Frequent flare events on the short-period M-type eclipsing binary BX Tri

We present long-term, multi-color photometric monitoring and spectroscopic observations of the short-period M-type eclipsing binary BX Tri. Six flare events were recorded in 4 years from 2014 to 2017. Three of them were detected on one night within an orbital cycle. The strongest one was identified on December 23, 2014. With the amplitudes of $\Delta$B=0.48 mag, $\Delta$V=0.28 mag, $\Delta$R=0.10 mag, $\Delta$I=0.02 mag, the total energy due to the flare event was measured to be 4.08 ($\pm$0.24) $\times$$10^{34}$ erg, exceeding the superflare level ($10^{34}$). Based on the observations, the evolutionary status of the binary system as well as the long-term orbital period changes were analyzed. It reveals that BX Tri is probably a semi-detached system with the primary component filling its Roche lobe. The extremely high occurrence of flare events of the binary could be related to the rapid mass transfer between components.


Introduction
Stellar flares are violent events of sudden energy releases in stellar atmospheres (Benz & Güdel 2010;Kowalski et al. 2010;Shibayama et al. 2013). These remarkable stellar activities are common on M dwarfs, presumably caused by magnetic reconnection in their atmospheres. Rotational periods and convective envelope depths are also suggested to be related to these phenomena (Silvestri et al. 2005;Browning 2008; Reiners et al. 2012). Recently, a large number of M-type stars with flare activity have been examined based on Kepler data Hawley et al. 2014;Lurie et al. 2015;Silverberg et al. 2016). The statistical characteristics of the flares for M dwarfs have presented strong correlations among the flare energy, duration, and amplitude and show that latetype M dwarfs have frequent flares (Shibata et al. 2013;Hawley et al. 2014;Chang et al. 2017;Yang et al. 2017).
Flare events have also been detected in close binaries. The strong interaction between the components in a binary system will typically generate magnetic activity (Noyes et al. 1984). Recently, 234 flare binaries out of 1049 binaries were identified in the Kepler Eclipsing Binary Catalog (Gao et al. 2016). Seven flares were detected from five RS CVn-type binaries (Pandey & Singh 2012). A few close binaries with flare events have been detected, such as EV Lac (Honda et al. 2018), GSC 02314−00530 (Dimitrov & Kjurkchieva 2010), GJ 3236 (Smelcer et al. 2017), CU Cnc (Qian et al. 2012), and CM Dra (Nelson & Caton 2007), and the frequency and energy of the flares were studied in detail.
The present paper concerns long-term flare monitoring of the M-type eclipsing binary BX Tri (also 1SWASP J022050.85 +332047.6 and GSC 02314−00530). We chose this target because it was classified as a W UMa binary with a short period of 0.19263 day (Terrell 2014). The short-period limit of contact binaries has been reported as being about 0.22 day (Rucinski 2007) and was widely discussed both observationally and theoretically (Rucinski & Pribulla 2008;Jiang et al. 2012;. Obviously, BX Tri can be a good example for studying the limit period of contact binaries. This target was also reported for its coincidence with the ROSAT X-ray source 1RXS J022050.7+332049 (Norton et al. 2007). Recently, flare activities have been detected by Dimitrov & Kjurkchieva (2010). Combining the radial-velocity curves, they determined the absolute physical parameters of BX Tri as = The flare activities of BX Tri were observed by Han et al. (2016), and its magnetic activities were discussed by . Their results revealed that BX Tri has strong magnetic activity. All of the information implies that BX Tri is a very active binary with M-type components and a very short period. Therefore, we carried out long-term, multicolor photometric monitoring and spectroscopic observations in order to study the flare characteristics of BX Tri. The details of observations and data reduction are given in Section 2. An analysis of a photometric solution is performed in Section 3. The behavior of the flare events is drawn in Section 4. Finally, we give our discussion and conclusion in Section 5.

