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.     

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 ^?α, where α = 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.     

The effect of turbulent fluctuations in the interstellar gas and magnetic field on Faraday rotation

The effect of fluctuations in both the interstellar electron number density and galactic magnetic field on the propagation of high frequency radio waves is discussed in terms of the frequency dependent Faraday rotation. It is shown that when the fluctuations are representative of large scale disturbances (1–10² pc) in the interstellar medium, then the observed Faraday rotation is not a measure of the line of sight integral of the product of the magnetic field with the electron number density.Since evidence has been presented elsewhere for believing that such large scale disturbances do exist in our galaxy, some care must be exercised in the physical interpretation of Faraday rotation measurements.Alfred P. Sloan Foundation Fellow.     

Determination of the coronal magnetic field and the radio-emitting electron energy from a Type IV solar radio burst

The intensity and frequency spectrum of gyro-synchrotron emission from energetic solar electrons radiating in coronal magnetic fields are calculated. These calculations, based on a recent study of the generation of gyro-synchrotron emission in a magnetoactive plasma, are applied to a Type IV radio burst originating at a high altitude in the solar corona. It is shown that the observed frequency spectrum of the burst, which exhibits very sharp low and high frequency cutoffs, can be best understood in terms of gyro-synchrotron emission in an ionized medium and that from the observed frequency spectrum and the ambient coronal density it is possible to deduce both the magnetic field at the site of the emission and the range of electron energies responsible for the burst.NAS-NASA Post-Doctoral Resident Research Associate.Research supported by the National Research Foundation under grant GP-849.     

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.     

Determination of ionospheric electron content from the Faraday rotation of geostationary satellite signals

Calculations using a wide range of model ionospheres (with a peak at 300 km) show that the integrated electron content up to the height of the satellite could be up to four times the value deduced from Faraday rotation measurements. However, using a fixed mean field height of 400 km, the observed Faraday rotation gives the electron content up to a height h_F of 2000 km with an accuracy of ±3 per cent. For observations at different magnetic and geographic latitudes, and geostationary satellites at different longitudes, the optimum value of h_F varies by only ±200 km. Night-time increases in the height of the ionosphere have little effect on h_F, but increase the mean field height to about 470 km. Using a fixed value of 420 km, with h_F = 2000 km, gives an accuracy of ±5 per cent under most conditions.     

Generation of low-frequency magnetic field disturbances in coronal loops by proton and electron beams

We consider the generation of low-frequency magnetic field disturbances in coronal loops when low density proton and electron beams propagate in them. Two mechanisms of low-frequency magnetic field perturbation generation are analyzed. The first mechanism is concerned with the longitudinal current generated by charged particles’ beams moving in the loop. It is shown that this mechanism of the Alfvén waves’ generation can lead to development of low-frequency perturbations even if the currents are very weak. It can facilitate the reconnection of magnetic fields and flare development. The second mechanism is not concerned with currents propagating in the coronal loop. It is shown that, in this case, the proton beams can cause an instability with significantly lower values of beam density. We found increments and criteria of the development of instabilities. Not only Alfvén-type perturbations can be generated as a result of development of those instabilities but also kinetic Alfvén-type perturbations can be generated.     

The shape of buoyant coronal loops in a magnetic field and the eruption of coronal transients and prominences

The equilibrium and non-equilibrium properties of a coronal loop embedded in a stratified isothermal atmosphere are investigated. The shape of the loop is determined by a balance between magnetic tension, buoyancy, and external pressure gradients. The footpoints of the loop are anchored in the photosphere; if they are moved too far apart, no equilibrium is possible and the loop erupts upwards. This critical separation is independent of the pressure differential between the loop and the external medium if the loop has enhanced magnetic field, but varies if instead the loop pressure is increased. The maximum width is proportional to the larger of the gravitational scale-height and the length-scale of the ambient field. In some circumstances, it is shown that multiple solutions exist for the tube path. These results may be relevant to the eruption of prominences during the preflare phase of two-ribbon flares and to the onset of coronal loop transients. Such eruptions may occur if the footpoint separation, internal pressure or internal magnetic field are too great.     

Lifetime,age, and rotation of coronal magnetic fields

The rotation of the solar electron corona is determined for intervals when nearly periodic variations dominated the polarization brightness record during 1964–1976. Coronal rotation rates derived for 765 intervals vary with height, latitude, and interval length. These rotation rates show a decrease of differential rotation with height and support earlier rotation studies which included much less stationary data. Analyses of the selected intervals and autocorrelation of the complete K-coronameter data set give quantitative estimates of the rotational effects of magnetic tracer age and lifetime. The principal effects detected are a relatively fast rotation of very long-lived tracers at high latitude and a relatively fast rotation of very short-lived tracers at low latitudes. The observations indicate that high-to-low latitude magnetic connections extending through the corona speed up rotation at high latitudes and retard it at low latitudes.     

