Evaluating Mean Magnetic Field in Flare Loops

We analyze multiple-wavelength observations of a two-ribbon flare exhibiting apparent expansion motion of the flare ribbons in the lower atmosphere and rising motion of X-ray emission at the top of newly-formed flare loops. We evaluate magnetic reconnection rate in terms of V _r B _r by measuring the ribbon-expansion velocity (V _r) and the chromospheric magnetic field (B _r) swept by the ribbons. We also measure the velocity (V _t) of the apparent rising motion of the loop-top X-ray source, and estimate the mean magnetic field (B _t) at the top of newly-formed flare loops using the relation 〈V _t B _t〉≈〈V _r B _r〉, namely, conservation of reconnection flux along flare loops. For this flare, B _t is found to be 120 and 60 G, respectively, during two emission peaks five minutes apart in the impulsive phase. An estimate of the magnetic field in flare loops is also achieved by analyzing the microwave and hard X-ray spectral observations, yielding B=250 and 120 G at the two emission peaks, respectively. The measured B from the microwave spectrum is an appropriately-weighted value of magnetic field from the loop top to the loop leg. Therefore, the two methods to evaluate coronal magnetic field in flaring loops produce fully-consistent results in this event.     

The self absorption of gyro-synchrotron emission in a magnetic dipole field: Microwave impulsive burst and hard X-ray burst

The gyro-synchrotron emission from a model source with a non-uniform magnetic field is computed taking into account the self absorption. This model seems adequate not only to interpret the radio spectrum and its time variation of microwave impulsive bursts but also to solve the discrepancy between the numbers of non-thermal electrons emitting radio burst and those emitting hard X-ray burst.The decrease of flux of radio burst with decreasing frequency at low microwave frequencies is due to the self absorption and/or the thermal gyro-absorption. In this frequency range, the radio source is optically thick even at weak microwave bursts. The weakness of the bursts may be rather due to the small size of the radio source and/or the weakness of the magnetic field than the small number density of the non-thermal electrons.The time variation of the flux of radio burst may be mainly attributed to the variation of source size in a horizontal direction ( direction) instead of the variation of the number density of non-thermal electrons itself, implying that the acceleration region progressively moves in the horizontal direction leaving the non-thermal electrons behind during the increasing phase of the radio burst.     

A comparison of the optical and microwave emissions of some major solar flares

In the first part of the paper, we study the relations between the frequency of maximum radio flux f _max and the magnetic field strength at the photosphere B _p and between the maximum radio flux F _max and the field and its scale L for two differing flares occurring above very different photospheric conditions. It is shown that the simple relations predicted by the gyro-synchrotron emission mechanism f _max B _p and F _max B ² L ² account for the fact that the flares produced microwave bursts of about the same F _max, but of differing f _max.The spectra of type IV radio bursts associated with three large proton flares with post-flare loops have been analyzed. It is found that the decimetric peak vanishes with the onset of the first optical loops. This is consistent with the model of Kopp and Pneuman (1976) which associates growing systems of loops with gradual fieldline reconnection above flaring regions.     

Ion-Sound Model of Microwave Spikes with Fast Shocks in the Reconnection Region

A new model for solar spike bursts is considered based on the interaction of Langmuir waves with ion-sound waves: l+st. Such a mechanism can operate in shock fronts, propagating from a magnetic reconnection region. New observations of microwave millisecond spikes are discussed. They have been observed in two events: 4 November 1997 between 05:52–06:10 UT and 28 November 1997 between 05:00–05:10 UT using the multichannel spectrograph in the range 2.6–3.8 GHz of Beijing AO. Yohkoh/SXT images in the AR and SOHO EIT images testify to a reconstruction of bright loops after the escape of a CME. A fast shock front might be manifested as a very bright line in T _e SXT maps (up to 20 MK) above dense structures in emission measure (EM) maps. Moreover one can see at the moment of spike emission (for the 28 November 1997 event) an additional maximum at the loop top on the HXR map in the AR as principal evidence of fast shock propagation. The model gives the ordinary mode of spike emission. Sometimes we observed a different polarization of microwave spikes that might be connected with the depolarization of the emission in the transverse magnetic field and rather in the vanishing magnetic field in the middle of the QT region. Duration and frequency band of isolated spikes are connected with parameters of fast particle beams and shock front. Millisecond microwave spikes are probably a unique manifestation of flare fast shocks in the radio emission.     

