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

Ryo Sasaki Department of Physics, Chuo University, 1-13-27 Kasuga, Bunkyo-ku,
Tokyo 112-8551, Japan  RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
Yohko Tsuboi  Department of Physics, Chuo University, 1-13-27 Kasuga, Bunkyo-
ku, Tokyo 112-8551, Japan  Wataru Iwakiri  Department of Physics, Chuo
University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan  RIKEN, 2-1
Hirosawa, Wako, Saitama 351-0198, Japan  Satoshi Nakahira  Institute of Space
and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1
Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan  Yoshitomo Maeda
Institute of Space and Astronautical Science, Japan Aerospace Exploration
Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan  Keith
Gendreau  X-ray Astrophysics Laboratory, NASA/Goddard Space Flight Center,
Greenbelt, MD, 20771, USA  Michael F. Corcoran  CRESST & the X-ray
Astrophysics Laboratory, NASA/Goddard Space Flight Center, Greenbelt, MD,
20771, USA  Institute for Astrophysics and Computational Science, The Catholic
University of America, 200 Hannan Hall, Washington, DC 20064  Kenji Hamaguchi
CRESST & the X-ray Astrophysics Laboratory, NASA/Goddard Space Flight Center,
Greenbelt, MD, 20771, USA  Department of Physics, University of Maryland
Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA  Zaven
Arzoumanian  X-ray Astrophysics Laboratory, NASA/Goddard Space Flight Center,
Greenbelt, MD, 20771, USA  Craig B. Markwardt  X-ray Astrophysics Laboratory,
NASA/Goddard Space Flight Center, Greenbelt, MD, 20771, USA  Teruaki Enoto
Extreme Natural Phenomena RIKEN Hakubi Research Team, RIKEN Cluster for
Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan  Tatsuki Sato
Department of Physics, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo
112-8551, Japan  Hiroki Kawai  Department of Physics, Chuo University, 1-13-27
Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan  Tatehiro Mihara  RIKEN, 2-1
Hirosawa, Wako, Saitama 351-0198, Japan  Megumi Shidatsu  Department of
Physics, Ehime University, 2-5, Bunkyocho, Matsuyama, Ehime 790-8577, Japan
Hitoshi Negoro  Department of Physics, Nihon University, 1-8 Kanda-Surugadai,
Chiyoda-ku, Tokyo 101-8308, Japan  Motoko Serino  Department of Physics and
Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara,
Kanagawa 229-8558, Japan

###### Abstract

We report that the RS CVn-type star GT Mus (HR4492, HD101379+HD101380) 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 eleven flares from GT Mus in eight
years of observations with MAXI (Monitor of All-sky X-ray Image) from 2009
August to 2017 August. The detected flare peak luminosities were 1–4 $\times$
1033 erg s-1 in the 2.0–20.0 keV band for its distance of 109.6 pc. The
durations of the flares ranged from 1–4 days. The flare energies are
calculated to be 1–8 $\times$ 1038 erg, which are at the upper end of the
observed stellar flare. We carried out X-ray follow-up observations for one of
the eleven flares with NICER (Neutron star Interior Composition Explorer) 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 5
$\times$ 1012 cm (or 70 $R_{\sun}$). The electron density is derived to be 6
$\times$ 109 cm-3, which is not inconsistent with the typical value of solar
and stellar flares (1010-12 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$\tau_{\rm cond}$.
Therefore, radiative cooling was dominant in this flare.

binaries: close — stars: flare — X-rays: stars

††journal: ApJ

##  1 Introduction

A stellar flare is an energetic explosion on the stellar surface and is
thought to occur by a release of magnetic energy accumulated around spots
(e.g., Shibata_Yokoyama:1999). The largest solar flares ever observed released
energies of the order of $10^{32}$ erg, whereas stellar flares have released
up to $10^{38}$ erg (e.g., Tsuboi:2016).

As for the flares on the stars other than the Sun, the same process is
inferred from mainly the time variation of physical parameters. For example,
we see the fast-rise and slow-decay in light curve of stellar flares, or we
see the flare temperature peaks before the Emission Measure (EM) does, i.e.,
harder emission peaks before softer emission, all of which are seen in the
solar flares as well. However, despite of the analogy, the geometries of the
reconnected magnetic loop are not fully understood in the case of large
flares, especially. For example, one proposed that the loops are connected
between binary components, and the other one assumed that they are connected
between the star and the circumstellar disk.

