The RS CVn type star GT Mus shows most energetic X-ray flares throughout the 2010s

We report that the RS CVn-type star GT Mus (HR 4492, HD 101379 + HD 101380) was the most active star in the X-ray sky in the last decade in terms of the scale of recurrent energetic flares. We detected 11 flares from GT Mus in 8 yr of observations with Monitor of All-sky X-ray Image (MAXI) from 2009 August to 2017 August. The detected flare peak luminosities were 1-4 $\times$ 10$^{33}$ erg s$^{-1}$ in the 2.0-20.0 keV band for its distance of 109.6 pc. Our timing analysis showed long durations ($\tau_{\rm r} + \tau_{\rm d}$) of 2-6 days with long decay times ($\tau_{\rm d}$) of 1-4 days. The released energies during the decay phases of the flares in the 0.1-100 keV band ranged 1-11 $\times$ 10$^{38}$ erg, which are at the upper end of the observed stellar flare. The released energies during whole duration time ranged 2-13 $\times$ 10$^{38}$ erg in the same band. We carried out X-ray follow-up observations for one of the 11 flares with Neutron star Interior Composition Explorer (NICER) on 2017 July 18 and found that the flare cooled quasi-statically. On the basis of a quasi-static cooling model, the flare loop length is derived to be 4 $\times$ 10$^{12}$ cm (or 60 R$_{\odot}$). The electron density is derived to be 1 $\times$ 10$^{10}$ cm$^{-3}$, which is consistent with the typical value of solar and stellar flares (10$^{10-13}$ cm$^{-3}$). The ratio of the cooling timescales between radiative cooling ($\tau_{\rm rad}$) and conductive cooling ($\tau_{\rm cond}$) is estimated to be $\tau_{\rm rad}$ $\sim$ 0.1$\tau_{\rm cond}$ from the temperature; thus radiative cooling was dominant in this flare.


INTRODUCTION
Stellar flares are thought to be a result of magnetic reconnection on a stellar surface (e.g., Shibata & Yokoyama 1999). The process has been actively studied in the case of solar flares, since we can see the flares directly. For the Sun, we can follow the evolution of X-arXiv:2103.16822v1 [astro-ph.HE] 31 Mar 2021 ray emission from plasma loops, which trace the shape of magnetic fields, and once an abrupt ignition occurs, we see how plasma starts to fill the loops. As for the flares on stars other than the Sun, on the other hand, the same process has been inferred from the time variation of physical parameters.
Since the beginning of X-ray astronomy, stellar flares have been observed with many instruments (e.g. Einstein, ROSAT, GINGA, ASCA etc.). These observations have detected the fast rise and slow decay in the light curves of stellar flares and detected that flare temperature peaks before the emission measure (EM), i.e., harder emission peaks before softer emission (e.g., Tsuboi et al. 1998), all of which are seen in the solar flares as well.
Through these studies, RS CVn systems and Young Stellar Objects have been recognized as active flare sources. As for the flares from RS CVn stars, in the last two decades, those from UZ Lib, HR 1099, σ Gem, λ And and EI Eri were detected with XMM-Newton (Pandey & Singh 2012a), those from HR 1099, II Peg, TZ CrB, XY UMa, and AR Lac were detected with Chandra (Nordon & Behar 2007;Drake et al. 2014;Gong et al. 2016); and those from II Peg were detected with Swift (Osten et al. 2007), for example. However, most of the studies were done with pointed observations, where the large flares can be detected only by chance, though there are some rare cases where the pointed observations started with a trigger by wide-field monitorings (e.g., a flare from II Peg observed with Swift; Osten et al. 2007).
Detection of large flares have increased thanks to the Monitor of All-sky X-ray Image (MAXI; e.g., Tsuboi et al. 2016). MAXI is an all-sky X-ray monitor that has been operating on the Japanese Experiment Module (JEM; Kibo) on the International Space Station (ISS) since 2009 August 15 (Matsuoka et al. 2009). It observes a large area of the sky once per 92 minute orbital cycle and makes it possible to search for transients effectively. Tsuboi et al. (2016) analyzed stellar flares detected in 2 yr of MAXI observations. The observed parameters of all of these MAXI/GSC flares are found to be near the upper range for observed stellar flares (see their Figure 4 and 5), with luminosities of 10 31−34 ergs s −1 in the 2-20 keV band, EMs of 10 54−57 cm −3 , e-folding times of 1 hr to 1.5 days, and total radiative energies of 10 34−39 ergs. They found a universal correlation between the flare duration and peak X-ray luminosity, combining the X-ray flare data of nearby stars and the Sun (their Figure 5).