A relationship between the brightness temperatures for type III bursts

Type III bursts often have brightness temperatures at the fundamental greater than 10⁹K. If the fundamental emission is due to scattering of Langmuir waves into transverse waves by thermal ions, this implies that induced scattering dominates over spontaneous scattering, which in turn requires that the energy density in Langmuir waves be greater than some minimum value, e.g. W ^l > 3 × 10^-10 erg cm^-3 for bursts at f _p = 100 MHz. Such Langmuir waves become isotropic on a time-scale shorter than the rise-time of type III bursts, e.g. < l s at f _p = 100 MHz. Consequently, their coalescence, leading to emission at the second harmonic, proceeds. The above inequalities would imply a brightness temperature at the second harmonic in excess of 10⁹K at f = 200 MHz.The predicted values of the brightness temperatures _T1 ^t and _T2 ^t (at the fundamental and second harmonic respectively) can be expressed in terms of an optical depth . After is eliminated a functional relation between _T1 ^t , _T2 ^t and the plasma frequency, f _p , remains. The form of this relation is not dependent on a quantitative theory of how the Langmuir waves are generated by the stream of electrons. Consequently, comparison with observed quantities should provide further insight into the detailed properties of the emission processes.     

Spectral distributions of microwave bursts

The lack of open literature publication of the distributional properties of the cm-λ spectra of solar microwave bursts has lead to some erroneous concepts of the typical characteristics of these spectra. To provide more accurate information, this paper sets forth various distributions of the peak flux density spectra of large numbers of bursts, based on observations of the Sagamore Hill Radio Observatory at nine discrete frequencies between 245 and 35000 MHz over the years 1968–1971. As a foundation for the distribution studies, the basic spectral classification system is outlined. The majority of burst spectra were found to contain a cm-λ component having a single spectral maximum in the 1400 to 35000 MHz range; such spectra are designated C type. A study of the correlation of the spectral maximum frequency f _max of the cm component and the photospheric magnetic field strength of the associated region shows a tendency for greater correlation at higher f _max for stronger magnetic sssfields. A study of the correlation for C type spectra between f _max and the quasi-cutoff frequency f _qc on the low-frequency side shows that for bursts of moderate peak flux density (50–500 sfu) f _qc is well correlated with f _max; a good fit to the relation f _max=A f _qc is found with A =3.4. The possible attenuating mechanisms responsible for the spectral shaping of the cm component are discussed.     

Circular radiation by a monopole around neutron stars

Radiation by a monopole which revolves round a neutron star is investigated in detail. Using radiant probabilityW _p ^t (k), we solve the radiant kinetic equation and proliferative equation of a monopole having the distribution functionf _p, and obtain the solution of wave numberN _k ^t (r) and distribution functionf _p. From these solutions, we know when the monopole moves round the neutron star; the exponential radiation is yielded with change of the motive orbit radiusr. As radiusr increases, the radiation appears as a saturated effect.     

A two-component model of impulsive microwave burst emission consistent with soft and hard X-rays

