Differential rotation and the structure and energy content of coronal magnetic fields

It is argued that differential rotation of the photospheric magnetic fields will induce currents in the corona. The work done against surface magnetic stresses will increase the energy content of the coronal magnetic field. The electrical conductivities are high and the foot points of field lines move with the differential rotation. The force-free field equations are solved with this constraint to obtain a minimum estimate of the energy increase for a quadrupole field. During a solar rotation the magnetic energy increases by 25%. Local release of this energy in the corona would have a significant effect. The expansion of field lines as a result of the differential rotation should increase the amount of flux and the field strength in the solar wind region.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

High resolution mapping of the magnetic field of the solar corona

High resolution KPNO magnetograph measurements of the line-of-sight component of the photospheric magnetic field over the entire dynamic range from 0 to 4000 gauss are used as the basic data for a new analysis of the photospheric and coronal magnetic field distributions. The daily magnetograph measurements collected over a solar rotation are averaged onto a 180 × 360 synoptic grid of equal-area elements. With the assumption that there are no electric currents above the photospheric level of measurement, a unique solution is determined for the global solar magnetic field. Because the solution is in terms of an expansion in spherical harmonics to principal index n = 90, the global photospheric magnetic energy distribution can be analyzed in terms of contributions of different scale-size and geometric pattern. This latter procedure is of value (1) in guiding solar dynamo theories, (2) in monitoring the persistence of the photospheric field pattern and its components, (3) in comparing synoptic magnetic data of different observatories, and (4) in estimating data quality. Different types of maps for the coronal magnetic field are constructed (1) to show the strong field at different resolutions, (2) to trace the field lines which open into interplanetary space and to locate their photospheric origins, and (3) to map in detail coronal regions above (specified) limited photospheric areas.The National Center for Atmospheric Research is sponsored by the National Science foundation.Kitt Peak National Observatory is operated by the Association of Universities for Research in Astronomy, Inc. Under contract with the National Science Foundation.     

The evolution of a coronal streamer and the photospheric magnetic field

A large equatorial coronal streamer observed in the outer corona (3R ) grew in brightness and size during successive limb passages between October 6, 1973 and January 10, 1974 (solar rotations 1606–1611). Unlike previous studies of streamers and their photospheric associations, no definite surface feature could be identified in the present case. This suggests that the streamer is associated with the large scale photospheric magnetic field. Comparison of the streamer growth with observed underlying photospheric magnetic flux changes indicated that as the streamer increased in brightness, areal extent, and density, the photospheric magnetic flux decreased. Three possible explanations for the streamer's growth are presented; the conceptually simplest being that the decrease in photospheric field results in an opening of the flux tubes under the streamer which permits an increased mass flux through the streamer.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Frequency of coronal transients and solar activity

The High Altitude Observatory's white light coronagraph aboard Skylab observed some 110 coronal transients - rapid changes in appearance of the corona - during its 227 days of operation. The longitudes of the origins of these transients were not distributed uniformly around the solar surface (51 of the 100 events observed in seven solar rotations arose from a single quadrant of longitude). Further, the frequency of transient production from each segment of the solar surface was well correlated with the sunspot number and Ca ii plage (area × brightness) index in the segment, rotation by rotation. This correlation implies that transients occur more often above strong photospheric and chromospheric magnetic fields, that is, in regions where the coronal magnetic field is stronger and, perhaps, more variable. This pattern of occurrence is consistent with our belief that the forces propelling transient material outward are, primarily, magnetic. A quantitative relation between transient production from an area and the Zürich sunspot number appropriate to that area is derived, and we speculate that the relation is independent of phase in the solar activity cycle. If true, the Sun may give rise to as many as 100 white light coronal transients per month at solar cycle maximum.Currently at Los Alamos Scientific Laboratory, Los Alamos, N.M., U.S.A.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Magnetic Activity Associated With Radio Noise Storms

As it crossed the solar disk in May and June 1998, AR 8227 was tracked by TRACE, Yohkoh, SOHO, and many ground-based observatories. We have studied how the evolution of the magnetic field resulted in changes in activity in the corona. In particular, we examine how the evolving field may have led to the acceleration of electrons which emit noise storms observed by the Nançay Radio Heliograph between 30 May and 1 June 1998, in the absence of any flare. The magnetic changes were related to moving magnetic features (MMFs) in the vicinity of the leading spot and are related to the decay of this spot. Within the limits of the instrumental capabilities, the location in time and space of the radio emissions followed the changes observed in the photospheric magnetograms. We have extrapolated the photospheric magnetic field with a linear force-free approximation and find that the active region magnetic field was very close to being potential. These computations show a complex magnetic topology associated to the MMFs. The observed photospheric evolution is expected to drive magnetic reconnection in such complex magnetic topology. We therefore propose that the MMFs are at the origin of the observed metric noise-storms.     

