3. Activity revealed by the observations of 1989-1993 in Arecibo

3.1. Reliability of the observing technique

Knowing that narrow-band stellar bursts () exist, the tuning frequencies of several antennas observing simultaneously should be spaced by less than about 10 MHz, otherwise the burst may be missed by one of the antennas. In addition, a day-to-day comparison of the data is especially useful in rejecting non-stellar emissions recorded by the antenna "ON". Therefore, when observing with a single-dish radiotelescope, the most reliable observations combine simultaneous ON and OFF-source antennas, tuned at the same frequency, both of wide bandwidth, high frequency and time resolutions, and daily comparison of the data recorded at the same hour angle. This is the technique used during a 200 hour observing campaign with an acousto-optical spectrograph as a receiver of the Arecibo telescope. In the course of this campaign, which started in July 1989 and ended in February 1993, nine dMe flare stars and one binary system of the type RS Canum Venaticorum (RS CVn) were observed at 6 and 21 cm (Lecacheux et al. 1993; Abada-Simon et al. 1994).

3.2. Number of bursts detected

Only AD Leo was detected during the Arecibo campaign, and no burst was detected from the other eight dMe flare stars observed, nor from the RS CVn system UX Ari. The details on each of the eleven bursts detected from AD Leo in 38.3 hours of data are recalled in Table 1 (click here) (from Abada-Simon et al. 1994). In summary, half of the bursts is circularly polarised, half is not; the bursts last between 6 and 90 s, and their peak flux density is between 8 and 63 mJy with an integration time of 1 s, but the strongest burst was in fact made of spikes reaching up to 350 mJy in 20 ms. Figure 1 (click here) shows a histogram of the eleven bursts' flux density. We have counted as "one individual burst" either an event isolated in a 5-min scan, or a burst separated from another one by a "non-detection time" lasting at least ten seconds: in this second case, it is possible that several "bursts" actually belong to the same event whose flux decreases below the detection threshold. The situation is different in the case of the event (counted as two bursts) recorded on 13 February 1993: the second burst is made of several brief bursts present over several minutes.

  
Figure 1: Histogram of the bursts' peak flux density detected from AD Leo at 21 cm between 1990 and 1993 in Arecibo by Abada-Simon et al. (1994)

 

Date Starting Duration (s) Peak Flux Peak Flux RCP (%) LCP (%)

Time (UT) Density in Density in

RCP (mJy) LCP (mJy)

11 Dec. 90 08:41:12 0 100 0

11 Dec. 90 09:05:10 0 100 0

13 Dec. 90 08:37:55 50 50

13 Dec. 90 09:40:28 50 50

13 Dec. 90 09:41:08 50 50

13 Dec. 90 09:42:19 43 57

13 Dec. 90 09:51:15 50 50

13 Dec. 90 09:53:03 57 43

12 Feb. 93 04:40:55 0 0 100

13 Feb. 93 04:12:53 0 100 0

13 Feb. 93 04:17:22 0 100 0

 

It is also interesting to note that the eleven bursts were detected in only a few days: two bursts on 11 December 1990 separated by less than 30 minutes, six bursts on 13 December 1990, among which five occurred over 15 min - maybe a unique event? -, one burst on 12 February 1993, and 7 minutes of activity on 13 February 1993. The six bursts recorded on 13 December 1990 cover a period of time  h 15 min, during which AD Leo rotates by an angle:

where days is AD Leo's rotation period, and is the inclination of its rotation axis to the line of sight (Pettersen et al. 1984). Assuming that these bursts are emitted from one "active region" and that the radiation is beamed toward the star's zenith, the size of this region is:

where R is AD Leo's radius. The size L may be smaller if the emitting region is not on the equator, but since radio bursts arise in the corona, i.e. up to about one stellar radius above the surface, the size L of the "active region" may be underestimated by a factor two. Within the same assumptions of beamed radiation toward zenith and of one "unique active region" for the consecutive radio bursts, it is interesting to note that, since AD Leo's rotation period is 2.7 days, the radio bursts detected on 13 December 1990 could come from the same region as that from which the radio bursts of 11 December 1990 originated, after the "active region" was not observable from the Earth on 12 December 1990; the bursts detected on 12 and 13 February 1993 could also come from one region (observable on both days). There could be several reasons why radio emission is not detected continuously when the hypothetical "active region" is observable from the Earth: i) the emission of radio bursts might be triggered only from time to time in the "active region"; ii) the radio emission may be below the detection threshold during part of the observing time; iii) the radio bursts are probably emitted in a narrow solid angle and toward directions which vary with time. Knowing that these bursts emission processes are coherent, the latter possibility (iii) seems more realistic than a radio radiation beamed toward zenith.

