magnetic field. Firstly, with the unique data from MDI/SOHO in an interval embodying solar cycle 23, we find three categories of small-scale magnetic elements, and their number variations shows no correlation, anti-correlation and correlation with sunspots, respectively. The possible sources for the three categories of small-scale magnetic elements are discussed. Secondly, by the observations from SOT on board Hinode, we study the properties of vector magnetic field in quiet Sun. The following results are summarized. (1) Two categories of horizontal magnetic elements are disclosed, and most of horizontal elements are associate with the emergence of U-loop. (2) The magnetic field of quiet region is obviously non-potential. The filigrees and network bright points are characterized by strong longitudinal field, large electric helicity and free energy density. (3) For quiet region, the intra-network region displays a predominance of weak field concentration, but network region shows the coexisting of weak field with strong field; For polar region, the strong field occupies 6.7% of the region. (4) On quiet region, the magnetic field mainly resides in the inter-granular lanes. By the observation, we reconstruct an average granular model, for which the detailed distributions of vector fields, Doppler velocity and intensity are obtained.

THE LATITUDE DISTRIBUTION OF SMALL-SCALE MAGNETIC ELEMENTS IN SOLAR CYCLE 23

With the unique data set from full-disk observations provided by Michelson Doppler Imager on board the Solar and Heliospheric Observatory in the interval embodying solar cycle 23, we have found that the cyclic variations of numbers and total flux of these small-scale magnetic elements covering fluxes of (2.9-32.0) Multiplication-Sign 10{sup 18} Mx and (4.27-38.01) Multiplication-Sign 10{sup 19} Mx show anticorrelation and correlation with sunspots, respectively. In this study, the time-latitude distributions of these anticorrelated and correlated elements are analyzed. The following results are disclosed: (1) for the correlated elements, the cyclic variations of the total flux in low-latitude and middle-latitude regions show a longer duration of cyclic maximum phase than that of an active region (AR) in the corresponding latitude region; the total flux of these elements shows the accordant south-north asymmetry with that of AR; the time-latitude distribution of their number displays a similar butterfly diagram but with a latitude distribution that is twice as wide as that of sunspots. (2) For the anticorrelated elements, the time-latitude distribution of number shows a solar cycle variation different from the sunspot butterfly diagram; in each latitude, the distribution of anticorrelated elements always shows the anticorrelated variation with that of sunspots; duringmore » solar cycle 23, the average speed of the peak latitudinal migration for anticorrelated elements reaches 7.5 deg year{sup -1}, almost three times that for sunspots. These results seem to imply that the correlated elements are the debris of decayed sunspots, and the anticorrelated elements have a different source but are affected or modulated by sunspot magnetic field.« less

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.

Intensity contrast from MHD simulations and HINODE observations

Changes in the solar surface area covered by small-scale magnetic elements are thought to cause long-term changes in the solar spectral irradiance, which are important for determining the impact on Earth's climate. To study the effect of small-scale magnetic elements on total and spectral irradiance, we derive their contrasts from 3-D MHD simulations of the solar atmosphere. Such calculations are necessary since measurements of small-scale flux tube contrasts are confined to a few wavelengths and suffer from scattered light and instrument defocus, even for space observations. To test the contrast calculations, we compare rms contrasts from simulations with those obtained with the broad-band filter imager mounted on the Solar Optical Telescope (SOT) onboard the Hinode satellite and also analyse centre-to-limb variations (CLV). The 3-D MHD simulations include the interaction between convection and magnetic flux tubes. They have been run with non-grey radiative transfer using the MURaM code. Simulations have an average vertical magnetic field of 0G, 50G, and 200G. Emergent intensities are calculated with the spectral synthesis code ATLAS9 and are convolved with a theoretical point-spread function to account for the properties of the observations' optical system. We find reasonable agreement for simulated and observed intensity distributions in the visible continuum bands. Agreement is poorer for the CN and G-Bands. The analysis of the simulations exhibits a potentially more realistic centre-to-limb behaviour than calculations based on 1-D model atmospheres. We conclude that starting from 3-D MHD simulations represents a powerful approach to obtaining intensity contrasts for a wide wavelength coverage and for different positions on the solar disk. This also paves the way for future calculations of facular and network contrast as a function of magnetic fluxes.

