Development of structure in pores and sunspots: flows around axisymmetric magnetic flux tubes

Flux elements, pores and sunspots form a family of magnetic features observed at the solar surface. As a first step towards developing a fully non-linear model of the structure of these features and of the dynamics of their interaction with solar convection, we conduct numerical experiments on idealized axisymmetric flux tubes in a compressible convecting atmosphere in cylindrical boxes of radius up to 8 times their depth. We find that the magnetic field strength of the flux tubes is roughly independent of both distance from the centre and the total flux content of the flux tube, but that the angle of inclination from the vertical of the field at the edge of the tube increases with flux content. In all our calculations, fluid motion converges on the flux tube at the surface. The results compare favourably with observations of pores; in contrast, large sunspots lie at the centre of an out-flowing moat cell. We conjecture that there is an inflow hidden beneath the penumbrae of large spots, and that this inflow is responsible for the remarkable longevity of such features.     

The rotation of sunspots in the solar active region NOAA 10930

The rotation of sunspots in the solar active region NOAA 10930 was investigated on the basis of the data on the longitudinal magnetic field and the Doppler velocities using magnetograms and dopplergrams taken with the Solar Optical Telescope installed aboard the HINODE mission. Under the assumption of axial symmetry, areally-mean vertical, radial, and azimuthal components of the magnetic field and velocity vectors were calculated in both sunspots. The plasma in the sunspots rotated in opposite directions: in the leading sunspot, clockwise, and in the following sunspot, counterclockwise. The magnetic flux tubes that formed sunspots of the active region on the solar surface were twisted in one direction, clockwise. Electric currents generated as a result of the rotation and twisting of magnetic flux tubes were also flowing in one direction. Azimuthal components of magnetic and velocity fields of both sunspot umbrae reached their maximum on December 11, 2006. By the start of the X3.4 flare (December 13, 2006), their values became practically equal to zero.     

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.     

The fine structure of the quiet Sun

The observed properties of the small-scale features visible in the quiet photosphere — the granulation, of convective origin, and the network bright points, associated with kG magnetic fields — are described. The known properties of the magnetic flux tubes associated with network bright points are also presented. Empirical models derived from the observations are discussed, as well as a few theoretical models of particular importance for the understanding of the origin of the small-scale features of the quiet photosphere. Finally, the observational evidences showing that the structure of the granulation and of the photospheric network are varying over the solar cycle are reported.     

prior to surface appearance of sunspot flux tubes and magneto-thermal pulsation of the Sun

We found an evidence that the luminosity of the Sun systematically decreased about 20 days before sunspot surface appearance by analysing time-lag correlation of time derivatives of running mean time profiles of the data of the Active Cavity Radiometer Irradiance Monitor (ACRIM) I experiment on board of Solar Maximum Mission (SMM) and of the data of the daily sunspot number. This indicates that sunspot flux tube cooling and heat transport blocking by the flux tubes start to take place in the interior of the solar convection zone well before the sunspot surface appearance. From this finding and our previous finding that the luminosity of the Sun systematically increased and the blocked heat appeared on the surface about 50 days after the sunspot surface appearance, a new view of sunspot formation and dynamics and a new view of the luminosity modulation emerged. (i) Sunspots of a solar cycle are formed from clusters of flux tubes which can be seen in the running mean time profile of the sunspot number as a peak with duration on the order of 100 to 200 days. (ii) Heat flow is blocked by the cluster of sunspot flux tubes inside the convection zone to decrease the luminosity about 20 days before the surface emergence of the sunspot cluster. (iii) The blocked heat appears on the surface about 50 days after the surface emergence of the cluster of sunspot flux tubes to heat up the surface. This appears as a thermal pulse in the running mean time profile of the ACRIM dat in between the peaks of the sunspot running mean time profile. This process of heating the surface makes the temperature gradient less steep and weakens the buoyancy of sunspot flux tubes below the surface. (vi) The radiative cooling of the surface layer by the excess heat release steepens the temperature gradient so that the buoyancy of the sub-surface magnetic flux tubes becomes stronger to cause the next surge of emergence of a cluster of sunspots and other magnetic activities, which creates a peak in the time profile of the sunspot number. We call this peak a magnetic pulse of the Sun and the coupled process of alternating pulsed appearance of heat and sunspots the magneto-thermal pulsation of the Sun.     