Stellar flares are thought to be a resultant of magnetic reconnection on a
stellar surface. The process can be watched in X-ray movies of the Sun; in the
movies, X-rays are emitted in plasma loops, which trace the shape of magnetic
fields, and with an abrupt ignitio n, plasma starts to fill the loops. As for
the flares on the stars other than the Sun, the same process is inferred from
mainly the time variation of physi cal parameters. For example, we see the
fast-rise and slow-decay in light curve of stellar flares, or we see the flare
temperature peak s before the Emission Measure (EM) does, i.e., harder
emission peaks before softer emission, all of which are seen in the sol ar
flares as well. However, despite of the analogy, the geometries of the
reconnected magnetic loops are not fully understood in the case of large
flares, especially. For example, one proposed that the loops are connected
between binary components, and the other one assumed that they a re connected
between the star and the circumstellar disk.

In order to investigate the origin of the giant flares, we have been
monitoring stars in the X-ray band with the Mon itor of All-sky X-ray Image
(MAXI; Matsuoka et al. 2009 Matsuoka+09). MAXI is a mission of an all-sky
X-ray moni tor operated in the Japanese Experiment Module (JEM; Kibo) on the
International Space Station (ISS) since 2009 August. It observes an area in
the sky once per 92 min orbital cycle, and enables us to search for stellar
flares effectively. Here, we report the results with the gas proportional
counters (GSC) of MAXI obtained in the first 10-year operation from 2009
August.

