On the polarization and anisotropy of solar X-radiation during flares

Starting from the idea that the electrons accelerated during a solar flare have originally a preferred direction, the angular distribution and the polarization of bremsstrahlung below 10 Å is calculated taking into account the influence of the magnetic field. The energy distribution of the nonthermal electrons is based on X-ray spectra measured by the Leicester group during flares in 1962 and 1967. In addition to the case of a fixed angle between the electron velocity and the magnetic field, an angular distribution of the form sin ⁿ is considered. The results may be used to test flare models. Recent measurements of the polarization of solar X-radiation yield the expected order of magnitude.Paper presented to the Int. Symp. on Solar-Terr. Phys., Leningrad, May 1970.     

The Hanle effect of the coronal Lα line of hydrogen: Theoretical investigation

This paper is devoted to a computation of the effect of a magnetic field on the linear polarization of the coronal L line of hydrogen. Recent works (Gabriel et al., 1971) have shown that the linear polarization of this line is due to resonant scattering of the incident chromospheric L line. The Hanle effect is the modification of this linear polarization, due to the magnetic field. After having briefly recalled the main features of this effect and the conditions of the coronal L line formation, we present the theoretical formalism to be used for Hanle effect computations. The effect of the hyperfine structure of the line is included. Then the results of our computations are given in terms of linear polarization as a function of the magnetic field. We get that the effect of the hyperfine structure on these results is negligible, although this is not evident a priori. When the hyperfine structure is neglected, the line structure is simplified and the Hanle effect can be expressed with analytical formulae, which we give in the last part of this paper. After integration along the line of sight, these formulae could be used for magnetic field determination in the solar corona from measurements of the linear polarization of the L line.     

The polarization of coronal emission lines

By means of a photographic polarimeter, we attempted to measure both the amount and direction of linear polarization of all emission lines between 3400 and 9000 Å in the inner corona (1.034 r/r ₀ 1.085). Only the green and red coronal lines have been analyzed in detail. Neither of these lines shows polarization exceeding the probable error of 1.0% for 5303 and 1.8% for 6374. None of the other 17 coronal lines observed during the 7 March, 1970 solar eclipse show any obvious (>5%) polarization.Presently at the Sacramento Peak Observatory.     

Polarization changes with time during solar microwave impulsive bursts

The evolution with time of circular polarization (t) from solar bursts at 7 GHz presents, in the majority of cases, a polarization degree peak before the maximum flux time. The subsequent evolution of (t) is continuous and usually increasing. The changes could be caused by superimposed polarization effects, due to the fast emissive electrons (dominant in the first phase), and to the propagation effects caused by the coronal condensation where the event occurred (dominant in the second phase). In an approximate approach, (t) is connected to the movement of the source in the second phase, being qualitatively sound, but limited to the lack of knowledge on acceleration processes and on magnetic field topology in the active region where the flares take place.     

SPECTROSCOPOLARIMETRIC SENSING OF ENERGY DEPOSITION INTO THE CHROMOSPHERE DURING SOLAR FLARES – I. Observations

Measurements of linear polarization in hydrogen H and H lines, made with the Large Solar Vacuum Telescope of Baikal Astrophysical Observatory and Automated Solar Telescope of Sayan Solar Observatory, affiliated with the Russian Institute of Solar and Terrestrial Physics, are reported in this paper. Short-term polarization associated with solar flares is found to be present in active regions. There is a significant tendency for the H polarization vector to be radial, i.e., in the flare-to-disk-center direction. This polarization may be due to atmospheric bombardment by hecta keV protons. On the other hand, the polarization vector is found to be perpendicular to the radial direction at some locations where the line profile has a typical mustache shape suggesting a bombardment by energetic electrons. The H line is also linearly polarized. However, no preferential direction of polarization is found in this line, which is formed more deeply in the solar atmosphere.     

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.     

Polarization of Lyman-alpha lines from hydrogen-like ions

The Oppenheimer-Penney theory to calculate the polarization of L lines from hydrogen-like ions, when the impact electrons are distributed such that their probability is more in the regions close to the magnetic field (f(cos ⁿ ), is applied by Chandra and Joshi (1984). The work of Chandra and Joshi (1984) has been reinvestigated for the pitch-angle distributionf()sin ⁿ . The degrees of polarization are still found to be independent of the atomic number of a hydrogen-like ion.     

Coronae around helium stars and X-ray sources

Calculations of the acoustic energy generation for helium-rich composition show that the maximum acoustic energy generation is located around 12000 K at logg=4 and 15000 K at logg=6. The author's suggestion in his last paper that a helium star Sgr may have a corona seems to be justified. X-ray from a corona around a helium star is strongest when the physical parameters of the star are logg6 andT _e15000 K. But the total energy flux is too small to account for the observed X-ray sources.Presented at the Trieste Colloquium on Mass Loss from Stars, September 12–16, 1968.     