High resolution observations of small-scale magnetic elements and interpretation

This contribution deals with the properties of small-scale magnetic elements in plages. Spectro-polarimetric observations, obtained with the highest possible spatial resolution with the German solar telescopes at the Observatorio del Teide on Tenerife, were analysed. We conclude from the spread of line parameters measured in the Stokes I and V profiles of Fe I and Fe II lines that a wide range of magnetic properties is realised in the solar atmosphere. The flow velocities in small-scale magnetic flux tubes, deduced from the zero-crossing of the V profiles at high spatial resolution, show a fluctuation of v _Doppler = 580 m s^-1. This is substantially smaller than the turbulent broadening velocities of v _Doppler = 2 – 3 km s^–1 commonly derived by fitting V profiles from flux tube models to low spatial resolution data, e.g. from a Fourier Transform Spectrometer. Attempts to explain the high resolution I and V profiles by models of hydrostatic flux tubes are discussed. It appears impossible to accomplish agreement between the modeled and observed radiation of lines with strong and weak magnetic sensitivity at the same time. We suggest a scenario in which small-scale magnetic elements possess substructure and are dynamic, with gas flows and magnetic field strengths varying in space and time.     

Small-scale magnetic structures on the Sun

Summary The Sun provides us with a unique astrophysics laboratory for exploring the fundamental processes of interaction between a turbulent, gravitationally stratified plasma and magnetic fields. Although the magnetic structures and their evolution can be observed in considerable detail through the use of the Zeeman effect in photospheric spectral lines, a major obstacle has been that all magnetic structures on the Sun, excluding sunspots, are smaller than what can be resolved by present-day instruments. This has led to the development of indirect, spectral techniques (combinations of two or more polarized spectral lines), which overcome the resolution obstacle and have revealed unexpected properties of the small-scale magnetic structures. Indirect empirical and theoretical estimates of the sizes of the flux elements indicate that they may be within reach of planned new telescopes, and that we are on the verge of a unified understanding of the diverse phenomena of solar and stellar activity.In the present review we describe the observational properties of the smallscale field structures (while indicating the diagnostic methods used), and relate these properties to the theoretical concepts of formation, equilibrium structure, and origin of the surface magnetic flux.On leave from Institute of Astronomy, ETH-Zentrum, CH-8092 Zürich, SwitzerlandThe National Center for Atmospheric Research is sponsored by the National Science Foundation     

The time-delayed solar cycle luminosity modulation by sub-surface magnetic flux tubes

In order to explore the mechanism of the solar cycle luminosity change observed by the Active Cavity Radiometer Irradiance Monitor (ACRIM) I experiment on board of the spacecraft Solar Maximum Mission, we examined running mean time profiles of the daily ACRIM data from the declining phase of solar cycle 21 to the rising phase of solar cycle 22. By comparing them with those of the daily sunspot number, integrated surface magnetic field flux, integrated He I 10830 Å line equivalent width data, and two kinds of data sets of the daily integrated Ca II K line index as indices of the surface magnetic activities, we found (i) that the running mean time profiles of the six independent data sets have several peaks and valleys in common in one solar cycle with time intervals on the order of a few hundreds of days, and (ii) that the peaks and valleys of the ACRIM data profiles followed the peaks and valleys of all the other five indices of the surface activities by 40 to 60 days. This time delay phenomenon suggests (i) that the luminosity modulation was not directly caused by dark and bright features of the surface magnetic activities that the other five indices represent, and (ii) that the missing sunspot radiative flux which was blocked by sub-surface magnetic flux tubes of sunspots and sunspot groups should be re-radiated 40 to 60 days after the surface emergence of the magnetic flux tubes. The concept of the time delay resolves the enigma of the missing sunspot radiative flux and the enigma of the ACRIM experiment that the luminosity dropped when a sunspot or a sunspot group appeared on the surface while the yearly mean of the luminosity decreased and increased along with the decrease and increase of the yearly sunspot number of the 11-year solar cycle. A model of the mechanism to understand these phenomena is presented and its application to other stars is suggested.     

Some characteristics of the development and decay of active region magnetic flux

Mount Wilson synoptic data of both plages and sunspots are examined in an effort to determine in some detail the manner of the appearance and disappearance of the magnetic flux of active regions at the solar surface. Separating regions into leading and following portions by magnetic polarity in the case of the plages and by position in the case of sunspots (for which there is no magnetic information available in this data set), various characteristics of these features are studied, namely their rotation, their relative longitudinal motions, and the east-west inclinations of their magnetic fields. The evidence, taken together, suggests that the magnetic flux loops which comprise a region rise to the surface at the time of its formation, and (at least some of them) sink back below the surface at the time of the decay of the region. It is likely that not all the magnetic flux that arises sinks again below the surface.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

黑子磁场的Stokes光谱反演技术

对太阳大气磁场的可靠测量有助于人们更好地理解太阳活动区内外的许多活动现象,如耀斑的触发和能量释放过程、黑子的形态和黑子大气的平衡、日珥的形成等.由于原子在磁场中的一些能级会产生分裂(Zeeman效应),使对应这些能级的谱线分裂成若干个具有不同偏振特性的分量,因此目前对黑子磁场的测量主要是通过偏振光,即Stokes参量I、Q、U、V的观测来实现的.该文主要介绍近30年来太阳黑子光谱反演的方法以及所取得的成就;同时也对光谱反演和滤光器型的望远镜矢量磁场的测量进行了简单的比较.     