lares from the other RS CVn-type stars; e.g. seven flares (UZ Lib, HR1099,
$\sigma$ Gem, $\lambda$ And and EI Eri) observed with XMM-Newton (7.2 $\times$
1035–4.2 $\times$ 1036 erg) (Pandey2012), five flares (HR1099, II Peg, TZ CrB,
XY UMa and AR Lac) observed with Chandra 6 $\times$ 1034–1.3 $\times$ 1036
erg) (Nordon:2007; Drake:2014; Gong:2016) and a II Peg flare observed with
Swift (6 $\times$ 1036 erg) (Osten:2007\parSofar;
themostcomprehensiveobservationsofstellarflareshavebeencarriedoutwiththeall-
skyX-raymonitorMAXI\cite[citep]{(MonitorofAll-skyX-rayImage;
\@@bibref{AuthorsPhrase1Year}{Matsuoka:2009}{\@@citephrase{;
}}{})}whichobservedstellarflareswithflareenergiesbetween10$^33$--10$^38$~ergfrom2009tothepresent(seeSection~\ref{subsec:maxi}fordetail).\cite[citet]{\@@bibref{AuthorsPhrase1YearPhrase2}{Tsuboi:2016}{\@@citephrase{(}}{\@@citephrase{)}}}analyzedstellarflaresdetectedintwoyearsofMAXIobservations.TheobservedparametersofalloftheseMAXI/GSCflaresarefoundtobeneartheupperrangeforobservedstellarflares;
withluminositiesof$10^31-34$ergss$^-1$inthe2--20keVband;
emissionmeasuresof10$^54-57$cm$^-3$; $e$-foldingtimesof1hourto1.5days;
andtotalradiativeenergiesof10$^34-39$ergs.TheyfoundauniversalcorrelationbetweentheflaredurationandpeakX-
rayluminosity; combiningtheX-rayflaredataofnearbystarsandtheSun.Recently;
somestellarflaresareobservedwithXMM-Newton;
ChandraandSwift\cite[citep]{(e.g.\@@bibref{AuthorsPhrase1Year}{Pandey2012;
Gong:2016}{\@@citephrase{; }}{})}.Especially;
anIIPegflareobservedwithSwiftshowed6$×$10$^36$erg\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Osten:2007}{\@@citephrase{;
}}{})}.ThisisoneofthelargestX-
rayflareobservedsofar.Theyarenotincludedin\cite[cite]{\@@bibref{AuthorsPhrase1YearPhrase2}{Tsuboi:2016}{\@@citephrase{(}}{\@@citephrase{)}}}.However;
theyarealsoconsistentwiththecorrelation.Moreover; theyfoundthattheMAXI-
detectedflaresextendedtheestablishedcorrelationbetweentheflare-
peakemissionmeasureandtemperatureforsolarflaresandsmallstellarflares\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Shibata_Yokoyama:1999}{\@@citephrase{;
}}{})}.Therecentflareworksarealsoconsistentwiththiscorrelation.Thesecorrelationsholdoverabroadrangeofenergies;
fromsolarmicroflarestolargestellarflares.Thiscorrelationsuggestsacommonmechanismconnectingflare-
triggeringandcoolingprocesses.\parAmongtheMAXI-detectedstellarflaresources;
theRSCVn-
typestarGTMuswasreportedtoshowremarkablyenergeticflareswithenergiesupto$∼$10$^38$~erg;
repeatedly.Sofar; MAXIhasdetectedflarecandidateswiththeMAXI``nova-
alertsystem''\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Negoro:2016}{\@@citephrase{;
}}{})}designedtodetecttransientsfromMAXIall-
skyimagesinrealtime.TheMAXIteamreportednineflarecandidatestotheMAXImailinglist.Amongthem;
theyreportedthreecandidatestotheastronomer'stelegram~(ATel)\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Nakajima:2010;
Kaneto:2015; Sasaki:2016}{\@@citephrase{;
}}{})}.Oneofthemhasbeenalreadyreportedin\cite[cite]{\@@bibref{AuthorsPhrase1YearPhrase2}{Tsuboi:2016}{\@@citephrase{(}}{\@@citephrase{)}}}.\par\parGTMus(HR4492)isaquadruplesystemconsistingoftwobinarysystemsnamedHD101379andHD101380;
locatedat(R.A.; Dec.)(J2000)=(11$^h$39$^m$29$^s$.497;
$-$65$°$23$′$52$″$.0135)atadistanceof109.594~pc\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Gaia:2016;
Gaia:2018}{\@@citephrase{;
}}{})}.Thetwobinaries(HD101379andHD101380)areseparatedby0.23~arcsec;
whichisspatiallyresolvedbyspecklemethods\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{McAlister:1990}{\@@citephrase{;
}}{})}.\parHD101379isanRSCVn-typesingle-
linedspectroscopicbinary\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Strassmeier:1988;
McAlister:1990}{\@@citephrase{;
}}{})}withaG5/8giantprimarywitharadiusof16.56~$R_☉$\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Gaia:2016;
Gaia:2018}{\@@citephrase{; }}{})}.ThisbinaryshowsstrongCaIIH; CaIIK;
andvariableH$α$emissions\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Houk:1975}{\@@citephrase{;
}}{})}.Moreover; itshowsaperiodicphotometricvariationof61.4days;
whichdominateanyothervariationsofGTMus.This61.4-dayvariationmaybeattributedtoarotationalmodulationofoneormorestarspotsonHD101379\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Murdoch:1995}{\@@citephrase{;
}}{})}.Thesefeaturesindicatehighmagneticactivity;
whichimpliesthattheflareobservedbyMAXImayhaveoriginatedonHD101379.\parTheothersystem;
HD101380; isabinaryconsistingofanA0andanA2main-
sequencestar\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Houk:1975;
Collier:1982b}{\@@citephrase{; }}{})}.InthefoldedV-bandGTMuslightcurve;
asmalldipisdetected\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Murdoch:1995}{\@@citephrase{;
}}{})}.Itisinterpretedtobeduetoaneclipseofthisbinarywithaperiodof2.75day.Novariationsbyspotshaveeverbeenobserved.Thus;
itisfeasibletospeculatethatHD101379hashigherchromosphericactivitythanHD101380.\par\par\parAllthereportedMAXIflaresfromGTMussofarhavebeendetectedbytheMAXI``nova-
alertsystem''\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Negoro:2016}{\@@citephrase{;
}}{})}.However;
thereisarealpotentialthatsomeflareshavebeenmissedbythisautomatedsystem.Giventhecurrentsmallnumber(23)intheMAXIstellarflaresample\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Tsuboi:2016}{\@@citephrase{;
}}{})}; andthehighlyactivenatureofGTMus;
GTMusprovidesagoodopportunitytostudythephysicalcharacteristicsofstellarflaresandtheirmechanism.\par\parInthiswork;
wecarryoutadetailedanalysisoftheMAXIdata(Section~\ref{sec:obs})ofGTMustosearchforX-
rayflares.Wesuccessfullydetectelevenflares(includingthethreethathavebeenalreadyreported);
allofwhichshowatotalreleasedenergyof10$^38$ergorhigher;
andperformunifiedanalysisforallofthem(Section~\ref{sec:res}).Inaddition;
wealsocarryoutfollow-upX-
