Force-free magnetic fields in the solar atmosphere

Reliable measurements of the solar magnetic field are restricted to the level of the photosphere. For about half a century attempts have been made to calculate the field in the layers above the photosphere, i.e. in the chromosphere and in the corona, from the measured photospheric field. The procedure is known as magnetic field extrapolation. In the superphotospheric parts of active regions the magnetic field is approximately force-free, i.e. electric currents are aligned with the magnetic field. The practical application to solar active regions has been largely confined to constant-α or linear force-free fields, with a spatially constant ratio, α, between the electric current and the magnetic field. We review results obtained from extrapolations with constant-α force-free fields, in particular on magnetic topologies favourable for flares and on magnetic and current helicities. Presently, different methods are being developed to calculate non-constant-α or nonlinear force-free fields from photospheric vector magnetograms. We also briefly discuss these methods and present a comparison of a linear and a nonlinear force-free magnetic field extrapolation applied to the same photospheric boundary data. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A search for the footpoints of solar magnetic fields

Solar Physics - High-resolution measurements of magnetic fields have been made in quiet and active regions in order to determine whether the photospheric fine-structures (‘crinkles’),...     

Relation between circular polarization of moving type IV bursts and polarity of photospheric magnetic fields

Two-dimensional, high-resolution observations of about 30 moving type IV bursts allow us to compare the polarization structure of the radio sources high in the corona with the distribution of magnetic fields measured at the photospheric level. Left- and right-handed circularly polarized moving type IV bursts are associated with active regions dominated by magnetic fields of plus and minus polarity respectively. The result suggests that the polarity of magnetic fields within the type IV source which moves high in the corona ( 1R above the photosphere) is closely related to the polarity of local magnetic fields at the photosphere. The above relation between the sense of polarization and the polarity of magnetic field is contrary to what would be expected from the generally accepted synchroton hypothesis. One way of resolving this conflict is to postulate that the magnetic field within the radio source has the opposite polarity to that of the ambient magnetic fields.     

Non-existence of linear polarization in type III solar bursts at 80 MHz

A search for linear polarization showing the effect of Faraday rotation has been made at 80 MHz in type III solar radio bursts. A novel autocorrelation technique was employed. The results were entirely negative, contrary to what was expected on the ground of earlier, less sophisticated experiments. However, there are convincing theoretical reasons why no linear polarization should be expected.Radiophysics Publication RPP 1642, September, 1972.     

Anisotropy and polarization of solar X-ray bursts

The effects of the Compton back-scattered X-ray flux from the photosphere on the directivity and polarization of flare X-rays between 15 keV and 150 keV are computed. The calculations are made with a thin target model for flares of De Jager-Kundu type with electrons spiralling downward around a vertical magnetic field and for an Isotropie source. The resulting polarization for an isotropic source is not higher than 4%. The resulting directivity of anisotropic sources is greatly reduced, particularly below 70 keV. The results of the statistical studies of the center-limb distribution of solar X-ray bursts are then compatible with the existing measures of polarization. The hypothesis for existence of De JagerKundu type flares is enforced.     

Interactions between solar neutrinos and solar magnetic fields

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

Electric fields in the solar atmosphere

The gross-structure of the force-free currents in the solar atmosphere and their possible dynamics have been discussed as caused by quasi short-circuited electric fields, generated by the motion of the solar magnetic features.     

Velocity fields in the solar atmosphere

Observations of velocity fields in the solar atmosphere made with the Mount Wilson solar magnetograph are analyzed. These observations, which were made with very high velocity sensitivity, cover nearly 250 hours and were made with apertures of several sizes and at various parts of the solar disk, and in strong and weak magnetic fields. The amplitudes of the 300-sec oscillations are about 25% weaker in regions where the magnetic field is greater than 80 gauss than where the field is less than 10 gauss. No difference in the frequencies of the oscillations could be found between strong-field and field-free regions. It is suggested that the oscillations occur only where the field is absent and the lower amplitude in a strong field represents the fraction of the magnetograph aperture occupied by a magnetic field. The element sizes for the 300-sec oscillations are probably at least 5–10 arc seconds.Observations made simultaneously with two lines formed at different depths in the solar atmosphere showed small phase differences in the 5-min oscillations. The upper level showed shorter period oscillations when the lower level oscillations underwent phase changes.A short period oscillation is found superposed on the 300-sec oscillation. These SPOs come in bursts that last for a minute or two and have average amplitudes that fall in the range 0.05–0.10 km/sec peak to peak. All attempts to explain them as instrumental or seeing effects have failed. Their periods fall in the range 1–5 seconds. The horizontal scale of these oscillations is smaller than that of the 300-sec oscillations, and the SPOs are more nearly isotropic oscillations than are these around 300 seconds. They do not represent a high-frequency tail of the latter. These observations did not have a digitizing interval short enough to analyze the SPOs for power spectra, but it is clear from the tracings that they are not a nearly monochromatic oscillation as are the longer waves. The amplitudes of the SPOs in the solar atmosphere must be very large and they contribute greatly to the non-radiative energy flux. It is suggested that they represent a large microturbulence line-broadening effect.     