Observations of the horizontal velocity field surrounding sunspots

During the summer and fall of 1971, Doppler spectroheliograms were obtained for several sunspots located near the solar limb. These observations confirm a previous result based on the study of only a few sunspots that in the plage-free photosphere surrounding sunspots the spatially-averaged, horizontal flow tends to be outward at 0.5–1.0 km s^–1 for distances typically 10000–20000 km beyond the outer boundary of the penumbra. It is suggested that these material motions are the means by which small-scale fragments of magnetic flux are carried away from sunspots.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Latitude-time distribution of 3 types of magnetic field activity in the global solar cycle

Large-scale solar activity is considered as a manifestation of 3 types of magnetic field activity which is demonstrated in the 22-year cycle (a) of small-scale flux emergence (polar faculae at latitudes > 40°), (b) of somewhat larger scale flux emergence (sunspots at latitudes < 40°), and (c) of the global magnetic neutral lines at all latitudes. The migration (poleward or equatorward) of the place of birth and/or of the phenomena themselves of these three types of manifestation of magnetic field is discussed. The poleward migration of the global field is explained in a phenomenological way.     

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.     

Nonlinear Force-Free Extrapolation of Emerging Flux with a Global Twist and Serpentine Fine Structures

We study the flux emergence process in NOAA active region 11024, between 29 June and 7 July 2009, by means of multi-wavelength observations and nonlinear force-free extrapolation. The main aim is to extend previous investigations by combining, as much as possible, high spatial resolution observations to test our present understanding of small-scale (undulatory) flux emergence, whilst putting these small-scale events in the context of the global evolution of the active region. The combination of these techniques allows us to follow the whole process, from the first appearance of the bipolar axial field on the east limb, until the buoyancy instability could set in and raise the main body of the twisted flux tube through the photosphere, forming magnetic tongues and signatures of serpentine field, until the simplification of the magnetic structure into a main bipole by the time the active region reaches the west limb. At the crucial time of the main emergence phase high spatial resolution spectropolarimetric measurements of the photospheric field are employed to reconstruct the three-dimensional structure of the nonlinear force-free coronal field, which is then used to test the current understanding of flux emergence processes. In particular, knowledge of the coronal connectivity confirms the identity of the magnetic tongues as seen in their photospheric signatures, and it exemplifies how the twisted flux, which is emerging on small scales in the form of a sea-serpent, is subsequently rearranged by reconnection into the large-scale field of the active region. In this way, the multi-wavelength observations combined with a nonlinear force-free extrapolation provide a coherent picture of the emergence process of small-scale magnetic bipoles, which subsequently reconnect to form a large-scale structure in the corona.     

The generation of magnetic fields in photospheric layers

Recent observations concerning the growth and decay of photospheric magnetic flux present a challenge to the conventional picture of the photosphere as a passive medium through which flux tubes emerge inertly. Rather, they suggest the possibility that interactions between the magnetic flux and the photospheric velocity fields may give rise to changes in the observed surface flux.In this paper the physics of flux changes are reviewed and the various terms in the hydromagnetic equation which give rise to the growth and decay of magnetic flux are examined. Several kinematic models for field changes are examined and it is shown that new flux loops may be generated by suitable oscillatory velocity fields near the boundaries of existing magnetic structures, thus increasing the gross flux through the photosphere. It is suggested that this mechanism may account for the appearance of moving magnetic features (knots of opposite polarities) at the boundaries of decaying sunspots.Other models are discussed and a tentative explanation of the apparently unbalanced growth of opposite polarities is given in terms of a current-sheet model.     

Observations of Unresolved Photospheric Magnetic Fields in Solar Flares Using Fe i and Cr i Lines

The structure of the photospheric magnetic field during solar flares is examined using echelle spectropolarimetric observations. The study is based on several Fe i and Cr i lines observed at locations corresponding to brightest Hα emission during thermal phase of flares. The analysis is performed by comparing magnetic-field values deduced from lines with different magnetic sensitivities, as well as by examining the fine structure of I±V Stokes-profiles’ splitting. It is shown that the field has at least two components, with stronger unresolved flux tubes embedded in weaker ambient field. Based on a two-component magnetic-field model, we compare observed and synthetic line profiles and show that the field strength in small-scale flux tubes is about 2?–?3 kG. Furthermore, we find that the small-scale flux tubes are associated with flare emission, which may have implications for flare phenomenology.     