rayobservationswithNICER\cite[citep]{(NeutronstarInteriorCompositionExplorer;
\@@bibref{AuthorsPhrase1Year}{Gendreau:2016}{\@@citephrase{; }}{};
seeSection~\ref{sec:obs})}foroneoftheflares; performtime-resolvedspectroscopy;
andgivemuchtighterconstraintsonthephysicalcharacteristics(Section~\ref{sec:res}).WethendiscussthecoolingprocessoftheflareobservedwithNICERandalsoGTMusflaresingeneralinabroadercontext(Section~\ref{sec:dis});
beforesummarizingourresult(Section~\ref{sec:sum}).\par\par\par\par\@@numbered@section{section}{toc}{Observations}\par\@@numbered@section{subsection}{toc}{MAXI}MAXI\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Matsuoka:2009}{\@@citephrase{;
}}{})}isanastronomicalX-
rayobservatorymountedontheInternationalSpaceStation(ISS).InthisanalysisweuseddatafromtheGasSlitCamera\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Mihara:2011}{\@@citephrase{;
}}{})}only; whichissensitiveinthe2--
30~keVband.Itconsistsoftwelveproportionalcounters; eachofwhichemployscarbon-
wireanodestoprovideone-
dimensionalpositionsensitivity.Apairofcountersformsasinglecameraunit;
andhencetheinstrumentconsistsof6cameraunits.Thesixcameraunitsareassembledintotwogroupswhosefieldofviews(FoVs)arepointedtowardthetangentialdirectionoftheISSmotionalongtheearthhorizonandthezenithdirection.TheFoVsare160$°$~$×$~3$°$;
whichcorrespondsto2%ofthewholesky.Thesecountersarenotoperatedintheregionswithhighparticle-
background;
suchastheSouthAtlanticAnomalyandatabsolutelatitudeshigherthan$∼$40$°$;
andthevicinityoftheSun(within$∼$5~$°$).HencetheGasSlitCamerahasanoperatingdutyratioof$∼$40$%$andscansabout85$%$ofthewholeskyperorbitoftheISS.\par\parInthiswork;
weusedtheMAXIon-
demandsystem~\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Nakahira:2013}{\@@citephrase{;
}}{})}toobtainimages; lightcurves;
andspectra.Weextractedsourcephotonsfromacircularregionwitharadiusof1$°$.5centeredontheGTMus;
theareaofwhichcorrespondstothepointspreadfunctionoftheGasSlitCamera.Thebackgroundphotonswereextractedfromacircularregionwitharadiusof4$°$.0centeredat(R.A.;
Dec)(J2000)=(11$^h$24$^m$3.7699$^s$; $-$67$°$4$′$42$″$.939);
excludingthesourceareaofradiusof2$°$.0centeredatthesamepositionasthesourceregion.Here;
thecenterofthebackgroundregionwasshiftedslightlyfromthatofthesourceregioninordertoavoidlightleakagefromnearbybrightsources(CenX-3andV830Cen).\par\par\par\@@numbered@section{subsection}{toc}{NICER}\parWecarriedoutfollow-
upobservationsofaGTMusflare(FN~11)withNICER.NICERisanon-imagingX-
raydetectorinstalledontheISSin2017June.X-raydetectorofNICER; theX-
rayTimingInstrument\cite[citep]{(XTI;
\@@bibref{AuthorsPhrase1Year}{Prigozhin:2012}{\@@citephrase{;
}}{})}consistsof56co-alignedX-rayconcentratoroptics(XRCs)andsilicon-
driftdetectors(SDDs).EachXRCcollectsX-
rayphotonsoveralargegeometricareafroma15arcmin$^2$areaofsky.TheXRCsconcentratephotonsontotheSDDs.TheSDDshaveasensitivityinthe0.2
--
12~keVbandwithanenergyresolutionof85~eVat1~keV.TheXTIsprovidealargeeffectiveareaof$∼$19;
00~cm$^2$at1.5~keV.Inpractice; outof56~XRCs;
52~XRCsareoperatedinorbit.\parTheNICERfollow-
upobservationwascarriedoutforFN~11.The``nova-
alertsystem''\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Negoro:2016}{\@@citephrase{;
}}{})}triggeredatransienteventfromGTMuson2017July1703:55UT.TheNICERfollow-
upobservationstartedon2017July1817:00UT; $∼$1.5daysafterthetrigger;
andendedon2017July2114:36UT.Duringtheobservation;
thecountratedecayedfrom300to140countspersecondinthe0.5--
10.0~keVband.After123~daysfromtheMAXItriggerforFN~11;
NICERobservedGTMusagain(from2017November18to2017November20).Duringthethree-
dayobservation; thecountratewasconstantat$∼$43countspersecondinthe0.5--
10.0~keVband.Nosignificantvariabilityduringtheobservationwasdetected(seeSection~\ref{sec:time_res}fordetail).Moreover;
thisisinagreementwiththecountrateofGTMusintheXMM-Newtonslew-
surveycatalog\cite[citep]{(\@@bibref{AuthorsPhrase1Year}{Freund:2018}{\@@citephrase{;
}}{})}; whereWebPIMMSwasemployedforthecount-rateconversion.Becauseofthat;
weconsideredthesedataasthequiescentstateofGTMus.\parWithNICER;
thespectralandtemporalparametersofstellarflarescanbedeterminedwithamuchhigherprecisionthanwithMAXI.Inpractice;
NICERcanswiftlyrespondtoemergentobservationsbecausetheISSisinreal-
timecontactfor$∼$70%ofaday;
thankstotheTrackingandDataRelaySatellite.\par\parInthiswork;
weusedallavailableGTMusNICERdata(observationIDsof1100140101--
1100140108).ThedatawerecalibratedandscreenedusingtheHEASARC'sHEAsoftpackage(v6.25);
whichincludesNICERDASversion5;
withtheNICERCALDBversion20181105.Weprocessedthedatausingthetasknicerl2;
whichgeneratesalistofcalibrated;
acceptedphotonsexcludingperiodsofespeciallyhighbackground.Bythiscleaning;
thedataofobservationID1100140105weretotallyexcluded.Weextractedsourcespectrafromthecleanedcalibratedevents.\parWeestimatedbackgroundspectraforeachoftheextractedsourcespectra.TheNICERbackgroundisproducedbychargedparticlesintheorbitoftheISS;
whichdependsonmagneticcut-offrigidityandspaceweatherconditions.Inaddition;
opticalloadingfromthesunlightfallingonthedetectorsalsocontributestobackgroundcontamination.Mostofthemappearintheenergyrangebelow0.4~keV.Toestimatebackground;
weextractedNICERphotoneventsfrommorethan970~ksecofNICERblank-
skyfieldobservationsthathavesimilarthecut-offrigidity; spaceweather; andsun-
angleconditionstothoseduringtheGTMusobservations.WeaccumulatedspectrafortheseextractedbackgroundeventsandsubtractedthesespectrafromtheGTMusspectraforspectralanalysis.Theestimatedbackgroundrateswere$<3$NICERXTIcountspersecondforalltheGTMusobservations.Weconservativelyusedthe0.5
--
10~keVenergybandintheanalysisexcludingthelowestandhighestenergybandsoftheSDDs;
inordertominimizetheeffectsofthelowenergynoiseandoflargecalibrationuncertaintyinthehighenergybandabove10~keV.\par\par\par\@@numbered@section{section}{toc}{Results}\par\par\<EMAIL_ADDRESS>are the most energetic flares ever.