Solar rotation as determined from OSO-4 EUV spectroheliograms

Spectroheliograms obtained in extreme ultraviolet (EUV) lines and the Lyman continuum are used to determine the rotation rate of the solar chromosphere, transition region, and corona. A cross-correlation analysis of the observations indicates the presence of differential rotation through the chromosphere and transition region. The rotation rate does not vary with height. The average sidereal rotation rate is given by (deg day^–1) = 13.46 - 2.99 sin² B where B is the solar latitude. This rate agrees with spectroscopic determinations of the photospheric rotation rate, but is slower by 1 deg day^–1) = 13.46 - 2.99 sin² than rates determined from the apparent motion of photospheric magnetic fields and from the brightest points of active regions observed in the EUV. The corona does not clearly show differential rotation as do the chromosphere and transition region.     

Differential rotation of the photospheric magnetic field

The differential rotation of the large-scale photospheric magnetic field has been investigated with an autocorrelation technique using synoptic charts of the photospheric field during the interval 1959–66. Near the equator the rotation period of the field is nearly the same as the rotation rate of long-lived sunspots studied by Newton and Nunn. Away from the equatorial zone the field has a significantly shorter rotation period than the spots. Over the entire range of latitudes investigated the average rotation period of the photospheric magnetic field was about 1 1/4 days less than the average rotation period of the material observed with Doppler shifts by Livingston and by Howard and Harvey. Near the equator the photospheric field results agree with the results obtained from recurrent sunspots, while above 15° the photospheric field rotation rates agree with the rotation rates of the K corona and the filaments.     

Coronal Flux Recycling Times

High-cadence, high-resolution magnetograms have shown that the quiet-Sun photosphere is very dynamic in nature. It is comprised of discrete magnetic fragments which are characterized by four key processes – emergence, coalescence, fragmentation and cancellation. All of this will have consequences for the magnetic field in the corona above. The aim of this study is to gauge the effect of the behavior of the photospheric flux fragments on the quiet-Sun corona. By considering a sequence of observed magnetograms, photospheric flux fragments are represented by a series of point sources and the resulting potential field arising from them is examined. It is found that the quiet-Sun coronal flux is generally recycled on time scales considerably shorter than the corresponding time scales for the recycling of photospheric flux. From the motions of photospheric fragments alone, a recycling time of coronal flux of around 3 h is found. However, it is found that the amount of reconnection driven by the motions of fragments is comparable to the amount driven by emergence and cancellation of flux, resulting in a net flux replacement time for the corona of only 1.4 h. The technique used in this study was briefly presented in a short research letter (R. M. Close et al., Astrophys. J., 612, L81, 2004); here the technique is discussed in far greater depth. Furthermore, an estimate is made of the currents required to flow along separator field lines in order to sustain the observed heating rates (assuming separator reconnection is the key mechanism by which the solar corona is heated).     

Magnetic Helicity Injection in Solar Active Regions

We present the evolution of magnetic field and its relationship with mag- netic(current)helicity in solar active regions from a series of photospheric vector magnetograms obtained by Huairou Solar Observing Station,longitudinal magne- tograms by MDI of SOHO and white light images of TRACE.The photospheric current helicity density is a quantity reflecting the local twisted magnetic field and is related to the remaining magnetic helicity in the photosphere,even if the mean current helicity density brings the general chiral property in a layer of solar active regions.As new magnetic flux emerges in active regions,changes of photospheric cur- rent helicity density with the injection of magnetic helicity into the corona from the subatmosphere can be detected,including changes in sign caused by the injection of magnetic helicity of opposite sign.Because the injection rate of magnetic helicity and photospheric current helicity density have different means in the solar atmosphere, the injected magnetic helicity is probably not proportional to the current helicity den- sity remaining in the photosphere.The evidence is that rotation of sunspots does not synchronize exactly with the twist of photospheric transverse magnetic field in some active regions(such as,delta active regions).They represent different aspects of mag- netic chirality.A combined analysis of the observational magnetic helicity parameters actually provides a relative complete picture of magnetic helicity and its transfer in the solar atmosphere.     

Correlation of photospheric magnetic field strength with coronal brightness on 7 March, 1970

The common observation that where photospheric magnetic fields are strong, the overlying corona is bright is examined quantitatively. White light coronal brightness is employed because it is independent of coronal temperature and is directly related to coronal electron density. Brightness data for the inner corona on 7 March, 1970, taken from isodensitometer traces having a resolution of 10 arc sec, are utilized. The data were obtained from photographs which exhibit distinct chromospheric features 5 arc sec or smaller. These data are quantitatively compared, using cross correlation and scatter plot techniques, with the corresponding photospheric magnetic field data provided by Kitt Peak National Observatory. Cross correlation coefficients are computed between latitudes ±55° at specified heights. In general, a statistically significant positive correlation is found. The correlation decreases with height in the corona. However, a range of values in several parameters remains to be investigated so the physical significance of the presently observed correlation is not yet entirely clear. We expect that refinement of our input parameters will produce a more sensitive correlation and lead to an expression for the relationship of electron density to photospheric magnetic field strength.NAS/NRC Research Associate.     

