Effects of turbulence on the electron cyclotron-maser mechanism for solar microwave spike bursts

It is shown that small magnetic perturbations can significantly alter the rates of cyclotron growth, absorption, mode conversion, and refraction because of the sensitive dependence of these processes on the field strength in narrow layers. In particular, growth lengths are increased, absorption depths decreased, mode conversion becomes more effective, and turbulent refraction leads to isotropization of the emission. The criteria for significant effects to occur are derived and it is shown that they can be met by the few-percent field perturbations observed in coronal loops. Relative to the theory of cyclotron-maser emission in smoothly varying plasmas, perturbations enable fundamental o-mode (o1) and second-harmonic x-mode (x2) radiation to saturate more effectively, increase the chance of x1, o1, and x2 radiation escaping to infinity through absorption and mode-coupling windows, and partially isotropize radiation emitted near the x-mode cutoff. It is concluded that o1 and x1 emission are both likely to be present, and that x2 emission is possible under some circumstances. However, x1 radiation can escape only at near-parallel propagation ( 0) or via mode conversion to the o-mode at 90°, whereas o1 and x2 emission can escape for a wide range of angles around = 0 and, under many circumstances, near = 90°.     

Polarization of fundamental type III radio bursts

The fundamental of type III bursts is only partially polarized, yet all theory for emission near the plasma frequency predicts pure o-mode emission. I argue depolarization is inherent in the burst itself. The o-mode radiation is intensely scattered and mode-converted when it temporarily falls behind its own source and finds itself in the medium that is already disturbed by the electron beam. In particular, mode conversion is very efficient and yet causes only modest angular scattering at the height were _p + 0.5.The predicted minimum polarization nearly equals the polarization of the harmonic, as observed. Spike polarization is naturally explained by the earlier arrival of the scattered o-mode. Additional residual polarization depends on the refraction at the site of emission; larger beam velocities imply higher polarization, as observed, because a larger fraction of the radiation escapes without mode-conversion. The polarization at the frequencies where U-bursts reverse is of particular interest.Support is acknowledged from the NSF Solar-Terrestrial Research Program.     

Microwave radiation from magnetic stars

Cyclotron microwave emission from magnetic stars is considered, assuming that they have coronae with the temperatureT10⁷ K and the emission measureEM10⁵⁴ cm^–3. It has been shown that the cyclotron radiation from a star with a dipole magnetic field has a specific spectrum with a maximum in the frequency rangesv _o/2 >v >sv _o/2 (s being the number of cyclotron harmonic, andv _o the gyrofrequency corresponding to the polar magnetic field) and radiation flux decreasing towards lower frequencies asv _4/3. The frequency of the spectrum maximum depends on the angle between the line-of-sight and the magnetic axis of the star. The observed radiation from a rotating magnetic star can be modulated with a modulation depth of about 0.2 at frequencies near maximum. The radiation is partially circularly-polarized in the sense of an extraordinary mode. The degree of polarization is almost constant at frequenciesv >sv _o/2 and increases with frequency atv >sv _o/2. The estimation of cyclotron radio fluxes of the nearest magnetic stars shows that they are observable in microwaves by means of modern radio astronomy.     

Electron-cyclotron maser emission in solar microwave spike bursts

A new model is developed for electron-cyclotron maser emission from flaring loops, which incorporates competition between driving of the instability and maser-induced relaxation, together with interactions between small neighboring regions of unstable plasma. This results in a picture in which radiation is emitted in bursts from regions whose length scale is determined self-consistently by previous bursts, while the unstable plasma fluctuates about the point, close to marginal stability, at which driving of the instability is balanced by relaxation due to maser-induced electron diffusion. Under the conditions applicable to flaring loops, time scales of fundamental x-mode (x1) driving and saturation are approximately equal at 1 ms, resolving a (10⁴–10⁶)-fold discrepancy in previous models and agreeing with the observed time scales of microwave spike bursts. Saturation effects are found to be especially effective in suppressing amplification of the most strongly growing modes. This suppression enables fundamental o-mode (o1) and second-harmonic x-mode (x2) emission to compete more effectively against x1 emission for the available free energy than has previously been estimated. Consideration of mode competition, burst time scales, suppression of growth due to overlap between amplification and absorption bands, and escape of radiation through absorption layers to the observer, implies that the observed radiation probably escapes from the corona principally in the o-mode, either emitted directly as o1 radiation or mode converted from x1 emission.     

