Study of polar faculae by means of spectro‐polarimetric observations and radiative transfer calculations

Polar faculae are of special interest for solar physics because of their close relationship to the global magnetic field of the Sun and to solar activity, and because of the recently found kilogauss magnetic fields, which are very unusual for the structures outside active regions at high latitudes of the Sun. The idea is that polar faculae can be represented by bundles of unresolved small‐scale magnetic flux tubes, which are characterized by sizes of about 100 km and strong magnetic fields. High resolution spectro‐polarimetric observations of the considered structures were performed and complemented by the radiation transfer calculations with oblique rays passing through an inhomogeneous magnetic medium. The recent results of observations and numerical calculations are presented.     

Differential rotation of solar magnetic fields

The connection of the differential rotation of solar magnetic fields with the field sign and strength is studied. The synoptic maps of magnetic fields over the last three solar cycles taken at the Kitt Peak Observatory served as input data for the study. The algorithm of magnetic field filtering over 14 chosen strengt intervals and successive 5-degree latitude zones was applied to these data. The Fourier transform of the time series obtained was then used. Analysis of the power spectra led to the conclusion that there are two types of magnetic fields. These differ in strength (0–50 and 50–700 G) and rotation characteristics. The rotation differentiality for strong magnetic field is almost twice as large as that for weak magnetic fields.     

Distribution of magnetic flux on the solar surface and low-degree p-modes

The frequencies of solar p-modes are known to change over the solar cycle. There is also recent evidence that the relation between frequency shift of low-degree modes and magnetic flux or other activity indicators differs between the rising and falling phases of the solar cycle, leading to a hysteresis in such diagrams. We consider the influence of the changing large-scale surface distribution of the magnetic flux on low-degree ( l ≤3) p-mode frequencies. To that end, we use time-dependent models of the magnetic flux distribution and study the ensuing frequency shifts of modes with different order and degree as a function of time. The resulting curves are periodic functions (in simple cases just sine curves) shifted in time by different amounts for the different modes. We show how this may easily lead to hysteresis cycles comparable to those observed. Our models suggest that high-latitude fields are necessary to produce a significant difference in hysteresis between odd- and even-degree modes. Only magnetic field distributions within a small parameter range are consistent with the observations by Jiménez-Reyes et al. Observations of p-mode frequency shifts are therefore capable of providing an additional diagnostic of the magnetic field near the solar poles. The magnetic distribution that is consistent with the p-mode observations also appears reasonable compared with direct measurements of the magnetic field.     

Dynamics of the solar magnetic field from SOHO/MDI

The investigation of the dynamics of magnetic fields from small scales to the large scales is very important for the understanding of the nature of solar activity. It is also the base for producing adequate models of the solar cycle with the purpose to predict the level of solar activity. Since December 1995 the Michelson Doppler Imager (MDI) on board of the Solar and Heliospheric Observatory (SOHO) provides full disk magnetograms and synoptic maps which cover the period of solar cycle 23 and the current minimum. In this paper, I review the following important topics with a focus on the dynamics of the solar magnetic field. The synoptic structure of the solar cycle; the birth of the solar cycle (overlapping cycles 23 and 24); the relationship of the photospheric magnetic activity and the EUV solar corona, polar magnetic fields and dynamo theory (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

What do the solar activity indices represent?

Sunspot number, sunspot area, and radio flux at 10.7 cm are the indices which are most frequently used to describe the long‐term solar activity. The data of the daily solar full‐disk magnetograms measured at Mount Wilson Observatory from 19 January 1970 to 31 December 2012 are utilized together with the daily observations of the three indices to probe the relationship of the full‐disk magnetic activity respectively with the indices. Cross correlation analyses of the daily magnetic field measurements at Mount Wilson observatory are taken with the daily observations of the three indices, and the statistical significance of the difference of the obtained correlation coefficients is investigated. The following results are obtained: (1) The sunspot number should be preferred to represent/reflect the full‐disk magnetic activity of the Sun to which the weak magnetic fields (outside of sunspots) mainly contribute, the sunspot area should be recommended to represent the strong magnetic activity of the Sun (in sunspots), and the 10.7 cm radio flux should be preferred to represent the full‐disk magnetic activity of the Sun (both the weak and strong magnetic fields) to which the weak magnetic fields mainly contribute. (2) On the other hand, the most recommendable index that could be used to represent/reflect the weak magnetic activity is the 10.7 cm radio flux, the most recommendable index that could be used to represent the strong magnetic activity is the sunspot area, and the most recommendable index that could be used to represent the full‐disk magnetic activity of the Sun is the 10.7cm radio flux. Additionally, the cycle characteristics of the magnetic field strengths on the solar disk are given. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Studying magneto‐convection by numerical simulation