A two-component (core-halo) emission model has been applied reconciling hard and soft X-ray burst emissions with the microwave burst radiation. The core region is represented by a nonthermal energy distribution (Maxwellian+power law tail) and assumed to be surrounded by a thermal halo. Parameters characterizing the energy distribution and emission measures have been derived numerically from soft and hard X-ray measurements. Using an artificial magnetic field model the microwave flux spectrum has been calculated on the basis of gyro-synchrotron emission and absorption by solving the equation of radiation transfer along the ray trajectories. Open parameters were used to adapt the spectrum to the radio measurements.Thus probable informations about the most appropriate magnetic field parameters as well as about the time- and frequency- dependent source diameters (yielding growth velocities of the core region during the impulsive phase) are deduced for the burst of 1972 May 18 as an example. A fit of the observed spectrum at the burst maximum is consistent with a magnetic field of 150O G at the core centre decreasing up to about 40 G at the top of the halo at a height of 50 000 km above the centre, a core density of 10¹⁰ cm^–3 decreasing to 10⁹ cm^–3 at the outer halo boundary, and a core diameter of 15 000 km (]20).Due to the simple geometry and emission process adopted,- the model refers primarily to special impulsive bursts. For the representation of broad band microwave bursts, e.g. type IV , events, a more complex source geometry and/or other variants of the emission mechanism must be invoked.     

Statistical Characteristics on SEPs,Radio-Loud CMEs,Low Frequency Type II and Type III Radio Bursts Associated with Impulsive and Gradual Flares

We have statistically analyzed a set of 115 low frequency (Deca-Hectometer wavelengths range) type II and type III bursts associated with major Solar Energetic Particle (SEP: E_p?>?10 MeV) events and their solar causes such as solar flares and coronal mass ejections (CMEs) observed from 1997 to 2014. We classified them into two sets of events based on the duration of the associated solar flares:75 impulsive flares (duration <?60 min) and 40 gradual flares (duration >?60 min).On an average, the peak flux (integrated flux) of impulsive flares?×?2.9 (0.32 J m^?2) is stronger than that of gradual flares M6.8 (0.24 J m^?2). We found that impulsive flare-associated CMEs are highly decelerated with larger initial acceleration and they achieved their peak speed at lower heights (??27.66 m s^?2 and 14.23 R_o) than the gradual flare-associated CMEs (6.26 m s^?2 and 15.30 R_o), even though both sets of events have similar sky-plane speed (space speed) within LASCO field of view. The impulsive flare-associated SEP events (R_t?=?989.23 min: 2.86 days) are short lived and they quickly reach their peak intensity (shorter rise time) when compared with gradual flares associated events (R_t?=?1275.45 min: 3.34 days). We found a good correlation between the logarithmic peak intensity of all SEPs and properties of CMEs (space speed: cc?=?0.52, SE_cc?=?0.083), and solar flares (log integrated flux: cc?=?0.44, SE_cc?=?0.083). This particular result gives no clear cut distinction between flare-related and CME-related SEP events for this set of major SEP events. We derived the peak intensity, integrated intensity, duration and slope of these bursts from the radio dynamic spectra observed by Wind/WAVES. Most of the properties (peak intensity, integrated intensity and starting frequency) of DH type II bursts associated with impulsive and gradual flare events are found to be similar in magnitudes. Interestingly, we found that impulsive flare-associated DH type III bursts are longer, stronger and faster (31.30 min, 6.43 sfu and 22.49 MHz h^?1) than the gradual flare- associated DH type III bursts (25.08 min, 5.85 sfu and 17.84 MHz h^?1). In addition, we also found a significant correlation between the properties of SEPs and key parameters of DH type III bursts. This result shows a closer association of peak intensity of the SEPs with the properties of DH type III radio bursts than with the properties DH type II radio bursts, atleast for this set of 115 major SEP events.

     

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 .     

Electron beams and associated rapid fluctuations in solar flares

Recent observations show that the rapid fluctuations in radio, hard X-ray, and H emissions are closely associated with type III and microwave (or decimetric) bursts during the impulsive and/or preimpulsive phases of solar flares.In order to clarify the physical processes of these observed phenomena, this paper proposes a tentative model of two acceleration regions A (source of type III bursts) and B (source of microwave or decimetric bursts) formed in the neutral sheet and at the top of a flaring loop, respectively; and also suggests that the electron beams streaming from region A and/or region B downward to the chromosphere are responsible for the rapid fluctuations in the different emissions mentioned above during the impulsive and/or pre-impulsive phases of solar flares.     

