Magnetic diffusion and flare energy buildup

Photospheric motion shears or twists solar magnetic fields to increase magnetic energy in the corona, because this process may change a current-free state of a coronal field to force-free states which carry electric current. This paper analyzes both linear and nonlinear two-dimensional force-free magnetic field models and derives relations of magnetic energy buildup with photospheric velocity field. When realistic data of solar magnetic field (B ₀ 10³ G) and photospheric velocity field (v _max 1 km s^–1) are used, it is found that 3–4 hours are needed to create an amount of free magnetic energy which is of the order of the current-free field energy. Furthermore, the paper studies situations in which finite magnetic diffusivities in photospheric plasma are introduced. The shearing motion increases coronal magnetic energy, while the photospheric diffusion reduces the energy. The variation of magnetic energy in the coronal region, then, depends on which process dominates.     

Connections Between the White-Light Eclipse Corona and Magnetic Fields over the Solar Cycle

Observations of ten solar eclipses (1973–1999) enabled us to reveal and describe mutual relations between the white-light corona structures (e.g., global coronal forms and most conspicuous coronal features, such as helmet streamers and coronal holes) and the coronal magnetic field strength and topology. The magnetic field strength and topology were extrapolated from the photospheric data under the current-free assumption. In spite of this simplification the found correspondence between the white-light corona structure and magnetic field organization strongly suggests a governing role of the field in the appearance and evolution of local and global structures. Our analysis shows that the study of white-light corona structures over a long period of time can provide valuable information on the magnetic field cyclic variations. This is particularly important for the epoch when the corresponding measurements of the photospheric magnetic field are absent.     

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.     

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.     

5303 Å Coronal Irradiance and Its Relation to the Photospheric Magnetic Activity

The association of Lomnický tít data of coronal green line irradiance (CI) to photospheric magnetic activity is studied for the years 1975–1994 using the Carrington rotation averaged photospheric magnetic flux data. It is found that the CI correlates well with photospheric magnetic flux of active regions and the total disk-integrated magnetic flux on longer time scales (11-year solar cycle) and fails (about 50% of the time) to show a strong dependence on shorter time scales. A comparison of the association of CI and of the 10.7 cm radio flux with the photospheric magnetic flux data indicated that the CI might basically represent the background coronal irradiance.     

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.     

Magnetic Field as a Tracer for Studying the Differential Rotation of the Solar Corona

The characteristics of differential rotation of the solar corona for the period 1976?–?2004 were studied as a function of the distance from the center of the Sun. For this study, we developed a method using the coronal magnetic field as a tracer. The field in a spherical layer from the base of the corona up to the source surface was determined from photospheric measurements. Calculations were performed for 14 heliocentric distances from the base of the corona up to 2.45 \(R_{\odot }\) solar radii (the vicinity of the source surface) and from the equator to \(\pm 75^{\circ }\) of latitude at \(5^{\circ }\) steps. For each day, we calculated three spherical components, which were then used to obtain the field strength. The coronal rotation periods were determined by the periodogram method. The rotation periods were calculated for all distances and latitudes under consideration. The results of these calculations make it possible to study the distribution of the rotation periods in the corona depending on distance, time, and phase of the cycle. The variations in the coronal differential rotation during the time interval 1976?–?2004 were as follows: the gradient of differential rotation decreased with the increase of heliocentric distance; the rotation remaining differential even in the vicinity of the source surface. The highest rotation rates (shortest rotation periods) were recorded at the cycle minimum at small heliospheric distances, i.e. small heights in the corona. The lowest rotation rate was observed at the middle of the ascending branch at large distances. At the minimum of the cycle, the differential rotation is most clearly pronounced, especially at small heliocentric distances. As the distance increases, the differential rotation gradient decreases in all phases. The results based on magnetic data and on the brightness of the coronal green line 530.3 nm Fe xiv used earlier show a satisfactory agreement. Since the rotation of the magnetic field at the corresponding heights in the corona is probably determined by the conditions in the field generation region, an opportunity arises to use this method for diagnostics of differential rotation in the subphotospheric layers.     