Two universal correlations are known with regard to the physical parameters of
stellar flares: $EM$ vs. $kT$ (e.g., Shibata_Yokoyama:1999; Tsuboi:2016) and
the intrinsic X-ray luminosity in the 0.1–100 keV band ($L_{\rm X\\_bol}$) vs.
$\tau_{\rm d}$ (Tsuboi:2016). We estimate $L_{\rm X\\_bol}$ of the GT Mus
flares identified in this work to be 1.5–5.1 $\times$ 1033 erg s-1, following
the calculation procedure described in the appendix of Tsuboi:2016. Then, the
GT Mus flares are located at the upper end in both of the universal
correlations.

###  3.2 High flare activity

It is likely that GT Mus was in an active phase during the 8-year period when
MAXI detected flares eleven times, though the possibility that GT Mus is
always active is not excluded. The Sun has an 11-years sunspot cycle
(Schwabe:1844). Its X-class flares ($\sim$1031 erg) tend to occur in the
period near the solar maximum, spanning about a half of a solar cycle
($\sim$5.5 years) (Aschwanden:2012). If the same trend applies to RS CVn-type
stars, the fact that GT Mus stayed active at least for eight years implies
that its activity cycle would be at least sixteen years long.

Activity cycles of other RS CVn-type stars have been reported in the past,
including a spot cycle of 14–20 years for HR1099 (V711 Tau) (Lanza:2006;
Muneer:2010; Perdelwitz:2018), 9.2 years from II Peg (Lindborg:2013), and 15
years from LQ Hya (Berdyugina:2002). Because a half of these activity cycles
shows the existence many/large spots, it can be considered as an active phase.
Although the spot cycle of GT Mus is unknown, the activity cycle of 16 years
or longer that we estimate is consistent with those of these other RS CVn-type
stars. Future monitoring observations will determine how long the active phase
of GT Mus lasts, if it indeed has a cycle like other active stars.

###  3.3 Cooling process of the GT Mus flares

Figure 1:  Plot of $T_{\rm hot\\_7}^{3.25}$/$EM_{\rm hot\\_54}$ against time
during flare FN 11, where $T_{\rm hot\\_7}$ and $EM_{\rm hot\\_54}$ denote the
temperature $T_{\rm hot}$ and emission measure $EM_{\rm hot}$ of the hot
component scaled with 107 K and 1054 cm-3, respectively. The horizontal lines
show the best-fit constant values (solid) with its 90% statistical errors
(dashed).

We investigate the cooling process of FN 11 with the NICER time-resolved
spectra. Here, we apply the quasi-static cooling model by vandenOord_Mewe:1989
as a simple approximation.

In the model, the ratio between the radiative-cooling timescale ($\tau_{\rm
r}$) and the conductive cooling timescale ($\tau_{\rm c}$) remains constant
during the flare decay phase. In general, the two timescales can be expressed
by the following formulae:

$\tau_{\rm r}=\frac{3n_{\rm e}kT}{n_{\rm e}^{2}\Psi(T)}$ (1) $\tau_{\rm
c}=\frac{3n_{\rm e}kT}{E_{\rm c}},$ (2)

where, $T$, $n_{\rm e}$, $\Psi(T)$ and $E_{\rm c}$ are the temperature,
electron density, emissivity of an optically-thin plasma, and mean conductive
energy loss rate, respectively.

