Structure and Evolution of Supergranulation from Local Helioseismology

Supergranulation is visible at the solar surface as a cellular pattern of horizontal outflows. Although it does not show a distinct intensity pattern, it manifests itself indirectly in, for example, the chromospheric network. Previous studies have reported significant differences in the inferred basic parameters of the supergranulation phenomenon. Here we study the structure and temporal evolution of a large sample of supergranules, measured by using local helioseismology and SOHO/MDI data from the year 2000 at solar activity minimum. Local helioseismology with f modes provides maps of the horizontal divergence of the flow velocity at a depth of about 1 Mm. From these divergence maps supergranular cells were identified by using Fourier segmentation procedures in two dimensions and in three dimensions (two spatial dimensions plus time). The maps that we analyzed contain more than 10⁵ supergranular cells and more than 10³ lifetime histories, which makes possible a detailed analysis with high statistical significance. We find that the supergranular cells have a mean diameter of 27.1 Mm. The mean lifetime is estimated to be 1.6 days from the measured distribution of lifetimes (three-dimensional segmentation), with a clear tendency for larger cells to live longer than smaller ones. The pair and mark correlation functions do not show pronounced features on scales larger than the typical cell size, which suggests purely random cell positions. The temporal histories of supergranular cells indicate a smooth evolution from their emergence and growth in the first half of their lives to their decay in the second half of their lives (unlike exploding granules, which reach their maximum size just before they fragment).     

A dependence on solar cycle of the size of the CA+ network

Calcium network diameters are shown to be smaller by 5% at solar maximum than at minimum. The average cell size at minimum is 22 115 ± 99 km. The average size at solar maximum is 20 920 ± 112 km, though individual maxima perform differently from each other depending probably on the dispersed remnant magnetic fields. The change in size of the network is interpreted in terms of changes in the size of the supergranular convective cell.     

Dynamics and Structure of Supergranulation

In this paper we investigate the temporal evolution and geometric properties of solar supergranular features. For this purpose we apply an automatic feature-tracking algorithm to a 6-day time series of 18 near-surface flowmaps containing 548 target objects. Lifetimes are calculated by measuring the time elapsing between the birth and death of each target. Using an exponential fit on the lifetime distribution of single supergranules we derived a mean lifetime of 22 hours. Based on the application of segmentation numerical procedures, we estimated characteristic geometric parameters such as area distributions of supergranular cells. We also derive the relationship between measured lifetime and the area of the supergranules.     

Time-Distance Helioseismology with f Modes as a Method for Measurement of Near-Surface Flows

Travel times measured for the f mode have been used to study flows near the solar surface in conjunction with simultaneous measurements of the magnetic field. Previous flow measurements of Doppler surface rotation, small magnetic feature rotation, supergranular pattern rotation, and surface meridional circulation have been confirmed. In addition, the flow in supergranules due to Coriolis forces has been measured. The spatial and temporal power spectra for a six-day observing sequence have been measured.     

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.     

Dependence of Supergranular Length-Scales on Network Magnetic Fields

In an earlier paper by Raju, Srikanth, and Singh (1998), the average size of chromospheric network cells has been shown to have a dependence on the solar latitude. This was presumed to be due to the reduction of supergranular length-scales by network magnetic field enhancements. It has been found that the network brightness enhancements over solar latitude support this finding. Significant negative correlations have been found between the average cell size and the network brightness enhancements. Since the brightness enhancements are essentially due to the magnetic field concentrations, it is suggested that the network magnetic fields reduce the network cell sizes. We have also obtained the variations of skewness of network brightness distributions over solar latitude, which follow the network field variations. This complements the findings of Caccin et al. (1998) that skewness of brightness distribution follows the solar cycle. The findings suggest that the dependence of supergranular sizes, network brightness, and skewness of network brightness distribution on solar latitude or on the phase of the solar cycle is due to the associated variation of network magnetic fields.     