The coronal and interplanetary magnetic fields at the time of the solar eclipse of 7 March, 1970

The magnetic field in the outer corona and in interplanetary space has been calculated from the photospheric magnetic fields measured around the time of the 7 March, 1970 eclipse. The field-line maps are compared with eclipse photographs showing coronal structures out to about 12 r . The projected field lines as well as the observed streamers appear straight. This is caused by the rapid expansion of the outer corona and is not an indication of corotation. The calculations show that the angular velocity of the coronal plasma decreases rapidly with distance.The relation between magnetic fields and density enhancements is discussed. The field strength in the photosphere seems to determine the amount of mechanical heating of the lower corona. The density structure higher up in the corona will, however, depend decisively on the topology of the field, particularly on whether we are on open or closed field lines, and not simply on field strength.The calculations show a sector structure of the interplanetary field, which agrees well with spacecraft observations. Also the magnitudes of the observed and calculated interplanetary field agree after the Mt. Wilson magnetograph data have been corrected to account for the temperature and saturation effects in the spectral line Fei 5250 Å.On leave from the Astronomical Observatory, Lund, Sweden.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.     

The mean coronal magnetic field determined from HELIOS Faraday rotation measurements

Coronal Faraday rotation of the linearly polarized carrier signals of the HELIOS spacecraft was recorded during the regularly occurring solar occultations over almost a complete solar cycle from 1975 to 1984. These measurements are used to determine the average strength and radial variation of the coronal magnetic field at solar minimum at solar distances from 3–10 solar radii, i.e., the range over which the complex fields at the coronal base are transformed into the interplanetary spiral. The mean coronal magnetic field in 1975–1976 was found to decrease with radial distance according to r ^–, where = 2.7 ± 0.2. The mean field magnitude was 1.0 ± 0.5 × 10 ^–5 tesla at a nominal solar distance of 5 solar radii. Possibly higher magnetic field strengths were indicated at solar maximum, but a lack of data prevented a statistical determination of the mean coronal field during this epoch.     

Analysis of EUV limb brightening observations from ATM

Magnetic fields in the low corona are the only plausible source of energy for solar flares. Other energy sources appear inadequate or uncorrelated with flares. Low coronal magnetic fields cannot be measured accurately, so most attention has been directed toward measurements of the photospheric magnetic fields from which coronal developments may be inferred. Observations of these magnetic fields are reviewed. It is concluded that, except possibly for the largest flares, changes in the photospheric magnetic fields in flaring centers are confined to evolutionary changes associated with emergence of new magnetic flux. Flare observations with the 10830 Å line of helium, in particular, are discussed. It is concluded that the brightest flare knots appear near points of emergent magnetic flux. Pre-flare activation and eruptions of H filaments are discussed. It is concluded that the rapid motions in filaments indicate unambiguously that the magnetic fields in the low corona are severely disrupted prior to most flares. The coronal signature of H filament eruptions is illustrated with soft X-ray photographs from the S-054 experiment of the NASA Skylab mission. An attempt is made, by studying X-ray flare morphology, to determine whether flares grow by reconnections between adjacent or intertwined magnetic elements or by triggering, in which each flaring loop drives adjacent loops to unstable states. It is concluded that successive loop brightenings are most easily interpreted as the result of magnetic field reconnections, although better time resolution is required to settle the question. A model of magnetic field reconnections for flares associated with filament activation and emerging magnetic flux is presented.     

Time–Latitudinal Development of the White-Light Coronal Structures over a Solar Cycle

Large-scale coronal structures (helmet streamers) observed in the white-light corona during total solar eclipses and/or with ground-based coronagraphs are mostly located only above quiescent types of prominences. These helmet streamers are maintained due to the magnetic fields of the Sun. Time–latitudinal distribution of prominences during a solar cycle, however, shows both the poleward and equatorward migrations, similar to the 530.3 nm emission corona (the green corona) intensities. Distribution of observed coronal helmet streamers during total solar eclipses, enlarged with the helmet streamers as were obtained by the ground-based coronagraph observations, are compared with the heliographic distribution of prominences and the green corona intensities for the first time. It is shown that the distribution of above-mentioned helmet streamers, reflects – roughly – the time–latitudinal distribution of prominences and emission corona branches, and migrates together with them over a solar cycle.     