A review of solar type III radio bursts

Solar type III radio bursts are an important diagnostic tool in the understanding of solar accelerated electron beams. They are a signature of propagating beams of nonthermal electrons in the solar atmosphere and the solar system. Consequently, they provide information on electron acceleration and transport, and the conditions of the background ambient plasma they travel through. We review the observational properties of type III bursts with an emphasis on recent results and how each property can help identify attributes of electron beams and the ambient background plasma. We also review some of the theoretical aspects of type III radio bursts and cover a number of numerical efforts that simulate electron beam transport through the solar corona and the heliosphere.     

The Hanle effect and the diagnostics of turbulent magnetic fields in the solar atmosphere

The theory of the Hanle effect is used to interpret the linear polarization measured in a number of spectral lines on the solar disk near the heliographic north and south poles, in search for a turbulent magnetic field in the solar atmosphere. The Hanle depolarization is separated from a number of other effects, including collisional depolarization and scattering geometry. Although the main aim of the paper is to elucidate the physics of the Hanle effect as applied to the Sun, our results indicate the existence of hidden or turbulent magnetic flux near the temperature minimum of the solar atmosphere, with a field strength between 10 and 100 G. This field is hidden in the sense that it is not seen in measurements of the longitudinal Zeeman effect (solar magnetograms). It carries more total magnetic flux than the kG network fields.     

Electric fields in the solar atmosphere: A review

Macroscopic electric fields in the solar atmosphere have received much less attention than magnetic fields, although they must play a role of comparable importance in plasma heating, and in charged particle acceleration and transport. We review various remote sensing techniques that have been developed, whose sensitivity is now 5–10 V cm ^–1 for measurement of the electric field component transverse to the line-of-sight. Our review of the processes most likely to produce observable fields in the solar atmosphere indicates that quasi-static, macroscopic values of E (the electric field component parallel to the magnetic vector) well above this detection threshold are predicted by the discharge model of flares, by models of return currents associated with flare particle beams, and by models of neutral sheets associated with two-ribbon flares and post-flare loops. In addition, both E and E components may be detectable in time dependent electric fields associated with MHD and plasma waves, and with plasma turbulence. The emission measures and time-scales associated with these electrified plasma volumes are as highly uncertain as our present understanding of the volumes, plasma conditions and processes involved in the liberation of flare energy. Observations of electric field vector intensities, orientations, time-behaviour and spatial distribution at the presently attained electric field sensitivity levels could provide new, direct information of great interest in the electrodynamics of solar magnetic structures.     

A dynamic theory of type III solar radio bursts

All four large EUV bursts (peak 10–1030 Å flux enhancements 2 ergs cm^–2 s^–1 at 1 AU as deduced from sudden frequency deviations), for which there were available concurrent white light observations of at least fair quality, were detected as white light flares. The rise times and maxima of the white light emissions coincided with rise times and maxima of the EUV bursts. The frequency of strong EUV bursts suggests that white light flares may occur at the rate of five or six per year near sunspot maximum. All of the white light flare areas coincided with intense bright areas of the H flares. These small areas appeared to be sources of high velocity ejecta in H. The white light flares occurred as several knots or patches of 2 to 15 arc-sec diameter, with bright cores perhaps less than 2 arc-sec diameter (1500 km). They preferred the outer penumbral borders of strong sunspots within 10 arc-sec of a longitudinal neutral line in the magnetic field. The peak continuum flux enhancement over the 3500–6500 Å wavelength range is about the same order of magnitude as the peak 10–1030 Å flux enhancement.     

The measurement of magnetic fields in the solar atmosphere above sunspots using gyroresonance emission

An analysis of the local sources (LS) structure of the S-component of solar radio emission confirms the presence of a core component which is characterized by strong circular polarization and a steep growing spectrum at shorter centimeter wavelengths. These details coincide in position with the sunspots' umbra and their height above the photosphere does not generally exceed about 2000 km. Gyroresonance emission of thermal electrons of the corona is generally accepted as being responsible for this type of emission. The spectral and polarization observations of LS made with RATAN-600 using high resolution in the wavelength range 2.0–4.0 cm, allow us to measure the maximum magnetic fields of the corresponding sunspots at the height of the chromosphere-corona transition region (CCTR). This method is based on determining the short wavelength limit of gyroresonance emission of the LS and relating it to the third harmonic of gyrofrequency.An analysis of a large number of sunspots and their LS (core component) has shown a good correlation between radio magnetic fields near the CCTR and optical photospheric ones. The magnetic field in CCTR above a sunspot is found only 10 to 20% lower than in the photosphere. The resulting gradient of the field strength is not less than 0.25 G km^–1. This result seems to contradict the lower values of magnetic fields generally found above sunspots using the chromospheric H line. Some possible ways of overcoming this difficulty are proposed.     