SIMULATION OF THE FORMATION OF A SOLAR ACTIVE REGION

We present a radiative magnetohydrodynamics simulation of the formation of an Active Region on the solar surface. The simulation models the rise of a buoyant magnetic flux bundle from a depth of 7.5 Mm in the convection zone up into the solar photosphere. The rise of the magnetic plasma in the convection zone is accompanied by predominantly horizontal expansion. Such an expansion leads to a scaling relation between the plasma density and the magnetic field strength such that $B\propto\varrho^{1/2}$. The emergence of magnetic flux into the photosphere appears as a complex magnetic pattern, which results from the interaction of the rising magnetic field with the turbulent convective flows. Small-scale magnetic elements at the surface first appear, followed by their gradual coalescence into larger magnetic concentrations, which eventually results in the formation of a pair of opposite polarity spots. Although the mean flow pattern in the vicinity of the developing spots is directed radially outward, correlations between the magnetic field and velocity field fluctuations allow the spots to accumulate flux. Such correlations result from the Lorentz-force driven, counter-streaming motion of opposite-polarity fragments. The formation of the simulated Active Region is accompanied by transient light bridges between umbrae and umbral dots. Together with recent sunspot modeling, this work highlights the common magnetoconvective origin of umbral dots, light bridges and penumbral filaments.

Empirical Modeling of Radiative versus 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 comparison of measured and simulated solar network contrast

AbstractLong-term trends in the solar spectral irradiance are important to determine the impact on Earth's climate. These long-term changes are thought to be caused mainly by changes in the surface area covered by small-scale magnetic elements. The direct measurement of the contrast to determine the impact of these small-scale magnetic elements is, however, limited to a few wavelengths, and is, even for space instruments, affected by scattered light and instrument defocus. In this work we calculate emergent intensities from 3-D simulations of solar magneto-convection and validate the outcome by comparing with observations from Hinode/SOT. In this manner we aim to construct the contrast at wavelengths ranging from the NUV to the FIR.

Observational evidences for multi-component magnetic field structure in solar flares

Two solar flares of 25 July 1981 and 5 November 2004 of importance 2N and M4.1/1B, respectively, were investigated using observational data obtained with the Echelle spectrograph of the Kyiv University Astronomical Observatory. Stokes I and V profiles of the FeI lines 5233, 5247.1, 5250.2, 5250.6, 5576.1 and of CrI 5247.6 A have been analyzed. We found several evidences for the existence of spatially unresolved magnetic field structures with kG strengths. In particular, the values of the measured average longitudinal field B ∥ depend on the Lande factors g of the lines: in general, B ∥ increases with increasing factor g. Analogously, the observed line ratio B ∥(5250.2)/B ∥(5247.1) is increasing with increasing distance Δλ from the line center. The observed Stokes V profiles show some deviations from that of an assumed homogeneous field, presented by the Stokes I gradient, dI/dλ. A comparison with the non-split line FeI 5576.1 A shows that some of these deviations are real and indicate the presence of subtelescopic magnetic elements with discrete field strengths of several kG. The lines with large Lande factors have considerable broadenings of the Stokes I profiles, indicating a strong background magnetic field of mixed polarity. On the basis of all these data we conclude that a four-component magnetic field structure is a possible explanation. The field strengths are about ±1.05 kG in the background field, and 1.3−1.5, 3.9−4.0, and 7.4−7.8 kG at level of middle photosphere (h ≈ 300 km) in the spatially unresolved, small-scale magnetic elements.

