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.     

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.     

A class of force-free magnetic fields for modeling pre-flare coronal magnetic configurations

Three-dimensional, quasi-static evolutions of coronal magnetic fields driven by photospheric flux emergence are modeled by a class of analytic force-free magnetic fields. Our models relate commonly observed photospheric magnetic phenomena, such as the formation and growth of sunspots, the emergence of an X-type separator, and the collision and merging of sunspots, to the three-dimensional magnetic fields in the corona above. By tracking the evolution in terms of a continuous sequence of force-free states, we show that flux emergence and submergence along magnetic neutral lines in the photosphere are essential processes in all these photospheric phenomena. The analytic solutions we present have a parametric regime within which the magnetic energy attained by an evolving force-free field may be of the order of 10³⁰ ergs to several 10³¹ ergs, depending on the magnetic environment into which an emerging flux intrudes. The commonly used indicators of magnetic shear in magnetogram interpretation are discussed in terms of field connectivity in our models. It is demonstrated that the crossing angle of the photospheric transverse magnetic field with the neutral line may not be a reliable indicator of the magnetic shear in the coronal field above, due to the complexity of three-dimensionality. The poorly understood constraint of magnetic-helicity conservation on the availability of magnetic free energy for a flare is briefly discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Propagation of magnetically guided acoustic shocks in the solar chromosphere

We study the propagation of a train of acoustic shocks guided by diverging magnetic fields through a static model of the solar chromospheric network and transition region. Our results show that for initial flux densities of the order 10⁶ ergs cm^–2 s^–1 in the lower chromosphere, the local efficiency of acoustic transmission into the corona can be much higher than calculated for a plane parallel atmosphere. Thus acoustic energy will tend to be deposited at higher chromospheric levels in diverging magnetic fields, and magnetic guiding may well influence the temperature profile of the network and plages. But the total flux that can be transmitted into the corona along such diverging fields is severely limited, since the magnetic elements occupy a small fractional area of the photosphere, and the transmission efficiency is a rapidly decreasing function of initial acoustic flux density. We conclude that diverging magnetic fields and a varying ratio of specific heats are not likely to allow high frequency shocks to dissipate high enough in a static atmosphere, to contribute significantly to the coronal energy balance. This result strengthens the view that acoustic waves do not heat the solar corona. However, the conclusion may be sensitive to the influence of observed mass motions, such as spicules.     

Properties of flux tubes and the relation with solar irradiance variability

At the solar surface the magnetic field is bundled into discrete elements of concentrated flux, often referred to as magnetic flux tubes, which cover only a small fraction of the solar surface. Flux tubes span a whole spectrum of sizes, ranging from sunspots to features well below the best currently obtainable spatial resolution. Whereas sunspots have been well studied, our knowledge of the true brightness of small-scale magnetic features is hampered by the insufficient spatial resolution of the observations. A better understanding of the thermal and magnetic properties of these small-scale features, however, is crucial for an understanding of (climate-relevant) long-term solar irradiance variations.     

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.     

Surface magnetic fields during the solar activity cycle

We examine magnetic field measurements from Mount Wilson that cover the solar surface over a 13 1/2 year interval, from 1967 to mid-1980. Seen in long-term averages, the sunspot latitudes are characterized by fields of preceding polarity, while the polar fields are built up by a few discrete flows of following polarity fields. These drift speeds average about 10 m s^-1 in latitude - slower early in the cycle and faster later in the cycle - and result from a large-scale poleward displacement of field lines, not diffusion. Weak field plots show essentially the same pattern as the stronger fields, and both data indicate that the large-scale field patterns result only from fields emerging at active region latitudes. The total magnetic flux over the solar surface varies only by a factor of about 3 from minimum to a very strong maximum (1979). Magnetic flux is highly concentrated toward the solar equator; only about 1% of the flux is at the poles. Magnetic flux appears at the solar surface at a rate which is sufficient to create all the flux that is seen at the solar surface within a period of only 10 days. Flux can spread relatively rapidly over the solar surface from outbreaks of activity. This is presumably caused by diffusion. In general, magnetic field lines at the photospheric level are nearly radial.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