Velocity Characteristics of Rotating Sunspots

A statistical study is carried out to investigate the detailed relationship between rotating sunspots and the emergence of magnetic flux tubes. This paper presents the velocity characteristics of 132 sunspots in 95 solar active regions. The rotational characteristics of the sunspots are calculated from successive SOHO/MDI magnetograms by applying the Differential Affine Velocity Estimator (DAVE) technique (Schuck, 2006, Astrophys. J. 646, 1358). Among 82 sunspots in active regions exhibiting strong flux emergence, 63 showed rotation with rotational angular velocity larger than 0.4° h⁻¹. Among 50 sunspots in active regions without well-defined flux emergence, 14 showed rotation, and the rotation velocities tend to be slower, compared to those in emerging regions. In addition, we investigated 11 rotating sunspot groups in which both polarities show evidence for co-temporary rotation. In seven of these cases the two polarities co-rotate, while the other four are found to be counter-rotating. Plausible reasons for the observed characteristics of the rotating sunspots are discussed.     

Phase-sensitive Holography of Solar Activity

Phase-correlation statistics comparing acoustic radiation coming out of a particular point on the solar photosphere with acoustic radiation going into it show considerably reduced sound travel times through the subphotospheres of active regions. We have now applied techniques in phase-sensitive seismic holography to data from the Solar Oscillations Investigation – Michelson Doppler Imager (SOI-MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft to obtain high resolution phase-correlation maps of a large, complex active region and the `acoustic moat' which surrounds it. We report the following new results: First, the reduced sound travel-time perturbations in sunspots, acoustic moats, and isolated plages increase approximately in proportion to the logarithm of the surface magnetic flux density, for flux densities above 10 G. This is consistent with an interpretation of the travel-time anomalies, observed with holographic and other local-helioseismic procedures, as caused by acoustic Wilson-like depressions in photospheres of magnetic regions. Second, we find that, compared with isolated plages, the acoustic moats have an additional sound travel-time reduction on the order of 3–5 s which may be explained by a thermal excess due to the blockage of convective transport by the sunspot photosphere. Third, the combined effect of the Wilson depression in plages, acoustic moats, and sunspots may explain the observed variation of global p-mode frequencies with the solar cycle. Fourth, we find that active regions, including sunspots, acoustic moats, and plages, significantly reflect p modes above the acoustic cut-off frequency, where the surface of the quiet Sun acts as a nearly perfect absorber of incident acoustic radiation.     

Latitudinal migration of sunspots based on the ESAI database

The latitudinal migration of sunspots toward the equator,which implies there is propagation of the toroidal magnetic flux wave at the base of the solar convection zone,is one of the crucial observational bases for the solar dynamo to generate a magnetic field by shearing of the pre-existing poloidal magnetic field through differential rotation.The Extended time series of Solar Activity Indices(ESAI)elongated the Greenwich observation record of sunspots by several decades in the past.In this study,ESAI's yearly mean latitude of sunspots in the northern and southern hemispheres during the years 1854 to 1985 is utilized to statistically test whether hemispherical latitudinal migration of sunspots in a solar cycle is linear or nonlinear.It is found that a quadratic function is statistically significantly better at describing hemispherical latitudinal migration of sunspots in a solar cycle than a linear function.In addition,the latitude migration velocity of sunspots in a solar cycle decreases as the cycle progresses,providing a particular constraint for solar dynamo models.Indeed,the butterfly wing pattern with a faster latitudinal migration rate should present stronger solar activity with a shorter cycle period,and it is located at higher latitudinal position,giving evidence to support the Babcock-Leighton dynamo mechanism.     

Three-Dimensional Structure of the Active Region Photosphere as Revealed by High Angular Resolution

Blue continuum images of active regions at ∼ 60° from the center of the solar disk obtained with the new Swedish 1-m Solar Telescope reveal heretofore unreported structure of the magnetized solar atmosphere. Perhaps the most striking aspect of these images is that, at an angular resolution of 0.12″, they show clearly the three-dimensional structure of the photosphere. In particular, the Wilson depression of the dark floors of pores is readily apparent. Conversely, the segmented structure of light bridges running through sunspots and pores reveal that light bridges are raised above the dark surroundings. The geometry of light bridges permits estimates of the height of their central (slightly darker) ridge: typically in the range 200–450 km. These images also clearly show that facular brightenings outside of sunspots and pores occur on the disk-center side of those granules just limbward of intergranular lanes that presumably harbor the associated plage magnetic flux. In many cases the brightening extends 0.5″ or more over those granules. Furthermore, a very thin, darker lane is often found just centerward of the facular brightening. We speculate that this feature is the signature of cool down flows that surround flux tubes in dynamical models. These newly recognized observational aspects of photospheric magnetic fields should provide valuable constraints for MHD models of the magnetized photosphere, and examination of those models as viewed from oblique angles is encouraged.