New Photometry
The key to the study of flares on active stars is sufficient observations such that complete samples can be collected. Therefore, we conducted detailed monitoring observations of BX Tri from 2014 to 2017, including photometric and spectroscopic observations. The new photometric observations of BX Tri were carried out in the B, V, R, and I bands with three small telescopes: the 85-cm reflecting telescope at Xinglong Station of NAOC 7 (hereafter XL 85 cm), the 50BiN prototype telescope at Delingha of PMO (hereafter DLH 50BiN), 8 and the 1 m telescope at Nanshan Station in Xingjiang (hereafter XJ 1 m). The details of the telescopes and the data reduction are described as follows.
XL 85 cm was equipped with an Andor 2K×2K CCD camera and a standard Johnson-Cousins-Bessel multicolor filter system (Zhou et al. 2009). The effective field of view is 35′×35′ and the pixel scale is  0. 96 pixel −1 . DLH 50BiN has two parallel optical systems. Each has an Andor 2K×2K CCD camera and provides a 20′×20′ field of view with a pixel scale of about 0 59 pixel −1 . Two standard Johnson-Cousins-Bessell BV filters were applied to simultaneous two-color photometry (Deng et al. 2013;Tian et al. 2016). XJ 1 m is equipped with a 4K×4K CCD camera giving a 1°.3×1°.3 field of view with a resolution of about  1. 13 pixel −1 (Liu et al. 2014). A total of 11 observational nights were obtained: eight nights from XL 85 cm with the BVRI bands, two nights from DLH 50BiN with the BV bands, and one night from XJ 1 m with the BV bands. The photometric observations are listed in Table 1.
All images were reduced preliminarily with the standard process, including subtracting the bias and dividing flat fields from the object frames. Then the instrument magnitudes of the stars were extracted from these images using aperture photometry of the IRAF. A star near the variable star was chosen as the comparison star (TYC 2314−1655), which has a brightness and color similar to the variable star. Another star in the same field of view was selected as the check star (TYC 2314−780). The differential magnitudes of these stars were extracted in each frame. Then, the instrumental magnitudes were converted to the standard system with the standard stars  Figure 1, where the yellow arrows indicate the flare events. Focusing on the B-band and V-band light curves, the color of B−V was calculated, shown below the light curve in Figure 1. The colors at the peaks of all flares are also presented in Table 6. We also calculated the epochs of minimum light with mean values of the B, V, R, and I filters determined by applying the KW method (Kwee & van Woerden 1956), as given in Table 2.

Spectroscopy
The spectroscopic observations were carried out with three instruments. The first one is the Beijing Faint Object Spectrograph and Camera (BFOSC; Fan et al. 2016) mounted on the 2.16 m telescope at Xinglong station of the National Astronomical Observatories of China (NAOC). BFOSC has a CCD with size 2048×2048. We adopted the grating E9 + G10 with wavelength range from 3740 Å to 10,200 Å and 1 6 width slit. The exposure time of each image was 30 minutes. The second one is the optical median resolution (OMR) spectrograph mounted on the 2.16 m telescope at Xinglong station of NAOC. We chose the grating of 600 lp/mm with the wavelength ranging from 3200 Åto 7500 Åand a slit width of 2 0. The exposure time was 20 minutes. The last one was on the 2.12 m telescope at the Observatory Astronomical National on the Sierra San Pedro Martir (OAN-SPM). We used a 2048×2048 E2V CCD to collect the high-resolution (the maximum resolution is R=18,000 at 5000 Å) ECHELLE spectra at the slit size 1 0. The wavelength range is from 3800 Åto 7100 Å. The exposure time was 40 minutes. No filter was used during the observations. The list of the spectroscopic observations is presented in Table 3. In the end, 12 spectra of BX Tri during 2016 December to 2017 November were obtained, which covered the whole orbital phase of BX Tri.
Reduction of the spectra was performed by the standard process using the IRAF/IMRED packages, including bias, flat calibration, and cosmic-ray removal. The wavelength calibration was made by taking the spectra of the Fe-Ar lamp, He-Ar lamp, and Th-Ar lamp for BFOSC, OMR of XL, and ECHELLE of OAN-SPM, respectively. Then, the data reduction was primarily performed using the IRAF/APALL package to obtain the normalized spectra. Figure 2 presents Hα, Hβ, and Hγ profiles at different phases. We can see that there is a clear asymmetry in the H alpha line at phase=0.1854. This spectra was observed by OAN-SPM in Mexico with a high resolution. The asymmetric profile is indeed a superposition of emission lines from both stars. It is consistent with the orbital velocity at the phase.