The emissivity $\Psi(T)$ in Equation 1, which is the combined emissivity of
X-ray emission lines and bremsstrahlung continuum spectrum, is given by
$\Psi(T)$ = $\Psi(T)_{0}~{}T^{-{\gamma}}$ = $10^{-24.73}~{}T^{1/4}$ erg cm3
s-1 when the flare plasma temperature is higher than 20 MK (e.g. Mewe:1985;
Mewe:1986). We assume that the flare geometry is one semicircular loop having
a constant cross section, as vandenOord_Mewe:1989 did. Under this assumption,
$E_{\rm c}$ in Equation 2 is expressed by

$E_{\rm c}=\frac{16\kappa_{0}T^{7/2}}{7L^{2}},$ (3)

where $\kappa_{0}$ and $L$ are the plasma thermal conductivity of 8.8 $\times$
$10^{-7}$ erg cm-1 s-1 K-7/2 (Spitzer:1962) and the flare loop full length,
respectively. In this case, the theoretical ratio $\tau_{\rm r}$/$\tau_{\rm
c}$ is 0.1, as derived from the scaling law in Kuin:1982 or Equations 19b,
19c, and 20 in vandenOord_Mewe:1989. Flare FN 11 should probably cools quasi-
statically because it has temperature of over 20 MK, providing that our
assumed loop geometry holds.

We verify the applicability of quasi-static cooling model from the observed
parameters of the hot component, which is the dominant flaring component,
where we assume that the aspect ratio ($a$ : diameter-to-length ratio) and $L$
do not change during a flare. Under this assumption, the fact that $\tau_{\rm
r}/\tau_{\rm c}$ is not time-variable means that $T^{13/4}/EM$ is not time-
variable either, from Equations 1, 2, and 3 (vandenOord_Mewe:1989) . Figure 1
shows the value of $T_{\rm hot\\_7}^{13/4}$/$EM_{\rm hot\\_54}$ as a function
of time, where $T_{\rm hot\\_7}$ and $EM_{\rm hot\\_54}$ are $T_{\rm
hot}$/(107 K) and EMhot/(1054 cm-3), respectively. We apply a constant
function to this plot and obtain an acceptable fit with $T_{\rm
hot\\_7}^{3.25}$/$EM_{\rm hot\\_54}$ = 2.9$\pm 0.3$, a $\chi_{\rm red}^{2}$
value of 0.8, and d.o.f. of 11. This result supports our assumption.

###  3.4 Flare Loop Geometry

Figure 2: Time variations of temperature ($kT_{\rm hot}$) and emission measure
($EM_{\rm hot}$). The first data points are the flare peak parameters of MAXI.
The other points are the NICER one. The dashed line was fitting result using
Equation 4 (see Section 3.4)

In this subsection, we estimate the geometrical parameters of the flare loop
for the assumed shape of one semicircular loop with a constant cross section
(as in the previous subsection) on the basis of quasi-static cooling. The key
parameter is the quasi-static cooling timescale ($\tau_{\rm qs}$), and we
estimate it from the observed time evolution of $kT_{\rm hot}$ and $EM_{\rm
hot}$ individually as follows. In the case of quasi-static flare cooling, the
decay timescale of $kT_{\rm hot}$ and $EM_{\rm hot}$ can be estimated on the
basis of a set of time-evolution formulae expressed in a form of

$F(t)=F(t^{\prime})\left(1+\frac{t-t^{\prime}}{3\tau_{\rm
qs}}\right)^{-\alpha}$ (4)

according to Equation 26 in vandenOord_Mewe:1989, where $F$ represents either
$kT_{hot}$ or $EM_{hot}$ as a function of time ($t$), and $t^{\prime}$ is the
epoch at which the $kT_{\rm hot}$ and $EM_{\rm hot}$ peaked during the flaring
event. The value of $\alpha$ depends on $F$: 8/7 or 26/7 for the cases where
$F$ is $kT_{\rm hot}$ and $EM_{\rm hot}$, respectively (vandenOord_Mewe:1989).
The parameter $t^{\prime}$ is set to -0.032, which corresponds to the epoch of
the flare peak observed with MAXI.