Propagation and absorption of cyclotron maser radiation in solar microwave spike bursts

It has been argued that the loss-cone-driven electron cyclotron maser instability can account for the properties of millisecond microwave spike bursts observed during some solar flares. However, as it propagates outward from the corona, maser radiation undergoes gyroresonance absorption when its frequency is a harmonic of the local electron-cyclotron frequency. Existing analytical models using slab geometries predict that this absorption should be sufficiently strong to prevent the radiation from being seen at the observed levels, except under highly restrictive conditions or for unrealistic plasma parameters. A more comprehensive analysis is presented here to determine if and when maser radiation can escape to produce microwave spike bursts. This analysis employs numerical raytracing and incorporates propagation and absorption of fundamental maser emission in a realistic model of a coronal flux loop. It is found that ranges of physical conditions do exist under which maser radiation can escape to an observer and that these conditions are much more limiting for fundamental emission in the extraordinary ()-mode than in the ordinary (o)-mode. Detailed investigation implies that escaping radiation in the -mode is highly directional and chiefly observable toward the center of the solar disk, while escapingo-mode radiation is found to emerge from the corona over a much wider range of directions, with some cases corresponding to radiation observable near the solar limb.     

Depolarization of solar bursts due to scattering by low-frequency waves

The possibility is explored that fundamental plasma emission in solar radio bursts of types I, II, and III is depolarized due to scattering off low-frequency waves. Three ways in which depolarization might occur are identified: (1) one or several large-angle scatters, (2) several small-angle scatters close to the plasma level, and (3) many small-angle scatters well above the plasma level. It is pointed out that the degree p of polarization (p = 1 initially) may be approximated by p() = cos after one large-angle scatter through an angle , and that for backscatter ( > /2) the sense of polarization changes (from o-mode to x-mode senses). Possibility (2) involves coupling between the o- and x-mode components through their longitudinal parts, and is explored in some detail. The wave vectors k required for the scatterings are identified, and it is suggested that ion-sound waves are suitable for possibility (1) and whistlers for possibility (2). The whistlers may be generated by the streaming electrons themselves.Large-angle scattering is favourable for depolarizing type I emission, as proposed by Wentzel, Zlobec, and Messerotti (1986). Scattering by whistlers near the plasma level is favourable for depolarizing type III bursts. Several predictions are made based on these possibilities.     

Magnetoacoustic-gravity surface waves

The linearized theory for the parallel propagation of magnetoacoustic-gravity surface waves is developed for an interface of a horizontal magnetic field above a field-free medium. The media either side of the interface are taken to be isothermal. The dispersion relation is obtained for the case of a constant Alfvén speed. In the absence of gravity the interface may support one or two surface modes, determined by the relative temperatures and magnetism of the two media. The effect of gravity on the modes is examined and dispersion diagrams and eigenfunctions are given. In the usual - k _x diagnostic diagram, the domain of evanescence is shown to be divided into two distinct regions determining whether a given mode will have a decaying or growing vertical velocity component. In the absence of a magnetic field the transcendental dispersion relation may be rewritten as a polynomial. This polynomial possesses two acceptable solutions only one of which may exist in any given circumstances (depending on the ratio of the densities). If the gas density within the field exceeds that in the field-free medium, then the f-mode may propagate. The f-mode exists in a restricted band of horizontal wavenumber and only when the field-free medium is warmer than the magnetic atmosphere. An analytical form for the wave speed of the f-mode is obtained for small values of the Alfvén speed. It is shown that the f-mode is related to the fast magnetoacoustic surface wave, merging into that mode at short wavelengths.     

Determination of intrinsic mode and linear mode coupling in solar microwave bursts

