Radial variation of differential rotation in the solar electron corona

Long-lived brightness structures in the solar electron corona persist over many solar rotation periods and permit an observational determination of coronal magnetic tracer rotation as a function of latitude and height in the solar atmosphere. For observations over 1964–1976 spanning solar cycle 20, we compare the latitude dependence of rotation at two heights in the corona. Comparison of rotation rates from East and West limbs and from independent computational procedures is used to estimate uncertainty. Time-averaged rotation rates based on three methods of analysis demonstrate that, on average, coronal differential rotation decreases with height from 1.125 to 1.5 R _S. The observed radial variation of differential rotation implies a scale height of approximately 0.7 R _S for coronal differential rotation.Model calculations for a simple MHD loop show that magnetic connections between high and low latitudes may produce the observed radial variations of magnetic tracer rotation. If the observed tracer rotation represents the rotation of open magnetic field lines as well as that of closed loops, the small scale height for differential rotation suggests that the rotation of solar magnetic fields at the base of the solar wind may be only weakly latitude dependent. If, instead, closed loops account completely for the radial gradients of rotation, outward extrapolation of electron coronal rotation may not describe magnetic field rotation at the solar wind source. Inward extrapolations of observed rotation rates suggest that magnetic field and plasma are coupled a few hundredths of a solar radius beneath the photosphere.     

Differential rotation of the solar electron corona

Autocorrelation analyses of K-coronameter observations made at Haleakala and Mauna Loa, Hawaii, during 1964–1967 have established average yearly rotation rates of coronal features as a function of latitude and height above the limb. At low latitudes the corona was found to rotate at the same rate as sunspots but at higher latitudes was consistently faster than the underlying photosphere. There were differences as large as 3–4% in the rate at specific latitudes from year to year and between the two hemispheres. In 1967 a nearly constant rotation was found for heights ranging from 1.125 to 2.0 R ₀. For 1966 there was a more complicated pattern of height dependence, with the rate generally decreasing with height at low latitudes and increasing at high latitudes.At Hawaii Institute of Geophysics.     

Determination of the temperature of the solar corona from the spectrum of the electron-scattering continuum

When the K-corona is formed by the scattering of photospheric radiation from free electrons, the Fraunhofer lines are greatly broadened by the thermal motions of the hot electrons. This paper discusses the possibility of measuring the coronal electron temperature from the residual depressions in the K-coronal spectrum. If the ratio of the intensities at 4100 Å and 3900 Å can be measured to an accuracy of ±1%, the coronal temperature can be inferred to an accuracy of ±0.2 MK. The temperature of a coronal inhomogeneity may also be measured by this method, provided the position angle is known.Now at Fraunhofer Institute, Freiburg, Germany.     

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.     

Temporal evolution of the equatorialK-corona

Observations of the equatorialK-coronal radiance at 2.5R from Sun center and its variation with time, on a daily basis, during the Skylab mission (May 1973–February 1974) are presented. The observations are subdivided into three periods, each characterized by a different variation of the radiance pattern with time. During the initial period, encompassing two solar rotations, there are several data gaps, but the radiance pattern shows a more or less smooth variation with time; however, during the second period (also about two solar rotations duration) the radiance signal is neither persistent on the short term nor recurrent from one limb passage to the next. Finally, during the last period, of five solar rotations duration, the radiance signal exhibits an orderly periodic behavior of increasing intensity. These results are interpreted as indicating a general simplification of the coronal magnetic field through the mission and, in comparison with harmonic analysis of the surface magnetic field (Levine, 1977), as indicating a rapid response of equatorial outer coronal structures to abrupt changes in the global surface field structure.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.     

Evolution of coronal helmets during the ascending phase of solar cycle 20

The principal polar-crown coronal helmet structures were selected from nearly three years (May, 1965–January, 1968) of K-coronameter observations made at Haleakala and Mauna Loa, Hawaii. Six isolated and long-lived helmet systems were found at latitudes of 45° and above. Their developments are compared with underlying chromospheric and photospheric activity and a simple phenomenological model is presented showing that a coronal system is formed over an active region. Thereafter the center of gravity of the system gradually drifts poleward with the trailing unipolar magnetic region (UMR), and it becomes a high latitude coronal helmet, arched over a polar crown filament.By comparison of these coronal helmets with observations of the outer corona (to circa 4 R ) made at solar eclipse, lunar sunset, and with balloon and rocket-borne externally occulted corona-graphs, it appears that ground-based K-coronameter measurements to a distance of 1.5–2.0 R are sufficient to detect the coronal streamers.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Electrons in the solar corona

