COMMISSION 27 OF THE I. A. U. INFORMATION BULLETIN ON VARIABLE STARS Number 2294 Konkoly Observatory Budapest 1983 March 14 HU ISSN 0374-0676 STATISTICAL ANALYSIS OF FLARE STAR OBSERVATIONS A large scale photoelectric monitoring program on five flare stars was carried out at the Stephanion Observatory, Greece during the period 1972-1976. The observations enable us to make some comments on these stars. I. One of the main problems of flare star observations is how to separate the flare events from the noises caused by the equipments used and by the instabilities of the Earth's atmosphere. In order to minimize the thermoionic effects we used dry carbondioxide ice for cooling. The observations were made in the B band. The fluctuation of the observations of the five flare stars has been measured at every certain interval of time DeltaT to avoid random values. The name of the stars and the number of points measured are given in Table I for the years 1973 and 1974, separately. The total monitoring time was 124 hours. Table I No. Name of the No. of measured No. of measured flare star points in 1973 points in 1974 1 BY Dra 265 89 2 EV Lac 144 87 3 BD +13deg2618 46 --- 4 BD +55deg1823 --- 213 5 AD Leo --- 52 sigma(m) and eta were calculated from the following formulae: sigma(m)=2.5 log((I0+sigma(I))/I0), where sigma(I)=((Ii-I)^2/(N-1))^(1/2) , Ii= measured intensity deflection (i=1,2,...,N) N I=1/N Sum Ii, I0= intensity deflection of the flare star at quiescence less i=1 background, and eta=Deltam/sigma(m), where Deltam= 2.5 log (If/I0), If=I0 + noise deflection. The distribution of eta for each observed flare star for the years 1973 and 1974, respectively are shown in Figs. 1 and 2. A careful and refined analysis of these figures gives the eta values which correspond to more than 99% confidence that the fluctuation is a flare event. The results are summarized in Table II. Table II No. Name of the eta with confidence more eta with confidence more flare star than 99%, in 1973 than 99%, in 1974 1 BY Dra 5.0 +/- 0.05 5.0 +/- 0.09 2 EV Lac 4.0 +/- 0.06 4.0 +/- 0.07 3 BD +13deg2618 6.0 +/- 0.16 --- 4 BD +55deg1823 --- 4.0 +/- 0.04 5 AD Leo --- 4.0 +/- 0.10 The mean value of eta= 4.57+/-0.30 i.e. eta~ 5, which is a suitable criterion for our photoelectric observations of flare event detection in the B- colour with a confidence more than 99%, i.e. if Deltam >= 5sigma(m), we can say with more than 99% confidence that the event is a flare. II. Kunkel (1973) defined a flare duration parameter Tq where the subscript q denotes the fraction of peak light at which the measurement was taken (e.g. T0.5 is the duration of a flare at half peak light, T0.2 is the duration at 20% of peak light, etc.). He found an empirical formula between the luminosity of the flare star of dMe type and the flare duration observed in the U - band: = -0.15 MV + 1.61 +/- 0.17 From our data for the flare star EV Lac which was observed from 1972 through 1976 and 75 flare events were detected in the B band, we were able to determine Kunkel's parameter Tq for q= 0.5, 0.2 and 0.1 (Table III). Omitting the very uncertain values of the events Nos 21,40,46,51 and 65 we obtain: = -0.092 +/- 0.036 = +0.186 +/- 0.046 = +0.375 +/- 0.052 Table III No. No. of flare events T0.5 T0.2 T0.1 of flare events T0.5 T0.2 T0.1 1 1.46m 3.50m 4.15m 39 2.32m 9.85m 12.60m 2 0.64 0.95 - 40 - - - 3 0.56 0.75 2.40 41 1.46 4.60 - 4 0.34 - - 42 1.30 4.85 5.85 5 1.44 2.00 7.05 43 0.74 1.75 3.20 6 0.36 0.60 2.95 44 1.62 1.90 2.10 7 0.94 1.20 2.09 45 0.60 - - 8 0.92 1.23 2.53 46 - - - 9 0.54 1.33 1.84 47 0.32 0.52 0.55 10 0.34 0.40 0.45 48 0.96 7.50 10.40 11 1.62 2.10 - 49 0.24 0.42 0.46 12 0.74 2.50 4.63 50 0.18 0.19 0.24 13 0.94 1.56 3.00 51 - - - 14 1.04 2.10 2.90 52 0.72 1.12 4.52 15 0.38 0.55 0.85 53 0.44 1.04 1.08 16 2.00 3.35 3.75 54 1.32 3.50 9.10 17 1.16 1.70 2.00 55 0.80 0.92 1.28 18 2.64 4.90 9.20 56 0.60 - - 19 0.28 0.55 - 57 1.04 4.00 5.40 20 0.58 - - 58 0.40 0.43 0.67 21 - - - 59 1.24 1.82 - 22 0.58 2.05 2.10 60 1.80 1.84 2.84 23 0.48 1.25 1.35 61 1.54 1.92 2.06 24 0.28 2.75 4.65 62 0.76 1.96 3.88 25 2.10 3.90 - 63 1.04 1.82 5.82 26 0.94 2.30 3.60 64 0.52 1.30 2.28 27 2.98 5.35 - 65 - - - 28 0.32 0.35 0.85 66 0.36 0.50 0.68 29 0.34 1.24 2.20 67 1.30 2.20 3.36 30 1.58 5.50 16.35 68 2.14 2.50 3.34 31 0.94 2.50 2.55 69 2.44 - - 32 0.64 0.80 2.20 70 0.30 0.38 0.45 33 1.30 3.40 4.75 71 2.78 - - 34 1.14 2.65 2.75 72 0.68 0.84 0.94 35 0.78 0.85 0.90 73 0.68 1.52 2.28 36 2.64 4.10 4.15 74 0.40 0.45 1.66 37 1.74 2.50 2.68 75 0.49 0.68 2.02 38 0.24 0.90 - Applying these values in Kunkel's formula we calculate the differences; DeltaMV(T0.5) = 0.31mag DeltaMV(T0.2) = 2.16 DeltaMV(T0.1) = 3.42 Our results for confirm Kunkel's empirical formula. [FIGURE 1] [FIGURE 2] Thanks are due to Prof. Dr. L.N. Mavridis, Head of the Department of Geodetic Astronomy, University of Thessaloniki, Greece, for supervising this research. F.M. MAHMOUD Helwan Institute of Astronomy and Astrophysics Cairo - Egypt Reference: Kunkel, W.E.: 1973, Ap.J. Suppl. 25.1 [BIBCODE 1973ApJS...25....1K ]