Large-scale horizontal flows in the solar photosphere IV. On the vertical structure of large-scale horizontal flows

In the recent papers, we introduced a method utilised to measure the flow field. The method is based on the tracking of supergranular structures. We did not precisely know, whether its results represent the flow field in the photosphere or in some subphotospheric layers. In this paper, in combination with helioseismic data, we are able to estimate the depths in the solar convection envelope, where the detected large-scale flow field is well represented by the surface measurements. We got a clear answer to question what kind of structures we track in full-disc Dopplergrams. It seems that in the quiet Sun regions the supergranular structures are tracked, while in the regions with the magnetic field the structures of the magnetic field are dominant. This observation seems obvious, because the nature of Doppler structures is different in the magnetic regions and in the quiet Sun. We show that the large-scale flow detected by our method represents the motion of plasma in layers down to ～10 Mm. The supergranules may therefore be treated as the objects carried by the underlying large-scale velocity field.     

On the development of magnetic fields in active regions

Transverse and longitudinal magnetic field scans together with K₂₃₂ spectroheliograms that cover the early phases of active region formation reveal the following:

1. The new active region forms near the periphery of an old magnetic region. There is evidence that the new region forms an interrelated system with the old magnetic structures on the sun.
2. Noticeable changes in the background magnetic field are seen nearly 3 days prior to the appearance of the sunspot. Magnetic hills of the longitudinal component appear along with bright localized K₂₃₂ emission. Subsequently the K₂₃₂ emission spreads along the boundary of one or two adjacent supergranules and at the time of sunspot formation occupies the whole supergranular cell.
3. Transverse fields with strengths of 100–150 gauss form closed regions in the area of the longitudinal component hills, in the very early phases of the region. These fields stretch and link up the two areas later, at which time the peak transverse fields with values near 250 gauss coincide with the zero line of the longitudinal field. When subsequently the spots appear in the new region, the transverse fields are located about the hills of the longitudinal field. The total field vectors just prior to sunspot formation are pressed to the surface. These are inclined about 45° to the surface after the spot appears. The findings indicate that the magnetic field of a new region emerges from the sub-photospheric layers. It is highly likely that the dynamics of a supergranule influences only the emergence of the magnetic field into the upper layers of the solar atmosphere.

     

Solar Cycle Phase Dependence of Supergranular Fractal Dimension

We study the complexity of supergranular cells using the intensity patterns obtained from the Kodaikanal Solar Observatory during the 23rd solar cycle. Our data consists of visually identified supergranular cells, from which a fractal dimension D for supergranulation is obtained according to the relation P?∝?A ^D/2, where A is the area and P is the perimeter of the supergranular cells. We find a difference in the fractal dimension between active and quiet region cells in the ascending phase, during the peak and in the descending phase which is conjectured to be due to the magnetic activity level.     

Geoeffectiveness of interplanetary shocks during solar minimum (1995–1996) and solar maximum (2000)

Plasma and magnetic field parameter variations across fast forward interplanetary shocks are analyzed during the last solar cycle minimum (1995–1996, 15 shocks), and maximum year 2000 (50 shocks). It was observed that the solar wind velocity and magnetic field strength variation across the shocks were the parameters better correlated with Dst. Superposed epoch analysis centered on the shock showed that, during solar minimum, B _z profiles had a southward, long-duration variation superposed with fluctuations, whereas in solar maximum the B _z profile presented 2 peaks. The first peak occurred 4 hr after the shock, and seems to be associated with the magnetic field disturbed by the shock in the sheath region. The second peak occurred 19 hr after the shock, and seems to be associated with the ejecta fields. The difference in shape and peak in solar maximum (Dst peak =−50 nT, moderate activity) and minimum (Dst peak =−30 nT, weak activity) in average Dst profiles after shocks are, probably, a consequence of the energy injection in the magnetosphere being driven by different interplanetary southward magnetic structures. A statistical distribution of geomagnetic activity levels following interplanetary shocks was also obtained. It was observed that during solar maximum, 36% of interplanetary shocks were followed by intense (Dst≤−100 nT) and 28% by moderate (−50≤Dst <−100 nT) geomagnetic activity. During solar minimum, 13% and 33% of the shocks were followed by intense and moderate geomagnetic activity, respectively. Thus, during solar maximum a higher relative number of interplanetary shocks might be followed by intense geomagnetic activity than during solar minimum. One can extrapolate, for forecasting goals, that during a whole solar cycle a shock has a probability of around 50–60% to be followed by intense/moderate geomagnetic activity.     

