New Approach to Study Extended Evolution of Supergranular Flows and Their Advection of Magnetic Elements

Using velocity and magnetogram data extracted from the full-disk field of view of MDI during the 1999 Dynamics Program, we have studied the dynamics of small-scale magnetic elements (3–7 Mm in size) over time periods as long as six days while they are readily visible on the solar disk. By exploiting concurrent time series of magnetograms and Doppler images, we have compared the motion of magnetic flux elements with the supergranular velocity field inferred from the correlation tracking of mesogranular motions. Using this new method (which combines the results from correlation tracking of mesogranules with detailed analysis of simultaneous magnetograms), it is now possible to correlate the motions of the velocity field and magnetic flux for long periods of time and at high temporal resolution. This technique can be utilized to examine the long-term evolution of supergranulation and associated magnetic fields, for it can be applied to data that span far longer time durations than has been possible previously. As tests of its efficacy, we are able to use this method to verify many results of earlier investigations. We confirm that magnetic elements travel at approximately 350 m s ^–1 throughout the duration of their lifetime as they are transported by supergranular outflows. We also find that the positions of the magnetic flux elements coincide with the supergranular network boundaries and adjust as the supergranular network itself evolves over the six days of this data set. Thus we conclude that this new method permits us to study the extended evolution of the supergranular flow field and its advection of magnetic elements. Since small-scale magnetic elements are strongly advected by turbulent convection, their dynamics can give important insight into the properties of the subsurface convection.     

The velocities of intranetwork and network magnetic fields

We analyzed two sequences of quiet-Sun magnetograms obtained on June 4, 1992 and July 28, 1994. Both were observed during excellent seeing conditions such that the weak intranetwork (IN) fields are observed clearly during the entire periods. Using the local correlation tracking technique, we derived the horizontal velocity fields of IN and network magnetic fields. They consist of two components: (1) radial divergence flows which move IN fields from the network interior to the boundaries, and (2) lateral flows which move along the network boundaries and converge toward stronger magnetic elements. Furthermore, we constructed divergence maps based on horizonal velocities, which are a good representation of the vertical velocities of supergranules. For the June 4, 1992 data, the enhanced network area in the field of view has twice the flux density, 10% higher supergranular velocity and 20% larger cell sizes than the quiet, unenhanced network area. Based on the number densities and flow velocities of IN fields derived in this paper and a previous paper (Wang et al., 1995), we estimate that the lower limit of total energy released from the recycling of IN fields is 1.2 × 10²⁸ erg s^–1, which is comparable to the energy required for coronal heating.     

Weak solar fields and their connection to the solar cycle

We discuss the weak solar magnetic fields as studied with the BBSO videomagnetograph (VMG). By weak fields we mean those outside active and unipolar regions. These are found everywhere on the Sun, even where there never have been sunspots. These fields consist of the network and intranetwork (IN) elements. The former move slowly and live a day or more; the latter move rapidly (typically 300 m s^–1) and live only hours. To all levels of sensitivity the flux is concentrated in discrete elements, and the background field has not been detected. The smallest detectable elements at present are 10¹⁶ Mx. The IN elements emerge in bipolar form but appear to flow in a random pattern rather than to the network edges; however, any expanding network element is constrained by geometry to move toward the edges.Because of the great number and short lifetime of the IN elements the total flux emerging in that form exceeds that emerging in the ER by two orders of magnitude and the flux in sunspots, by a factor 10⁴. However, the flux separation is small and there is no contribution to the overall field. In contrast with our earlier results, merging of IN fields is more important than the ephemeral regions as a source of new network elements.The conjecture that all solar magnetic fields are intrinsically strong is discussed and evidence pro and con presented. For the IN fields the evidence suggests they cannot exceed 100 G. For the network fields there is evidence on either side.Reconnection and merging of magnetic fields takes place continually in the conditions studied.Because there is a steady state distribution, the amout of new elements created by merging or emergence must balance that destroyed by reconnection or fission and diffusion of the stronger elements.Solar Cycle Workshop Paper.     

Solar Intranetwork Magnetic Elements: Intrinsically Weak or Strong?