Constructing the Coronal Magnetic Field By Correlating Parameterized Magnetic Field Lines With Observed Coronal Plasma Structures

A method is presented for constructing the coronal magnetic field from photospheric magnetograms and observed coronal loops. A set of magnetic field lines generated from magnetogram data is parameterized and then deformed by varying the parameterized values. The coronal flux tubes associated with this field are adjusted until the correlation between the field lines and the observed coronal loops is maximized. A mathematical formulation is described which ensures that (i) the normal component of the photospheric field remains unchanged, (ii) the field is given in the entire corona over an active region, (iii) the field remains divergence-free, and (iv) electric currents are introduced into the field. It is demonstrated that a parameterization of a potential field, comprising a radial stretching of the field, can provide a match for a simple bipolar active region, AR 7999, which crossed the central meridian on 1996 November 26. The result is a non-force-free magnetic field with the Lorentz force being of the order of 10^–5.5 g cm s^–2 resulting from an electric current density of 0.079 A m^–2. Calculations show that the plasma beta becomes larger than unity at a relatively low height of 0.25 r supporting the non-force-free conclusion. The presence of such strong non-radial currents requires large transverse pressure gradients to maintain a magnetostatic atmosphere, required by the relatively persistent nature of the coronal structures observed in AR 7999. This scheme is an important tool in generating a magnetic field solution consistent with the coronal flux tube observations and the observed photospheric magnetic field.     

To the problem of solar coronal heating

We consider the adequacy of various solar coronal heating models. We show that the correlation between the intensity of the coronal Fe XIV 530.5 nm green line and the calculated magnetic field strength in the solar corona can be a useful tool for this purpose. We have established this correlation for coronal structures and magnetic fields of large spatial and temporal scales. The correlation found exhibits a strong dependence on both solar cycle phase and heliolatitude. The efficiency of a particular coronal heating mechanism is probably determined by the relative area occupied by low and high loops (including open structures). The direct current models based on slow field dissipation (DC) and the wave models based on Alfvén and magnetosonic wave dissipation (AC) are more efficient in the equatorial and polar zones, respectively.     

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.     

Green coronal intensity enhancements and their relation to the underlying photospheric/chromospheric activity

Analysis of the photospheric and chromospheric activity at the sites of enhanced 5303 Å coronal intensity revealed some important aspects of their association. We have examined the daily maps of 5303 Å coronal line intensity of Lomnický tít for the low sunspot activity years 1985 and 1986 in association with the cotemporal daily maps of sunspots, plages and Stanford magnetograms and identified strong field gradients at the sites of enhanced intensity regions. We found that the peak intensity does not depend on the strength of the underlying magnetic field though the coronal intensity-enhanced feature is almost sure to occur at the locations of sunspots with strong magnetic fields and at the locations of plages having larger areas.     

Coronal line intensity as an integrated index of solar activity

The relation between coronal green line intensity and high-speed streams of solar wind emitted by coronal holes or by loop structures of the corona is studied. As well as these exclusive regions of coronal radiative emission, other factors of solar activity have been taken into account in this relation, such as proton events, sunspot number, faculae, and solar magnetic fields.Although the investigated time period (1964–1974) is very short, because of lack of data, we attempted to define the intensity of the coronal green line as an integrated index of the solar activity which can express all the photospheric and coronal phenomena of the Sun. The contraction of the low-density coronal-hole regions and the presence of bright loops during solar maximum provide a theoretical explanation of the above-mentioned relation.     