Period Study
We have collected all of the available times of light minima from the database O-C gateway (http://var.astro.cz/ocgate/) and the literature to calculate the orbital period. With the 33 times of light minima we observed, 131 times of light minima were collected in total. All of the data are observed using the CCD method. Table 4 presents all of the times of light minima and the types of eclipses, where "p" and "s" refer to the primary minima and the secondary minima, respectively. The corresponding epoch and O-C values are based on the new linear ephemeris: The values for epoch and O-C are shown in Table 4. The O-C diagram for BX Tri is plotted in the upper panel of Figure 3 with solid lines. The observed data are plotted with open circles. The bottom panel displays the residuals between the ephemeris and the observed data. It seems that there is a continuous secular decrease in this system. The period decrease rate = -´-dP dt 1.42 10 7 days yr 1 was derived from Equation (2). Since it is composed of two late-type components, BX Tri is a chromospheric active binary (CAB). This type of system usually has strong magnetic activity. The period decrease may be due to the loss of angular momentum via a magnetized wind, also called magnetic braking (Stepien 1995;Demircan 1999;Luo et al. 2010). The mass transfer can also lead to the period decrease. Based on a Wilson-Devinney model simulation, the BX Tri system was probably a semidetached binary with a primary component filling its Roche lobe (see Section 3.2). Therefore, mass transfer from primary to secondary components can lead to a period decrease over a long timescale. So the period decrease of BX Tri is most likely caused by mass transfer from the primary to the secondary component.

Photometric Solution of BX Tri
In order to find the proper photometric solution, the light curves with and without flare phenomena are calculated. Here, our four-color light curves were simultaneously analyzed using the Wilson-Devinney (WD) program (Wilson & Devinney 1971;Wilson 1979Wilson , 1990Wilson , 1994Wilson , 2012Wilson & Van Hamme 2003). During the process, we assumed the effective temperature to be T 1 =3735 K for the primary component, which was determined from the color index and taking into account that the temperature of the primary component T 1 is higher than the mean temperature of the binary (Dimitrov & Kjurkchieva 2010). The initial mass ratio q is fixed to the spectroscopic mass ratio q=0.509(±0.02) obtained by Rucinski & Lu (1999). The gravity-darkening exponents were set to 0.32 according to the stellar temperatures given by Claret (2000). The bolometric albedos A1=A2=0.5 (Rucinski 1969) were used because BX Tri is cool. A nonlinear limbdarkening law with a logarithmic form was applied in the light curve synthesis. The initial bolometric (X 1 , X 2 , Y 1 , Y 2 ) and monochromatic limb-darkening coefficients (x 1 , x 2 , y 1 , y 2 ,) of the components were taken from Van Hamme (1993). The adjustable parameters of the photometric solutions are listed in Table 5.
We started with light curves without flare activities on 2016 December 14 and 15 (named as solution A without flares). In the light curve, the light maxima obviously not being equal implies an O'Connell effect; it has been widely suggested that this effect is associated with magnetic activity (O'Connell 1951; Wilsey & Beaky 2009). Consequently, a cool-spot model was introduced into the primary component. At first, mode 2 (detached binary) was used, and the surface potential of the primary component reached its Roche limits. Then, we changed to mode 4 (semidetached) in the program and obtained the bestfit model for the B-, V-, R-, and I-band photometric data simultaneously. The observed data (red, green, blue, and purple circles mark the B, V, R, and I bands, respectively) and the bestfit light curves (black solid lines) are shown in Figure 4. The results and the parameters of the cool spot are shown as solution A in Table 5.