A Model for the Total Solar Irradiance Based on Active Region Decay

We present a model for the total solar irradiance. The model takes the observed location, timing, and area of emerging active regions as input and produces a time-evolving size distribution of magnetic structures over the solar surface. We assume that the bright magnetic structures (faculae), which counteract the irradiance deficit caused by sunspots, consist of the products of active region decay. We simulate the decay process as a combination of fragmentation and boundary erosion of large-scale magnetic structures. The model has several adjustable parameters that control the decay processes and the irradiance contribution from the quiet Sun and the small-scale magnetic elements that are produced during the decay process. We use a genetic algorithm to estimate these parameters by fitting to the observed irradiance and daily sunspot area time series over the 1978-2007 time interval. Given the simplifications associated with the model, the resultant parameter values are well constrained within the imposed ranges. In addition, the irradiance and daily sunspot area time series produced by the best-fit models agree very well with the observations, although the sunspot area fits tend to perform better than the irradiance fits. However, it is evident that the model is neglecting a significant source of excess brightness, which manifests itself in two ways. First, the optimal values for the lifetime and intensity contrast of the bright, small-scale flux elements are both larger than expected. Second, the synthetic irradiance consistently underestimates the observations during the ascending phase of a cycle, despite the daily sunspot area fitting the observations quite well during these times. We also show that this genetic forward modeling approach can be used to detect a long-term trend of decadal timescale in the quiet-Sun irradiance. Assuming a constant quiet-Sun irradiance, we reconstruct the total solar irradiance over the 1874-1978 time interval, for which observational data of emerging active regions are available.

On Absorption and Scattering of P Modes by Small-Scale Magnetic Elements

The solar surface is characterised everywhere by the presence of small-scale magnetic structures. Their collective behaviour in the form of active regions is known to have strong influence on p-mode power. For example, sunspots and plages are strong absorbers of acoustic waves. This paper studies the effects of individual small-scale magnetic elements to understand the details of absorption of p-mode power. For this, we consider a thin magnetic flux tube and calculate the phase shifts and the absorption coefficients by numerically solving the linearised MHD equations. The phase shifts calculated from the Born Approximation are then compared for the same range of degrees. The results are discussed with a view to understanding the physical mechanism.

Supergranulation as an Emergent Length Scale

We have developed an n-body diffusion-limited aggregation model to simulate the dispersal and interaction of small-scale magnetic elements at the solar surface. The model is highly simplified and is based on the observation that small-scale magnetic elements are passively advected by the granular flow, which we approximate as a random walk. With a great many magnetic elements executing this random walk simultaneously, collisions are inevitable. We assume that these collisions lead to the aggregation of the colliding magnetic elements (if they have the same polarity) or mutual cancellation (if opposite polarity). In a similar fashion, the resulting clusters can subsequently interact with more magnetic elements or with other clusters. The clusters also undergo a random walk. However, the step size is reduced and the lifetime is increased in order to mimic the observation that larger magnetic flux concentrations move slower and live longer than smaller ones. The essential finding is that this process can produce a spatial distribution of clusters comparable to the supergranule cell pattern (depending on model parameters). The characteristic length scale associated with the spatial distribution of the clusters is quite sensitively dependent on the injection rate of fresh magnetic elements—when the injection rate is high (low) the length scale is small (large). This property provides a natural explanation for the observation that supergranule cells tend to be smaller when and where the level of magnetic activity is higher. We also find that at length scales similar to supergranulation the dominance of a given polarity tends to be enhanced, in comparison to the case where the same clusters are situated randomly in space. This is potentially testable by observation.