The high spatial resolution observation of a quiet region taken with the Solar Optical Telescope/Spectro-Polarimeter aboard the Hinode spacecraft is analyzed. Based on the Milne?CEddington atmospheric model, the vector magnetic field of the quiet region is derived by fitting the full Stokes profiles of the Fe i 630 nm line pair. We extract intranetwork (IN) region from the quiet region and identify 5058 IN magnetic elements, and study their magnetic properties. As a comparison, the magnetic properties of network (NT) region are also analyzed. The main results are as follows. i)?The IN area displays a predominance of weak (hecto-gauss) field concentration, i.e., 99.8?% of IN area shows the weak field. Moreover, the vector magnetic field exhibits concentration toward horizontal direction. However, for the NT region, we discover the coexistence of weak field and strong (kilo-gauss, kG) field. In the IN and NT regions, the filling factor shows almost the same probability distribution function with the peak at about 0.28. ii)?All IN magnetic elements show field strength less than 1?kG. However, some NT elements display the coexistence of weak field and strong field. Regardless of NT or IN elements, about 20?% of elements lies in the Doppler blue-shift region. Our results imply that not all magnetic elements lie in the down-draft sites.     

The Relation of Ca II K FEATURES TO MAGNETIC FIELD

We studied quantitatively the relation between the intensity of Caii K-line bright features and the intensity of the associated magnetic elements using two data sets obtained at the Big Bear Solar Observatory. Both network and intranetwork (IN) structures were considered. Magnetic field changes always affected the K-line emission; for example, the appearance of new bipoles was always followed by enhanced K-line emission. There is an almost linear correlation between the K-line intensity and the magnetic field strength of the stronger network elements (elements with absolute field strength higher than 11–19.5 G). We identified two classes of intranetwork K-line elements: magnetic and non-magnetic ones. The number of the magnetic K-line IN elements above a 1-sigma threshold was only 5%–10% of the number of the non-magnetic ones. The magnetic K-line IN elements were almost 3 to 4 times brighter compared to the non-magnetic elements. On the other hand, the non-magnetic elements were moving with typical velocities of 35–40 km s^–1 while the velocities of the magnetic K-line elements were of the order of 1 km s^–1.     

On the relationship between magnetic fields and supergranule velocity fields

We studied the size, correlation lifetime and horizontal velocity amplitude of supergranules in regions with different magnetic activity. We found that the supergranule velocity cells have similar scale, correlation lifetime and horizontal velocity amplitude in the unipolar enhanced magnetic network regions and in the mixed-polarity quiet Sun. However, the correlation lifetime of magnetic structure is much longer in the enhanced network. We investigated the velocity pattern of moving magnetic features (MMF) surrounding a decaying sunspot. The velocity of MMFs is consistent with the outflow surrounding the sunspot as measured by Dopplergrams. The velocity cell surrounding the sunspot has a much larger velocity amplitude and a longer lifetime than regular supergranule cells. We found that ephemeral regions (ER) have a slight tendency to emerge at or near boundaries of supergranules. Almost all the magnetic flux disappears at the supergranule boundaries. In most cases, two poles of cancelling features with opposite magnetic polarities approach along the boundaries of supergranules.     

Solar Intranetwork Magnetic Elements: Flux Distributions

The current study aims at quantifying the flux distributions of solar intranetwork (IN) magnetic field based on the data taken in four quiet and two enhanced network areas with the Narrow-band Filter Imager of the Solar Optical Telescope on board the Hinode satellite. More than 14000 IN elements and 3000 NT elements were visually identified. They exhibit a flux distribution function with a peak at 1?–?3×10¹⁶ Mx (maxwell) and 2?–?3×10¹⁷ Mx, respectively. We found that the IN elements contribute approximately to 52 % of the total flux and an average flux density of 12.4 gauss of the quiet region at any given time. By taking the lifetime of IN elements of about 3 min (Zhou et al., Solar Phys. 267, 63, 2010) into account, the IN fields are estimated to have total contributions to the solar magnetic flux up to 3.8×10²⁶ Mx per day. No fundamental distinction can be identified in IN fields between the quiet and enhanced network areas.     