Then, the photometric solutions of the light curves of BX Tri with flare activities were calculated based on solution A. Four nights in total have been observed with flare activities on 2014 November 22 and 23 (named as solution B with flares) and on 2017 November 10 and 12 (named as solution C with flares). In the beginning, we tried to use the best-fit results of solution A to fit the light curves of solutions B and C simultaneously, but the results were unsatisfactory. Then, solutions B and C were simulated. The initial and basic parameters of solutions B and C are the same as for solution A, including the effective temperature, the gravity-darkening coefficients, the bolometric albedos, and the mass ratio. We still used mode 4 with a cool spot in the WD program in solutions B and C. Finally, the best simulation results were obtained, which are clearly shown in Figure 5, with the same open circles and solid lines as in Figure 4. The detailed photometric solutions of solutions B and C are given in Table 5. We can see that the observed data and the theoretical data have a good match in Figure 5. In the simulation process, the light curves of solutions A, B, and C must be separately fitted with the cool-spot mode, meaning that the light curves of BX Tri vary over time. This phenomenon was also reported by . After investigating the results of photometric solutions since 2010, we find that almost all of the parameters are similar, except for the position of the cool spots. This implies that BX Tri is an active system with a long-lived active region on the components.

The Flare Events
Flare activity is one typical characteristic of BX Tri. We have collected all of the flare events from the literature and analyzed the statistical properties. Thirteen flares in total were collected, including six flares from our observations and seven from the literature (see Table 6). This is a large sample for an individual object with ground-based multicolor observations. Therefore, we discuss the statistical properties of these flares, including the average frequency of flares, flare energies, durations, amplitudes, and the long-term behavior of flare timing with respect to the observed stellar phase.

Flare Frequency
The average occurrence frequency of flares can be estimated from the number of observed flares and the length of the observation period, which can partly reflect the activity of the  (Lacy 1977;Metcalfe et al. 1996;Kim et al. 1997;Kozhevnikova et al. 2004). The amplitude range is from 0.02 to 0.7 mag, and the frequency is around 0.02-0.05 flare per hour.
The first observation of a flare in BX Tri was reported by Dimitrov & Kjurkchieva (2010), who reported six flares. Then, Han et al. (2016) captured another flare event. By the end of 2017 November, 13 outbursts of this binary had been reported by different observers. The brightness of BX Tri was monitored for about 144 hr between 2010 November and 2017 November, including 40 hr by Dimitrov & Kjurkchieva (2010), 24 hr by Han et al. (2016), and 80 hr in this work. If we assume that the eruptions are evenly distributed in time, the flare frequency would be about 0.09 flares per hour. This value is larger than those of CM Dra and GJ 3236. An overview of all of the observed flares is given in Table 6. It is shown in our data set that the repeated occurrence of flares lasted for days, and several flare events were detected in a single night during an orbital cycle. In 2014, the flares lasted two days from November 22 to 23, and there were three events within one period. The period of this system is 0.1926359 days, so we obtained that a flare occurred only about every 1.54 hr. In 2017, the first flare was observed on November 10 and the second flare was detected on November 12. Although there were no data on November 11 because of the weather, such a flare occurrence indicates that the star has a continued flare outburst. It suggested that this system has a high flare frequency, which implies strong magnetic activity.

Flare Duration, Amplitude, Energy, and Color
Flares are usually described by several parameters: amplitude, duration, the equivalent duration, and energy. The schematic diagram of a typical flare is shown in Figure 6 based on the flare on 2014 November 22 at the B band. From the shape of the flare in Figure 6, we can see that the flare has a rapid rise followed by a slowing exponential decay. This flare takes just about 851 s to rise to maximum light, and the decay process takes 2267 s. The duration is 3118 s, which is the sum of the rise time and the decay time. The range of the duration for all flares is from 240 to 3232 s. The amplitude is one of the parameters that reflects how strong the flare is. It was calculated by comparing the observed light curve (red line) and the light curve model (black line) with no flares. The light curve model is calculated using the WD code. It can be calculated as where M peak is the flare peak with the lowest-magnitude value from observation, and M model is the value in the light curve model. In Figure 6, M peak and M model are marked with blue and green circles, respectively. Finally, the amplitude of every flare in different bands was calculated. The difference in different bands is very clear in Table 6. It clearly shows that the amplitudes of the flares gradually decrease from the B to the I band. The largest amplitude among those flares is detected in the B band (0.476 mag), V band (0.325 mag), R band (0.056 mag), and I band (0.015 mag). The amplitude range of all flares is from 0.013 to 0.476 mag.
