Abstract

The results of U-filter flare monitoring of the binary flare star FL Vir = Wolf 424 is presented. 57 flares with energies between 2 × 1028 and 2 × 1031 erg were recorded in 20 h of observation. The properties of flare occurrence and flare time-scales are analysed, and the flare activity level in 1980 April is determined to be Lf(U) = 8.0 × 1026 erg s−1. This is larger than previously published results and may indicate a variation in the flare activity level on a time-scale of years. An analysis of existing data indicates that the flare activity level correlates with the relative orbital positions of the stars.

1 INTRODUCTION

The close visual binary Wolf 424 = Gliese 473 AB = FL Vir contains two equally bright dM6e flare stars with MV= 15.0 (e.g. Henry et al. 1999). Revised orbital parameters were derived from Hubble Space Telescope data (Schultz et al. 1998; Torres et al. 1999), and imply an eccentric orbit (e= 0.295) with a period of 15.6 yr and masses of 0.13 and 0.14 M.

Flaring was discovered by Kunkel (1967). Further U-filter photometry was made by Moffett (1973, 1974, 1975) and Beskin et al. (1988). Moffett's data from 1972 and 1974 (16 flares in 6.7 h) imply a flare luminosity of Lf(U) = 3.5 × 1026 erg s−1, while those of Beskin et al. (15 flares in 9.5 h) a factor of 2 smaller during observations in 1983-1984. We present extended photometry from 1980 (57 flares with 98 individual maxima in 20.3 h) yielding Lf(U) = 8.0 × 1026 erg s−1, a factor of 2 larger than Moffett. This makes FL Vir slightly more active than other binary flare stars of similar mass and luminosity, e.g. UV Cet AB, V780 Tau and EI Cnc (Pettersen 1990). In 1980, 19 per cent of the U-filter output from FL Vir was due to flare activity.

2 OBSERVATIONS

FL Vir = Wolf 424 = Gliese 473 AB was observed on seven nights in 1980 April with the 2.1-m Struve reflector at McDonald Observatory. A computer-controlled high-speed photometer was used to collect data through eight filters. Here, we analyse only the U-filter data. Each data point is the result of a 1-s integration. They are separated in time by 9 s. Both components of the binary were included in the diaphragm. The detailed observation log is given in Table 1.

Table 1

U-filter observing log for FL Vir.

Date (utMonitoring Intervals (utCoverage (s) 
1980 April 08 04:27:45–04:31:05 04:32:16–06:53:52  
06:55:52–07:40:22 07:41:34–08:21:46  
08:24:01–08:40:31  14768 
1980 April 09 04:39:08–04:44:23 04:45:53–05:03:26  
05:05:32–05:24:44 05:25:56–06:14:41  
06:16:02–06:45:08 06:46:46–07:13:47  
07:15:44–07:39:35 07:40:56–07:51:53 10899 
1980 April 10 04:39:52–04:58:19 04:59:31–05:19:28  
05:20:40–05:36:15 05:37:28–06:07:19  
06:08:40–06:26:22 06:27:34–05:48:25  
06:49:46–07:14:48 07:16:00–07:39:35 10261 
1980 April 11 04:51:21–04:54:57 04:56:09–05:23:18  
05:24:30–06:54:48 06:56:00–07:35:00  
07:36:21–08:06:21 08:07:42–08:11:54 11655 
1980 April 22 03:18:53–03:22:29 03:23:59–03:28:20  
03:29:37–03:43:54 03:46:00–05:03:55  
05:05:25–05:30:10 05:31:22–06:28:22  
06:29:35–06:44:52 06:46:22–06:47:07  
06:48:10–07:16:49 07:18:01–07:33:37 14471 
1980 April 23 05:04:52–05:20:19 05:22:25–06:08:37  
06:09:40–06:54:22  6381 
1980 April 25 03:41:29–03:44:02 03:45:05–04:06:41  
04:07:53–04:13:17 06:43:44–06:47:29  
06:48:41–07:33:23  4680 
Date (utMonitoring Intervals (utCoverage (s) 
1980 April 08 04:27:45–04:31:05 04:32:16–06:53:52  
06:55:52–07:40:22 07:41:34–08:21:46  
08:24:01–08:40:31  14768 
1980 April 09 04:39:08–04:44:23 04:45:53–05:03:26  
05:05:32–05:24:44 05:25:56–06:14:41  
06:16:02–06:45:08 06:46:46–07:13:47  
07:15:44–07:39:35 07:40:56–07:51:53 10899 
1980 April 10 04:39:52–04:58:19 04:59:31–05:19:28  
05:20:40–05:36:15 05:37:28–06:07:19  
06:08:40–06:26:22 06:27:34–05:48:25  
06:49:46–07:14:48 07:16:00–07:39:35 10261 
1980 April 11 04:51:21–04:54:57 04:56:09–05:23:18  
05:24:30–06:54:48 06:56:00–07:35:00  
07:36:21–08:06:21 08:07:42–08:11:54 11655 
1980 April 22 03:18:53–03:22:29 03:23:59–03:28:20  
03:29:37–03:43:54 03:46:00–05:03:55  
05:05:25–05:30:10 05:31:22–06:28:22  
06:29:35–06:44:52 06:46:22–06:47:07  
06:48:10–07:16:49 07:18:01–07:33:37 14471 
1980 April 23 05:04:52–05:20:19 05:22:25–06:08:37  
06:09:40–06:54:22  6381 
1980 April 25 03:41:29–03:44:02 03:45:05–04:06:41  
04:07:53–04:13:17 06:43:44–06:47:29  
06:48:41–07:33:23  4680 

Total coverage = 73115 s = 20.31 h.

