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Astron. Astrophys. 328, 390-398 (1997)

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5. Discussion

We have shown that fast flare electrons with a power-law energy distribution trapped in magnetic loops are generating plasma waves at the upper hybrid frequency which is here considered as the source of the solar decimetric continuum. Evidently this source is located near a flaring loop and its magnetic field should be sufficiently weak satisfying the condition [FORMULA]. This condition is necessary in order to prevent a strong gyroresonance absorption at the layers [FORMULA] and [FORMULA] at the escape of the radiation from the source region.

The absorption of the decimetric continuum due to free-free transitions in the corona at [FORMULA] is rather high, which favours emission at the second harmonic of the plasma frequency [FORMULA]. This emission turns out to be polarized in the ordinary sense within a wide cone of angles [FORMULA] between the (perpendicular) magnetic field and the direction to the observer.

The direct vicinity of the source of the decimetric continuum to the flare loop (or system of flare loops, cf. Fig. 3) allows to explain the good temporal and spatial correlation between the decimetric continuum and the microwave bursts. This circumstance allows to conclude that both components are feeded by one and the same source of fast electrons originating during the flare process.

The main difference between our results and the conclusion by Benz & Kuijpers (1974) is connected with the problem of the use of a distribution function with a sharp boundary of the loss cone. A loss cone with a smooth boundary appears physically more realistic and gives the main contribution to the instability since it provides a part of a positive derivative [FORMULA] in Eq. (1) for the growth rate of the instability.

In order to obtain an instability for plasma waves from fast flare-electrons with a power-law energy spectrum, Benz & Kuijpers (1974) investigated the deformation of the initial distribution function by collisions of the fast electrons with particles of the background plasma. According to their estimations the time necessary for producing the instability is about 37 s for plasma parameters corresponding to the source region of the decimetric continuum. In our case, collisions of fast electrons with particles of the background plasma should not have an essential influence on the instability because the characteristic time of the formation of the loss cone for the distribution function of the fast electrons after their injection into the trap is of the order [FORMULA] s. This caracteristic time was found using the following values for the characteristic length of the magnetic trap [FORMULA] and the mean velocity of the fast electrons v: [FORMULA] cm and [FORMULA] - [FORMULA] cm s-1. The characteristic time of the development of the instability is [FORMULA] s [cf. Eq. (16)]. After the generation of the instability a further evolution of the distribution function takes place due to the interaction of the electrons with the plasma waves as a quasilinear effect, which is a more rapid process than the collisions of the fast electrons with the particles of the background plasma.

We estimated the total number of fast electrons needed for the generation of the decimetric continuum with an observed brightness temperature [FORMULA] K to be of order [FORMULA]. In order to compare this quantity with the number of electrons necessary for the generation of the related microwave burst, one can use the formula for the maximum frequency of the spectrum of gyrosynchrotron radiation from electrons with a power-law energy distribution (Dulk & Marsh 1982):


From Eq. (54) follows that for [FORMULA] GHz, [FORMULA] G, and [FORMULA] we obtain [FORMULA] cm-2. Taking a characteristic size of the microwave-burst source [FORMULA] cm we obtain [FORMULA] cm-3 and the total number of fast electrons [FORMULA]. The estimation of the number [FORMULA] made in Sect. 4.2 for the solar decimetric continuum is of the order of 20 % of this quantity. Hence a non-negligible part of the fast flare electrons should be injected into the source region of the decimetric continuum to provide brightness temperatures up to [FORMULA] K, as observed.

The formation of an instability of plasma waves inside the source of the microwave burst at a temperature of the background plasma [FORMULA] - [FORMULA] K appears less likely because this would require a relatively high density of fast electrons [FORMULA], although for sufficiently large events this possibility cannot be excluded.

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© European Southern Observatory (ESO) 1997

Online publication: March 24, 1998