The Influence of a Uniform Magnetic Field of Arbitrary Strength on Turbulence

The spectral tensor of turbulent motion in an infinite conductive incompressible medium is given in the case of a uniform magnetic field of any strenght affecting a homogeneous turbulence. With the help of BOCHNER 's theorem we make sure that the trace u_i(x, t) u_i(x, t) is non-negative. The presence of a weak magnetic field causes a damping of the turbulence, in some cases a strengthening. For strong magnetic fields the norms of the velocity vectors parallel and perpendicular to B approach one and the same value. Compared with the correlation length measured perpendicular to the magnetic field the correlation length measured along the magnetic field increases. Furthermore, our formulas have allowed to calculate the dependence of the α-effect on the magnetic field.     

Two Regularities in the Coronal Green-Line Brightness – Magnetic Field Coupling and the Heating of the Corona

To study the quantitative relationship between the brightness of the coronal green line 530.5 nm Fe xiv and the strength of the magnetic field in the corona, we have calculated the cross-correlation of the corresponding synoptic maps for the period 1977 – 2001. The maps of distribution of the green-line brightness I were plotted using every-day monitoring data. The maps of the magnetic field strength B and the tangential B _t and radial B _r field components at the distance 1.1 R _⊙ were calculated under potential approximation from the Wilcox Solar Observatory (WSO) photospheric data. It is shown that the correlation I with the field and its components calculated separately for the sunspot formation zone ±30° and the zone 40 – 70° has a cyclic character, the corresponding correlation coefficients in these zones changing in anti-phase. In the sunspot formation zone, all three coefficients are positive and have the greatest values near the cycle minimum decreasing significantly by the maximum. Above 40°, the coefficients are alternating in sign and reach the greatest positive values at the maximum and the greatest negative values, at the minimum of the cycle. It is inferred that the green-line emission in the zone ±30° is mainly controlled by B _t, probably due to the existence of low arch systems. In the high-latitude zone, particularly at the minimum of the cycle, an essential influence is exerted by B _r, which may be a manifestation of the dominant role of large-scale magnetic fields. Near the activity minimum, when the magnetic field organization is relatively simple, the relation between I and B for the two latitudinal zones under consideration can be represented as a power-law function of the type I ∝ B ^q. In the sunspot formation zone, the power index q is positive and varies from 0.75 to 1.00. In the zone 40 – 70°, it is negative and varies from −0.6 to −0.8. It is found that there is a short time interval approximately at the middle of the ascending branch of the cycle, when the relationship between I and B vanishes. The results obtained are considered in relation to various mechanisms of the corona heating.     

Modelling p-Mode Interaction with a Spreading Sunspot Field

Sunspots absorb and scatter incident p modes. The dominant mechanism is still uncertain. One possibility, mode conversion to slow magneto-acoustic waves, has been shown to yield results in agreement with observations for the f mode only. Absorption of p modes in simple vertical magnetic field models is too weak by an order of magnitude or more. Here we report on numerical calculations of p modes encountering a simple sunspot model with field which spreads with height. It is found that p-mode absorption is greatly enhanced by field spread, to a level consistent with observations, and it appears that it occurs preferentially in the outer regions of the spot, in line with recent results from acoustic holography.     

On the Possible Connection between Photospheric 5-Min Oscillation and Solar Flare Microwave Emission

Dynamic spectra of low-frequency modulation of microwave emission from solar flares are obtained. Data of 15 bursts observed in 1989–2000 with Metsähovi radio telescope at 37 GHz have been used. During 13 bursts a 5-min modulation of the microwave emission intensity was detected with the frequency of ν _I = 3.2± 0.24 (1σ) mHz. Five bursts revealed a 5-min wave superimposed on a ～1 Hz, linear frequency modulated signal generated, presumably, by coronal magnetic loop, this wave frequency is ν_fm = 3.38± 0.37 (1σ) mHz. Both intensity and frequency modulations detected are in good agreement with the data on 5-min global oscillations of photosphere and with the data on the umbral velocity oscillations observed in the vicinity of sunspots. Possible role of p-mode photospheric oscillations in modulation of microwave burst emission is discussed.     