During 20.31 h of observations, we detected 57 flares, the characteristics of which are given in Table 2. The time of maximum is only accurate to within the time resolution of 9 s. Column 4 gives the rise time of the flares (in seconds) from the quiescent pre-flare brightness level to maximum, and the next column gives the time elapsed from maximum till the intensity of the flare light reached half of the maximum intensity. These quantities, when time resolved, are usually determined to better than twice the time resolution. Column 6 gives the total duration of the flare. Due to the slow decline phase towards the end of most flares, this quantity may have an uncertainty of up to 1 min. The flare amplitude in intensity units measured relative to the quiet star is given in Column 7, and the standard deviation of the measurements of the quiet star is given in Column 8. The last column contains the U-filter energy emitted during each flare event. This quantity is taken to be EU= RE LU (in erg), where forumla is the relative energy of the flare in units of seconds, obtained by numerically integrating the flare light curve. The area included in this integration is bounded by the level representing the quiescent stellar brightness before and after the flare, and the flare light curve bounded by its start and end times. This area is normalized by an area corresponding to the quiescent output of the star in 1 s, thus yielding RE. For flares lasting a few minutes, the change of airmass is small and causes no measurable change in the observed quiescent brightness level. For long duration events lasting several tens of minutes, we detect changes in brightness level due to the change of airmass. Thus, we have applied extinction corrections to all time-series before deriving the flare parameters of Table 2. The U-filter extinction coefficient was determined each night from observations of FL Vir outside of flares. The second quantity, LU, represents the absolute flux emitted by the quiescent star in the U bandpass. The average U magnitude from a number of literature sources is 15.57 ± 0.07. A parallax of 0.2278 ± 0.0049 arcsec (van Altena, Lee & Hoffleit 1995) yields MU= 17.36 ± 0.12 for the absolute magnitude of the system, which implies LU= 4.15 × 1027 erg s−1 (cf. Moffett 1974).

Table 2

Sample of U-filter flare characteristics for FL Vir (The full table is available as Supplementary Material in the on-line article).

Flare no. Date (utFlare max (uttrise (s) t0.5(s) tdur (s) Flare amplitude Noise σ/I0 log EU(erg) 
01 1980 April 08 04:38:42 27 36 450 1.49 0.07 29.71 
02 1980 April 08 04:48:54 18 909 6.12 0.07 30.15 
03 A 1980 April 08 05:07:58 23  1.71 0.07  
03 B 1980 April 08 05:08:34 18 396 0.80 0.07 29.68 
04 A 1980 April 08 05:36:19  2.58 0.05  
04 B 1980 April 08 05:36:46  284 1.28 0.05 29.67 
05 1980 April 08 05:58:12 18 63 0.34 0.07 28.66 
06 1980 April 08 06:00:10 18 54 153 0.42 0.07 29.14 
Flare no. Date (utFlare max (uttrise (s) t0.5(s) tdur (s) Flare amplitude Noise σ/I0 log EU(erg) 
01 1980 April 08 04:38:42 27 36 450 1.49 0.07 29.71 
02 1980 April 08 04:48:54 18 909 6.12 0.07 30.15 
03 A 1980 April 08 05:07:58 23  1.71 0.07  
03 B 1980 April 08 05:08:34 18 396 0.80 0.07 29.68 
04 A 1980 April 08 05:36:19  2.58 0.05  
04 B 1980 April 08 05:36:46  284 1.28 0.05 29.67 
05 1980 April 08 05:58:12 18 63 0.34 0.07 28.66 
06 1980 April 08 06:00:10 18 54 153 0.42 0.07 29.14 

The average flare detection rate in this time-series corresponds to one event every 21 min. One-third of the outbursts were complex and had several maxima. All together, 98 individual flares were recorded, i.e. an average of one flare every 12 min. The actual time intervals between flares were sometimes observed to be less than 1 min and could be as long as 46 min. The average value of flare time spacing from Tables 1 and 2 is 7.0 ± 7.3 min. The statistical time distribution is well fitted by a Poissonian, which is confirmed by a χ2 test at the 95 per cent confidence level. Flares on FL Vir are randomly distributed in time.

The flare rise time varies from unresolved to 1.5 min, with an average of 20 ± 16 s for 95 flares. The decay time t0.5 varies from unresolved to 2 min (but one slow flare at 18 min), with an average of 90 flares of 25 ± 23 s. The two distributions are very similar and are well fitted by Poissonians. This is confirmed by χ2 tests at the 95 per cent confidence level. Flare time scales thus appear to distribute randomly within a range of two orders of magnitude.