There are many different methods to estimate the energy of a flare. The key is how to get the bolometric luminosity. Recently, many works on flares in the Kepler field have been published. They usually assume that the light flare on the star can be described by a blackbody radiation model (Kretzschmar 2011;Czesla et al. 2014;Gao et al. 2016;Osten et al. 2016) with a specific effective temperature. Then, based on the Kepler response function, the area of the flare can be obtained. Finally, the total energy can be calculated by integrating over the duration.
In this paper, we also use the blackbody radiation model. The difference is that our data are in multiple bands of the Johnson-Cousins system. At first, the basic equation of magnitude was used as follows: where m and F are the visual magnitude in the V band and the flux, respectively. The subscripts f, tot, and * represent the flux from the flare, from both the star and flares, and from the star, respectively. In order to calculate the total energy, we need to know the bolometric luminosity of the flare: where BC V is the bolometric correction in the V band. Then we obtained the bolometric luminosity as where  L is the solar luminosity, and  M is the absolute magnitude of the Sun and equal to 4.75 mag. The distance d equals 95 pc, and BC V equals −1.73 (Dimitrov & Kjurkchieva 2010). Combining Equations (4)- (7), we can obtain the bolometric luminosity of the flares, L bol,f . The peak L bol,f values of the flares are presented in Table 6, denoted as L peak . At last, the total bolometric energy of the flares, E tot,f , can be obtained from the integral of L f bol, over the duration: The values of the flare energy E tot,f are presented in the 10th column of Table 6. We can see that the range of the total energy is from 3.02(±0.84)×10 33 to 6.70(±0.31)×10 34 erg, which reaches the superflare level (10 34 or more; Walkowicz et al. 2011;Candelaresi et al. 2014;Hawley et al. 2014;Chang et al. 2017). To obtain the error of the energies, we perform a Monte Carlo simulation. We first estimate the photometry uncertainties using the deviation from the light curve modeled before and after the flare. Then we assign an additional random Gaussian error with the sigma of the uncertainty of the photometry to each point of the flares and estimate the energy with the mock data. We run this 100 times and calculate the standard deviation of the energy as the uncertainty. The distributions of rise and decay duration compared with the total duration are analyzed in all filters (see Figure 8). The red triangles mark the decay durations, and the blue dots mark the rise durations. The black lines are linear fits. They show that the rise duration is nearly constant, while the decay duration increases as the flare duration increases. It seems to be that the flares of BX Tri take almost the same time to reach the peak luminosities, but have different decay times. Of course, this phenomenon needs to confirmed by more accurate data, especially on the time resolution.
Based on the B-band and V-band light curves, the colors of B−V were calculated, shown below the light curve in Figure 1. The change in color during the flare is obvious, and the color at the peak of each flare was computed and listed in Table 6. We can see that the B−V values for the two strongest flares are 0.769 mag and 0.839 mag, which are the bluest compared with the other flares. Tofflemire et al. (2017) also discussed the color of the flares and showed that the peak emission from a stellar flare is bluer than accretion radiation. They found the peak of the flares is significantly bluer than other measurements, which they attributed to accretion. Actually, the bluest color in our paper is even redder than their reddest color. Therefore, the flares of the BX Tri system are likely coming from accretion.
We also investigated the distribution of flares as a function of orbital phase. The phases where flares occur are listed in Table 6, and the distribution of these phases is shown in Figure 9. We can see that the flares occur more at phase ∼0.6, and the strongest flare events also happen at this phase. An obvious gap exists at phase ∼0.5, at which almost all of the  light comes from the primary. Combined with the color investigation of the flares and the period analysis, all of this information implies that the flares likely occur on the massaccreting secondary.

Spectrographic Solution of BX Tri
In addition to photometric monitoring, we also obtained a series of spectroscopic observations with full phase coverage for BX Tri (see Table 3). The strong emission lines were detected during our observational run, that is, the Hα, Hβ, and Hγ emission lines, as shown in Figure 2, as well as CaII HK lines (not shown in Figure 2). Such lines (in particular Hα) are commonly used as chromospheric activity indicators for lowmass stars (e.g., Reid et al. 1995b;Bochanski et al. 2007;Walkowicz & Hawley 2009;West et al. 2015).