Among the MAXI-detected stellar flare sources, the RS CVn-type star GT Mus showed remarkably energetic flares with energies up to ∼10 38 erg, repeatedly. So far, MAXI has detected flare candidates with the MAXI "nova-alert system" (Negoro et al. 2016) designed to detect transients from MAXI all-sky images in real time. The MAXI team reported nine flare candidates to the MAXI mailing list. Among them, they reported three candidates to the astronomer's telegram 1 (ATel) (Nakajima et al. 2010;Kanetou et al. 2015;Sasaki et al. 2016). One of them has already been reported in Tsuboi et al. (2016).
The RS CVn-type single-lined spectroscopic binary HD 101379 (Strassmeier et al. 1988;McAlister et al. 1990) has a G5/8 giant primary with a radius of 16.56 R (Gaia Collaboration et al. 2016. This binary shows strong CaII H, CaII K, and variable Hα emissions (Houk & Cowley 1975). Moreover, it shows a periodic photometric variation of 61.4 days, which dominates any other variations of GT Mus. This 61.4 day variation may be attributed to a rotational modulation of one or more starspots on HD 101379 (Murdoch et al. 1995). These features indicate high magnetic activity, which implies that the flare observed by MAXI may have originated on HD 101379.
The other system, HD 101380, is a binary consisting of an A0 and an A2 main-sequence star (Houk & Cowley 1975;Collier 1982). In the folded V-band GT Mus light curve, a small dip is detected (Murdoch et al. 1995). It is interpreted to be due to an eclipse of this binary with a period of 2.75 day. No variations by spots have ever been observed. Thus, it is feasible to speculate that HD 101379 has higher chromospheric activity than HD 101380.
All of the reported MAXI flares from GT Mus so far have been detected by the MAXI "nova-alert system" (Negoro et al. 2016). However, there is a real potential that some flares have been missed by this automated system. Given the current small number (23) in the MAXI stellar flare sample ) and the highly active nature of GT Mus, GT Mus provides a good opportunity to study the physical characteristics of stellar flares and their mechanism.
In this work, we carry out a detailed analysis of the MAXI data (Section 2) of GT Mus to search for X-ray flares. We successfully detect 11 flares (including the three that have been already reported), all of which show a total released energy of 10 38 erg or higher, and perform a unified analysis for all of them (Section 3). In addition, we also carry out follow-up X-ray observations with Neutron star Interior Composition Explorer (NICER, see Section 2; Gendreau et al. 2016) for one of the flares, perform time-resolved spectroscopy, and give much tighter constraints on the physical characteristics (Section 3). We then discuss the cooling process of the flare observed with NICER and also GT Mus flares in general in a broader context (Section 4), before summarizing our result (Section 5).
2. OBSERVATIONS 2.1. MAXI MAXI (Matsuoka et al. 2009) is an astronomical Xray observatory mounted on the International Space Station (ISS). In this analysis, we used data from the Gas Slit Camera (Mihara et al. 2011) only, which is sensitive in the 2-30 keV band. It consists of 12 proportional counters, each of which employs carbon-wire anodes to provide one-dimensional position sensitivity. A pair of counters forms a single camera unit; hence the instrument consists of 6 camera units. The six camera units are assembled into two groups whose field of views (FoVs) are pointed toward the tangential direction of the ISS motion along the earth horizon and the zenith direction. The FoVs are 160 • × 3 • , which corresponds to 2% of the whole sky. These counters are not operated in the regions with high particle background, such as the South Atlantic Anomaly and at absolute latitudes higher than ∼40 • , and the vicinity of the Sun (within ∼5 • ). Hence the Gas Slit Camera has an operating duty ratio of ∼40% and scans about 85% of the whole sky per orbit of the ISS.