Inductive magnetic footpoint tracking by combining the minimum energy fit with the local correlation tracking and doppler velocity

Time-dependent magneto-hydrodynamic simulations of active region coronal magnetic field require the underlying photospheric magnetic footpoint velocities. The minimum energy fit (MEF) is a new velocity inversion technique to infer the photospheric magnetic footpoint velocities using a pair of vector magnetograms, introduced by Longcope (2004). The MEF selects the smallest overall flow from several consistent flows by minimizing an energy functional. The inferred horizontal and vertical flow fields by the MEF can be further constrained by incorporating the partial or imperfect velocity information obtained through independent means. This hybrid method is expected to give a velocity close to the true magnetic footpoint velocity. Here, we demonstrate that a combination of the MEF, the local correlation tracking (LCT) and Doppler velocity is capable of inferring the velocity close to the photospheric flow.     

Anchor depths of flux elements and depths of flux sources in relation to the two rotation profiles of the sun's surface magnetic fields

It is known for over two decades now that the rotation of the photospheric magnetic fields determined by two different methods of correlation analysis leads to two vastly differing rotation laws - one the differential and the other rigid rotation. Snodgrass and Smith (2001) reexamining this puzzle show that the averaging of the correlation amplitudes can tilt the final profile in favour of rigid rotation whenever the contribution of the rigidly rotating large-scale magnetic structures (the plumes) to the correlation dominates over that of the differentially rotating small-scale and mesoscale features. We present arguments to show that the large-scale unipolar structures in latitudes >40 deg, which also show rigid rotation (Stenflo, 1989), are formed mainly from the intranetwork magnetic elements (abbreviated as IN elements). We then estimate the anchor depths of the various surface magnetic elements as locations of the Sun's internal plasma layers that rotate at the same rate as the flux elements, using the rotation rates of the internal plasma layers given by helioseismology. We infer that the anchor depths of the flux broken off from the decay of sunspot active regions (the small-scale and mesoscale features that constitute the plumes) are located in the shallow layers close to the solar surface. From a similar comparison with helioseismic rotation rates we infer that the rigid rotation of the large-scale unipolar regions in high latitudes could only be coming from plasma layers at a radial distance of about 0.66–0.68 R _⊙ from the Sun's centre. Using Stenflo's (1991) ‘balloon man’ analogy, we interpret these layers as the source of the magnetic flux of the IN elements. If so, the IN flux elements seem to constitute a fundamental component of solar magnetism.     

A study of supergranulation using a Diode Array Magnetograph

The evolution of the velocity and magnetic fields associated with supergranulation has been investigated using the Sacramento Peak Observatory Diode Array Magnetograph. The observations consist of time sequences of simultaneous velocity, magnetic field, and chromospheric network measurements. From these data it appears that the supergranular velocity cells may have lifetimes in excess of the accepted value of 24 hours. Magnetic field motions associated with supergranulation were infrequent and seem to be accompanied by changes in the velocity field. More prevalent were the slow dissipation and diffusion of stationary flux points. Vertical velocity fields of 200 m s–1 appear to be confined to downflows in magnetic field regions at supergranular boundaries. These downflows are only observed using certain absorption lines. Corresponding upflows in the center of supergranules of less than 50 m s^–1 may be present but cannot be confirmed.     

The Polarity Distribution of Intranetwork and Network Fields

We have studied the relative polarity distribution of intranetwork (IN) and network (NW) fields for the first time, using very deep magnetograms obtained at Big Bear Solar Observatory (BBSO) and Huairou Solar Observation Station (HSOS). We found 80 network cells and measured the polarities of intranetwork and network magnetic flux within each cell. The analysis reveals that, in enhanced networks, the signed sum of the IN flux in a cell and the signed sum of the network flux on the boundary of the cell is opposite with 90% probability; in mixed-polarity network, the corresponding signed fluxes are opposite with a probability of 75%. We suggest that:(1) Some of the excess flux within a cell may connect to a weak field component of the IN field that is below the detection limit.(2) Some IN flux, preferentially close to the cell boundary, may be topologically connected to the network field.(3) Some observational effects might produce this anti-correlation.     