Following a brief overview of the two main approaches to investigate the interaction between magnetic fields and convective flows near the solar surface layers by numerical simulation, namely idealized model problems and ‘realistic’ large‐eddy simulations, we present first results obtained with a newly developed MHD code. The first example concerns the realistic simulation of the magnetic field dynamics in a solar plage region while the second example demonstrates small‐scale dynamo action in idealized compressible convection.     

The 1.5 meter solar telescope GREGOR

The 1.5 m telescope GREGOR opens a new window to the understanding of solar small‐scale magnetism. The first light instrumentation includes the Gregor Fabry Pérot Interferometer (GFPI), a filter spectro‐polarimeter for the visible wavelength range, the GRating Infrared Spectro‐polarimeter (GRIS) and the Broad‐Band Imager (BBI). The excellent performance of the first two instruments has already been demonstrated at the Vacuum Tower Telescope. GREGOR is Europe’s largest solar telescope and number 3 in the world. Its all‐reflective Gregory design provides a large wavelength coverage from the near UV up to at least 5 microns. The field of view has a diameter of 150″. GREGOR is equipped with a high‐order adaptive optics system, with a subaperture size of 10 cm, and a deformable mirror with 256 actuators. The science goals are focused on, but not limited to, solar magnetism. GREGOR allows us to measure the emergence and disappearance of magnetic flux at the solar surface at spatial scales well below 100 km. Thanks to its spectro‐polarimetric capabilities, GREGOR will measure the interaction between the plasma flows, different kinds of waves, and the magnetic field. This will foster our understanding of the processes that heat the chromosphere and the outer layers of the solar atmosphere. Observations of the surface magnetic field at very small spatial scales will shed light on the variability of the solar brightness (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the solar rotation and activity

The interaction between differential rotation and magnetic fields in the solar convection zone was recently modelled by Brun (2004). One consequence of that model is that the Maxwell stresses can oppose the Reynolds stresses, and thus contribute to the transport of the angular momentum towards the solar poles, leading to a reduced differential rotation. So, when magnetic fields are weaker, a more pronounced differential rotation can be expected, yielding a higher rotation velocity at low latitudes taken on the average. This hypothesis is consistent with the behaviour of the solar rotation during the Maunder minimum. In this work we search for similar signatures of the relationship between the solar activity and rotation determined tracing sunspot groups and coronal bright points. We use the extended Greenwich data set (1878–1981) and a series of full-disc solar images taken at 28.4 nm with the EIT instrument on the SOHO spacecraft (1998–2000). We investigate the dependence of the solar rotation on the solar activity (described by the relative sunspot number) and the interplanetary magnetic field (calculated from the interdiurnal variability index). Possible rotational signatures of two weak solar activity cycles at the beginning of the 20th century (Gleissberg minimum) are discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Night‐time science with large solar telescopes: The magnetic Sun through time

Today the Sun has a regular magnetic cycle driven by a dynamo action. But how did this regular cycle develop? How do basic parameters such as rotation rate, age, and differential rotation affect the generation of magnetic fields? Zeeman Doppler imaging (ZDI) is a technique that uses high‐resolution observations in circularly polarised light to map the surface magnetic topology on stars. Utilising the spectropolarimetric capabilities of future large solar telescopes it will be possible to study the evolution and morphology of the magnetic fields on a range of Sun‐like stars from solar twins through to rapidly‐rotating active young Suns and thus study the solar magnetic dynamo through time. In this article I discuss recent results from ZDI of Sun‐like stars and how we can use night‐time observations from future solar telescopes to solve unanswered questions about the origin and evolution of the Sun's magnetic dynamo (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

What SDO tells us about structure and evolution of coronal bright points

Using magnetograms and coronal images from two instruments on board the Solar Dynamics Observatory (SDO), we study structure and evolution of a limited number of coronal bright points (CBPs). Our results show that the relation between CBPs and their magnetic footpoints is not simple. In some cases, CBP may appear as a bright portion of a larger loop (with clearly identifiable footpoints), and in some cases, an isolated CBP may develop between magnetic poles, which might not be the closest ones to each other or which might not be involved in the magnetic flux cancellation. We suggest that the magnetic connectivity responsible for formation of isolated coronal bright points is governed by the orientation of the large‐scale magnetic field. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Turbulent dynamo near tachocline and reconstruction of azimuthal magnetic field in the solar convection zone

