Saturation Levels for White-Light Flares of Flare Stars: Variation of Minimum Flare Duration for Saturation

Abstract

Taking into account results obtained from models and from statistical analyses of obtained parameters, we discuss flare activity levels and flare characteristics of five UV Ceti stars. We present the parameters of unpublished flares detected over two years of observations of V1005 Ori. We compare parameters of the U-band flares detected over several seasons of observations of AD Leo, EV Lac, EQ Peg, V1054 Oph, and V1005 Ori. Flare frequencies calculated for all program stars and maximum energy levels of the flares are compared, and we consider which is the most correct parameter as an indicator of flare activity levels. Using the One Phase Exponential Association function, the distributions of flare equivalent duration versus flare total duration are modeled for each program star. We use the Independent Samples t-Test in the statistical analyses of the parameters obtained from the models. The results reveal some properties of flare processes occurring on the surfaces of UV Ceti type stars. (1) Flare energies cannot be higher than a specific value regardless of the length of the flare total duration. This must be a saturation level for white-light flares occurring in flare processes observed in the U band. Thus, for the first time it is shown that white-light flares have a saturation in a specific energy range. (2) The span values, which are the difference between the equivalent durations of flares with the shortest and longest total durations, are almost equal for each star. (3) The half-life values, minimum flare durations for saturation, increase toward the later spectral types. (4) Both maximum total durations and maximum rise times computed from the observed flares decrease toward the later spectral types among the UV Ceti stars. According to the maximum energy levels obtained from the models, both EV Lac and EQ Peg are more active than the other three program stars, while AD Leo is the most active flare star according to the flare frequencies.

The statistical analyses of flares detected in B band photometry of UV Ceti type stars

“…In addition, the distributions of flare equivalent durations versus flare total durations were obtained for each star to compare the behaviours of flare activity among programme stars. Using the method described by Dal & Evren (2010b) for U band flares, all the distributions were modelled by the One Phase Exponential Association (hereafter OPEA) (Motulsky, 2007;Spanier & Oldham, 1987) function. The results obtained from the models were tested by a statistical analysis method, Independent Samples t-Test (hereafter t-Test) (Wall & Jenkins, 2003;Dawson & Trapp, 2004;Motulsky, 2007).…”

Statistical Analysis and the OPEA Model of the White-Light Flares Occurring on Krüger 60B (DO Cep)

“…If this case is valid, the timescales derived from the white-light flares can also give some clues about the flaring loop geometry or the flaring area geometry (at least for the photosphere). The obtained timescales from the observations of DO Cep demonstrated that the flaring loop or area is smaller than those seen on the stars from the earlier spectral types, because the obtained maximum flare duration for DO Cep flares is 3472 s. The observed maximum durations are 5236 s for V1005 Ori and 4164 s for AD Leo (Dal and Evren 2011a). The flare timescales of both stars are dramatically longer than that of DO Cep.…”

“…The regression analyses demonstrated that the OPEA function (Motulsky 2007;Spanier & Oldham 1987) given by Equation 6 is the best model fit. According to Dal and Evren (2011a), this is actually an expected case. The case demonstrates that the flares occurring on the surface of DO Cep have an upper limit for producing energy.…”

“…In this respect, the flare equivalent duration was based on the analyses in this study in order to determine the behaviour of the white-light flares of DO Cep. The method recently developed by Dal and Evren (2011a) is based on the modelling the distributions of the flare equivalent durations versus flare total durations. The authors demonstrate that the best function is the onephase exponential association function (hereafter the OPEA) to model the distribution.…”

“…As is seen in the OPEA model, the flare equivalent durations cannot be higher than a specific value, and the flare's total duration does not matter. Dal and Evren (2011a) defined this level as an indicator for the saturation level for the white-light flare processes. In fact, white-light flares are detected in some large active regions, where compact and two-ribbon flares are occurring on the surface of the Sun (Rodono 1990;Benz and Güdel 2010).…”