We fit our NICER data with the equations for the two cases of $F(t)$, i.e.,
$kT_{\rm hot}(t)$ and $EM_{\rm hot}(t)$ to estimate $kT_{\rm hot}(t^{\prime})$
and $EM_{\rm hot}(t^{\prime})$ and their corresponding cooling timescales
(referred to as $\tau_{\rm qs,kT}$ and $\tau_{\rm qs,EM}$, respectively). As a
result, we obtain $kT_{\rm hot}(t^{\prime})=$4.6$\pm$0.3 keV, $\tau_{\rm
qs,kT}$=300$\pm$150 ksec with $\chi_{\rm red}^{2}$/d.o.f.=0.78/11 for the
former, and $EM_{\rm hot}(t^{\prime})$=97$\pm 5\times 10^{54}$ cm-3,
$\tau_{\rm qs,EM}$=180$\pm$10 ksec with $\chi_{\rm red}^{2}$/d.o.f.=0.68/11
for the latter. In this formulation, the two timescales ($\tau_{\rm qs,kT}$
and $\tau_{\rm qs,EM}$) are expected to be the same when the flare cools
quasi-statically (see the previous subsection), and we confirm it is indeed
the case within the errors; $\tau_{\rm qs,kT}$ $\approx$ $\tau_{\rm qs,EM}$.
In the following discussion, we use $\tau_{\rm qs,EM}$ as the cooling
timescale of FN 11, for it is better constrained than $\tau_{\rm qs}$.

We estimate from these values the three geometric parameters of FN 11 of the
flare loop length $L$, aspect ratio of the loop $a$, and electron density
$n_{\rm e}$, using the following equations of the quasi-static cooling model
(vandenOord_Mewe:1989; Tsuboi:2000),

$\displaystyle a=$ $\displaystyle 1.38\left(\frac{\tau_{\rm qs}}{10~{}{\rm
ks}}\right)^{-1/2}$ (5) $\displaystyle\left\\{\frac{kT_{\rm
hot}(t^{\prime})}{\rm keV}\right\\}^{-33/16}\left\\{\frac{EM_{\rm
hot}(t^{\prime})}{10^{54}~{}{\rm cm}^{-3}}\right\\}^{1/2},$
$L=1.0R_{\sun}\frac{\tau_{\rm qs}}{10~{}{\rm ks}}\left\\{\frac{kT_{\rm
hot}(t^{\prime})}{\rm keV}\right\\}^{7/8},$ (6) $n_{\rm e}=4.4\times
10^{10}{\rm cm}^{-3}\left(\frac{\tau_{\rm qs}}{10~{}{\rm
ks}}\right)^{-1}\left\\{\frac{kT_{\rm hot}(t^{\prime})}{\rm
keV}\right\\}^{4/3},$ (7)

and obtain the following:

$\displaystyle a$ $\displaystyle=$ $\displaystyle 0.14\pm 0.02$ (8)
$\displaystyle L$ $\displaystyle=$ $\displaystyle(4.8\pm 0.4)\times 10^{12}\ \
[\mathrm{cm}]\ \ (69\pm 6R_{\sun})$ (9) $\displaystyle n_{\rm e}$
$\displaystyle=$ $\displaystyle(7.6\pm 0.6)\times 10^{9}\ \
[\mathrm{cm^{-3}}].$ (10)

The estimated loop length $L$ is much larger, by two orders of magnitude, than
that of the typical solar flare, 109–1010 cm (Kontar:2011). The derived length
is then almost four times larger than the stellar radius, 16.56$R_{\sun}$ (1.2
$\times$ 1012 cm) (Gaia:2016; Gaia:2018). According to Tsuboi:2016, the
MAXI/GSC sources 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 others MAXI
stellar flares. The derived loop length is more than one order of magnitude
larger than that of 1010.0–1011.4 cm for the flares from other RS CVn-type
stars (Pandey2012 and the references therein.) Note that the binary separation
of HD101379 is unknown, and hence we are unable to tell whether the loop is
connected between the RS CVn-type stars.

Another estimated parameter, $a$, is within the range for solar active-region
loops (0.06–0.2; Golub:1980). The footprints of the loop cover $\sim$4.2% of
the stellar surface ($7.6~{}\times~{}10^{23}$ cm2). The estimated density
$n_{\rm e}$ is almost consistent with the typical solar and stellar flares of
1010–1011 cm-3 (Aschwanden:1997; Reale:2007).

Finally, we calculate the ratio $\tau_{\rm r}/\tau_{\rm c}$ to be $\sim$0.1,
substituting the obtained plasma parameters to Equations 1 and 2. This means
that 90% of the thermal energy was lost by radiation. It is consistent with
the theoretical prediction by vandenOord_Mewe:1989 for quasi-static cooling.

###  3.5 Coronal magnetic activity

Figure 3: Scatter plot of the X-ray to bolometric luminosity ratio ($L_{\rm
X}$/$L_{\rm bol}$) vs. Rossby number ($R_{\rm o}$). Dots and plus symbols are
for late-type main-sequence single and binary stars, respectively. The solar
symbol is for the Sun (Wright:2011). Squares are for G- and K-type giant
binaries (Gondoin:2007). GT Mus is shown by the star symbol.

