T. Takakura

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 (Φ 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.

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 θ, 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 θ especially at small values of θ.

Dynamics of a cloud of fast electrons travelling through the plasma

Numerical analysis of quasi-linear relaxation has been made for four models of electron beam with a finite length travelling through the plasma. In Model 4, a model atmosphere of the corona is adopted and also an increase in the cross-section of the electron beam is taken into account. The electron velocity distribution generally becomes a quasi-plateau form in limited velocity and time ranges. If, however, collisional decay of the fast electrons is too strong and the initial beam density is not high enough, the plateau does not appear. Collisional damping of plasma waves cannot be neglected, since the growth rate of the waves is strongly suppressed by the appearance of the quasi-plateau.An approximate formula for the velocity distribution of the solar electrons passing through the corona has been derived analytically taking into account not only the interaction with plasma waves, but also the collisional damping of the plasma waves and collisions with thermal particles. By the use of this formula, we can easily compute the time profile of the plasma waves caused by these solar electrons at any given place in the interplanetary space. The validity of this semi-analytical approach is checked by the numerical analysis of Model 4, showing a satisfactory fit between the numerical and semi-analytical results.The direct application of this method to the problems of type III radio bursts is left to a later paper.

INTERPRETATION OF TIME CHARACTERISTICS OF SOLAR X-RAY BURSTS REFERRING TO ASSOCIATED MICROWAVE BURSTS.

It has been controversial whether the flare-associated hard X-ray bursts are thermal emission or non-thermal emission. Another controversial point is whether or not the associated microwave impulsive burst originates from the common electrons emitting the hard X-ray burst.It is shown in this paper that both the thermal and non-thermal bremsstrahlung should be taken into account in the quantitative explanation of the time characteristics of the hard X-ray bursts observed so far in the photon energy range of 10–150 keV. It is emphasized that the non-thermal electrons emitting the hard X-rays and those emitting the microwave impulsive burst are not common. The model is as follows, which is also consistent with the radio observations.At the explosive phase of the flare a hot coronal condensation is made, its temperature is generally 107 to 108K, the number density is about 1010 cm−3 and the total volume is of the order of 1029 cm3. A small fraction, 10−3–10−4, of the thermal electrons is accelerated to have power law distribution. Both the non-thermal and thermal electrons in the sporadic condensation contribute to the X-ray bursts above 10 keV as the bremsstrahlung. Fast decay of the harder X-rays (say, above 20 keV) for a few minutes is attributed to the decay of non-thermal electrons due to collisions with thermal electrons in the hot condensation. Slower decay of the softer X-rays including around 10 keV is attributed to the contribution of thermal component.

The location and size of a solar hard X-ray burst on September 27, 1969

The location and size of a solar impulsive hard X-ray burst have been determined in one dimension to a considerable precision with a balloon-borne X-ray modulation collimator. The center of the X-ray source is on the line passing through the center of a big Hα flare region of 3 arc min. The size of the X-ray source is remarkably smaller and may be one arc min or less.

Acceleration of electrons and solar flares due to quasi-static electric field

The storage of flare energy, efficient acceleration of electrons and the trigger of the flares are suggested to be attributed to a quasi-static electric field caused by a gas motion near the photosphere without satisfying the frozen condition. The primary cause of the onset of flares would be the acceleration of electrons due to the electric field above a critical strength. The electrons excite plasma waves which make the conductivity lower by several orders in the lower corona, so that the electro-magnetic energy I2L stored before the onset of the flare would be rapidly converted into the heat due to the ohmic loss in about 10 s.

Vertical Structure of Hard X-ray Flare

This paper presents studies of the vertical structure of hard X-ray flares for two contrasting examples. The 1981 May 13 flare contained a coronal hard X-ray source which was located above 50000 km above the photosphere. On the other hand, the 1981 July 20 flare had a chromospheric double source structure in the initial phase. Electrons in this case were able to stream freely from the corona to the chromosphere.

X-ray imaging of a solar limb flare on 1982 January 22

Simultaneous X-ray images in hard (20–40 keV) and softer (6.5–15 keV) energy ranges were obtained with the hard X-ray telescope aboard the Hinotori spacecraft of an impulsive solar X-ray burst associated with a flare near the solar west limb.The burst was composed of an impulsive component with a hard spectrum and a thermal component with a peak temperature of 2.8 × 107 K. For about one minute, the impulsive component was predominant even in the softer energy range.The hard X-ray image for the impulsive component is an extended single source elongated along the solar limb, rather steady and extends from the two-ribbon Hα flare up to 104 km above the limb. The centroid of this source image is located about 10″ (7 × 103 km) ± 5″ above the neutral line. The corresponding image observed at the softer X-rays is compact and located near the centroid of the hard X-ray image.The source for the thermal component observed in the later phase at the softer X-rays is a compact single source, and it shows a gradual rising motion towards the later phase.

Time variation of the spectrum of Gyro-synchrotron emission from the Sun

The emission spectra and their time variations of gyro-synchrotron emission from an ensemble of energetic electrons are computed for some initial power-law distributions of the electron energies N(ε)dε=ε−γ with γ=2 or 4. The spectra and decay curves of the emission are compared with solar microwave bursts in order to separately estimate the magnetic field H and γ. From a limited number of observations, we have γ≈ 3 and H ≈ 103 gauss for the microwave impulsive bursts, and γ≈ 2 and H ≈ (500–1000) gauss for the microwave type-IV bursts.

Long time delay between the peaks of intense solar hard X-ray and microwave bursts

It is shown that the long time delays more than five seconds between the peaks of intense hard X-ray and microwave bursts are concerned with two independent phenomena. One is the energy dependent time delays in X-rays and the other is the frequency dependent time delays in microwaves.The time delays of 5 s to 10 s between the peaks of solar hard X-ray burst (≲100 keV) obtained with Hinotori spacecraft and microwave burst at 17 GHz were observed exceptionally in three intense events with a spectral maximum at about 17 GHz. It is found that the peak of harder X-rays (≳300 keV) also delays in these events by about the same amount with respect to the softer X-rays (≲100 keV), so that the peak at 17 GHz nearly coincides (≲4s) with that of the harder X-rays. This is quite reasonable because the gyro-synchrotron emissions from the electrons below about 100 keV in the solar flares are generally negligible at high microwave frequencies (≳10 GHz). The optical thickness of the radio source decreases with frequency and is unity generally at about 10–20 GHz in intense bursts as inferred from the radio spectrum. Further delay of the peaks at the lower microwave frequencies is attributed to the temporal increase in the effective size of radio source which is optically thick at the lower frequencies.