In this work, we used the MAXI on-demand system 2 (Nakahira et al. 2013) to obtain images, light curves, and spectra. We extracted source photons from a circular region with a radius of 1 • .5 centered on the GT Mus, the area of which corresponds to the point spread function of the Gas Slit Camera. The background photons were extracted from a circular region with a radius of 4 • .0 centered at (R.A., Dec)(J2000) = (11 h 24 m 3 s .7699, −67 • 4 42 .939), excluding the source area of radius of 2 • .0 centered at the same position as the source region.
Here the center of the background region was shifted slightly from that of the source region in order to avoid 2 http://maxi.riken.jp/mxondem/ light leakage from nearby bright sources (Cen X-3 and V830 Cen).

NICER
We carried out follow-up observations of a GT Mus flare (FN 11) with NICER. NICER is a nonimaging Xray detector installed on the ISS in 2017 June. X-ray detector of NICER, the X-ray Timing Instrument (XTI, Prigozhin et al. 2012) consists of 56 co-aligned X-ray concentrator optics (XRCs) and silicon-drift detectors (SDDs). Each XRC collects X-ray photons over a large geometric area from a 15 arcmin 2 area of sky. The XRCs concentrate photons onto the SDDs. The SDDs have a sensitivity in the 0.2-12 keV band with an energy resolution of 85 eV at 1 keV. The XTIs provide a large effective area of ∼1,900 cm 2 at 1.5 keV. In practice, out of 56 XRCs, 52 XRCs are operated in orbit.
The NICER follow-up observation was carried out for FN 11. The "nova-alert system" (Negoro et al. 2016) triggered a transient event from GT Mus on 2017 July 17 03:55 UT. The NICER follow-up observation started on 2017 July 18 17:00 UT, ∼1.5 days after the trigger, and ended on 2017 July 21 14:36 UT. During the observation, the count rate decayed from 300 to 140 counts per second in the 0.5-10.0 keV band. After 123 days from the MAXI trigger for FN 11, NICER observed GT Mus again (from 2017 November 18 to 2017 November 20). During the 3 day observation, the count rate was constant at ∼43 counts s −1 in the 0.5-10.0 keV band. No significant variability during the observation was detected (see Section 3.3 for details). Moreover, this is in agreement with the count rate of GT Mus in the XMM-Newton slew survey catalog (Freund et al. 2018), where Web PIMMS 3 was employed for the count rate conversion. Because of that, we considered these data as the quiescent state of GT Mus.
With NICER, the spectral and temporal parameters of stellar flares can be determined with a much higher precision than with MAXI. NICER can swiftly respond to emergent observations because the ISS is in real-time contact for ∼70% of a day, thanks to the Tracking and Data Relay Satellite.
In this work, we used all available GT Mus NICER data (observation IDs of 1100140101-1100140108). The data were calibrated and screened using the HEASARC's HEAsoft package (v6.25), which includes NICERDAS version 5, with the NICER CALDB version 20181105. We processed the data using the task nicerl2, which generates a list of calibrated, accepted photons excluding periods of especially high background. By this cleaning, the data of observation ID 1100140105 were totally excluded. We extracted source spectra from the cleaned calibrated events.
We estimated background spectra for each of the extracted source spectra. The NICER background is produced by charged particles in the orbit of the ISS, which depends on magnetic cutoff rigidity and space weather conditions. In addition, optical loading from the sunlight falling on the detectors also contributes to background contamination. Most of them appear in the energy range below 0.4 keV. To estimate the background, we extracted NICER photon events from more than 970 ksec of NICER blank-sky field observations that have similar the cutoff rigidity, space weather, and sunangle conditions to those during the GT Mus observations. We accumulated spectra for these extracted background events and subtracted these spectra from the GT Mus spectra for spectral analysis. The estimated background rates were < 3 NICER XTI counts per second for all the GT Mus observations. We conservatively used the 0.5-10 keV energy band in the analysis excluding the lowest and highest energy bands of the SDDs, in order to minimize the effects of the low-energy noise and of large calibration uncertainty in the high-energy band above 10 keV.