The flux-rope-fibre theory of solar magnetic fields

The flux-rope theory of solar magnetic fields is reviewed briefly and, together with the dynamo theory, compared with various observational results. Dynamo and related theories are based on fields controlled by the plasma, and it is shown that such fields cannot account for the strong surface fields or even emerge without becoming tangled. Observations which appear uniquely explicable in terms of powerful (4000 G), helically twisted flux ropes and their many twisted flux fibres (3×10¹⁸ Mx) are listed as follows. (i) Emerging magnetic flux is seen first as pairs of small, closely spaced flux concentrations whose motions suggest magnetic control to provide bipolar regions of extent10⁵ km. The associated system of arch filaments rotates on the disk as would a series of emerging flux fibres twisted into a rope. (ii) Sunspots form by the accretion of pores and magnetic knots of like polarity, sometimes moving along curved paths between stationary elements of opposite polarity. (iii) Fluxes of10²² Mx in large sunspots must have been concentrated to strengths of4000 G before emerging, and also strongly helically twisted to avoid the flute instability. (iv) The trumpet-shaped flux-rope-fibre sunspot model (Figure 6) accounts readily for the phenomena of the moat convection, the sunspot energy deficit, the complex Evershed flow, penumbral filaments (flux 3×10¹⁸ Mx) and temporary light bridges. (v) Asymmetries in sunspot groups (in spot size, lifetime and proper motion) show that the spot fields are extensions of two submerged magnetic structures comprising strong fields. (vi) Sunspots decay by the loss of magnetic knots with strong fields and flux 5×10¹⁸ Mx. These must be isolated flux tubes, twisted to account for their stability. (vii) Flux fibres leaving a spot are prone to the kink instability, thus accounting for their sudden appearance in pairs, the transport of total flux several times that of the spot and net flux equal to that of the spot. (viii) Ephemeral active regions and X-ray bright points are explained similarly without invoking improbably huge quantities of new flux. (ix) Atmospheric structures show a high prevalence of helical twists (force-free fields) and rotary motions on all scales from spicules to large prominences. It is difficult to account for these twists unless they are present in emerging flux. (x) In and above the photosphere the flux fibres (3×10¹⁸ Mx) fray into loose associations of flux threads (3×10¹⁷ Mx) to provide a simple, selfconsistent model of the solar filigree and the chromospheric rosette (bush) with its group of mottles (spicules). (xi) Global patterns of surface and coronal magnetic fields reveal puzzling features such as the migration of large unipolar regions and the freedom from differential rotation of some structures. Submerged flux ropes peeling out of the Sun provide a starting point for explaining these effects. These results provide a strong case for the flux-rope theory against the entrenched dynamo theory, and suggest that more observations should be made of the above ten phenomena. Where possible, simultaneous observations should be made of Zeeman effects and of plasma distributions and velocity field seen in white light and spectral lines.     

Twists and rotations of solar magnetic fields

Evidence is reviewed and extended that most, if not all, solar magnetic fields emerge as highly concentrated (4000 gauss)helically twisted flux ropes, made up of hundreds or thousands of individually twisted flux fibers. The pitch angles of the twists are estimated as 10° in the submerged flux ropes and roughly 1° in the flux fibers, but increase by large factors during and following emergence. The upward transmission of magnetic stresses and motions from the submerged flux-rope sections are major factors in solar physics. The helical twists account for the creation of sunspots and for their stability, fine structure, and mode of decay. They are basic features of the atmospheric structures, from the largest prominences and flare events down to arch filament systems and the smallest network components.     

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.     

An essay on sunspots and solar flares

The presently prevailing theories of sunspots and solar flares rely on the hypothetical presence of magnetic flux tubes beneath the photosphere and the two subsequent hypotheses, their emergence above the photosphere and explosive magnetic reconnection, converting magnetic energy carried by the flux tubes for solar flare energy.In this paper, we pay attention to the fact that there are large-scale magnetic fields which divide the photosphere into positive and negative (line-of-sight) polarity regions and that they are likely to be more fundamental than sunspot fields, as emphasized most recently by McIntosh (1981). A new phenomenological model of the sunspot pair formation is then constructed by considering an amplification process of these largescale fields near their boundaries by shear flows, including localized vortex motions. The amplification results from a dynamo process associated with such vortex flows and the associated convergence flow in the largescale fields.This dynamo process generates also some of the familiar “force-free” fields or the “sheared” magnetic fields in which the magnetic field-aligned currents are essential. Upward field-aligned currents generated by the dynamo process are carried by downward streaming electrons which are expected to be accelerated by an electric potential structure; a similar structure is responsible for accelerating auroral electrons in the magnetosphere. Depending on the magnetic field configuration and the shear flows, the current-carrying electrons precipitate into different geometrical patterns, causing circular flares, umbral flares, two-ribbon flares, etc. Thus, it is suggested that “low temperature flares” are directly driven by the photospheric dynamo process.     