Narrow-band imaging in the CN band at 388.33 nm

We promote the use of narrow-band (0.05 -- 0.20 nm FWHM) imaging in the molecularvCN band head at 388.33 nm as an effective method for monitoring small-scale magnetic field elements because it renders them with exceptionally high contrast. We create synthetic narrow-band CN filtergrams from spectra computed from a three-dimensional snapshot of a magnetohydrodynamic simulation of the solar convection to illustrate the expected high contrast and explain its nature. In addition, we performed observations with the horizontal slit spectrograph at the Dunn Solar Tower at 388.3 nm to experimentally confirm the high bright-point contrast, and to characterize and optimize the transmission profile of a narrow-band (0.04 FWHM) Lyot filter, which was built by Lyot and tailored to the CN band at Sacramento Peak in the early 70's. The presented theoretical computations predict that bright-point contrast in narrow-band (0.04 FWHM) CN filtergrams is more than 3 times higher than in CN filtergrams taken with 1 nm FWHM wide filters, and in typical G-band filtergrams.

Polar magnetic field reversals on the Sun

AbstractThe polar magnetic fields on the Sun have been an attractive subject for solar researches since Babcock measured them in solar cycle 19. One of the remarkable features of the polar magnetic fields is their reversal during the maxima of 11-year sunspot cycles. I have present results of the investigations of the polar magnetic field using SOHO-mdi data. It is found, that the polar magnetic field reversal is detected with mdi data for polar region within 78°–88°. The North Pole has changed polarity in CR1975 (April 2001). The South reversed later in CR1980 (September 2001). The total unsigned magnetic flux does not show the dramatic decreasing during the polar reversals due to omnipresent bi-polar small-scale magnetic elements. The observational and theoretical aspects of the polar magnetic field reversals are discussed.

A comparison of solar proxy-magnetometry diagnostics

Aims. We test various proxy-magnetometry diagnostics, i.e., brightness signatures of small-scale magnetic elements, for studying magnetic field structures in the solar photosphere. Methods. Images are numerically synthesized from a 3D solar magneto-convection simulation for, respectively, the G band at 430.5 nm, the CN band at 388.3 nm, and the blue wings of the Hα, Hβ, Caii H, and Ca ii 854.2 nm lines. Results. Both visual comparison and scatter diagrams of the computed intensity versus the magnetic field strength show that, in particular for somewhat spatially extended magnetic elements, the blue Hα wing presents the best proxy-magnetometry diagnostic, followed by the blue wing of Hβ. The latter yields higher diffraction-limit resolution. Conclusions. We recommend using the blue Hα wing to locate and track small-scale photospheric magnetic elements through their brightness appearance.

A comparative study of the contrast of solar magnetic elements in CN and CH

Photospheric bright points were investigated in three different wavelength bands using interference filters centered at 436.5 nm (continuum), 430.5 nm (Fraunhofer's G-band dominated by absorption due to CH), and 388.7 nm (absorption band of CN). Such bright points serve as proxies of small-scale solar magnetic elements. Near diffraction limited imaging was achieved by real-time frame selection and subsequent joint phase diverse speckle reconstruction. Comparison of the filtergrams of NOAA0670 taken in CH and CN shows that the contrast of bright points is on average 1.4 times higher in CN than in G-band, which is in good quantitative agreement with the predictions of Berdyugina et al. (2003, A&A, 412, 513) and Rutten et al. (2001, ASP Conf. Ser., 236, 445).

Solar flares: self-organization of active region to the critical state

Results of modern multi-wavelength observations of large solar non-stationary events are briefly summarized. Such events consist of a puls, an eruption (surge or CME) and a long-living system of giant arches.Observations demonstrate often that the pulse arises as a result of “avalanche” of interaction of small-scale magnetic elements, while the dynamic system transforms into a state of self-organizing criticality (SOC) on the post-eruptive phase. We developed new code for the avalanche model where it is possible to consider a transition of the active region as a dynamic system in a state of SOC. Derived solutions show, firstly, that the avalanche is naturally developed nearby spots during the pulse. Secondly, during long-duration events, occuring along the neutral line of the longitudinal magnetic field, behaviour of the large-scale coronal magnetic field is characterized by a state of SOC.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html