During a balloon flight in France on September 13, 1971, at altitude 32 000 m, the solar corona was cinematographed from 2 to 5R during 5 hr, with an externally occulted coronagraph.Motions in coronal features, when they occur, exhibit deformations of structures with velocities not exceeding a few 10 km s^–1; several streamers were often involved simultaneously; these variations are compatible with magnetic changes or sudden reorganizations of lines of forces.Intensity and polarization measurements give the electron density with height in the quiet corona above the equator. Electron density gradient for one of the streamers gives a temperature of 1.6 × 10⁶ K and comparisons with the on-board Apollo 16 coronal observation of 31 July, 1971 are compatible with the extension of this temperature up to 25 R _bd.Three-dimensional structures and localizations of the streamers are deduced from combined photometry, polarimetry and ground-based K coronametry. Three of the four coronal streamers analysed have their axis bent with height towards the direction of the solar rotation, as if the upper corona has a rotation slightly faster than the chromosphere.     

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.     

Coronal Field Opens at Lower Height During the Solar Cycles 22 and 23 Minimum Periods: IMF Comparison Suggests the Source Surface Should Be Lowered

The solar cycle 23 minimum period has been characterized by a weaker solar and interplanetary magnetic field. This provides an ideal time to study how the strength of the photospheric field affects the interplanetary magnetic flux and, in particular, how much the observed interplanetary fields of different cycle minima can be understood simply from differences in the areas of the coronal holes, as opposed to differences in the surface fields within them. In this study, we invoke smaller source surface radii in the potential-field source-surface (PFSS) model to construct a consistent picture of the observed coronal holes and the near-Earth interplanetary field strength as well as polarity measurements for the cycles 23 and 22 minimum periods. Although the source surface value of 2.5 R _⊙ is typically used in PFSS applications, earlier studies have shown that using smaller source surface heights generates results that better match observations during low solar activity periods. We use photospheric field synoptic maps from Mount Wilson Observatory (MWO) and find that the values of ≈ 1.9 R _⊙ and ≈ 1.8 R _⊙ for the cycles 22 and 23 minimum periods, respectively, produce the best results. The larger coronal holes obtained for the smaller source surface radius of cycle 23 somewhat offsets the interplanetary consequences of the lower magnetic field at their photospheric footpoints. For comparison, we also use observations from the Michelson Doppler Imager (MDI) and find that the source surface radius of ≈ 1.5 R _⊙ produces better results for cycle 23, rather than ≈ 1.8 R _⊙ as suggested from MWO observations. Despite this difference, our results obtained from MWO and MDI observations show a qualitative consistency regarding the origins of the interplanetary field and suggest that users of PFSS models may want to consider using these smaller values for their source surface heights as long as the solar activity is low.     

Solar coronal streamers

A unique combination of photographic and K-coronameter data were used to study the structure and evolution of two known coronal streamers. In addition, two other K-coronameter enhancements were studied as representing ideal second examples of the known streamers. As a general rule the observations indicate that these features were direct coronal manifestations of photospheric bipolar magnetic regions (BMR) and were of two basic types:active region, by which is meant a coronal streamer which develops radially over a low-latitude active region; andhelmet which denotes a streamer whose structure and development appear to be a consequence of a long-lived complex of activity, composed of both trailing magnetic fields and a parent center of disk activity.The similarity of growth rates during the first solar rotation of life led to derivation of a total streamer density of 4–5 × 10⁸ cm^–3 atr = 1.125R . This density may represent a characteristic maximum density at the base of streamers. The intensity gradient of the inner (r1.5R ) corona was used to establish a qualitative evolutionary model of streamers which synthesizes the observations. Briefly, streamers initially develop over active regions; the streamer growth rate may be as rapid as the disk activity, or at worst lags flare activity by solar rotation. The streamer can be the cause of interplanetary and geomagnetic effects at 1 AU within a solar rotation after birth. Thereafter the streamer follows an evolution dictated by the underlying solar magnetic fields. In any case the lowest level of the coronal enhancement has a lifetime not exceeding that of the solar disk activity.     

Solar-cycle dependence of galactic cosmic ray flux

The coronal green line intensity is inappropriate for correlation studies of galactic cosmic ray variations. Being a non-monotonic function of coronal temperature, the green line intensity is a good index of neither coronal temperature nor solar wind speed. A more appropriate measure of coronal activity is the intensity of the electron corona. Two-dimensional observations of the K-corona trace changes in coronal morphology during the solar cycle. An index based on four years of K-coronal measurements made in Hawaii shows that activity in the lower corona is not better correlated than sunspot number with long-term modulation. Correlation analysis defines the time lag of modulation much too poorly to permit its use in estimating the size of the heliosphere.     