On the appearance of magnetic flux in the solar photosphere

Ideas and models for the appearance of photospheric magnetic structure are confronted with observational data. Some findings are: The magnetic flux emerging in an active region consists of a bundle of flux tubes which were already concentrated before penetrating into the photosphere. A model of a rising bunch of flux tubes joining into a few strands at larger depths describes the coalescence of spots near the leading and following edges of the active region while more flux may surface near the center of the region. There is no observational evidence for appreciable helical twists in the flux bundles.Throughout the region's lifetime the magnetic elements move coherently, the whole magnetic structure rotates faster than the quiet photosphere. In active regions the convective flow at scales larger than the granulation is arrested by the magnetic structure. The long-lived supergranular cells around spots and in the enhanced network in turn determine the decay properties of spots and facular clusters. The modulation of the convective flow by the magnetic structure explains the slow dispersal of faculae.The hierarchy of magnetic elements (sunspots-pores-knots-facular clusters-facular points) may be explained by a set of magnetostatic flux tube models in the top of the convection zone. The underlying assumptions are that the heat flow along the magnetic field is reduced and that there is no heat exchange across the field except by radiation.A tentative model is proposed to account for the amplification, ascent and emergence of intense flux bundles. The assumptions are: (i) the field is concentrated in toroidal bundles by differential rotation, (ii) in the deep convection zone flux bundles are contained by the external turbulent pressure, and (iii) for field strengths up to the equipartition value efficient lateral heat exchange is possible. After a loop has surfaced radiative cooling and subsequent convective downflow reduce the temperature in the top of the flux tubes which then contract to field strengths well above the local equipartition value. There the heat flow is channelled along the field, which creates the conditions for the magnetostatic flux tube models without requiring a blocking of the heat flow somewhere within the tubes.The paper contains a brief review on the evolution of the magnetic field from the emergence in active regions up to the enigmatic disappearance, and a list of topics for further observational investigation.     

The velocity pattern of weak solar magnetic fields

We have measured the proper motion of magnetic elements on the quiet Sun by means of local correlation tracking. The existence of a pattern in the intranetwork (IN) flow is confirmed. This velocity field is consistent with the direct Doppler measurement of the horizontal component of the supergranular velocity field. The IN elements generally move toward the network boundaries. By tracking test points we confirm that the magnetic elements converge in areas corresponding to the magnetic network. But because the IN elements are of random polarity, they cannot contribute to the growth or maintenance of the magnetic network.By calculating the cross correlation between the magnetogram and Dopplergram, we confirm that the supergranule boundaries and the magnetic network are roughly correlated.     

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.     

Interactions between solar neutrinos and solar magnetic fields

We attempt to correlate all of the available solar-neutrino data with the strong magnetic fields these neutrinos encounter in the solar interior along their Earth-bound path. We approximate these fields using the photospheric, magnetograph-measured flux from central latitude bands, time delayed to proxy the magnetic fields in the solar interior. Our strongest evidence for anticorrelation is for magnetic fields within the central ±5° solar-latitude band that have been delayed by 0.85 ± 0.55 yr. Assuming a neutrino-magnetic interaction, this might indicate that interior fields travel to the solar surface in this period of time. As more solar-neutrino flux information is gathered, the question of whether this result arises from a physical process or is merely a statistical fluke should be resolved, providing that new data are obtained spanning additional solar cycles and that correlation studies focus on these same regions of the solar magnetic field.     