Flare search with MAXI
We searched for flares from the MAXI GT Mus light curve using data from 2009 August 15 to 2017 August 14. First, we applied an adaptive binning with a Bayesian block algorithm (Scargle et al. 2013) to a oneorbit light curve. Then, we identified statistically significant variations in the binned light curve with a simple nonparametric model (Figure 1), where the false positive rate (i.e., probability of falsely detecting a change point) was set to p 0 = 0.1, which follows that the significance of a change point is 90% (= 1 − p 0 ). In Figure 1, the data points with time bin less than 0.15 day are deleted, because with such short time bin, the error of the background-subtracted events cannot be approximated to Gaussian. As flare candidates, the bins with a photon flux higher than 0.05 photons s −1 cm −2 are selected. We further filtered out dubious flare candidates using the spatial significance-checking method employed in Uzawa et al. (2011) and Tsuboi et al. (2016), in which the threshold significance was set to 5σ, where σ is the standard deviation of the X-ray counts of the background region in each MAXI image in the 2.0-10.0 keV band, scaled to the source area. We applied this method because the background count rates in the source region are higher than the source count rates in the quiescent state by a factor of 6. Consequently, we found 11 flares. Figure 1 shows the binned light curve with the 11 flares indicated, and Table 1 summarizes the parameters of the flares, including the 2.0-10.0 keV photon flux (see Section 3.2 for details) and the detection significance.

MAXI light curves and spectra
For each of the 11 flares detected with MAXI, we performed time series and then spectral analyses. The duration, or e-folding time (τ d ), of each flare was determined from the 2.0-10.0 keV light curve with each time bin of half a day ( Figure 2 and Table 2). Each light curve was fitted with a burst model, which consists of a linear rise followed by an exponential decay component with an additional constant component. The constant component was fixed to the photon flux of the quiescent emission, 0.013 photons s −1 cm −2 , which was the average value of the over 100 days bin with the Bayesian block process.
The fitting model was expressed by Here t, c(t), ST, PT, and PC are time, count rates, the time when the count rate starts to increase, the time when the count rate is the highest, and the count rate at PT, respectively. Because of the poor statistics, we were not able to determine ST and PT independently. Therefore, we fixed the peak time to the timing of the bin that has the highest photon flux. The exceptions are FN 01 and FN 05, whose rising phases were not observed. They were fitted instead with an exponential plus the constant function that describes the quiescent emission. The result showed that τ d was 100-360 ks (1-4 day).
To determine the physical parameters of the individual flares, we analyzed the spectra at their peaks (see Figure 2 for the extracting time regions). In this analysis, we used the optically thin thermal plasma model apec (Smith et al. 2001) to fit the spectra. Given insufficient photon count statistics of the MAXI data, the metal abundance (Z) and the interstellar absorption (N H ) in the model were fixed at 0.35 Z and 4.4 × 10 20 cm −3 , respectively, the values derived from the NICER time-resolved spectra (see Section 3.3 for details). The redshift was fixed at zero. The best-fit parameters are shown in Table 2. As a result of the fitting,  Table 1.  the absorption-corrected flare peak luminosity in the 2-20 keV band (L X,peak ), temperature (kT ), and EM were derived to be 1-4 × 10 33 erg s −1 , 4-11 keV and 7-23 × 10 55 cm −3 , respectively. The released flare energies are separately shown, separated for the rise phase and decay phases. The flare energy during the rise phase (E rise ) was 3-16 × 10 37 erg, while that during the decay phase (E decay ) was 9-73 × 10 37 erg. Then, the emission in the decay phase is a majority of the energy released during the flare.  Figure 3. Note that since the flare peak was missed with NICER, the MAXI peak data were added into the Figure 3, after conversion to the NICER count rate with Web PIMMS 4 . The NICER light curve was fitted with an exponential function with the decay constant τ d and a constant function, the latter of which was fixed to the NICER count rate in the quiescent state of 6.3 count s −1 in the 2.0-10.0 keV band. The period for the quiescent state is 3 days from 2017 November 18 to 2017 November 20 (see Section 2.2). As a result, the decay constant τ d was derived to be 174±3 ks. The reduced χ 2 (χ 2 red ) and degrees of freedom (d.o.f.) were 1.8 and 10, respectively. The derived τ d is consistent with the value derived from the MAXI light curve.