Improved values for the solar micro- and macro-turbulent filter functions

The contributions of any arbitrary photospheric velocity field to (macroturbulent) line displacement, and to (microturbulent) line broadening can be expressed by the macro- and micro-turbulent filters f _M (k) and f _t(_k), where _k is the wavenumber of the energy spectrum in which the line-of-sight component of the velocity field can be decomposed. As a correction to a previous computation of f _M and f _t we give in this Note improved values for the filter functions for weak lines in LTE. An example of the way to use the filter functions is given.     

Impulsive and hot thermal solar flares

Some X-class flares (hot thermal flares, HTF) observed with the Hinotori satellite show unique behavior: slow time variability, a compact hard X-ray source containing dense (n > 10¹¹ cm^–3) and hot (T > 3 × 10⁷ K) plasma, and unusually weak microwave emission in spite of the intense magnetic field (B > 330 G) required theoretically to sustain the hot plasma. These observations show that HTF's have essentially thermal characteristics throughout the flare evolution, while in impulsive flares, there is a transition in the energy release mode from particle acceleration (impulsive phase) to plasma heating (gradual phase). This behavior can be explained in a unified manner by employing parallel DC electric field acting over large distances.     

Time Evolution of the Turnover Frequency for Diagnosis of the Coronal Magnetic Field

Two impulsive microwave bursts observed by Owens-Valley Solar Arrays (OVSA)are studied.The fast time variation of the turnover frequency in these bursts is quite different from the constant value in the earlier conclusion.The observational turnover frequencies are consistent with the calculations using the non-thermal gyro- synchrotron radiation model.We find the turnover frequency may play an important role for calculating the coronal magnetic field on the basis of Dulk and Marsh's ap- proximations.     

Radio and soft X-ray evidence for dense non-potential magnetic flux tubes in the solar corona

The source positions of solar radio bursts of spectral types I, III(U) and III(J) and V observed by the Culgoora radioheliograph are found to lie almost radially above soft X-ray loops on pictures taken by the S-056 telescope aboard Skylab. The radio source positions and the X-ray loops occur near magnetic loops on computed potential field maps. However, the magnetic induction required to explain the radio observations is much greater than the computed potential field value at that height. Dense current-carrying magnetic flux tubes emanating from active regions on the Sun and extending to 1.5R above the photosphere provide a satisfactory model for the radio bursts.     

Instability of Electrons Trapped by the Coronal Magnetic Field and Its Evidence in the Fine Structure (Zebra Pattern) of Solar Radio Spectra

Solar radio emission is a significant source of information regarding coronal plasma parameters and the processes occurring in the solar atmosphere. High resolution frequency, space, and time observations together with the developed theory make it possible to retrieve physical conditions in the radiation source and recognize the radiation mechanisms responsible for various kinds of solar radio emission. In particular, the high brightness temperature of many bursts testifies to coherent radiation mechanisms, that is, to plasma instabilities in the corona. As an example, the fine structure of solar radio spectra looking like a set of quasi-harmonic stripes of enhanced and lowered radiation, which is observed against the type IV continuum at the post-flare phase of activity, is considered. It is shown that such emission arises from a trap-like source filled with a weakly anisotropic equilibrium plasma and a small addition of electrons which have a shortage of small velocities perpendicular to the magnetic field. For many recorded events with the mentioned fine spectral structure the instability processes responsible for the observed features are recognized. Namely, the background type IV continuum is due to the loss-cone instability of hot non-equilibrium electrons, and the enhanced striped radiation results from the double-plasma-resonance effect in the regions where the plasma frequency f _p coincides with the harmonics of electron gyrofrequency f _B ; f _p=sf _B . Estimations of the electron number density and magnetic field in the coronal magnetic traps, as well as the electron number density and velocities of hot electrons necessary to excite the radiation with the observed fine structure, are given. It is also shown that in some cases several ensembles of non-equilibrium electrons can coexist in magnetic traps during solar flares and that its radio signature sensitively depends on the parameters of the distribution functions of the various ensembles.