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)     

Current sheet models of solar flares

Current sheets have been suggested as the site for flare energy release because they can convert magnetic energy very rapidly into both heat and directed plasma energy. Also they contain electric fields with the potential of accelerating particles to high energies.The basic properties of current sheets are first reviewed. For instance, magnetic flux may be carried into a current sheet and annihilated. An exact solution for such a process in an infinitely long sheet has been found; it describes the annihilation of fields which are inclined at any angle, not just 180°. Moreover, field lines which are expelled from the ends of a current sheet can be described as having been reconnected. The only workable model for fast reconnection in the solar atmosphere, namely Petschek's mechanism, has recently been put on a firm foundation; it gives a reconnection rate which depends on the electrical conductivity but is typically a tenth or a hundredth of the Alfvén speed. A current sheet may be formed when the sources of an initially potential field start to move; a simple analytic technique for finding the position and shape of such a sheet in two dimensions now exists. Finally, a sheet with no transverse magnetic field component is subject to the tearing-mode instability, which rapidly produces a series of loops in the field.The main ways in which current sheets have been used for solar flare models is described. Syrovatskii's mechanism relies on the increase of the electric current density during the formation of a sheet, to a value in excess of the critical value j ^* for the onset of microinstabilities. But Anzer has recently demonstrated that the critical value is most unlikely to be reached during the initial formation process. Sturrock, on the other hand, has advocated the occurrence of the tearing-mode instability in an open streamer-like configuration (which may result from the eruption of a force-free field). But recent observations do not point to that as the relevant configuration. Rather, they suggest that flares are triggered by the emergence of new magnetic flux from below the solar photosphere. This has led Heyvaerts, Priest, and Rust (1976) to propose a new emerging flux model, according to which, as more and more flux emerges, so reconnection occurs, producing some preflare heating. When the current sheet reaches such a height (around the transition region) that its current density exceeds j ^*, then the impulsive phase of the flare is triggered. The main phase is caused by an enhanced level of magnetic energy conversion in a turbulent current sheet. The type of flare depends on the magnetic environment in which the emerging flux finds itself. A surge flare results if the flux appears near a strong unipolar region such as a simple sunspot, whereas a two ribbon flare may be produced by flux emergence near an active region filament, in which case the main phase energy is released from the field that surrounds the filament.     

Solar Magnetic Carpet I: Simulation of Synthetic Magnetograms

This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar magnetic fields. In the model, the basic evolution of the magnetic elements is governed by a supergranular flow profile. In addition, magnetic elements may evolve through the processes of emergence, cancellation, coalescence and fragmentation. Model parameters for the emergence of bipoles are based upon the results of observational studies. Using this model, several simulations are considered, where the range of flux with which bipoles may emerge is varied. In all cases the model quickly reaches a steady state where the rates of emergence and cancellation balance. Analysis of the resulting magnetic field shows that we reproduce observed quantities such as the flux distribution, mean field, cancellation rates, photospheric recycle time and a magnetic network. As expected, the simulation matches observations more closely when a larger, and consequently more realistic, range of emerging flux values is allowed (4×10¹⁶ – 10¹⁹ Mx). The model best reproduces the current observed properties of the magnetic carpet when we take the minimum absolute flux for emerging bipoles to be 4×10¹⁶ Mx. In future, this 2D model will be used as an evolving photospheric boundary condition for 3D non-potential modeling.     

Flows around sunspots and pores

We report on three sequences of high-resolution white-light and magnetogram observations obtained in the summer of 1989. The duration of sub-arcsecond seeing was three to four hours on each day. Study of the white-light and magnetogram data yields the following results:

1. For all but one of the sunspots we have observed, both dark fibrils and bright grains in the inner part of the penumbra of sunspots move toward the umbra with a speed of about 0.5 km s^-1. In the outer part of the penumbra, movement is away from the umbra. The one exception is a newly formed spot, which has inflow only in its penumbra.
2. Granular flows converge toward almost every pore, even before its formation. Pores are observed to form by the concentration of magnetic flux already existing in the photosphere. The pores (or small sunspots), in turn, then move and concentrate to form bigger sunspot.
3. We followed an emerging flux region (EFR) from 29 to 31 July, 1989 that was composed of a large number of bipoles with magnetic polarities mixed over a large area in the first day of its birth. As time went on, polarities sorted out: the leading polarity elements moved in one direction; the following, the opposite. During the process a large number of cancellations occurred, with some sub-flares and surges observed simultaneously. After about 24 hours, the positive and negative fluxes were essentially separated.
4. We find two kinds of photospheric dark alignments in the region of new flux emergence: (a) alignments connecting two poles of opposite magnetic polarity form the tops of rising flux tubes; (b) alignments corresponding to the magnetic flux of one polarity, which we call elongated pores.