The cyclical variation of energy flux and photospheric magnetic field strength from coronal holes

We measured the average soft X-ray emission from coronal holes observed on images obtained during AS & E rocket flights from 1974 to 1981. The variation of this emission over the solar cycle was then compared with photospheric magnetic flux measurements within coronal holes over the same period. We found that coronal hole soft X-ray emission could be detected and that this emission appeared to increase with the rise of the sunspot cycle from activity minimum to maximum. Our quantitative results confirmed previous suggestions that the coronal brightness contrast between holes and large-scale structure decreased during this period of the cycle. Gas pressures at the hole base were estimated for assumed temperatures and found to vary from about 0.03 dyne cm^–2 in 1974 to 0.35 dyne cm^–2 in 1981. The increase in coronal hole X-ray emission was accompanied by a similar trend in the surface magnetic flux of near-equatorial holes between 1975 and 1980 (Harvey et al., 1982).     

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.     

Theoretical scaling law of coronal magnetic field and electron power-law index in solar microwave burst sources

It is first proposed a theoretical scaling law respectively for the coronal magnetic field strength \(B\) and electron power-law index \(\delta\) versus frequency and coronal height in solar microwave burst sources. Based on the non-thermal gyro-synchrotron radiation model (Ramaty in Astrophys. J. 158:753, 1969), \(B\) and \(\delta\) are uniquely solved by the observable optically-thin spectral index and turnover (peak) frequency, the other parameters (plasma density, temperature, view angle, low and high energy cutoffs, etc.) are relatively insensitive to the calculations, thus taken as some typical values. Both of \(B\) and \(\delta\) increase with increasing of radio frequency but with decreasing of coronal height above photosphere, and well satisfy a square or cubic logarithmic fitting.     

Hourglass magnetic field from a survey of current density profiles

Modeling the magnetic field in prestellar cores can serve as a useful tool for studying the initial conditions of star formation. The analytic hourglass model of Ewertowski and Basu (2013) provides a means to fit observed polarimetry measurements and extract useful information. The original model does not specify any radial distribution of the electric current density. Here, we perform a survey of possible centrally-peaked radial distributions of the current density, and numerically derive the full hourglass patterns. Since the vertical distribution is also specified in the original model, we can study the effect of different ratios of vertical to radial scale length on the overall hourglass pattern. Different values of this ratio may correspond to different formation scenarios for prestellar cores. We demonstrate the flexibility of our model and how it can be applied to a variety of magnetic field patterns.     

Computation of inner coronal magnetic fields from longitudinal field components on a spherical photosphere

A method is developed which for a certain day permits the approximate calculation of closed small and large scale magnetic field lines. From the photospheric longitudinal components of the magnetic field measured at this day normal components are derived taking into account the curvature of the solar surface. The magnetic fields are assumed to be potential or force-free fields.The method is applied to observations of September 5 and September 7, 1973. The projected magnetic field lines are compared with the loop structures which are visible in XUV pictures taken on these days. In the cases where no good agreement could be obtained for potential fields, force-free fields are calculated and fitted to the observed structures.     

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.     

Latitudinal variability of large-scale coronal temperature and its association with the density and the global magnetic field

In this paper we utilize the latitude distribution of the coronal temperature during the period 1984–1992 that was derived in a paper by Guhathakurta et al, 1993, utilizing ground-based intensity observations of the green (5303 Fe XIV) and red (6374 Fe X) coronal forbidden lines from the National Solar Observatory at Sacramento Peak, and estabish its association with the global magnetic field and the density distributions in the corona. A determination of plasma temperature,T, was estimated from the intensity ratio Fe X/Fe XIV (whereT is inversely proportional to the ratio), since both emission lines come from ionized states of Fe, and the ratio is only weakly dependent on density. We observe that there is a large-scale organization of the inferred coronal temperature distribution that is associated with the large-scale, weak magnetic field structures and bright coronal features; this organization tends to persist through most of the magnetic activity cycle. These high-temperature structures exhibit time-space characteristics which are similar to those of the polar crown filaments. This distribution differs in spatial and temporal characterization from the traditional picture of sunspot and active region evolution over the range of the sunspot cycle, which are manifestations of the small-scale, strong magnetic field regions.affiliated to USRA     

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.     

The importance of photospheric magnetic field complexity for coronal energy storage

Possibilities for the storage of energy in coronal electric currents in different magnetic background field configurations are investigated in the framework of the solar flare energy build-up model of Van Tend and Kuperus (1978). The results are compared to characteristics of filaments and X-ray loops. Empirical flare predictors are interpreted theoretically.