Statistical research of hyper X-ray flares detected with MAXI
– a correlation between the quiescent luminosity and the largest flare energy –Ryo Sasaki,1 Yohko Tsuboi,1 Satoru Katsuda,1 Ken Yabuki1Yumiko Nakamura1 Yasuharu Sugawara2 Masaru Matsuoka3 and the MAXI team1

Department of Physics, Facilty of Science and Engineeriong, Chuo University,
1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
2ISAS, JAXA, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 229-8510, Japan
3
MAXI team, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
E-mail(RS): sasaki@phys.chuo-u.ac.jp
Abstract
MAXI started its operation in 2009 August. Thanks to its unprecedentedly high sensitivity as an allsky X-ray monitor and to its capability of real-time data transfer, we have detected 106 strong ﬂares fromtwenty-seven active stars (fourteen RS CVn systems, one Algol systems, nine dMe stars, one dKe star, one
Young Stellar Object and one K-type variable star). X-ray energies of these ﬂares were 6 × 1033 –9 × 1038
erg in the 2–20 keV band. These ﬂares can be high ends of their own categories (Tsuboi et al. 2016).
Quiescent state X-ray emissions is thought to originate from the magnetic activity as well as stellar ﬂares.
In response to this, we compared the largest X-ray ﬂare energy in 7.25 years (running period of MAXI
until 2016 November) for each object (Etot,max ) with quiescent state X-ray luminosity (Lx,q ). Each Lx,q
was extracted from ROSAT All-Sky Survey Bright Source Catalogue (Voges et al.1999). As a result, wediscovered a correlation of Etot,max ∝ L1.26
x,q , for the ﬁrst time. With this correlation, we can predict thehighest ﬂare energy in 7.25 years from Lx,q for all stars.
Key words: stars:ﬂares — stars:RS-CVn type — stars:dMe

1. Introduction
Stellar ﬂares are caused by magnetic reconnection
which is speculated by numerous preceding solar studies. Flares often accelerate electrons and protons over
MeV and GeV, respectively. The particles precipitate
along the magnetic ﬁelds into the chromosphere, suddenly heating the plasma at the bottom of the magnetic
loop up to very high temperatures.
A large number of solar and stellar ﬂares were detected
so far. MAXI detected many stellar ﬂares. These ﬂares
are located at the high ends in correlation for both theduration time (τ ) vs. X-ray luminosity (Lx ) and theemission measure vs. temperature (Tsuboi et al. 2016).
Preceding works have discovered that a distribution ofstellar ﬂare energy can be approximated by a power-low
N(E > Etot ) = A E−αtotτobs

year−1 ,(1)where N(E > Etot ) and τobs are the number of eventswith energy larger than the ﬂare energy (Etot ) and observed years, respectively. The index α is 0.6 on RS

CVn system (Osten and Brown 1999), 0.52 and 0.7 on
M dwarfs (Collura et al. 1988 and Pallavicini et al. 1990).
Quiescent state X-ray emissions is thought to originate
from the magnetic activity as well as stellar ﬂares. In
response to this, the distribution of stellar ﬂare, which
ought to be typiﬁed by the largest ﬂare energy in a certain period of time, can be considered to be related withquiescent X-ray emissions. To resolve the relevance, wefocused on the largest ﬂare energy which detected withMAXI in the running period of MAXI.
2. Result
MAXI has been observing the all sky in 7.25 years whichis from 2009 August to 2016 November. MAXI has detected 106 strong ﬂares from twenty-seven active stars(fourteen RS CVn systems, one Algol system, nine dMestars, one dKe star, one Young Stellar Object and one
K-type variable star). The locations of these stars on
all-sky map are shown in Figure 1. The energies of theseﬂares range from 6 × 1033 to 9 × 1038 erg in the 2–20 keVband, as shown in Figure 2. The ﬂare energies detectedwith MAXI are more than two orders of magnitude larger

40■■■ ■■ ■■♦36●■■▲

▲

▲

▲

■

▲

★

▲

▲

■ RS CVn♦ Algol▲

34log (Etot,max [erg])

38

×■
■
■ ■

▲ dMe

▲

★ dKe
● YSO× K-type

32

Fig. 1. Location of ﬂare stars detected with MAXI on all-sky map
2830log (Lx,q [erg s−1])

32

Fig. 3. The correlation between Etot,max and Lx,q .

Fig. 2. The ﬂare energy histgram detected with MAXIthan the maximum solar ﬂare (≈ 1032 erg).
Fig. 4. The diﬀerence of the ﬂare energy distribution of each star.
Star A, B, C are arranged in order from a smaller Etot,max .

3. Discussion
3.1. The maximum flare energy prediction
The obtained ﬂares can be high ends of their own categories (Tsuboi et al. 2016). We compared the maximum
ﬂare energy in running period of MAXI for each object (Etot,max ) with quiescent X-ray luminosities (Lx,q ).
Flare energies are derived by multiplying Lx by τ . Thevalue of τ were not measured for seven stars. For theseﬂares, we used a correlation of τ ∝ L0.2x that was discovered in Tsuboi et al. (2016). We plotted the seven stars
by open mark. On the other hand, each Lx,q was extracted from ROSAT All-Sky Bright Source Catalogue(Voges et al. 1999). We ﬁtted all the data in Figure 3 bya power-law model and obtained the best-ﬁt function ofEtot,max = 10

−2.04±1.12

L1.26±0.04x,qerg.

(2)

The error of the coeﬃcient and the power are 1–σ conﬁdence level. The best-ﬁt model is shown in Figure 3.
With this correlation, we are able to predict the maximum X-ray ﬂare energy of individual stars during theobserving span of 7.25 years from their Lx,q .
3.2. Flare energy distribution
The equation 2 implies that ﬂare mechanisms among theall stellar systems are intrinsically the same. Assumingthat all stellar ﬂare systems obey the same index “α”of equation 1, we ﬁxed the index to 0.6. The N is 1,
because Etot,max occurred once in τobs (7.25 years). The
schematic view of this idea is shown in Figure 4. The
equation of the number of ﬂares is1(E ≥ Etot,max ) = A E−0.6tot,max
7.25 years

year−1 . (3)Etot,max With the equation 2, we were able to derive thenormalization “A”.
A = 1.38 × 1019.38 × (Lx,q)0.72
30
10 erg s−1(4)

In this way, we also succeeded in predicting the number of ﬂares in 7.25 years of each star from the quiescentstate X-ray luminosity.
References
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Osten, R A., Brown, A. 1999, ApJ, 515, 746
Tsuboi, Y. et al. 2016, PASJ, 68, 90
Voges, W. et al. 1999, A&A, 349, 389