In order to extend the abilities of the αΩ dynamo model to explain the observed regularities and anomalies of the solar magnetic activity, the negative buoyancy phenomenon and the magnetic quenching of the α effect were included in the model, as well as newest helioseismically determined inner rotation of the Sun were used. Magnetic buoyancy constrains the magnitude of toroidal field produced by the Ω effect near the bottom of the solar convection zone (SCZ). Therefore, we examined two “antibuoyancy” effects: i) macroscopic turbulent diamagnetism and ii) magnetic advection caused by vertical inhomogeneity of fluid density in the SCZ, which we call the ∇ρ effect. The Sun's rotation substantially modifies the ∇ρ effect. The reconstruction of the toroidal field was examined assuming the balance between mean‐field magnetic buoyancy, turbulent diamagnetism and the rotationally modified ∇ρ effect. It is shown that at high latitudes antibuoyancy effects block the magnetic fields in the deep layers of the SCZ, and so the most likely these deep‐rooted fields could not become apparent at the surface as sunspots. In the near‐equatorial region, however, the upward ∇ρ effect can facilitate magnetic fields of about 3000 – 4000 G to emerge through the surface at the sunspot belt. Allowance for the radial inhomogeneity of turbulent velocity in derivations of the helicity parameter resulted in a change of sign of the α effect from positive to negative in the northern hemisphere near the bottom of the SCZ. The change of sign is very important for direction of the Parker's dynamo‐waves propagation and for parity of excited magnetic fields. The period of the dynamo‐wave calculated with allowance for the magnetic quenching is about seven years, that agrees by order of magnitude with the observed mean duration of the sunspot cycles. Using the modern helioseismology data to define dynamo‐parameters, we conclude that north‐south asymmetry should exist in the meridional field. At low latitudes in deep layers of the SCZ, the αΩ dynamo excites most efficiency the dipolar mode of the meridional field. Meanwhile, in high‐latitude regions a quadrupolar mode dominates in the meridional field. The obtained configuration of the net meridional field is likely to explain the magnetic anomaly of polar fields (the apparent magnetic “monopole”) observed near the maxima of solar cycles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An interpretation of rapid changes in the magnetic field associated with solar flares

The energy source of a flare is the magnetic field in the corona. A topological model of the magnetic field is used here for interpreting the recently discovered drastic changes in magnetic field associated with solar flares. The following observational results are self‐consistently explained: (1) the transverse field strength decreases at outer part of active regions and increases significantly in their centers; (2) the center‐of‐mass positions of opposite magnetic polarities converge towards the magnetic neutral line just after flares onset; (3) the magnetic flux of active regions decreases steadily during the course of flares. For X‐class flares, almost 50% events show such changes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability of the solar tachocline with magnetic fields

The stability of magnetic fields in the solar tachocline is investigated. We present stability limits for higher azimuthal wave numbers and results on the dependence of the stability on the location of toroidal magnetic fields in latitude. While the dependence of the wave number with the largest growth rate on the magnetic field strength and the magnetic Prandtl number is small, the dependence on the magnetic Reynolds number Rm indicates that lowest azimuthal modes are excited for very high Rm. Upon varying the latitudinal position of the magnetic field belts, we find slightly lower stability limits for high latitudes, and very large stability limits at latitudes below 10°, with little dependence on latitude in between. An increase of the maximum possible field was achieved by adding a poloidal field. The upper limit for the toroidal field which can be stored in the radiative tachocline is then 1000 G, compared to about 100 G for a purely toroidal field as was found in an earlier work. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The rise of twisted magnetic flux tubes

Sunspots are caused by the eruption of magnetic flux tubes through the solar photosphere: current theories of the internal magnetic field of the Sun suggest that such tubes must rise relatively unscathed from the base of the convection zone. In order to understand how the structure of the magnetic field within a buoyant flux tube affects its stability as it rises, we have considered the quasi-two-dimensional rise of isolated magnetic flux tubes through an adiabatically stratified atmosphere. The magnetic field is initially helical; we have investigated a range of initial field configurations, varying the distribution and strength of the twist of the field.     