We performed time-resolved spectroscopy using the NICER data divided into 12 time intervals, which cor-respond to 12 ISS orbits, in the 0.5-10 keV band listed in Table 3. Figure 4 shows all of the time-resolved spectra and the best-fit model. Since the spectra are the sum of the quiescent and flare emissions, the modeling of the quiescent emission was fixed to the bestfit values given in Section 3.3.2. For the flare component, we first adopted an absorbed one-temperature optically thin thermal plasma model. Here we used TBabs (Wilms et al. 2000) and apec for the absorption and the thin thermal plasma models, respectively. We also fixed the red-shift to zero. However, this model was rejected with χ 2 red >2. Then, we fitted the flare component with an absorbed two-temperature optically thin thermal plasma model with the metal abundances (Z) of the cool and hot plasma components assumed to be the same. The spectra were found to be well reproduced by this model. Table 3 and Figure 5 summarize the best-fit parameters and their time variations, respectively.
To check the potential time variations of these NICER spectral parameters, we fitted the time series of the hydrogen column density (N H ), Z, the kT of the cool component (kT cool ), and the EM of the cool component (EM cool ) with a constant model and found that all of these parameters were constant from flare to flare within the statistics. Table 4 shows the fitting results of the time series of the four parameters summarized in Table 3. By contrast, the parameters EM and kT of the hot component (EM hot and kT hot ) showed clear declining trends. We study them in detail in Section 4.3.

Quiescent state analysis
We analyzed a quiescent-state spectrum as follows, using the time-averaged spectra for 3 days (from 2017 Errors, upper limits, and lower limits refer to 90% confidence intervals. a Flare peak luminosity in the 2-20 keV band. The absorption is corrected. b χ 2 red and d.o.f. stand for reduced chi-square and degrees of freedom, respectively. Please note that some fittings have very low χ 2 red , primarily due to the low d.o.f., which came from the limited photon statistics. c τr is flare rise time, which is difference between flare start time and its peak time. d Because the kT was not derived when we made it free, we fixed to the average value of the other flares.  Table 3 for time intervals). The upper panel shows the MAXI photon flux. The lower panel shows the NICER count rate, together with that obtained with MAXI (the first bin). The MAXI data was converted to the NICER count rate with Web PIMMS. The horizontal axis is the number of days since MJD=57,952 (2017 July 18 UT). The solid lines show the fitting function (see text for details).
November 18 to 2017 November 20). The total exposure was 5 ks. The spectrum is shown in Figure 6. The spectrum could be fitted with the absorbed two thin thermal plasma models. As a result, the kT hot,q , EM hot,q , kT cool,q , and EM cool,q values, where the subscript "q" means the quiescent state, were determined to be 3.13 +0.06 −0.07 keV, 8.7 +0.02 −0.01 × 10 54 cm −3 , 1.02±0.01 keV and 1.98±0.02 × 10 54 cm −3 , respectively. The parameters N H,q and Z q were 5.9 ± 0.3 × 10 20 cm 3 and 0.24 +0.01 −0.02 Z , respectively. The absorption-corrected quiescent X-ray luminosity in the 0.5-10.0 keV band was 1.09±0.01 × 10 32 erg s −1 . The resultant χ 2 red and d.o.f. were 1.30 and 308, respectively. The cool component in the quiescent state can be intrinsically interpreted as the same as the cool component during the flare, having a similar temperature and EM (see Table 4).     Table 3 for time intervals). In each panel, the data and componentseparated best-fit model (total model, the flare hot-/cool-temperature components and the quiescent hot-/cool-temperature components shown by solid, dotted, and dashed lines, respectively) are shown in the upper panel, whereas the χ values are shown in the lower panel.

Flare Parameters of GT Mus
Using MAXI, we have detected 11 flares from GT Mus. From the X-ray spectroscopy, GT Mus was found to have large EMs and high plasma temperatures when it is flaring. Both of the parameters are confirmed to be located at the upper end of the universal EM-kT correlation when we plot them into the Figure 4 of Tsuboi et al. (2016).