As shown in Figure 2, all spectra in different orbital phases show evident emission in the Hα, Hβ, and Hγ lines. The equivalent widths of total emissions of Hα and Hβ (EW Hα and EW Hβ , respectively) at each orbital phase are plotted in Figure 10. It shows that the total Hα emission varied irregularly in the range EW Hα ∼2.5-4 Å. On average, EW Hβ has a smaller value, but with similar variation behavior. It seems that these two Balmer emissions are smaller around the first quadrature (though there are few observations) than around the second quadrature; a similar Hα variation was previously reported by Dimitrov & Kjurkchieva (2010). More interestingly, the Hβ has equivalent-width values that are comparable to that of Hα in several orbital phases (e.g., around the second    quadrature), a phenomenon reminiscent of the enhancements in higher Balmer lines during flare-like events (Huenemoerder & Ramsey 1987;Hawley & Pettersen 1991;Johns-Krull et al. 1997;Allred et al. 2006;Bochanski et al. 2007). For example, while Hβ is enhanced during a flare-like event, Hα is not proportionally increased in strength. In fact, the ratio of energy emitted in Hα to Hβ is widely used as an indicator of the presence of flare-like events; the typical energy ratio value is less than 2 in flare-like events, and it then becomes 3 or larger for quiescent chromospheres (e.g., Huenemoerder & Ramsey 1987). The EW Hα /EW Hβ with values of 4/4Åaround the second quadrature indicates an energy ratio value of about 2, assuming the Hα and Hβ continuum fluxes of BX Tri are comparable to that of a dwarf star with = T 3700 eff K. Thus the Hβ enhancements in these phases seem to be due to flare-like events. Unfortunately, we did not have simultaneous photometric observations during these spectroscopic observing runs, so we cannot reach a solid conclusion that these Hβ enhancements indeed result from flare-like events.
To check the respective contribution to the Hβ enhancements for each component, we fitted each profile of Hα and Hβ with a two-Gaussian model, followed the fitting procedure of Dimitrov & Kjurkchieva (2010). We ran a Markov chain Monte Carlo sampling with EMCEE (Foreman-Mackey et al. 2013) to obtain the best-fitted intensities and their uncertainties. The measurements are presented in Figure 10, where red and black symbols denote the Hα (squares) and Hβ (triangles) emissions for the primary and secondary, respectively. Figure 10 shows that the total emissions were mainly from the primary component (in particular around the second quadrature), with just one or two exceptions. In addition, it seems that the variation trend of emission from the primary star is opposite that of emission from the secondary; for example, as the emissions from the primary become higher around the second quadrature, the emissions from the secondary decrease. For the primary component, there are evident Hβ enhancements in several orbital phases (e.g., 0.661, 0.753), indicating that the primary star might suffer some flarelike events in these phases. For the secondary star, there is no evident Hβ enhancement in these phases; instead, we detected evident Hβ enhancements probably due to flare-like events in other phases (e.g., 0.0127). If our measurements for each component are reasonable, it then appears that flares can occur on both components of BX Tri. However, the flare events, as we have discussed in Section 4, are probably from the secondary star. Therefore, more observations are required for confirmation.

Discussions and Conclusions
In this paper, new long-term photometric and spectroscopic observations of the short-period eclipsing system BX Tri have been used to determine its flare activity. Until 2017 December, 13 flares of BX Tri had been reported: six of them are from our observations from 2014 December to 2017 December, and the other seven flares are from other published works (Han et al. 2016;Dimitrov & Kjurkchieva 2010). The durations of all flares from all authors ranged from 566 to 3232 s with amplitudes from 0.013 to 0.476 mag. If we assume the eruptions of BX Tri are evenly distributed in time, then the frequency is roughly 0.09 flares per hour based on all collected flares. We need to emphasize that in our observation on 2014 December 22, three flares were detected in one night with one period, which means that a flare occurred every 1.54 hr. We can infer that this binary system has a high occurrence frequency of flares compared to CM Dra and GJ 3236.