Finally, in addition to the nine dMe flare stars, the RS CVn-type UX Arietis was also observed but no burst was detected during the campaign of 1989-1993 in Arecibo. In fact, UX Ari's flares are generally on a timescale of hours to days, as it has been observed by the VLA, but it can emit relatively short bursts. Its flux density at 5 GHz can increase from 16 to 21 mJy in about 10 min and decrease again to 16 mJy in 10 min (Lefèvre et al. 1993): this kind of variability is too low and too slow to be easily identified with the Arecibo radiotelescope. Since UX Ari could not be tracked more than 1h15min (at 21 cm) with this instrument, its long duration flares cannot be observed; our result is that it emitted no short burst in 2.8 hr of observation.

3.3. Comparison between the dMe stars observed in Arecibo

 

Spec- Flux Flux

tral Number dens. at dens. at

Star Type Dis- of P(0) P(1) P(2) P(3) diff. dist. diff. dist.

tance observin (%) (%) (%) (%) of a burst of a burst

(pc) g hours of 8 mJy of 64

at 1.4 at 4.9 pc mJy at

GHz 4.9 pc

Wolf 424 M5.5Ve 4.3 10.7 4.6 14.2 21.9 22.4 10.4 83.2

TZ Ari M5Ve 4.5 3.3 36.7 34.8 16.5 5.2 9.5 76

AD Leo M4Ve 4.9 38.3 <2.10^-5 <2.10^-4 0.1 0.4 8 64

YZ CMi M4.5Ve 6.0 7.7 11.0 24.2 26.8 19.7 5.3 42.4

EQ Peg M4Ve 6.5 3.6 35.6 36.8 19.0 6.6 4.5 36 M6Ve

Gl 569 M0 10.4 4.4 28.3 35.7 22.6 9.5 1.8 14.4

YY Gem M1Ve 14.5 3.1 41.1 36.5 16.3 4.8 0.9 7.2

V371 Ori M3Ve 15.2 2.9 43.5 36.2 15.1 4.2 0.8 6.4

VW Com M4Ve 17.5 2.0 57.4 33.0 9.5 1.8 0.6 4.8

 

Before comparing the flare occurrence rates deduced from our observations to those found in the literature, let us see if the non-detection of eight stars among the nine dMe stars observed in Arecibo in 1989-1993 is surprising, assuming that their behaviour is totally comparable to that observed on AD Leo. Table 2 (click here) shows the number of observing hours (Col. 4) of each star (name in Col. 1) whose spectral type and distance are recalled in Cols. 2 and 3 (resp.). Columns 5, 6, 7 and 8 indicate the probability to detect 0, 1, 2 and 3 bursts (respectively), under the following conditions. Eleven bursts were detected from AD Leo in 38.3 hr, and we assume that:

- the nine studied stars emit bursts of equal strength,
- the other eight stars have the same flare rate occurrence as AD Leo,
- they are observed at the distance of AD Leo (4.9 pc), and
- their probability of burst emission follows the Poisson statistics law.

According to Poisson's law, the probability that n bursts are emitted is:

where a is a parameter describing the distribution of bursts. For a star observed for N hours, this parameter is, in the case of 12 bursts emitted by AD Leo in 38.3 hr:

As an additional information, Cols. 9 and 10 indicate, for each star "placed at its real distance", the corresponding flux density of a burst of 8 and 64 mJy (respectively) when observed at 4.9 pc.

In the frame of the former hypotheses, we can see that, during the observations of 1989-1993, we had a maximum probability to detect no burst from VW Com, V371 Ori and YY Gem; we had a maximum probability to detect one burst from Gl 569; we had approximately equal probabilities to detect zero or one burst from EQ Peg and TZ Ari, one or two bursts from YZ CMi, and two or three bursts from Wolf 424: for these two latter stars, the probability to detect no burst was relatively low. However, apart from Wolf 424 and TZ Ari, the six other stars are further than AD Leo.

If we consider that the weakest burst from AD Leo (peak flux density of 8 mJy) is the weakest detectable at 21 cm by the Arecibo telescope (with the observing technique used in 1989-1993), it is obvious that if the six stars which are further than AD Leo emitted such a low burst during the observations of 1989-1993, it could not be detected. Among these six stars, only YZ CMi, which was observed for more than twice the time of the five others, could have emitted a second burst, but if it were as weak as the "second weaker" burst of AD Leo (10 mJy, that is 6.6 mJy at YZ CMi's distance), we might not have detected it either. We have just taken the most pessimistic hypotheses, assuming that the stars would have emitted the weakest bursts of AD Leo.

In summary, if the nine observed dMe stars were comparable, we could not be surprised by having detected no burst from TZ Ari and the six stars further than AD Leo, but we may be more surprised by knowing that bursts much stronger than the weakest ones assumed can be emitted. On the other hand, there is a maximum probability to detect three bursts from Wolf 424. However, the papers about flares from dMe stars show that some stars which are further than others are more active and emit stronger bursts than other stars which are closer.