The large EMs and the plasma temperatures give the large X-ray luminosities. The intrinsic X-ray luminosities in the 0.1-100 keV band, derived with the procedure described in the appendix of Tsuboi et al. 2016, are in the range of 2-5 × 10 33 erg s −1 . Our timing analysis showed long durations (τ r +τ d ) of 2-6 days with long decay times (τ d ) of 1-4 days. We plotted both parameters on the τ d -L X diagram of Tsuboi et al. (2016) (their Figure 5), adding the samples of RS CVn binaries detected with XMM-Newton (Pandey & Singh 2012b), Chandra (Nordon & Behar 2007;Drake et al. 2014;Gong et al. 2016), and Swift (Osten et al. 2007) after converting  (Table 3). Dotted lines are the best-fit models summarized in Table 4. (Right) Time variation of the parameters obtained for the hot component. The first bin is from MAXI data, while the other bins are from NICER data. From the top, the luminosity in the 0.5-10 keV band, the temperature, the EM, and the ratio of T 3.25 hot /EM hot are shown. Dotted lines in the panels for T hot and EM hot show the best-fit model for Equation 4. The dotted line in the luminosity plot is calculated from the models for T hot and EM hot . In all the panels, the NICER and MAXI data are shown by triangles and circles, respectively. their luminosity ranges to the 0.1-100 keV band by using their temperatures and EMs. The results are shown in Figure 8. In the diagram, the GT Mus flares are located at the upper end of the universal correlation obtained by Tsuboi et al. (2016).
The large X-ray bolometric luminosities and the decay time scales give the large X-ray released energies during the flares. In Figure 8, the dashed lines indicate the same energies. The energy released in the GT Mus flare decay phase is in the range 1-11 × 10 38 erg in the 0.1-100 keV band, and that for the whole duration (τ r +τ d ) is in the range 2-13 × 10 38 erg. They are about more than an order of magnitude larger than the other observed stellar flares. We further show the observed flare energy distribution obtained with MAXI (this work and Tsuboi et al. 2016) in Figure 7. Here also, the extremely large energies of the GT Mus flares are shown. All these results indicate that the GT Mus flares are among the hottest, longest, and brightest flares ever observed.

High flare activity
During the MAXI 8-year observation period, the large flares were detected every year. Although the possibility that GT Mus is always active is not excluded, it is likely that GT Mus was in an active phase over 8 yr.
It is well known that the Sun has an 11-years sunspot cycle (Schwabe 1844). Its X-class flares (∼10 31 erg) tend to occur in the period near the solar maximum, spanning about a half of a solar cycle (∼5.5 years) (Aschwanden & Freeland 2012). On the other hand, activity cycles of other RS CVn-type stars have been obtained from a spot number/area as 14-20 years for HR 1099 (V711 Tau) (Lanza et al. 2006;Muneer et al. 2010;Perdelwitz et al. 2018), 9.2 years from II Peg (Lindborg et al. 2013), and 15 years from LQ Hya (Berdyugina et al. 2002). During the half of these activity cycles, the stars are active, which is indicative from the existence many/large spots.
If the same trend of the activity-phase ratio applies to GT Mus, the activity cycle of GT Mus would be at least sixteen years long. Future monitoring observations will determine how long the active phase of GT Mus lasts, if it indeed has a cycle like other active stars.

Cooling process of the GT Mus flares
We investigate the cooling of the hot component of FN 11, which is the dominant flaring event in the observed flares. Here we apply the quasi-static cooling model of van den Oord & Mewe (1989) as a simple approximation.
In the model, the ratio between the radiative-cooling timescale (τ r ) and the conductive-cooling timescale (τ c ) remains constant during the flare decay phase. The two timescales can be expressed by the following formulae: τ r = 3n e kT n 2 e Ψ(T ) (1) where T , n e , Ψ(T ), and E c are the temperature, electron density, emissivity of an optically thin thermal plasma, and mean conductive energy loss rate, respectively. Here Ψ(T ) in Equation 1 is a combination of X-ray emission lines and bremsstrahlung continuum spectrum. In the case of the hot component of FN 11, it is given by Ψ(T ) = Ψ(T ) 0 T −γ = 10 −24.73 T 1/4 erg cm 3 s −1 , since the flare plasma temperature is higher than 20 MK (e.g. Mewe et al. 1985Mewe et al. , 1986) throughout the observation. We assume that the flare geometry is one semicircular loop having a constant cross section, as van den Oord & Mewe (1989) did. Under this assumption, E c in Equation 2 is expressed by where κ 0 and L are the plasma thermal conductivity of 8.8 × 10 −7 erg cm −1 s −1 K −7/2 (Spitzer 1962) and the flare loop full length, respectively. In this case, from the hydrodynamic equations of conservation of mass, momentum, and energies, the solution yields the scaling law in Kuin &Martens (1982) or Equations 19b, 19c, and20 in van den Oord &Mewe (1989), and then the ratio τ r /τ c of 0.1. When we assume that the aspect ratio (a : diameterto-length ratio) and L do not change during a flare, the fact that τ r /τ c is not time-variable means that T 13/4 /EM is not time-variable either, from Equations (1)-(3) in this work (they are corresponding to Equations 7, 8, 9 and 10 in van den Oord & Mewe 1989). The bottom right panel of Figure 5 shows the value of T 13/4 hot 7 /EM hot 54 as a function of time, where T hot 7 and EM hot 54 are T hot /(10 7 K) and EM hot /(10 54 cm −3 ), respectively. We apply a constant function to this plot and obtain an acceptable fit with T 3.25 hot 7 /EM hot 54 = 2.9±0.3, a χ 2 red value of 0.8, and a d.o.f. of 11. Then the FN 11 flare can be described with the model.