Anomalies in the evolution of global and large-scale solar magnetic fields as the precursors of several upcoming low solar cycles

Anomalies in the solar magnetic fields of various scales are studied. The polar magnetic field strength is shown to have decreased steadily during the last three solar cycles. This is because the increase in the dipole magnetic moment observed from 1915 to 1976 has changed into a decrease in the last three cycles. At the same time, the medium scale magnetic fields (like those of isolated coronal holes) have been unusually strong in the last cycle. As a result, the tilt of the heliospheric current sheet is still about 30°. The large effective contribution from the medium scale fields to the total energy of the large-scale fields is also confirmed by our calculations of the effective multipolarity index. The aa-index at the cycle minima is correlated with the height of the succeeding maxima. The set of data considered may be indicative of the possible approach of a sequence of low solar cycles.     

The Hβ Chromospheric Magnetic Field in a Quiescent Filament

We observed the line-of-sight magnetic field in the chromosphereand photosphere of a large quiescent filament on the solar disk on September 6, 2001 using the Solar Magnetic Field Telescope in Huairou Solar Observing Station. The chromospheric and photospheric magnetograms together with Hβ filtergrams of the filament were examined. The filament was located on the neutral line of the large scale longitudinal magnetic field in the photosphere and the chromosphere. The lateral feet of the filament were found to be related to magnetic structures with opposite polarities. Two small lateral feet are linked to weak parasitic polarity. There is a negative magnetic structure in the photosphere under a break of the filament. At the location corresponding to the filament in the chromospheric magnetograms, the magnetic strength is found to be about 40-70 Gauss (measuring error about 39 Gauss). The magnetic signal indicates the amplitude and orientation of the internal magnetic field in the filament. We discuss several possible causes which may produce such a measured signal. A twisted magnetic configuration inside the filament is suggested .     

On the Relationship between Flux Emergence and CME Initiation

We present in this paper a statistical study aimed at understanding the possible relationship between surface magnetic field variation and CME initiation. The three samples studied comprise 189 CME-source regions, 46 active regions, and 15 newly emerging active regions. Both large-scale and small-scale variations of longitudinal magnetic fields of these regions are studied. To quantitatively study these variations, three physical quantities are calculated: the average total magnetic flux (ATF), the flux variation rate (FVR), and the normalized flux variation rate (NFVR). Our results show that 60% of the CME-source regions are found to have magnetic flux increases during 12 hours before CME eruptions and 40% are found to have magnetic flux decreases. The NFVR of CME-source regions are found to be statistically identical to those of active regions, averaged over 111 hours, and significantly smaller than those of newly emerging active regions. In addition 91% of the CME-source regions are found to have small-scale flux emergence, whereas small-scale flux emergences are also easily identified in active regions during periods with no solar surface activity. Our study suggests that the relationship between flux emergence and CME eruption is complex and the appearance of flux emergence alone is not unique for the initiation of CME eruption.     

Predicting solar ‘climate’ by assimilating magnetic data into a flux-transport dynamo

Observational and theoretical knowledge about global-scale solar dynamo ingredients have reached the stage that it is possible to calibrate a flux-transport dynamo for the Sun by adjusting only a few tunable parameters. The important ingredients in this class of model are differential rotation (Omega-effect), helical turbulence (alpha-effect), meridional circulation and turbulent diffusion. The meridional circulation works as a conveyor belt and governs the dynamo cycle period. Meridional circulation and magnetic diffusivity together govern the memory of the Sun's past magnetic fields. After describing the physical processes involved in a flux-transport dynamo, we will show that a predictive tool can be built from it to predict mean solar cycle features by assimilating magnetic field data from previous cycles. We will discuss the theoretical and observational connections among various predictors, such as dynamo-generated toroidal flux integral, cross-equatorial flux, polar fields and geomagnetic indices. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Subdiffusive transport in intergranular lanes on the Sun. The Leighton model revisited

In this paper we consider a random motion of magnetic bright points (MBP) associated with magnetic fields at the solar photosphere. The MBP transport in the short time range [0–20 minutes] has a subdiffusive character as the magnetic flux tends to accumulate at sinks of the flow field. Such a behavior can be rigorously described in the framework of a continuous time random walk leading to the fractional Fokker-Planck dynamics. This formalism, applied for the analysis of the solar subdiffusion of magnetic fields, generalizes the Leighton’s model.