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 Faraday rotation of the Crab Nebula, 1971–1975

We observed Faraday rotation of linearly polarized radio waves from the Crab Nebula (Tau A) at 4170 MHz during solar coronal occultations in June 1971–75. Mean amplitudes of the variations of position angle are larger in an active phase of the solar cycle than in a quiet phase. In occultations in 1971 and 1973, the position angle of the polarization varied oscillatory by 20–50 degrees due to local magnetic structures in the corona with a typical scale-length of about 0.5 R . In 1974, we observed a typical variation of position angle of polarization which is expected from a Y-shaped field configuration in coronal streamers.The Faraday rotation is enhanced when the line of sight to Tau A passes through strong coronal magnetic fields computed from magnetograph observations, while the rotation is suppressed when the line of sight passes through large coronal holes observed in X-rays. Short-time oscillation of the rotation angle observed in 1971 and 1973 suggests that neutral sheets in coronal streamers oscillate at a period of 3 hours with an amplitude of 1 R at a distance of 10 R from the Sun.     

The differential rotation of the corona as indicated by coronal holes

The rotation of the corona can be determined either directly by using Doppler methods or indirectly by using tracers, i.e., structures within the corona. In this study the rotational characteristics of the corona are determined using coronal holes as tracers, for the period 1978–1991. The coronal data used here are from an atlas of coronal holes mapped in Hei 10830 data. A comparison is made between our results and previous determinations of the coronal rotation rate, e.g., by Sime (1986), using white-light K-coronameter observations, by Timothy, Krieger, and Vaiana (1975), using soft X-ray observations, and by Shelke and Pande (1985) and Navarro-Peralta and Sanchez-Ibarra (1994), using Hei 10830 data. For the atlas of coronal holes used in this study the nature of the coronal hole distributions in number and latitude, in yearly averages, has been determined. These distributions show that at solar minimum the polar coronal holes dominate and the few non-polar holes are confined to a narrow band near the equator. At solar maximum, however, mid-latitude coronal holes dominate, with a large spread in latitudes. Given these distributions we consider the differential rotation data only as an average over a solar cycle. This removes spurious effects caused by having only a small number of coronal holes contributing to the results, or by having a narrow latitude band for the observations, thus limiting the results to that narrow latitude band. By considering these coronal holes as tracers of the differential rotation we show that the mid-latitude corona rotates more rigidly than the photosphere, but still exhibits significant differential rotation, with an equatorial rate of 13.30 ± 0.04° day^–1, and at 45° latitude a rate of 12.57 ± 0.13° day^–1. These results are comparable, within errors, to the Sime (1986) results which have an equatorial rate of approximately 13.2 ± 0.2° day^–1 and a rate of approximately 12.9 ± 0.3° day^–1 at 45° latitude.     

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.     

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.     

A study of the background corona near solar minimum

The white light coronagraph data from Skylab is used to investigate the equatorial and polarK andF coronal components during the declining phase of the solar cycle near solar minimum. Measurements of coronal brightness and polarization brightness product between 2.5 and 5.5R during the period of observation (May 1973 to February 1974) lead to the conclusions that: (1) the equatorial corona is dominated by either streamers or coronal holes seen in projections on the limb approximately 50% and 30% of the time, respectively; (2) despite the domination by streamers and holes, two periods of time were found which were free from the influences of streamers or holes (neither streamers nor holes were within 30° in longitude of the limb); (3) the derived equatorial background density model is less than 15% below the minimum equatorial models of Newkirk (1967) and Saito (1970); (4) a spherically symmetric density model for equatorial coronal holes yields densities one half those of the background density model; and (5) the inferred brightness of theF-corona is constant to within ±10% and ±5% for the equatorial and polar values, respectively, over the observation period. While theF-corona is symmetric at 2R it begins to show increasing asymmetry beyond this radius such that at 5R the equatorialF-coronal brightness is 25% greater than the polar brightness.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Comparative Analyses of the CSSS Calculation in the UCSD Tomographic Solar Observations

We describe a new method to derive the interplanetary magnetic field (IMF) out to 1 AU from photospheric magnetic field measurements. The method uses photospheric magnetograms to calculate a source surface magnetic field at 15R_⊙. Specifically, we use Wilcox Solar Observatory (WSO) magnetograms as input for the Stanford Current-Sheet Source-Surface (CSSS) model. Beyond the source surface the magnetic field is convected along velocity flow lines derived by a tomographic technique developed at UCSD and applied to interplanetary scintillation (IPS) observations. We compare the results with in situ data smoothed by an 18-h running mean. Radial and tangential magnetic field amplitudes fit well for the 20 Carrington rotations studied, which are largely from the active phase of the solar cycle. We show exemplary results for Carrington rotation 1965, which includes the Bastille Day event.     

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.