On the dissipation rates for Alfvén waves in the solar transition region

The present paper concerns Alfvén waves, in a resistive and viscous atmosphere, under a steep temperature gradient (Section 1). The dissipative Alfvén wave equation is deduced assuming uniform vertical background magnetic field, and allowing for arbitrary profiles of Alfvén speed, and viscous and resistive diffusivities as functions of altitude (Section 2). A three-parameter family of temperature profiles, allowing for independent choice of initial and asymptotic temperature, and of initial temperature gradient, is used to re-write the wave equation, with the temperature as the independent variable, instead of altitude (Section 3). It is shown that, for the conditions prevailing in the solar transition region between the chromosphere and corona, two approximations of the dissipative wave equations may be considered, the simplest leading to solution in terms of Gaussian hypergeometric functions (Section 4). The exact analytical solution allows calculation of the (i) velocity and (ii) magnetic field perturbations, (iii) kinetic, (iv) magnetic and (v) total energy density, (vi) energy flux, (vii) rate-of-strain and (viii) electric current, and (ix) viscous, (x) resistive and (xi) total rate of dissipation (Section 5). These are plotted versus temperature, across the transition region from the chromosphere to the corona, for the quiet and active Sun (Section 6). The feasibility of heating of the transition region by dissipation of Alfvén waves is discussed (Section 7), by comparing empirical heating rates, with theoretical values for a range of physical conditions, including initial velocity perturbations 5 to 15 km s ^–1, background magnetic field 12 to 120 G, wave periods 60 to 300 s, thickness of the transition region 100 to 300 km, resistive and anomalous diffusivities to 100 and viscous and turbulent diffusivities to 100 . The conclusion is that dissipation of Alfvén waves is not an effective heating mechanism for the transition region and corona, although it may be for the chromosphere (see Campos and Mendes, 1995, and references therein).     

Precise determination of the orientation of the plane of polarization in the solar corona

It has been shown by Molodensky (1973), that precise measurements of the position of the plane of polarization in the corona may allow us to observe overthermal electrons in the solar corona. For such measurements during the eclipse of 10 July 1972, a method based on the photographic recordings of the corona by means of a cineset and with an automatically rotating polaroid has been developed. A technique has also been developed for determining the position of the plane of polarization by means of isophotes obtained with polarization filters. This technique uses the photometric data for determining phase shifts between the apparent intensity variation curve and a similar curve expressing the rotation phase of the polaroid. The results of the measurements for h/r _⊙ =0.5 to 0.9 allow us to conclude that:

1. The plane of polarization (E-vector position) coincides very exactly with the tangential direction in the region of N-W limb. The maximum deviations of this plane amounts to 1–1.5°, and the mean-square deviations in this region amount to ～0,3° at h/R _⊙ ≈1. This coronal region was the least active one and there were no spots there.
2. The corona near the E limb consisted of two ‘fans’ divided by a thin beam. In that region some deviations of the plane of polarizarion from the tangential direction were revealed. Those deviations were of the order of 3°. During the time of the eclipse there were some groups of spots behind the E limb (but close to this limb). The observed deviations were apparently connected with those groups.
3. Calculations have been made of the turn of the plane of polarization caused by an inhomogeneity in the radiation field from the photosphere and due to the presence of spots. The effect qualitatively coincided with that shown by the measurements.

     

Observations and discussions concerning ‘high’ polarization features in the solar corona

Photographic observations were obtained of the radial and tangential polarization of the solar corona for the 1970, March 7, solar eclipse. The corona was photographed using a neutral density filter and rotating linear polaroid sectors to allow the polarization structure to be seen from 1 to 6 solar radii. Anomalously high polarizations were found for structures with the E-tangential intensity being predominantly larger than the E-radial intensity. These structures are generally filamentary in nature and radial in direction. One case with a high radial polarization was also found. The photographs were calibrated accurately against the Earth shine from the Moon. Possible source mechanisms are discussed that may explain this new component in the solar corona. Most sources may be ruled out on physical grounds. One possibility appears to be synchrotron radiation from 10 GeV electrons in a 0.4 G field. The existence of these electrons, however, is unlikely in that spacecraft observations at 1 AU do not confirm their presence.     