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.     

On the variations in the parameters of high-degree acoustic modes with solar cycle

We analyze the pattern of behavior of p-mode wave packets with solar cycle using TON one-day helioseismic data with a high spatial resolution. The time—distance method is used to perform this task. We make an attempt to determine the variations in the travel time of acoustic waves at maximum and minimum solar activity; at maximum activity, this time decreases by 2 s compared to that at minimum activity to a depth of 0.8R_⊙. In addition, the correlation amplitudes of acoustic wave packets from minimum to maximum solar activity were found to decrease by 10–20% for all angular distances.     

Ca II resonance lines in non-homogeneous chromospheres

Profiles of the K line of Caii are computed for a two component solar chromosphere, chosen to simulate with a simple geometry the chromospheric supergranular network. Each component rises above the BCA photosphere, the boundary component representing the bright network with a sharp temperature rise and the cell component representing the darker region with an extended temperature minimum. Theoretical intensity profiles of the Can K core, calculated as weighted averages over the projected areas of the components, are produced for = 0.6 and 0.3. The line source function and the optical depth are obtained from a self-consistent treatment of the steady state and radiative transfer equations, with complete redistribution assumed for scattering in the line. The atomic model consists of two bound levels and a continuum. It is found that a 4600 K minimum can lead to the successful theoretical prediction of the observed limb darkening and 4300 K radiation temperature of the K1 feature only when very large values of turbulent velocity are assumed to exist in the cell region.Publications of the Goethe Link Observatory, Indiana University, No. 95.     

An exploratory two-dimensional study of the coarse structure of network magnetic fields

Magnetograms in lines originating high in the solar atmosphere show, away from disk center, diffuse fringes of reverse polarity on the limbward side and diffuse centerwards extensions of normal polarity wherever the field is strong. Analysis of a Mg b₂ magnetogram reveals that, in active regions (and, hence, wherever the magnetic network is well developed) fields cover associated supergranules completely at heights mostly below 500–600 km (zero height is at ₅₀₀₀ = 1) but possibly up to 700–800 km at great distances (e.g. >10⁴km) from the network. These lie much lower than previously believed, mostly around the solar average temperature minimum. Near plagettes, the low-lying field has been measured out to 6000–7000 km. One consequence is that in active regions and plagettes, the chromosphere-corona transition region probably penetrates below 600 km; another is that potential theory is inapplicable at coronal heights below about 15 000 km.A more accurate analysis requires a specific atmospheric model for magnetic regions. Attention is drawn to the need for studying the consequences for acoustic wave propagation, reflection and dissipation in regions of strong network fields.Visiting Astronomer, Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

The Sun’s Large-Scale Magnetic Field and Its Long-Term Evolution

The Sun’s large-scale external field is formed through the emergence of magnetic flux in active regions and its subsequent dispersal over the solar surface by differential rotation, supergranular convection, and meridional flow. The observed evolution of the polar fields and open flux (or interplanetary field) during recent solar cycles can be reproduced by assuming a supergranular diffusion rate of 500 – 600 km² s⁻¹ and a poleward flow speed of 10 –20 m s⁻¹. The nonaxisymmetric component of the large-scale field decays on the flow timescale of ∼1 yr and must be continually regenerated by new sunspot activity. Stochastic fluctuations in the longitudinal distribution of active regions can produce large peaks in the Sun’s equatorial dipole moment and in the interplanetary field strength during the declining phase of the cycle; by the same token, they can lead to sudden weakenings of the large-scale field near sunspot maximum (Gnevyshev gaps). Flux transport simulations over many solar cycles suggest that the meridional flow speed is correlated with cycle amplitude, with the flow being slower during less active cycles.     