In this section, we examine magnetic activity of GT Mus. As for low-mass
($<$1.5$M_{\sun}$) main-sequence stars, one of the indicators of magnetic
activity, the X-ray to bolometric luminosity ratio ($L_{\rm X}$/$L_{\rm
bol}$), is well known to show good correlation to the Rossby number ($R_{\rm
o}$), which is the ratio of the rotation period to the convective turnover
timescale (e.g. Wright:2011). Whereas the data show a distinctive log-linear
relation between $L_{\rm X}$/$L_{\rm bol}$ and $R_{\rm o}$ for $R_{\rm o}$
$\gtrsim$ 0.1, the relationship is flat for $R_{\rm o}$ $\lesssim$ 0.1. This
flattening indicates saturation of magnetic activity. However, no significant
relation is known for intermediate-mass giant binaries like GT Mus; the mass
of the G-type giant star (the primary star of HD101379) in GT Mus is
$M_{\ast}$ = 2.7$M_{\sun}$ (Tokovinin:2008). We plot the data points for 20 G-
and K-type intermediate-mass giant binaries taken from the sample in
Gondoin:2007, where $R_{\rm o}$ and $L_{\rm bol}$ are calculated with the
stellar parameters taken from literature (Schrijver:1991; Strassmeier:1993;
McDowell:1994; Hummel:1994; Voges:1999; Kovri:2001; Williamon:2005) and
$L_{\rm X}$ is derived from the ROSAT bright source catalog (Voges:1999). 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 3).
Therefore, the magnetic activity of G- and K-type giant binaries seem to
follow the same relation as that of late-type main-sequence stars in the
$L_{\rm X}$/$L_{\rm bol}$-$R_{\rm o}$ diagram.

We then evaluated GT Mus in the diagram. The value $R_{\rm o}$ of GT Mus is
derived to be 0.614 from the rotation period of 61.4 days (Murdoch:1995) and
the convective turnover timescale of 100 days, calculated from the effective
temperature of 4761 K (Gaia:2016; Gaia:2018). From the effective temperature
and stellar radius of 16.56 $R_{\sun}$, the $L_{\rm bol}$ was calculated to be
4.9 $\times$ 1035 erg. With extrapolation of the quiescent-state spectrum of
NICER, the value of $L_{\rm X}$ is estimated to be 7.18 $\pm 0.02$ $\times$
1032erg s-1 in 0.1–2.4 keV. Figure 3 compares the location of GT Mus with
other stars in the $L_{\rm X}$/$L_{\rm bol}$-$R_{\rm o}$ 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. GT Mus shows considerably
higher $L_{\rm X}$/$L_{\rm bol}$ ratio than the other giant binaries in the
diagram. This high X-ray fraction may suggest that GT Mus is in an active
phase.

##  4 Summary

  1. 1.

MAXI detected eleven flares from the RS CVn type star GT Mus in its eight
years of all-sky X-ray monitoring observations. The flare energies ranged
between 0.9–7.3 $\times$ 1038 erg, which is higher than any other stellar
flares detected in two years of monitoring observations with MAXI
(Tsuboi:2016). The flare parameters ($kT$, $EM$, $L_{\rm X\\_bol}$, and
$\tau_{\rm d}$) are found to be located at the upper end of the known
parameter-correlation plot of stellar flares (Tsuboi:2016), suggesting that
these flares have the largest energy ever observed from stellar flares.

  2. 2.

We performed a three-day follow-up X-ray observation of GT Mus with NICER from
2017 July 18, 1.5 days after MAXI detection of a large flare. The time-
resolved spectra suggest that the flare cooled quasi-statistically during the
NICER observation. On the basis of a quasi-static cooling model, the flare
loop size is estimated to be 5.1$\pm$0.4 $\times$ 1012 cm (73$\pm 6$
$R_{\sun}$). This size is a 2–3 orders of magnitude larger than that of the
typical solar-flare loop of 109–1010 cm.

  3. 3.

We found that the G- and K-giant binaries are consistent with the low-mass
stars in the diagram of X-ray to bolometric luminosity ratio versus Rossby
number. The Rossby number and log($L_{\rm X}$/$L_{\rm bol}$) 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. GT Mus shows a
considerably higher $L_{\rm X}$/$L_{\rm bol}$ 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.

## Acknowledgments

This research used MAXI data provided by RIKEN, JAXA and the MAXI team. This
work was supported by NASA through the NICER team and the Astrophysics
Explorers Program. It used data and software provided by the High Energy
Astrophysics Science Archive Research Center (HEASARC), a service of the
Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics
Division of the Smithsonian Astrophysical Observatory. R.S. acknowledges
financial support from the Junior Research Associate Program in RIKEN, JSPS
Overseas Challenge Program for Young Researchers and Research Assistant
Program in Chuo University. Y.T. acknowledges financial support from JSPS
KAKENHI Grant Number JP17K05392. W.I. acknowledges support from the Special
Postdoctoral Researchers Program in RIKEN and JSPS KAKENHI Grant Number
JP16K17717. Y.M. gratefully acknowledges funding from the Tanaka Kikinzoku
Memorial Foundation.