Solar Intranetwork Magnetic Elements: Evolution and Lifetime

Based on Hinode SOT/NFI observations with greatly improved spatial and temporal resolution and polarization sensitivity, the lifestory of the intranetwork (IN) magnetic elements are explored in a solar quiet region. A total of 2282 IN elements are followed from their appearance to disappearance and their fluxes measured. By tracing individual IN elements their lifetimes are obtained, which fall in the range from 1 to 20 min. The average lifetime is 2.9±2.0 min. The observed lifetime distribution is well represented by an exponential function. Therefore, the e-fold characteristic lifetime is determined by a least-square fitting to the observations, which is 2.1±0.3 min. The lifetime of IN elements is correlated closely with their flux. The evolution of IN elements is described according to the forms of their birth and disappearance. Based on the lifetime and flux obtained from the new observations, it is estimated that the IN elements have the capacity of heating the corona with a power of 2.1×10²⁸ erg s⁻¹ for the whole Sun.     

Magnetic Field Elements at High Latitude: Lifetime and Rotation Rate

Using one-minute cadence time-series full disk magnetograms taken by the SOHO/MDI, we have studied the magnetic field elements at high latitude (poleward of 65° in latitude). It is found that an average lifetime of the magnetic field elements is 16.5 h during solar minimum, much longer than that during solar maximum (7.3 h). During solar minimum, number of the magnetic field elements with the dominant polarity is about 3 times as that of the opposite polarity elements. Their lifetime is 21.0 h on average, longer than that of the opposite polarity elements (2.3 h). It is also found that the lifetime of the magnetic field elements is related with their size, consistent with the magnetic field elements in the quiet sun at low latitude found by Hagenaar et al. (Astrophys. J. 511:932, 1999). During solar maximum, the polar regions are equally occupied by magnetic field elements with both polarities, and their lifetimes are roughly the same on average. No evidence shows there is a correlation between the lifetime and size of the magnetic field elements. Using an image cross-correlation method, we also measure the solar rotation rate at high latitude, up to 85° in latitude. The rate is ω=2.914−0.342sin ² φ−0.482sin ⁴ φ μrad s⁻¹ sidereal. It agrees with previous studies using the spectroscopic and image cross-correlation methods, and also agrees with the results using the element tracking method when the sample of the tracked magnetic field elements is large. The consistency of those results strongly suggests that this rate at high latitude is reliable.     

The chromospheric magnetograph

By comparison of photoelectric magnetograms with high resolution Hα pictures it is possible to formulate a set of rules by which the magnetic field may be derived directly from the filtergrams. This is possible because of the regularities of magnetic field configurations on the sun and because chromospheric morphology is determined by the magnetic field. Off-band pictures (preferably 0.5 Å red) show a well-defined enhanced chromospheric network, the boundaries of which coincide with the 5 G contour of longitudinal field on the Mt. Wilson magnetograms. The actual fields are presumably more concentrated along the dark structure of the network. Higher fields are marked by filled-in cells. Regions of predominantly transverse fields may be inferred from the absence of normal network structure and the presence of chromospheric fibrils. The quiet chromosphere is recognized by the presence of oscillatory motion and the absence of fibrils or strong network structure. Thus, the chromosphere may be divided into three types of regions: enhanced network, horizontal field, and quiet network. The polarity of the magnetic field may be recognized by plage-antiplage asymmetry; that is, the fact that only following magnetic fields show bright plage in the center of Hα.     

Study of supergranules

Results of a detailed study on supergranule lifetime and velocity fields are presented. We show the correlation between the observed downdraft velocity and the network magnetic flux elements on the quiet sun. After excluding areas with magnetic flux density 25 G, we find that the upper limit of the supergranule vertical speed is 0.1 km s^–1 for both downdraft and updraft, and the r.m.s. speed is 0.03 km s^–1. By observing the evolution of individual supergranules, we find that the average lifetime of supergranules might be 50 hours. We describe different ways of formation and decay of supergranular cells. New cells usually form in an area containing no pre-existing supergranule velocity fields. Cells may disappear in two ways: fragmentation and fading away.     