Chromospheric rotation

The dependence of solar rotation on the size of the chromospheric tracers is considered. On the basis of an analysis of Ca ii K₃ daily filtergrams taken in the period 8 May–14 August, 1972, chromospheric features can be divided into two classes according to their size. Features with size falling into the range 24 000–110 000 km can be identified with network elements, while those falling into the range 120 000–300 000 km with active regions, or brightness features of comparable size present at high latitudes. The rotation rate is determined separately for the two families of chromospheric features by means of a cross-correlation technique which directly yields the average daily displacement of tracers due to rotation. Before computing the cross-correlation functions, chromospheric brightness data have been filtered with appropriate bandpass and highpass filters for separating spatial periodicities whose wavelengths fall into the two ranges of size, characteristic of the network pattern and of the activity centers. A difference less than 1% of the rotation rate of the two families of chromospheric features has been found. This is an indication for a substantial corotation at chromospheric levels of different short-lived features, both related to solar activity and controlled by the convective supergranular motions.     

Initial Venus Express magnetic field observations of the magnetic barrier at solar minimum

Although there is no intrinsic magnetic field at Venus, the convected interplanetary magnetic field piles up to form a magnetic barrier in the dayside inner magnetosheath. In analogy to the Earth's magnetosphere, the magnetic barrier acts as an induced magnetosphere on the dayside and hence as the obstacle to the solar wind. It consists of regions near the planet and its wake for which the magnetic pressure dominates all other pressure contributions. The initial survey performed with the Venus Express magnetic field data indicates a well-defined boundary at the top of the magnetic barrier region. It is clearly identified by a sudden drop in magnetosheath wave activity, and an abrupt and pronounced field draping. It marks the outer boundary of the induced magnetosphere at Venus, and we adopt the name “magnetopause” to address it. The magnitude of the draped field in the inner magnetosheath gradually increases and the magnetopause appears to show no signature in the field strength. This is consistent with PVO observations at solar maximum. A preliminary survey of the 2006 magnetic field data confirms the early PVO radio occultation observations that the ionopause stands at ∼250 km altitude across the entire dayside at solar minimum. The altitude of the magnetopause is much lower than at solar maximum, due to the reduced altitude of the ionopause at large solar zenith angles and the magnetization of the ionosphere. The position of the magnetopause at solar minimum is coincident with the ionopause in the subsolar region. This indicates a sinking of the magnetic barrier into the ionosphere. Nevertheless, it appears that the thickness of the magnetic barrier remains the same at both solar minimum and maximum. We have found that the ionosphere is magnetized ∼95% of the time at solar minimum, compared with 15% at solar maximum. For the 5% when the ionosphere is un-magnetized at solar minimum, the ionopause occurs at a higher location typically only seen during solar maximum conditions. These have all occurred during extreme solar conditions.     

The heating of the solar transition region

The temperature curve in the solar chromosphere has puzzled astronomers for a long time.Referring to the structure of supergranular cells,we propose an in ductive heating model.It mainly includes the following three steps.(1) A small-scale dynamo exists in the supergranulation and produces alternating small-scale magnetic fluxes;(2) The supergranular flow distributes these small-scale fluxes according to a regular pattern;(3) A skin effect occurs in the alternating and regularly-distributed magnetic fields.The induced current is concentrated near the transition region and heats it by resistive dissipation.     

太阳宁静区磁场的功率谱分析

利用１９９８年１０月３日北京天文台怀柔太阳观测站的高质量磁图,对给定的太阳宁静区两种不同极性的磁场进行了功率谱分析．结果表明,空间功率谱在超米粒和中米粒尺度具有明显的尖峰结构,这对应于空间周期性分布的网络和内网络磁结构．结果也显示出,超米粒边缘所包含的两种极性场中,其中的一种极性占优势．通过瞬态功率谱的分析,得出网络和内网络场寿命之间的比例关系,这一结果和其他学者得出的超米粒和中米粒对流寿命之间的关系相符．     

Study of calcium-K network evolution from Antarctica

To study the evolution of large convective cells known as supergranules, a solar telescope was set up at Maitri, Indian permanent station in Antarctica region, during the local summer months (December 1989 through March 1990). A continuous sequence of calcium K-line filtergrams for 106 hours spaced at intervals of about 10 min was obtained. The analysis of the data indicates that the most probable lifetime of the calcium-K network is about 22 hours. The lifetime depends upon the size of the cell and is larger for bigger cells. The data also show that cells (of a given size) associated with remnant magnetic field regions live longer than those in the field-free region. This may mean that the magnetic field plays an important role in the confinement of these structures.