Flare Loop Geometry
In the case of quasi-static flare cooling, the decay timescale of kT hot and EM hot can be estimated on the basis of a set of time-evolution formulae expressed in the form of according to Equation 26 and 27 in van den Oord & Mewe (1989), where F represents either kT hot or EM hot as a function of time (t). Here τ qs is called the quasistatic time scale, the specific timescale that determines the decay of both kT hot and EM hot . The value of α depends on F : 8/7 or 26/7 for the cases where F is kT hot and EM hot , respectively (van den Oord & Mewe 1989). We fit the time variation of kT hot and EM hot obtained with MAXI and NICER with Equation 4 simultaneously, with the common parameter τ qs free. The parameter t is set to -0.032 (MJD=57,951.968), which corresponds to the epoch at which the peak of kT hot and EM hot were observed with MAXI. Then we obtained τ qs =130±4 ksec, kT hot (t ) =5.7±0.2 keV, EM hot (t )=99±2 with χ 2 red /d.o.f.=0.89/22. The bestfit models are shown in the time variation of kT hot and EM hot in the right panel of Figure 5, while the model for L X,hot is calculated from those for kT hot and EM hot , and inserted in the upper right panel.
We estimate from these values the three geometric parameters of FN 11 of flare loop length L, aspect ratio of the loop a, and electron density n e using the following equations of the quasi-static cooling model ( n e = 4.4 × 10 10 cm −3 τ qs 10 ks −1 kT hot (t ) keV and obtain the following: The estimated loop length L is much larger, by two orders of magnitude, than that of the typical solar flare, 10 9 -10 10 cm (Kontar et al. 2011). Pandey & Singh (2012a) made a comprehensive loop length comparisons of RS CVn-type stars using pointed observations (e.g. XMM-Newton). They found loop lengths of 10 10 -10 12 cm. On the other hand, MAXI has observed large flares from RS CVn type stars that have a loop length of 10 11 -10 13 cm . The derived loop length in this work is among the highest in the MAXI flare sample. The derived GT Mus loop length is then almost four times larger than the stellar radius, 16.56 R (1.2 × 10 12 cm) (Gaia Collaboration et al. 2016. There are the MAXI/GSC sources that have flares with loop lengths of up to an order of magnitude larger than the stellar radius; our derived ratio of L relative to the stellar radius of GT Mus ranges within the nominal range for these other MAXI stellar flares. Note that the binary separation of HD 101379 is unknown; hence, we are unable to tell whether the loop is connected between the RS CVn-type stars. The estimated parameter, a, is within the range for solar active-region loops (0.06-0.2; Golub et al. 1980). The footprints of the loop cover ∼3.7% of the stellar surface (6.7 × 10 23 cm 2 ). The estimated density n e is consistent with the typical solar and stellar flares of 10 10 -10 13 cm −3 (Aschwanden & Benz 1997;Güdel 2004;Reale 2007).

Coronal magnetic activity
In this section, we examine the magnetic activity of GT Mus. As for low-mass (<1.5M ) main-sequence stars, one of the indicators of magnetic activity, the X-ray to bolometric luminosity ratio (L X /L bol ), is well known to show a good correlation to the Rossby number (R o ), which is the ratio of the rotation period to the convective turnover timescale (e.g. Wright et al. 2011). Figure 9. Scatter plot of the X-ray to bolometric luminosity ratio (LX/L bol ) vs. Rossby number (Ro). Dots and plus signs are for late-type main-sequence single and binary stars, respectively. The solar symbol is for the Sun (Wright et al. 2011). Squares are for G-and K-type giant binaries (Gondoin 2007). The star indicates GT Mus.