Weak solar fields and their connection to the solar cycle

We discuss the weak solar magnetic fields as studied with the BBSO videomagnetograph (VMG). By weak fields we mean those outside active and unipolar regions. These are found everywhere on the Sun, even where there never have been sunspots. These fields consist of the network and intranetwork (IN) elements. The former move slowly and live a day or more; the latter move rapidly (typically 300 m s^–1) and live only hours. To all levels of sensitivity the flux is concentrated in discrete elements, and the background field has not been detected. The smallest detectable elements at present are 10¹⁶ Mx. The IN elements emerge in bipolar form but appear to flow in a random pattern rather than to the network edges; however, any expanding network element is constrained by geometry to move toward the edges.Because of the great number and short lifetime of the IN elements the total flux emerging in that form exceeds that emerging in the ER by two orders of magnitude and the flux in sunspots, by a factor 10⁴. However, the flux separation is small and there is no contribution to the overall field. In contrast with our earlier results, merging of IN fields is more important than the ephemeral regions as a source of new network elements.The conjecture that all solar magnetic fields are intrinsically strong is discussed and evidence pro and con presented. For the IN fields the evidence suggests they cannot exceed 100 G. For the network fields there is evidence on either side.Reconnection and merging of magnetic fields takes place continually in the conditions studied.Because there is a steady state distribution, the amout of new elements created by merging or emergence must balance that destroyed by reconnection or fission and diffusion of the stronger elements.Solar Cycle Workshop Paper.     

Meridional drift of the large-scale solar magnetic fields in different phases of solar activity

An analysis is made of mean latitudinal profiles of the meridional drift of the large-scale solar magnetic fields. The previously detected equatorward migration of the drift pattern in the course of a cycle is confirmed. Evidence for the existence of a near-equatorial narrow zone ±7° with an equatorward drift with a rate of about 1 m s^-1 is obtained. The study revealed a significant difference in shapes and variations of average drift profiles for the large-scale magnetic field and small magnetic features (Komm, Howard, and Harvey, 1993).     

On the observation of linear polarization of solar microwave bursts

It is known that mode coupling may occur in quasi-transverse magnetic field regions of the solar corona, which produces linear polarization at microwave frequencies. A microwave polarimeter measuring all 4 Stokes parameters at 8.918 GHz simultaneously at three different highfrequency bandwidths (40 kHz, 400 kHz and 5 MHz) has been developed in order to observe the linear component and its Faraday rotation. The respective minimum detectable changes of the Stokes parameters I, Q, U and V are 9, 3 and 1 solar flux unit at an integration time of 1 s. For burst intensities greater than 300 solar flux units, the minimum detectable degree of linear and circular polarization is 1 %–3 %, depending on the bandwidth. Observations of 68 bursts showed that most of the bursts were circularly polarized. No linear polarization could be found within the limits of accuracy of our polarimeter. Two possible explanations for this result are discussed. The possibility of mode coupling however cannot be excluded from these first observations.     

Type III solar radio bursts and the fundamental-harmonic hypothesis

The observational evidence is reviewed for the occurrence of type III solar radio bursts in pairs with frequency ratio two to one. We show that the observations can be explained under the hypothesis that there is a tendency for a type III burst to be followed by a second burst within approximately one second. This explanation leads to fewer difficulties than the hypothesis that type III bursts occur in pairs, one member being emitted at the fundamental of the local coronal plasma frequency, the other at its second harmonic. We conclude that in general, type III bursts are emitted at the second harmonic of the plasma frequency and that type III theories should account for this and only under very special circumstances (which are rare) for the emission at the fundamental and the second harmonic.     

Source heights of metre wavelength bursts of spectral types I and III

Direct measurements by the Culgoora radioheliograph of the apparent source heights of type I and type III bursts at the solar limb are described. The average observed height is approximately the same for type I and type III sources. The heights are somewhat larger than previous estimates. After refraction effects are removed the present results give an electron density model for the source region below 3 R with densities on the average between 8 and 10 times the values for corresponding heights in the quiet K-corona.