3 ANALYSIS AND RESULTS

In Fig. 1, we have plotted the cumulative distribution of flare energy versus flare frequency. Above EU= 1030 erg, there is a linear trend with slope very close to unity,

 
formula

where N is the number of flares and T is the observing time in seconds. This slope is not contradicted by the data of Moffett (1973, 1974, 1975) and Beskin et al. (1988), but their distributions (and especially that of the latter) are shifted to the left relative to our plot. This is reflected in the frequency of flares with energy larger than log EU≥ 29.5 erg, where Moffett's data from 1972 and 1974 indicate 1.4 ± 0.5 flares per hour, the data of this work indicate 1.2 ± 0.3 flares per hour, and the data of Beskin et al. from 1983 and 1984 indicate 0.4 ± 0.2 flares per hour. The flare luminosity values are Lf(U) = 3.5 × 1026, 8.0 × 1026 and 1.6 × 1026 erg s−1, respectively. Thus, for any given flare energy, Beskin et al. (1988) detected about half the number of flares per time unit than did Moffett (1973, 1974, 1975), who detected about half the number of flares than did this work.

Figure 1

The cumulative energy distribution of flares on FL Vir from U-filter observations in 1980.

Figure 1

The cumulative energy distribution of flares on FL Vir from U-filter observations in 1980.

If the same data are broken into (smaller) annual data sets, we find flare frequencies as listed in Column 4 of Table 3. The uncertainty estimates reflect the number of flares above log EU= 29.5 erg in each sample. The time distribution of flare frequency between 1972 and 1984 is plotted in Fig. 2. We have used the orbital solution of Torres et al. (1999) to compute a curve showing the distance between the component stars as a function of time for an elliptical orbit with e= 0.295 and a= 4.06 au. A least-squares adjustment was made to fit the two scales in Fig. 2, i.e. the distribution of flare frequency data points to the temporal variation of the orbital distance between the two binary components of FL Vir. Noting the large error bars, there exists an anticorrelation in the sense of high flare frequency near periastron and a reduced flare rate by a factor of 3–4 at apastron.

Table 3

Flare statistics for FL Vir.

  Epoch  Telescope  forumla   forumla  
Moffett (1973)  1972.2  2.1 m  1.1 ± 0.7 h−1  26.2 ± 0.2 erg 
Moffett (1975)  1974.1  0.9 & 0.8 m  1.5 ± 0.6 h−1  26.1 ± 0.1 erg 
This work  1980.3  2.1 m  1.2 ± 0.3 h−1  26.3 ± 0.1 erg 
Beskin et al. (1988)  1983.22  6 m  0.3 ± 0.3 h−1  25.9 erg 
Beskin et al. (1988)  1984.17  6 m  0.5 ± 0.3 h−1  25.8 ± 0.1 erg 
  Epoch  Telescope  forumla   forumla  
Moffett (1973)  1972.2  2.1 m  1.1 ± 0.7 h−1  26.2 ± 0.2 erg 
Moffett (1975)  1974.1  0.9 & 0.8 m  1.5 ± 0.6 h−1  26.1 ± 0.1 erg 
This work  1980.3  2.1 m  1.2 ± 0.3 h−1  26.3 ± 0.1 erg 
Beskin et al. (1988)  1983.22  6 m  0.3 ± 0.3 h−1  25.9 erg 
Beskin et al. (1988)  1984.17  6 m  0.5 ± 0.3 h−1  25.8 ± 0.1 erg 
Figure 2

The time variability of flare frequency for log EU≥ 29.5 erg is shown as dots. The vertical scale to the right shows number of flares per hour (cf. Table 3). The curved line is the change of separation between the two stellar components of the binary, computed from the orbital solution of Torres et al. (1999). The linear distance is given on the vertical scale to the left in units of m. The adjustment of the two scales was obtained by a least-squares solution.

Figure 2

The time variability of flare frequency for log EU≥ 29.5 erg is shown as dots. The vertical scale to the right shows number of flares per hour (cf. Table 3). The curved line is the change of separation between the two stellar components of the binary, computed from the orbital solution of Torres et al. (1999). The linear distance is given on the vertical scale to the left in units of m. The adjustment of the two scales was obtained by a least-squares solution.

4 CONCLUSIONS

Flares on FL Vir are randomly distributed in time. With a signal-to-noise ratio of 10–20, as obtained in our observations, we detected an average of five flares per hour. One-third of them were clustered in complex events with several maxima following each other before the star eventually returned to its pre-flare brightness level.

The flaring power spans a range of 5, from 1.6 to 8.0 × 1026 erg s−1, when data sets from different epochs are compared. Our extensive observing (more than all others combined) has yielded a U-filter flare luminosity of 8 × 1026 erg s−1, which is larger than that of other results. The frequency of flares with energy above a chosen lower limit (N/T in Fig. 2 is plotted for flares larger than 3 × 1029 erg) appears to vary with the orbital phase of the binary components.

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SUPPLEMENTARY MATERIAL

The following supplementary material is available for this article online:

Table 2. U-filter flare characteristics for FL Vir.

This material is available as part of the on-line article from http:www.blackwell-synergy.com.