Whereas the data show a distinctive log-linear relation between L X /L bol and R o for R o 0.1, the relationship is flat for R o 0.1. This flattening indicates saturation of magnetic activity. In contrast, as for the intermediatemass giant binaries like GT Mus, which has the mass of M * = 2.7M (Tokovinin 2008), the relation has not yet been established, though some studies exist for a period-activity relationship using the other parameters (e.g. Gondoin 2007).
We replotted the data points of 20 G-and K-type intermediate-mass giant binaries in Gondoin (2007), changing the vertical axis of the surface X-ray flux to L X /L bol , and keeping the independent variable as R o (see their Figure 2, right panel). Here R o and L bol are used from Gondoin (2007), calculated with the stellar parameters taken from the literature (Schrijver & Zwaan 1991;Strassmeier et al. 1993;McDowell et al. 1994;Hummel et al. 1994;Voges et al. 1999;Kovári et al. 2001;Williamon et al. 2005). Each L X is taken from the ROSAT bright source catalog (Voges et al. 1999) in order to unify the X-ray band with that used in Wright et al. (2011), 0.1-2.4 keV. The distribution of data points for the giant binaries is found to agree with the relation derived from that of late-type main-sequence stars (see Figure 9).
We then evaluated GT Mus in the diagram. The value R o of GT Mus is derived to be 0.614 from the rotation period of 61.4 days (Murdoch et al. 1995) and the convective turnover timescale of 100 days, the latter of which was obtained from a function of effec-tive temperature during the evolution of a 2.2 M star (Gunn et al. 1998). Here the effective temperature (4761 K) is taken from the Gaia Collaboration et al. (2016,2018). The L bol was calculated to be 4.9 × 10 35 erg from the effective temperature and stellar radius of 16.56 R . With extrapolation of the quiescentstate spectrum of NICER, the value of L X is estimated to be 7.18 ±0.02 × 10 32 erg s −1 in the 0.1-2.4 keV band. Figure 9 compares the location of GT Mus with other stars in the L X /L bol -R o diagram.
We find that GT Mus is consistent with the trend followed by late-type main-sequence stars and G-and K-type giant binaries. However, we note that GT Mus shows considerably higher L X /L bol ratio than the other giant binaries in the diagram. This high X-ray fraction supports the idea that GT Mus is in an active phase. 5. SUMMARY 1. MAXI detected 11 flares from the RS CVn type star GT Mus in its 8 yr of all-sky X-ray monitoring observations. The released energies during the decay phases of the flares were in the range of 1-11 × 10 38 erg in the 0.1-100 keV band, which is higher than any other stellar flares detected in 2 yr of monitoring observations with MAXI ) as well as the other flares detected with the other missions. The released energies during whole duration (τ r + τ d ) ranged 2-13 × 10 38 erg in the same band. The flare parameters (kT , EM, Xray luminosity in the 0.1-100 keV band, and τ d ) are found to be located at the upper end of the known parameter correlation plot of stellar flares compiled by Tsuboi et al. (2016), suggesting that these flares have the largest energy ever observed from stellar flares.
2. We performed a 3 day follow-up X-ray observation of GT Mus with NICER from 2017 July 18, 1.5 days after the MAXI detection of a large flare. The time-resolved spectra suggest that the flare cooled quasi-statically during the NICER observation. On the basis of a quasi-static cooling model, the flare loop size is estimated to be 4.2±0.2 × 10 12 cm (61±5 R ). This size is a 2-3 orders of magnitude larger than that of the typical solar flare loop of 10 9 -10 10 cm.
3. For the first time, we plotted the G and K giant binary samples in the diagram of X-ray to bolometric luminosity ratio versus Rossby number and obtained a consistent distribution with those for the low-mass stars. The Rossby number and log(L X /L bol ) of GT Mus are 0.614 and −3.5, respectively, which puts GT Mus in line with the relation derived from low-mass and giant binary stars in the diagram. It shows a considerably higher L X /L bol than other giant binaries. This high X-ray fraction suggests that GT Mus is at a high magnetic activity level, which is consistent with what is inferred from its recurring large flares.