Culgoora radio and skylab euv observations of emerging magnetic flux in the lower corona

Detailed comparisons of Culgoora 160 MHz radioheliograms of solar noise storms and Skylab EUV spectroheliograms of coronal loop structures are presented. It is concluded that: (1) there is a close association between changes in large-scale magnetic fields in the corona and the onset or cessation of noise storms; (2) these coronal changes result from the emergence of new magnetic flux at the photospheric level; (3) although new magnetic flux at the photospheric level is often accompanied by an increase in flare activity the latter is not directly responsible for noise storm activity; rather the new magnetic flux diffuses slowly outwards through the corona at rates 1–2 km s^–1 and produces noise storms at 160 MHz 1–2 days later; (4) the coronal density above or in large-scale EUV loop systems is sufficiently dense to account for noise storm emission at the fundamental plasma frequency; (5) the scatter in noise storm positions can be accounted for by the appearance and disappearance of individual loops in a system.     

The Importance of Photospheric Intense Flux Tubes for Coronal Heating

Dissipation of magnetic energy in the corona requires the creation of very fine scale-lengths because of the high magnetic Reynolds number of the plasma. The formation of current sheets is a natural possible solution to this problem and it is now known that a magnetic field that is stressed by continous photospheric motions through a series of equilibria can easily form such sheets. Furthermore, in a large class of 3D magnetic fields without null points there are locations, called quasi-separatrix layers (QSLs), where the field-line linkage changes drastically. They are the relevant generalisation of normal separatrices to configurations without nulls: along them concentrated electric currents are formed by smooth boundary motions and 3D magnetic reconnection takes place when the layers are thin enough. With a homogenous normal magnetic field component at the boundaries, the existence of thin enough QSL to dissipate magnetic energy rapidly requires that the field is formed by flux tubes that are twisted by a few turns. However, the photospheric field is not homogeneous but is fragmented into a large number of thin flux tubes. We show that such thin tubes imply the presence of a large number of very thin QSLs in the corona. The main parameter on which their presence depends is the ratio between the magnetic flux located outside the flux tubes to the flux inside. The thickness of the QSLs is approximately given by the distance between neighbouring flux tubes multiplied by the ratio of fluxes to a power between two and three (depending on the density of flux tubes). Because most of the photospheric magnetic flux is confined in thin flux tubes, very thin QSLs are present in the corona with a thickness much smaller than the flux tube size. We suggest that a turbulent resistivity is triggered in a QSL, which then rapidly evolves into a dynamic current sheet that releases energy by fast reconnection at a rate that we estimate to be sufficient to heat the corona. We conclude that the fragmentation of the photospheric magnetic field stimulates the dissipation of magnetic energy in the corona.     

Preliminary observations of coronal magnetic fields before and after solar proton events

Maps of the coronal magnetic field before and after several proton flares were examined. There are indications that large scale changes occur in both the photospheric and coronal magnetic field as a consequence of large proton flares.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.     

Evolution of photospheric magnetic field patterns during skylab

The evolution of the photospheric magnetic field pattern over eleven solar rotations preceding a minimum of the activity cycle is shown to be characterized by abrupt changes of the dominant geometrical patterns of the field. These changes are associated with the onset and end of a sudden increase in the calculated total energy content of the field, which is otherwise decreasing through the period. The calculated geometrical rearrangements correspond in time to observed restructurings of the corona, the interplanetary field, and the solar rotation pattern.     

Evolution of the Fine Structure of Magnetic Fields in the Quiet Sun: Observations from Sunrise/IMaX and Extrapolations

Observations with the balloon-borne Sunrise/Imaging Magnetograph eXperiment (IMaX) provide high spatial resolution (roughly 100 km at disk center) measurements of the magnetic field in the photosphere of the quiet Sun. To investigate the magnetic structure of the chromosphere and corona, we extrapolate these photospheric measurements into the upper solar atmosphere and analyze a 22-minute long time series with a cadence of 33 seconds. Using the extrapolated magnetic-field lines as tracer, we investigate temporal evolution of the magnetic connectivity in the quiet Sun’s atmosphere. The majority of magnetic loops are asymmetric in the sense that the photospheric field strength at the loop foot points is very different. We find that the magnetic connectivity of the loops changes rapidly with a typical connection recycling time of about 3±1 minutes in the upper solar atmosphere and 12±4 minutes in the photosphere. This is considerably shorter than previously found. Nonetheless, our estimate of the energy released by the associated magnetic-reconnection processes is not likely to be the sole source for heating the chromosphere and corona in the quiet Sun.     