Solar Wind Speed and Expansion Rate of the Coronal Magnetic Field during Carrington Rotation 1909

The synoptic map of the solar wind speed (SWS) estimated by the computer-assisted tomography (CAT) method with interplanetary scintillation observations is constructed for the 1909 Carrington rotation. A similar synoptic map of expansion rate (RBR) of the coronal magnetic field calculated by the so-called 'potential model' with the photospheric magnetic field is also constructed under the radial field assumption (RF model). These maps consist of 64800 (180×360) data points of equal area. We examine for the first time relations between the SWS estimated by the CAT technique and the RBR calculated by the RF model. A highly significant correlation is found between the SWS and the RBR. A simple correlation coefficient is about –0.72; that is, high-velocity winds emanate from photospheric areas corresponding to a low expansion rate of the coronal magnetic field, and low-velocity winds emanate from photospheric areas of high expansion rate. This result suggests that there is some acceleration mechanism relating to the coronal field expansion.     

Towards Calibration of the Mean Magnetic Field of the sun

The 1968–2000 data on the mean magnetic field (MMF, longitudinal component) of the Sun are analysed to study long-time trends of the Sun's magnetic field and to check MMF calibration. It is found that, within the error limits, the mean intensity of photospheric magnetic field (the MMF strength, |H|), did not change over the last 33 years. It clearly shows, however, the presence of an 11-year periodicity caused by the solar activity cycle. Time variations of |H| correlate well with those of the radial component, |B _r|, of the interplanetary magnetic field (IMF). This correlation (r=0.69) appears to be significantly higher than that between |B _r| and the results of a potential source-surface extrapolation, to the Earth's orbit, of synoptic magnetic charts of the photosphere (using the so-called `saturation' factor <sup>–1</sup> for magnetograph measurements performed in the line Fei 525.0 nm; Wang and Sheeley, 1995). It seems therefore that the true source surface of IMF is the `quiet' photosphere – background fields and coronal holes, like those for MMF. The average `effective' magnetic strength of the photospheric field is determined to be about 1.9 G. It is also shown that there is an approximate linear relation between |B <sub>r</sub>| and MMF intensity |H| (in gauss)|B <sub>r</sub>|(H <sub>0</sub>)<sub>min</sub>×(1+C|H|)where =1.5×10<sup>–5</sup> normalizes the photospheric field strength to 1 AU distance from the Sun, (H <sub>0</sub>)<sub>min</sub>=1.2 G is some minimal `effective' intensity of photospheric background fields and C=1.3 G^–1 an empirical constant. It is noted that good correlation between time variations of |H| and |B _r| makes suspicious a correction of the photospheric magnetic fields with the use of saturation factor ^–1.     

Solar Wind Speed and Expansion Rate of the Coronal Magnetic Field in Solar Maximum and Minimum Phases

Relationships between solar wind speed and expansion rate of the coronal magnetic field have been studied mainly by in-ecliptic observations of artificial satellites and some off-ecliptic data by Ulysses. In this paper, we use the solar wind speed estimated by interplanetary scintillation (IPS) observations in the whole heliosphere. Two synoptic maps of SWS estimated by IPS observations are constructed for two Carrington rotations CR 1830 and 1901; CR 1830 starting on the 11th of June, 1990 is in the maximum phase of solar activity cycle and CR 1901 starting on the 29th of September, 1995 is in the minimum phase. Each of the maps consist of 64800 (360×180) data points. Similar synoptic maps of expansion rate of the coronal magnetic field (RBR) calculated by the so-called potential model are also constructed under a radial field assumption for CR 1830 and CR1901. Highly significant correlation (r=–0.66) is found between the SWS and the RBR during CR1901 in the solar minimum phase; that is, high-speed winds emanate from photospheric areas corresponding to low expansion rate of the coronal magnetic field and low speed winds emanate from photospheric areas of high expansion rate. A similar result is found during CR 1830 in solar maximum phase, though the correlation is relatively low (r=–0.29). The correlation is improved when both the data during CR 1830 and CR 1901 are used together; the correlation coefficient becomes –0.67 in this case. These results suggest that the correlation analysis between the SWS and the RBR can be applied to estimate the solar wind speed from the expansion rate of the coronal magnetic field, though the correlation between them may depend on the solar activity cycle. We need further study of correlation analysis for the entire solar cycle to get an accurate empirical equation for the estimation of solar wind speed. If the solar wind speed is estimated successfully by an empirical equation, it can be used as an initial condition of a solar wind model for space weather forecasts.