For each of the nine dMe flare stars listed above, we have counted the number of bursts reported in the literature, taking into account the methods used to prove the stellar origin of the bursts and the total number of observing hours. Many radio bursts were detected in the metre range, but we have focussed on the observations near 21 cm in order to have data comparable to our observations. On the other hand, an important part of bursts was detected at 6 cm (mainly with the Very Large Array - VLA), and many of them are reported in the same papers as for the bursts near 21 cm (see for example the large survey by White et al. 1989). In particular, very weak detections (about 1 mJy) with the VLA have been reported in the publications. All these reports might have contributed to the impression that radio bursts could easily be detected from flare stars.
Assuming that the activity of the nine studied stars has not changed since they are observed at decimetric wavelengths, the burst rates inferred from the literature should be the same as the rates deduced from the reliable technique used between 1989 and 1993 (Lecacheux et al. 1993; Abada-Simon et al. 1994), under the two following conditions on the bursts reported in the publications: firstly, we only take into account the bursts for which the stellar origin is proven; secondly, we take into account only the bursts reaching at least 8 mJy, which is the peak flux density of the weakest burst detected during the Arecibo campaign.
We have considered that the stellar origin of a burst is proven when one of the three following
techniques is used:
i) use of an interferometer (mainly the VLA): this kind of instrument allows to create a map of the
observed star and the surrounding sky region, and only an emission recorded by all the antennas can
produce a "consistent" signal appearing at the position of the star. In addition, a map is useful in
identifying sources which are close to the observed star and which are known to radiate at 21 cm too: this
prevents from the source confusion problem of single-dish telescopes; for example, there is a well-known
extra-galactic source detected in a direction close to that of AD Leo: the emission of T1017+201 (flux
density of 200 mJy, e.g. Jackson et al. 1989) is within the primary beam of the Arecibo
telescope, and occasionally needs to be distinguished from a possible stellar burst;
ii) recording simultaneously a burst with several (single-dish) radiotelescopes observing all near 21 cm;
iii) observing simultaneously the star ("ON") and another close direction in the sky ("OFF") with two
antennas (mostly single-channel) tuned at almost equal frequencies (near 21 cm).
We have not taken into account the bursts detected by a single-dish telescope for which the stellar origin was not proven by one of the above criteria, especially when a burst is recorded with a single- frequency channel receiver. However, we cannot reject some bursts as definitely not stellar. In particular, one can find apparent rapid "spikes", without being able to prove their stellar origin. Such "false" spikes were discovered in the data during the campaign of 1989-1993 in Arecibo (Lecacheux et al. 1992). Finally, the (quasi-)simultaneity of a radio event with a flare at other wavelengths may not be a sufficient proof of its stellar origin.
One problem is that the precise number of bursts detected is not always specified by the authors, and another one is that the total number of observing hours is not always given. We report such incomplete data but we cannot use them to estimate the rate of activity in radio. In addition, the observing techniques used in the past may have had different sensitivity thresholds, so that the weakest bursts were probably missed. The different time resolutions used on various instruments such as the VLA and the Arecibo telescope also suggest to be careful in comparing the bursts' fluxes. Furthermore, in the past, only the most intense bursts were reported, whereas weaker bursts might have been present in the data without being searched for (private communication). Some real bursts may also have been rejected because they didnot exhibit the typical characteristics expected from a star (e.g. strong polarisation, drift of the emission frequency with time). Finally, some detections of weak bursts were never reported in the literature after many days of observation (e.g. Bastian, private communication). All these facts may lead us to underestimate the rate of radio bursts per hour. On the other hand, it may be overestimated by the fact that some non-detections following many hours of observation were never reported. Finally, we might have missed some publications on the subject.
Another difficulty - that we also encountered during the observations of 1989-1993 in Arecibo - rests in counting the "real" bursts. There is no "strict" distinction between a quiescent emission (i.e. weak and slowly varying) and a burst (stronger and more rapid). Indeed, quiescent emission from UV Ceti, the prototype of dMe stars, was recorded up to 18 mJy (Bastian & Bookbinder 1987), and this value is higher than many bursts. On the other hand, YZ CMi is a good example of a dMe star exhibiting gradual increases and decreases which can hardly be classified as quiescence or burst: how can one estimate the number of individual bursts in a "weakly varying event" of YZ CMi, as decreasing from 12 to 6 mJy during 5 hours (see Kundu et al. 1986)? Another difficulty is then to distinguish several "independent" bursts which are close in time from several bursts which actually belong to the same "single event".
In the tables of Appendix 1, we present our findings for eight of the nine dMe stars listed in Sect. 1 (we could not find any report on a detection of V371 Ori near 21 cm). One can see in Appendix 1 a case when AD Leo was observed simultaneously at four frequencies by the VLA: a burst reached 80 mJy at 1415 MHz but it was not detected at 1515 MHz, nor at 5 GHz (Kundu et al. 1986). Since a reliable observing technique was used, this result suggests that the bandwidth of the burst did not extend to frequencies higher than 1415 MHz, but it may extend to lower frequencies.
In summary, AD Leo emitted 6 bursts in excess of 8 mJy in 31 hours, EQ Peg more than 5 in 16 hr, and YZ CMi more than 13 in 34 hr; Wolf 424 and YY Gem exhibited no burst in 14 and 15 hr (respectively), nor did TZ Ari, Gl. 569 and VW Com (in only 0.4 hr). Let us see if the observations of 1989-1993 are in agreement with the preceding publications.