Gyro-synchrotron emission in a magnetic dipole field for the application to the center-to-limb variation of microwave impulsive bursts

In order to interpret the observed center to limb variations of spectrum and polarization of microwave impulsive bursts, gyro-synchrotron emission from nonthermal electrons trapped in a magnetic dipole field is computed. The theoretical spectrum and polarization are consistent with observed ones if we put an outer boundary of the radio source at a layer of 100-60 G or (7–9) × 10⁴ km in height. Rather small observed center-limb variations in intensity and polarization are attributed to the distribution of , an angle between the magnetic field and the direction of observer, in the radio source emitting the burst, though the intensity and polarization depend strongly on especially at small values of .     

Transport of cosmic rays in the solar corona

A model is proposed to explain the transport of energetic protons in the solar corona. The particles are assumed to undergo an enhanced gradient-B drift along thin current sheets separating discontinuous field structures in the corona. These discontinuities may represent the extension into the corona of photospheric granular and supergranular cell boundaries. We have made a quantitative analysis of this process by assuming that the particle propagation can be described by a diffusion equation. Comparison of predictions of the model with cosmic ray observations at 1 AU provide some support for the model.     

Excitation of high-frequency Alfvén waves by plasma outflows from coronal reconnection events

We study a kinetic excitation mechanism for high-frequency dispersive Alfvén waves in the solar corona by magnetic reconnection events. The ion-cyclotron and Cerenkov kinetic effects are important for these waves which we call the ion-cyclotron kinetic Alfvén waves (IC KAWs). The plasma outflowing from the reconnection site sets up a neutralized proton beam in the surrounding plasma, providing free energy for the excitation of waves. The dependence of the phase velocity of the IC KAW on the parallel wavenumber is different from that on the perpendicular wavenumber. The phase velocity is an increasing function of the perpendicular wavenumber and overtakes the Alfvén velocity for sufficiently large values of k . However, the phase velocity is a decreasing function of k , and sufficiently large values of k result in a phase velocity below the Alfvén velocity. As a result, the IC KAWs can undergo the Cerenkov resonance with both super- and sub-Alfvénic particles, and for the waves to be excited the outflow velocity does not need to be super-Alfvénic, as for KAWs, but the beam/Alfvén velocity ratio can span a wide range of values. High growth rates of the order of 10⁴ s^–1 are found for the values of the plasma parameters typical for the low solar corona. The waves excited by (sub-)Alfvénic beams are damped mainly due to kinetic wave-particle interactions with ions at the cyclotron resonance (ion-cyclotron damping), and with ions and electrons at the Cerenkov resonance (Landau damping). Therefore, IC KAWs can heat the plasma species of the corona in both the parallel and perpendicular direction, giving rise to an anisotropic heating of the ions. The observational consequences of the processes under study are discussed.     

Some features of the solar microwave emission and their connection with geomagnetic activity

The quiet component of the 9.1-cm solar radio emission is studied from the Stanford radioheliograms covering the period April–October 1964. The distribution of the brightness temperature in heliographic coordinates is not entirely uniform, but positive and negative departures from the average value appear at a number of stable locations. The most important negative departure crosses the central meridian 4 days before the maximum of the recurrent geomagnetic activity. Two out of three less important brightness depressions are connected with geomagnetic disturbances in the same manner. It is suggested that the brightness depressions are identical with M-regions.The result is confirmed by the construction of polytrope models for the solar wind, for various values of the parameters (the polytrope index) and T (the temperature in the inner corona). The velocities near the earth's orbit and in the inner corona are computed as functions of the model parameters, the density results from the observed proton flux at 1 AU. For quiet conditions the model with T = 1.26 × 10⁶ K and = 1.10 is appropriate. The corresponding density and temperature in the corona lead to a value of 4000 K for the contribution of the corona to the 9-cm brightness. For disturbed conditions the suitable model has the parameters T 2.0 × 10⁶ K, a 1.04. It being given that the proton flux at 1 AU is relatively constant, the equation of continuity leads to a low coronal density because of the high solar-wind velocity. The corresponding coronal contribution to the 9-cm brightness is of the order of 10 K. This confirms that the brightness temperature is considerably reduced in the regions where the enhanced solar wind originates. We suggest the name coronal depression for such regions.Papers II and III will appear in forthcoming issues of this journal.     

