Solar flares accelerate particles, and their distribution is usually non-thermal. Non-thermal electrons are prone to velocity space instabilities driving various plasma waves which, in turn, couple into observable radio waves. Such coherent emissions are the result of the combined action of many electrons organized by kinetic plasma waves and can therefore be extremely efficient. Small coherent radio bursts at the limit of present routine observations emit an energy of some 10¹⁵ erg. Even if the conversion of particle energy into radio emission may occur at a ratio as low as 10^-6, the energy in the electron population that excites coherent radio emission is a tiny fraction of the flare energy. Thus a slight deviation from an isotropic Maxwellian electron distribution in the course of acceleration, as a result of particle propagation or magnetic trapping, may be sufficient to cause coherent radio emission.

Radio-quiet flares should be infrequent!

It is not surprising that many radio bursts are not accompanied with X-ray emission as observed with present sensitivity. More astonishing are reports of radio-quiet flares. Simnett and Benz (A&A 165, 1986) found no coherent radio emission between 100 and 1000 MHz in 15% of the events having count rate >1000 cts/s at photon energies >25 keV observed by the Hard X-Ray Burst Spectrometer (HXRBS) on the Solar Maximum Mission. The detection ratio did not improve in statistics based on more sensitive radio observations and larger frequency range, extending up to 4000 MHz: In 17% of the X-ray events observed by the Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) , no coherent radio emission was associated in Phoenix-2 observations between 100 and 4000 MHz (Benz et al., Solar Physics 226, 2005). The enhanced sensitivity and the larger search range of frequencies must have increased the association rate. On the other hand, the extension to smaller events in X-ray magnitude from HXRBS to RHESSI may have decreased the association rate. The two opposing effects have apparently cancelled out. The existence of such ‘radio-quiet’ flares puts severe constraints on the acceleration and containment of energetic flare electrons.

Some correlate well! A more typical case of correlation between X-rays and coherent radio emission in the 100 to 4000 MHz range, observed on 2002-04-25 by Phoenix-2 in Zurich and RHESSI.

Analysis of the radio-quiet flares

So, what about these radio-quiet flares? We have analyzed them in detail and find the following properties:

• Out of a total number of 201 coincident flares (RHESSI – Phoenix-2) having a GOES class >C5, 29 flares were found initially radio-quiet in the 100–4000 MHz range. A closer inspection with increased sensitivity by integration yielded radio emission in only one case. Thus radio-quiet is a yes/no property.
• A surprising number of 22 (76%) out of the 29 radio-quiet events occurred at a radial distance of more than 800″ from disk center, indicating that radio waves associated with a limb flare may be completely absorbed.
• The remaining 7 radio-quiet flares that occurred within 800″ had a property in common: All of them were accompanied with metric type III radio emission below 100 MHz, as reported by the spectrometers in Culgoora, IZMIRAN, Learmont, Ondrejov, Potsdam or San Vito.
• These 7 radio-quiet flares occurring within 800″ had another startling property: All of them had no RHESSI counts above 25 keV. Thus they had weak non-thermal emission in general or were soft in their non-thermal X-ray spectrum. In fact, there is evidence for both: the radio-quiet flares were all below C7.0 class except for one event. There were two events with a large count rate at 12–25 keV (> 300 cts/s). Thus they must have been very soft to vanish at 25 keV.

So how does a flare become radio-quiet?

What does a flare have to do to remain undetected by current radio instruments? The best idea is to stay small. Only one flare out of 11 with GOES class larger than M1 was radio-quiet. A good idea is furthermore to occur at the limb. Assuming a random distribution of flare positions, 33.4 flares out of the total number of 201 are expected to occur at the limb (>800″). The fact that 22 of the radio-quiet flares were indeed found at the limb, indicates that 66% of the limb flares larger than C5 are radio-quiet. A third idea is to be soft in non-thermal electron distribution. The duration, impulsive or extended, does not seem to help, however. Of course, the gyrosynchrotron emission in centimeter waves and thermal emission in millimeter waves cannot escape detection given a large enough instrument, but these radiations are not the issue here.

The cloak of invisibility of the flare process against radio detection in the 100–4000 MHz range — small, on the limb and soft — may be interpreted by reduced emission and/or absorption.

1. In limb events, the propagation path is initially nearly horizontal. The dwelling time of the radio waves in a region having a plasma frequency close to the radiation frequency is much longer near the limb. Thus the absorption is higher, as well as the chances to meet an occulting region having a plasma frequency above the radiation frequency. Limb events are evidently more likely to be absorbed or occulted.
2. Soft electron energy distributions are less likely to become loss-cone unstable and need a longer beam propagation time to develop a bump-on-tail instability. Thus hard X-ray events originating from a soft energy distribution are less likely to have decimetric loss-cone or beam-propagation emissions.
3. The most difficult characteristic to interpret seems to be the smallness of radio-quiet flares. Remember that the radio emission of the smallest detectable X-ray flare constitutes a minute fraction of its energy. Thus, it may not be the lack of energy in small flares that reduces the association rate, but the smaller number of elements yielding fewer chances for radio emission to escape.

Conclusions

Our conclusions:

• There are no really radio-quiet flares >C5 if the full meter and decimeter wave ranges are surveyed and the source is observed from above (i.e. not from the limb).
• There is no evidence for purely thermal flares >C5 without super-thermal electrons. Given enough propagation path length, all these flares produce coherent radio emission at least by electron beams.
• A comparison of radio and X-ray emissions from the flare electron accelerator must focus on events near the center.
• The results motivate to compare radio and X-ray emissions not only in association, but in position. Future multi-frequency radio capabilities necessary to accomplish this, combined with soft and hard X-ray imaging, could make a break-through in the understanding of flares.

Based on a paper recently submitted to Solar Physics by Arnold O. Benz, Roman Brajša, and Jasmina Magdalenić