Solar Intranetwork Magnetic Elements: Bipolar Flux Appearance

This study aims to quantify characteristic features of the bipolar flux appearance of solar intranetwork (IN) magnetic elements. To attack this problem, we use the Narrowband Filter Imager (NFI) magnetograms from the Solar Optical Telescope (SOT) on board Hinode; these data are from quiet and enhanced network areas. Cluster emergence of mixed polarities and IN ephemeral regions (ERs) are the most conspicuous forms of bipolar flux appearance within the network. Each of the clusters is characterized by a few well-developed ERs that are partially or fully coaligned in magnetic axis orientation. On average, the sampled IN ERs have a total maximum unsigned flux of several 10¹⁷ Mx, a separation of 3 – 4 arcsec, and a lifetime of 10 – 15 minutes. The smallest IN ERs have a maximum unsigned flux of several 10¹⁶ Mx, separations of less than 1 arcsec, and lifetimes as short as 5 minutes. Most IN ERs exhibit a rotation of their magnetic axis of more than 10 degrees during flux emergence. Peculiar flux appearance, e.g., bipole shrinkage followed by growth or the reverse, is not unusual. A few examples show repeated shrinkage–growth or growth–shrinkage, like magnetic floats in the dynamic photosphere. The observed bipolar behavior seems to carry rich information on magnetoconvection in the subphotospheric layer.     

Magnetic Energy and Helicity Fluxes at the Photospheric Level

The source of coronal magnetic energy and helicity lies below the surface of the Sun, probably in the convective zone dynamo. Measurements of magnetic and velocity fields can capture the fluxes of both magnetic energy and helicity crossing the photosphere. We point out the ambiguities which can occur when observations are used to compute these fluxes. In particular, we show that these fluxes should be computed only from the horizontal motions deduced by tracking the photospheric cut of magnetic flux tubes. These horizontal motions include the effect of both the emergence and the shearing motions whatever the magnetic configuration complexity is. We finally analyze the observational difficulties involved in deriving such fluxes, in particular the limitations of the correlation tracking methods.     

The smallest observable elements of magnetic flux

We have followed disappearing elements of magnetic flux to determine the smallest elements detectable with the Big Bear videomagnetograph. All the elements followed were disappearing through interaction with elements of opposite polarity. The last remaining visible segment of magnectic field of such features can be used to infer the total magnetic flux of these and other small flux elements visible on the magnetograms.We used both photographic and digital videomagnetograms combining 4096 Zeeman frames made at Big Bear. Fifteen elements were measured near the vanishing point, in a 2–8 hr period. The minimum observable fluxes fall in the range of 1.0 × 10¹⁶ to 1.4 × 10¹⁷ Mx, and the apparent size of these elements is in the range of 1 to 9 square arc sec. The process of disappearance appears to be a smooth one. The smallest detectable elements of network field and ephemeral regions (ER) appear to be the same as the small intra-network (IN) field elements. The present limit is still instrumental; elements smaller than 1 × 10¹⁶ would not have been detected.Visiting Associates from Beijing Observatory, Academia Sinica, Beijing, China.     

On the Influence of a Large-scale Magnetic Field on Turbulent Motions in an Electrically Conducting Medium

This paper deals with turbulent motions in a homogeneous incompressible electrically conducting medium in the presence of a magnetic field which is on average homogeneous and stationary. Using a model in which the turbulence is produced by a stochastic body force, and supposing a weak interaction between motion and magnetic field, a method is developed for calculating the pair correlation tensor of the velocity field from that occuring in a zero magnetic field. As an example, the pair-correlation tensor for a homogeneous stationary turbulence, which is isotropic and mirror-symmetric for zero magnetic field, is determined. With obvious assumptions on the correlation for zero field, two results are obtained. Firstly, the turbulent velocity is reduced by the magnetic field, the component parallel to the field, however, less than those perpendicular to it. Secondly, the correlation length parallel to the field turns out to be greater than the one perpendicular to it, indicating a tendency towards two-dimensional motion. Finally, the possibility of special situations is briefly discussed in which the turbulent velocity is enhanced by the magnetic field, and the anisotropies of the velocity components and the correlation lengths are opposite to those above.     

Flares and velocity fields in AR 5528, AR 5629, and AR 6891

By analysing the relationship between flares and the morphology of velocity and magnetic fields in active regions AR 5528, AR 5629, and AR 6891, we found that initial brightening points at the earliest phase and flare ribbons at the maximum phase are more closely related to the velocity field patterns than to magnetic field patterns. We also found that the velocity patterns related to the flares are different from Evershed flows in the chromosphere. Finally, a model of vortex-induced reconnection has been applied to solar flares and some preliminary results are discussed.