Effects of diverging coronal fields on the solar wind expansion

The expansion of the solar wind in divergent flux tubes is calculated by taking into account a magnetic acceleration of the particles, analogous to the magnetic mirror effect.The resulting force term included in the magnetohydrodynamical equations describes a conversion of thermal into kinetic energy. This causes an additional acceleration of the solar wind plasma which has never been taken into account before. The force is directed opposite to the magnetic field gradient. Consequently, in this case the solar wind velocity increases faster to its asymptotic value than it does for corresponding nonmagnetic solutions. Therefore inside and close to the solar corona markedly higher velocities are found. Compared to strictly hydrodynamical models, the critical point is shifted towards the Sun, and the radial decrease of the ratio of thermal to kinetic energy is faster.The necessary prerequisites for these calculations are (a) that the gyroperoid _g of the plasma particles is much shorter than the Coulomb collision time _c , and (b) that the collision time _c is shorter than the characteristic time _d in which an appreciable amount of thermal anisotropy is built up. Thus it is (a) insured that the particles have established magnetic moments and follow the guiding center approximation, and (b) an almost isotropic velocity distribution function is maintained which, in this first approximation of a purely radial expansion, justifies the use of isotropic pressures and temperatures.Both (a) and (b) are shown to be fulfilled in a region around the Sun out to about 20R , and thermal anisotropies developing outside of this region could explain the observed magnetically aligned anisotropies at 1 AU.     

Interpretation of type I- and IV mB-bursts and noise storms by mode coupling in the warm plasma

The circular polarization of radiation emitted from the solar type I- and IV mB-bursts and noise storms is not understood very well. For an attempted new explanation the dispersion equations for the ordinary (left-handed) and the extraordinary (right-handed) wave are derived from the well-known tensor conductivity of warm plasma proposing a very small angle between magnetic field and propagation direction, and the plasma parametersX1,Y1. Taking into account a plasma temperature different from zero, conditions of a coupling point (Budden, 1961) are attained very nearly even if the very small collision frequency is neglected. It is shown, that the observed ordinary (left-handed) polarization may be explained by a process of mode-coupling between the originally emitted extraordinary (right-handed) wave and the resulting ordinary wave. The source of the right-handed radiation may be gyro-radiation or erenkov-radiation. The proposed mechanism is in accordance with the main observational facts. It remains open, whether the known magnetic asymmetry of active regions accounts for the prevailing left-handed polarization.     

Forerunners: Outer rims of solar coronal transients

The large loop or blob-like transient events viewed in the white-light corona are rimmed by broad regions where the density is slightly enhanced above the pre-transient corona. Every one of the Skylab events studied for which sufficiently good Skylab coronagraph coverage is available shows this effect. The upper boundaries of these forerunners blend gradually into the background corona 1 to 2R above the transients' leading edges. In any single event, the coronal mass enhancement represented by the forerunner comprises up to 25% of the total excess mass present in the coronagraph's field of view and includes a much larger volume of the corona than previously attributed to the underlying transient. We have not yet seen a forerunner without an accompanying transient. Clearly, forerunners must be reckoned with in any proposed models of discrete outward coronal mass motions, because they indicate the presence of disturbed corona far ahead of the denser portions of the event.Skylab Solar Workshop Postdoctoral Appointee 1975–78. The Skylab Solar Workshops are sponsored by NASA and NSF and managed by the High Altitude Observatory.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Ray-type spectra of plasma turbulence in coronal magnetic loops

The problem of stationary spectra of Langmuir, l, and electromagnetic, t, waves excited in a magnetic trap (loop) by a group of suprathermal electrons, whose velocity distribution includes a loss cone, is considered. Within the framework of weak turbulence theory, accurate spectra of l- and t-waves are found. These spectra have the form of thin rays in wavevector space. Forms of plasma emission radio lines of a homogeneous source near the plasma frequency and its second harmonic are determined.     

Alfvén waves in the solar atmosphere

The linearized propagation of axisymmetric twists on axisymmetric vertical flux tubes is considered. Models corresponding to both open (coronal hole) and closed (active region loops) flux tubes are examined. Principal conclusions are: Open flux tubes: (1) With some reservations, the model can account for long-period (T 1 hr) energy fluxes which are sufficient to drive solar wind streams. (2) The waves are predicted to exert ponderomotive forces on the chromosphere which are large enough to alter hydrostatic equilibrium or to drive upward flows. Spicules may be a consequence of these forces. (3) Higher frequency waves (10 s T few min) are predicted to carry energy fluxes which are adequate to heat the chromosphere and corona. Nonlinear mechanisms may provide the damping. Closed flux tubes: (1) Long-period (T 1 hr) twists do not appear to be energetically capable of providing the required heating of active regions. (2) Loop resonances are found to occur as a result of waves being stored in the corona via reflections at the transition zones. The loop resonances act much in the manner of antireflectance coatings on camera lenses, and allow large energy fluxes to enter the coronal loops. The resonances may also be able to account for the observed fact that longer coronal loops require smaller energy flux densities entering them from below. (3) The waves exert large upward and downward forces on the chromosphere and corona.The National Center for Atmospheric Research is sponsored by the National Science Foundation.