Computation of solar magnetic fields from photospheric observations

The observational difficulties of obtaining the magnetic field distribution in the chromosphere and corona of the Sun has led to methods of extending photospheric magnetic measurements into the solar atmosphere by mathematical procedures. A new approach to this problem presented here is that a constant alpha force-free field can be uniquely determined from the tangential components of the measured photospheric flux alone. The vector magnetographs now provide measurements of both the solar photospheric tangential and the longitudinal magnetic field. This paper presents derivations for the computation of the solar magnetic field from these type of measurements. The fields considered are assumed to be a constant alpha force-free fields or equivalent, producing vanishing Lorentz forces. Consequently, magnetic field lines and currents are related by a constant and hence show an identical distribution. The magnetic field above simple solar regions are described from the solution of the field equations.     

Center-to-limb profiles of the aluminum autoionization lines in the solar spectrum

The rotation of the solar corona has been studied using recurrence properties of the green coronal line (5303 Å) for the interval 1947–1970. Short-lived coronal activity is found to show the same differential rotation as short-lived photospheric magnetic field features. Long-lived recurrences show rigid rotation in the latitude interval ±57°.5. It is proposed that at least part of the variability of rotational properties of the solar atmosphere may be understood as a consequence of coexistence of differential and rigid solar rotation.On leave from Torino University, Italy, as an ESRO-NASA Fellow.     

Differential Rotation of the Solar Corona from Magnetic Field Data

A method for investigating the differential rotation of the solar corona using the coronal magnetic field as a tracer is proposed. The magnetic field is calculated in the potential approximation from observational data at the photospheric level. The time interval from June 24, 1976, to December 31, 2004, is considered. The magnetic field has been calculated for all latitudes from the equator to ±75? with a 5? step at distances from the base of the corona 1.0 R_⊙ to 2.45 R_⊙ near the source surface. The coronal rotation periods at 14 distances from the solar center have been determined by the method of periodogram analysis. The coronal rotation is shown to become progressively less differential with increasing heliocentric distance; it does not become rigid even near the source surface. The change in the coronal rotation periods with time is considered. At the cycleminimumthe rotation has been found to bemost differential, especially at small distances from the solar center. The change in coronal rotation with time is consistent with the tilt of the solar magnetic equator. The results from the magnetic field are compared with those obtained from the brightness of the green coronal Fe XIV 530.3 nm line. The consistency between these results confirms the reliability of the proposed method for studying the coronal rotation. Studying the rotation of the coronal magnetic field gives hope for the possibility of using this method to diagnose the differential rotation in subphotospheric layers.     

On the reality of potential magnetic fields in the solar corona

Global magnetic field calculations, using potential field theory, are performed for Carrington rotations 1601–1610 during the Skylab period. The purpose of these computations is to quantitatively test the spatial correspondence between calculated open and closed field distributions in the solar corona with observed brightness structures. The two types of observed structures chosen for this study are coronal holes representing open geometries and theK-coronal brightness distribution which presumably outlines the closed field regions in the corona. The magnetic field calculations were made using the Adams-Pneuman fixed-mesh potential field code based upon line-of-sight photospheric field data from the KPNO 40-channel magnetograph. Coronal hole data is obtained from AS&E's soft X-ray experiment and NRL's Heii observations and theK-coronal brightness distributions are from HAO'sK-coronameter experiment at Mauna Loa, Hawaii.The comparison between computed open field line locations and coronal holes shows a generally good correspondence in spatial location on the Sun. However, the areas occupied by the open field seem to be somewhat smaller than the corresponding areas of X-ray holes. Possible explanations for this discrepancy are discussed. It is noted that the locations of open field lines and coronal holes coincide with the locations ofmaximum field strength in the higher corona with the closed regions consisting of relatively weaker fields.The general correspondence between bright regions in theK-corona and computed closed field regions is also good with the computed neutral lines lying at the top of the closed loops following the same general warped path around the Sun as the maxima in the brightness. One curious feature emerging from this comparison is that the neutral lines at a given longitude tend systematically to lie somewhat closer to the poles than the brightness maxima for all rotations considered. This discrepancy in latitude increases as the poles are approached. Three possible explanations for this tendency are given: perspective effects in theK -coronal observations, MHD effects due electric currents not accounted for in the analysis, and reported photospheric field strengths near the poles which are too low. To test this latter hypothesis, we artificially increased the line-of-sight photospheric field strengths above 70° latitude as an input to the magnetic field calculations. We found that, as the polar fields were increased, the discrepancy correspondingly decreased. The best agreement between neutral line locations and brightness maxima is obtained for a polar field of about 30 G.The National Center for Atmospheric Research is sponsored by the National Science Foundation.