An explicit equation of the propagational angle of microwave emission between the line-of-sight and the local magnetic field is newly derived based on the approximated formulae of nonthermal gyrosynchrotron emission (Dulk and Marsh in Astrophys. J. 259, 350, 1982). The existence of the solution of propagational angle is clearly shown under a series of typical parameters in solar microwave observations. It could be used to determine the intrinsic mode and linear mode coupling in solar microwave bursts by three steps. (1) The mode coupling may happen only when the angle approximately equals to 90 degrees, i.e., when the emission propagates through the quasi-transverse region (Cohen in Astrophys. J. 131, 664, 1960). (2) The inversion of polarization sense due to the weakly mode coupling takes place only when the transition frequency defined by Cohen (1960) is larger than the frequency of microwave emission, and an observable criterion of the weakly mode coupling in flaring loops was indicated by the same polarization sense in the two footpoints of a flaring loop (Melrose and Robinson in Proc. Astron. Soc. Aust. 11, 16, 1994). (3) Finally, the intrinsic mode of microwave emission is determined by the observed polarization and the calculated direction of local magnetic field according to the general plasma dispersion relation, together with the mode coupling process. However, a 180-degree ambiguity still exists in the direction of longitudinal magnetic field, to produce an uncertainty of the intrinsic mode. One example is selected to check the feasibility of the method in the 2001 September 25 event with a loop-like structure nearby the central meridian passage observed by Nobeyama Radio Heliograph and Polarimeters. The calculated angle in one footpoint (FP) varied around 90^° in two time intervals of the maximum phase, which gives a direct evidence of the emission propagating through a quasi-transverse region where the linear mode coupling took place, while, the angle in another FP was always smaller than 90^° where the mode coupling did not happen. Moreover, the right-circular sense at 17 GHz was always observed in both two FPs during the event, which supports that the transition frequency should be larger than 17 GHz in the first FP together with strong magnetic field of over 2000 Gauses in photosphere, where the weakly coupled case should happen. Moreover, there are two possibilities of the intrinsic mode in the two FPs due to the 180-degree ambiguity. (1) The emission of extraordinary (X) mode from the first FP turns to the ordinary (O) mode in the two time intervals of the maximum phase, while, the X-mode is always emitted from the second FP. (2) The inversion from O-mode to X-mode takes place in the first FP, while the O-mode keeps in the second FP. If the magnetic polarities in photosphere and corona are coincident in this event, the intrinsic mode belongs to the second case.     

Polarization of loop-top and footpoint sources in microwave bursts

The polarization is analyzed in four microwave bursts with one loop-top and two footpoint sources observed at 17 GHz with the Nobeyama Radioheliograph (NoRH). The loop-like structure of the four events is confirmed by simultaneous SOHO/MDI magnetograms and TRACE/EUV images or Yohkoh/SXT images. The heliocentric distance of the four events is greater than 30°. The three microwave sources in each given burst are polarized in the same sense. This may be interpreted in terms of extraordinary mode emission, taking into account the polarity of the underlying magnetic field and propagation effects, which may lead to inversion of the sense of polarization in the limbward foot and loop-top source of the flaring loop.     

Flare SOL2012-07-06: On the Origin of the Circular Polarization Reversal Between 17 GHz and 34 GHz

The new generation of multiwavelength radioheliographs with high spatial resolution will employ microwave imaging spectropolarimetry to recover flare topology and plasma parameters in the flare sources and along the wave propagation paths. The recorded polarization depends on the emission mechanism and emission regime (optically thick or thin), the emitting particle properties, and propagation effects. Here, we report an unusual flare, SOL2012-07-06T01:37, whose optically thin gyrosynchrotron emission of the main source displays an apparently ordinary mode sense of polarization in contrast to the classical theory that favors the extraordinary mode. This flare produced copious nonthermal emission in hard X-rays and in high-frequency microwaves up to 80 GHz. It is found that the main flare source corresponds to an interaction site of two loops with greatly different sizes. The flare occurred in the central part of the solar disk, which allows reconstructing the magnetic field in the flare region using vector magnetogram data. We have investigated the three possible known reasons of the circular polarization sense reversal – mode coupling, positron contribution, and the effect of beamed angular distribution. We excluded polarization reversal due to contribution of positrons because there was no relevant response in the X-ray emission. We find that a beam-like electron distribution can produce the observed polarization behavior, but the source thermal density must be much higher than the estimate from to the X-ray data. We conclude that the apparent ordinary wave emission in the optically thin mode is due to radio wave propagation across the quasi-transverse (QT) layer. The abnormally high transition frequency (above 35 GHz) can be achieved reasonably low in the corona where the magnetic field value is high and transverse to the line of sight. This places the microwave source below this QT layer, i.e. very low in the corona.     