The total energy of our detected flares was determined to range from 3.02(±3.02)×10 33 erg to 6.70(±0.31)×10 34 erg. This energy reaches the superflare energy of 10 34 (e.g., Walkowicz et al. 2011;Notsu et al. 2013;Shibayama et al. 2013;Candelaresi et al. 2014;Hawley et al. 2014;Chang et al. 2017). The flares on the surface of a star are usually associated with the magnetic energy. The magnetic energy accumulates on the stellar surface, accompanied by more frequently occurring and larger star spots when the magnetic energy-releasing flare erupts (Shibata & Magara 2011;Candelaresi et al. 2014.) Meanwhile, because the photometric solution suggests a semidetached configuration for BX Tri with the primary star filling the Roche lobe, mass transfer may also affect the flare eruption. Therefore, we analyzed the period variations and estimated the energy caused by the mass transfer for the BX Tri system. The rate of period decrease of = -dP dt 1.42 -10 7 days yr 1 has been calculated in Section 3. The continuous period decrease can be explained by mass transfer from the primary to the secondary. By considering a conservative mass transfer from primary to secondary, a calculation with the Notes. a T rise and T decay are the durations of the rise (between the beginning and maximum) and decay (between the maximum and end) phases of the flare, respectively. b L peak is the maximum luminosity of the flare. c E flare is the total energy of the flare at the full-wave band. 1 . At last, the luminosity caused by the accreting mass would be approximately represented as the following expression (Zhai & Fang 1995;Zhang et al. 2002): where L acc is the accretion luminosity, M 2 is the mass of the secondary star, dm dt means the mass transfer rate, Ω 2 and Ω in are the dimensionless potentials of the stellar surface and the critical Roche lobe, A is the distance between the two components, and G is the gravitational constant. All of the parameters are known from the photometric results and the period analysis. Finally, the value of L acc was computed as 2.65×10 33 erg s −1 . The average duration of flares can be   We can see that the flares occurred relatively more at phase 0.6, and the strongest flare events also occur at this phase and have a gap near phase 0.5. Figure 10. Equivalent widths of Hα and Hβ emission lines of the primary and secondary components at different phases. Red squares and triangles mark the Hα and Hβ of the primary, respectively. Black squares and triangles mark the Hα and Hβ of the secondary, respectively. obtained from our observations as 2113 s, so the energy caused by the accreting mass can be determined approximately as E acc =5.6×10 36 erg. The largest energy in our observation is E obs =6.70(±0.31)×10 34 erg. Comparing E acc and E obs , we can see that E acc is 100 times bigger than E obs , which means the accreting energy from mass transfer is bigger than flare energy from our observation. It can be understood that mass transfer can motivate such a large flare outburst, but not all of this energy is used in the flare outburst.
The energy, amplitude, and duration are strongly corrected in Figure 7. The larger the energy, the greater the amplitude and the longer the duration. If a star has strong magnetic energy, it takes a longer time to release it and then will show a high amplitude. If the magnetic energy is strong enough, a superflare will occur with a higher amplitude and a longer duration. The distributions of rising and decay time versus the flare duration are analyzed in all filters, shown in Figure 8. The results show that the rising time is flat, while the decay time increases with the duration. It implies that the flares of BX Tri take almost the same time to reach the highest luminosity no matter how long the duration. Then they decay with a time proportional to the flare duration.
We also investigated the distribution of flares as a function of orbital phase in Figure 9. We can see that the flares occur more frequently at phase 0.6, and the strongest flare events also occur at this phase. No flares have been found at phase 0.5, which means all of the light is from the primary at this phase. On the other hand, the results of photometric solutions of BX Tri and the period variation analysis show that this system is a semidetached binary with a continuous orbital period decrease. BX Tri has a mass transfer from the primary to the secondary. Based on this information, we infer that the flares likely occur on the secondary component. Moreover, we identified that the flare is attributed to accretion from the primary to the secondary component based on analysis of the B−V color in Section 4.2, which seems to be further evidence to support our point. Nonetheless, more solid and exclusive evidence is still required from good quality, highresolution spectroscopic observation, in particular simultaneous photometric monitoring, in the future.
To summarize, the M-type eclipsing binary BX Tri with a short period is a magnetically active binary system. Based on our new photometric and spectroscopic observations, we find that it is a semidetached binary with high flare frequency and high energy. In the meantime, the strong emission lines Hα, Hβ, and Hγ imply that BX Tri has strong chromospheric densities and strong magnetic activity.