Microwave emission from a sunspot

From the gyroresonance brightness temperature spectrum of a sunspot, one can determine the magnetic field strength by using the property that microwave brightness is limited above a frequency given by an integer-multiple of the gyrofrequency. In this paper, we use this idea to find the radial distribution of magnetic field at the coronal base of a sunspot in the active region, NOAA 4741. The gyroresonance brightness temperature spectra of this sunspot are obtained from multi-frequency interferometric observations made at the Owens Valley Radio Observatory at 24 frequencies in the range of 4.0–12.4 GHz with spatial resolution 2.2″–6.8″. The main results of present study are summarized as follows: first, by comparison of the coronal magnetic flux deduced from our microwave observation with the photospheric magnetic flux measured by KPNO magnetograms, we show that theo-mode emission must arise predominantly from the second harmonic of the gyrofrequency, while thex-mode arises from the third harmonic. Second, the radial distribution of magnetic fieldsB(r) at the coronal base of this spot (say, 2000–4000 km above the photosphere) can be adequately fitted by $$B(r) = 1420(1 \pm 0.080)\exp \left[ { - \left( {\frac{r}{{11.05''(1 \pm 0.014)}}} \right)^2 } \right]G,$$ wherer is the radial distance from the spot center at coronal base. Third, it is found that coronal magnetic fields originate mostly from the photospheric umbral region. Fourth, although the derived vertical variation of magnetic fields can be approximated roughly by a dipole model with dipole moment 1.6 × 10³⁰ erg G^?1 buried at 11000 km below the photosphere, the radial field distribution at coronal heights is found to be more confined than predicted by the dipole model.     

Noise storms and the structure of microwave emission of solar active regions

Solar radio and microwave sources were observed with the Very Large Array (VLA) and the RATAN-600, providing high spatial resolution at 91 cm (VLA) and detailed spectral and polarization data at microwave wavelengths (1.7 to 20 cm - RATAN). The radio observations have been compared with images from the Soft X-ray Telescope (SXT) aboard theYohkoh satellite and with full-disk phoptospheric magnetic field data from the Kislovodsk Station of the Pulkovo Observatory. The VLA observations at 91 cm show fluctuating nonthermal noise storm sources in the middle corona. The active regions that were responsible for the noise storms generally had weaker microwave emission, fainter thermal soft X-ray emission, as well as less intense coronal magnetic fields than those associated with other active regions on the solar disk. The noise storms did, however, originate in active regions whose magnetic fields and radiation properties were evolving on timescales of days or less. We interpret these noise storms in terms of accelerated particles trapped in radiation belts above or near active regions, forming a decimetric coronal halo. The particles trapped in the radiation belts may be the source of other forms of nonthermal radio emission, while also providing a reservoir from which energetic particles may drain down into lower-lying magnetic structures.Presented at the CESRA-Workshop on Coronal Magnetic Energy Release at Caputh near Potsdam in May 1994.     

A simulation study of the solar wind including the solar rotation effect

An axisymmetric solar wind structure including the solar rotation effect is studied by the method of MHD computer simulation. For the case of the radial magnetic field configuration, the simulation result is fairly well coincident with the steady-state solution. For the case of the dipole magnetic field configuration, the properties of the solution depend on the ratio of the gas pressure to the magnetic pressure-ratio) in the model. If the-ratio is small, a clearly defined stagnation region appears in the wind, in which the flow speed is very small and the azimuthal magnetic field is very weak because of the corotation of the plasma. If the-ratio is greater than 1, the plasma is not effectively trapped by the magnetic field so that the stagnation region is not clearly defined in the solution.     

Coronal emission line polarization

A discussion of a program for the computation of coronal emission line polarization is presented. The starting point is a general formulation of the scattering function for magnetic dipole transitions between any two total angular momentum levels, J J, J ± 1. Illustration of the behavior of the scattering function for different transitions is given. The integration of the scattering function over the solar disk and along the line of sight accounting for arbitrary distribution of magnetic fields as well as an inhomogeneous temperature and density structure of the corona is considered next.Sample results are presented for the numerical computation of the angle of maximum polarization and the degree of maximum polarization to be expected from idealized magnetic field configurations such as radial and dipole. A computation is included for a realistic field configuration predicted to exist at the time of the 1966 eclipse. The magnetic field input to the scattering calculation is based upon the potential field extension of photospheric magnetic fields. It is the purpose of the sample calculations to demonstrate how the measurement of emission polarization measurements can be interpreted in terms of the direction of coronal magnetic fields. Factors which lend ambiguity to such interpreations are clearly illustrated from the examples. These include the Hanle-effect depolarization and the depolarization at the Van Vleck angle.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Probing Twisted Magnetic Field Using Microwave Observations in an M Class Solar Flare on 11 February, 2014

This work demonstrates the possibility of magnetic-field topology investigations using microwave polarimetric observations. We study a solar flare of GOES M1.7 class that occurred on 11 February, 2014. This flare revealed a clear signature of spatial inversion of the radio-emission polarization sign. We show that the observed polarization pattern can be explained by nonthermal gyrosynchrotron emission from the twisted magnetic structure. Using observations of the Reuven Ramaty High Energy Solar Spectroscopic Imager, Nobeyama Radio Observatory, Radio Solar Telescope Network, and Solar Dynamics Observatory, we have determined the parameters of nonthermal electrons and thermal plasma and identified the magnetic structure where the flare energy release occurred. To reconstruct the coronal magnetic field, we use nonlinear force-free field (NLFFF) and potential magnetic-field approaches. Radio emission of nonthermal electrons is simulated by the GX Simulator code using the extrapolated magnetic field and the parameters of nonthermal electrons and thermal plasma inferred from the observations; the model radio maps and spectra are compared with observations. We have found that the potential-magnetic-field approach fails to explain the observed circular polarization pattern; on the other hand, the Stokes-\(V\) map is successfully explained by assuming nonthermal electrons to be distributed along the twisted magnetic structure determined by the NLFFF extrapolation approach. Thus, we show that the radio-polarization maps can be used for diagnosing the topology of the flare magnetic structures where nonthermal electrons are injected.     

Radio emission from stellar flares

An overview is given of the observations of stellar radio flares, defined as radio emission which is both variable in time and created by explosive releases of magnetic energy. The main sources of such flares are late-type Main-Sequence stars, classic close binaries, X-ray binaries, and pre-Main-Sequence stars.We summarize the interpretations of these observations in terms of the various incoherent and coherent emission mechanisms. The possible importance of a coherent emission process in electrostatic double layers is pointed out.We briefly indicate the diagnostic importance of radio emission for the flare process in classic and compact stars. In particular we discuss the possible production of radio flares from interactions between an accretion disk and the magnetic field of the central object.     

Mode Conversion of Solar <Emphasis Type="Italic">p</Emphasis>-Modes in Non-Vertical Magnetic Fields

Sunspots absorb and scatter incident f- and p-modes. Until recently, the responsible absorption mechanism was uncertain. The most promising explanation appears to be mode conversion to slow magnetoacoustic-gravity waves, which carry energy down the magnetic field lines into the interior. In vertical magnetic field, mode conversion can adequately explain the observed f-mode absorption, but is too inefficient to account for the absorption of p-modes. In the first paper of the present series we calculated the efficiency of fast-to-slow magnetoacoustic-gravity wave conversion in uniform non-vertical magnetic fields. We assumed two-dimensional propagation, where the Alfvén waves decouple. In comparison to vertical field, it was found that mode conversion is significantly enhanced in moderately inclined fields, especially at higher frequencies. Using those results, Cally, Crouch, and Braun showed that the resultant p-mode absorption produced by simple sunspot models with non-vertical magnetic fields is ample to explain the observations. In this paper, we further examine mode conversion in non-vertical magnetic fields. In particular, we consider three-dimensional propagation, where the fast and slow magnetoacoustic-gravity waves and the Alfvén waves are coupled. Broadly speaking, the p-mode damping rates are not substantially different to the two-dimensional case. However, we do find that the Alfvén waves can remove similar quantities of energy to the slow MAG waves.     

Electrostatic Wave Instability and Plasma Radiation from Coronal Loops

Polarization properties of solar and stellar radio emission require, in some cases, emission below the third or fourth coronal electron gyro level, < 3,_c; 4, _c. In the context of plasma radiation, the source parameters should be such that the intermediate magnetic field condition 1 < _p ² / _c ² < 3 is satisfied. Supposing this condition, we investigate the generation of electrostatic waves in a warm background plasma with a high-energy component of magnetically trapped electrons. We invoke the conversion of upper-hybrid waves and Bernstein waves into electromagnetic radiation as being responsible for intense radio emission from a coronal magnetic loop. Moreover, odd-half harmonic emissions in the solar radio spectrum as well as the o-mode polarization at the second harmonic of the plasma frequency are natural consequence of this proposed model.     

Spectropolarimetric Observations of the Unique White Dwarf GD 356 on the 6-m BTA

The results of spectropolarimetric observations of a unique magnetic white dwarf with emission lines, GD 356, on the 6-m BTA are presented. The star's magnetic field is estimated and it is shown not to rotate over times of 5 yr. Allowance for magnetic deformation of the star's surface, resulting an a nonuniform temperature distribution over its surface, showed that in the region of the magnetic poles the conditions may be satisfied for a radiative diskon in the form of a plasma jet, originating from the action of cyclotron radiation pressure. It is shown that the effect of nonuniformity of the surface temperature distribution of the white dwarf can produce the observed broad-band and resonance polarization of the stellar emission.     

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.