LETTER

PASJ: Publ. Astron. Soc. Japan 62, L55–L60, 2010 December 25
c 2010. Astronomical Society of Japan.
Bright X-Ray Flares from the BL Lac Object Markarian 421,
Detected with MAXI in 2010 January and February
Naoki I SOBE,1 Kousuke S UGIMORI,2 Nobuyuki K AWAI,2,3 Yoshihiro U EDA,1 Hitoshi N EGORO,4
Mutsumi S UGIZAKI,3 Masaru M ATSUOKA,3,5 Arata DAIKYUJI,6 Satoshi E GUCHI,1 Kazuo H IROI,1
Masaki I SHIKAWA,5 Ryoji I SHIWATA,4 Kazuyoshi K AWASAKI,5 Masashi K IMURA,7 Mitsuhiro KOHAMA,3,5
Tatehiro M IHARA,3 Sho M IYOSHI,4 Mikio M ORII,2 Yujin E. NAKAGAWA,3 Satoshi NAKAHIRA,8 Motoki NAKAJIMA,9Hiroshi O ZAWA,4 Tetsuya S OOTOME,3 Motoko S UZUKI,3 Hiroshi T OMIDA,5 Hiroshi T SUNEMI,7 Shiro U ENO,5
Takayuki YAMAMOTO,3 Kazutaka YAMAOKA,8 Atsumasa YOSHIDA,8 and the MAXI TEAM
1 Department of Astronomy, Kyoto University, Kitashirakawa, Oiwake-cho, Sakyo-ku, Kyoto 606-8502

n-isobe@kusastro.kyoto-u.ac.jp
2 Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551
3 Coordinated Space Observation and Experiment Research Group,
Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198
4 Department of Physics, Nihon University, 1-8-14 Kanda-Surugadai, Chiyoda-ku, Tokyo 101-8308
5 ISS Science Project Office, Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA),
2-1-1 Sengen, Tsukuba, Ibaraki 305-8505
6 Department of Applied Physics, University of Miyazaki, 1-1 Gakuen Kibanadai-nishi,
Miyazaki, Miyazaki 889-2192
7 Department of Earth and Space Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043
8 Department of Physics and Mathematics, Aoyama Gakuin University,
5-10-1 Fuchinobe, Chuo-ku, Sagamihara 252-5258
9 School of Dentistry at Matsudo, Nihon University, 2-870-1 Sakaecho-nishi, Matsudo, Chiba 101-8308(Received 2010 June 3; accepted 2010 October 1)

Abstract
Strong X-ray flares from the blazar Mrk 421 were detected in 2010 January and February through 7-monthmonitoring with the MAXI GSC. The maximum 2–10 keV flux in the January and February flares was measured
to be 120 ˙ 10 mCrab and 164 ˙ 17 mCrab, respectively; the latter is the highest among those reported from theobject. A comparison of the MAXI and Swift BAT data suggests a convex X-ray spectrum with an approximatedphoton index of Γ & 2. This spectrum is consistent with a picture that MAXI is observing near the synchrotron peakfrequency. The source exhibited a spectral variation during these flares, slightly different from those in previous
observations, in which the positive correlation between the flux and hardness was widely reported. By equating thehalving decay timescale in the January flare, td  2.5  104 s, to the synchrotron cooling time, the magnetic field wasevaluated to be B  4.5  102 G (ı=10)1=3, where ı is the jet beaming factor. Assuming that the light crossing timeof the emission region is shorter than the doubling rise time, tr . 2  104 s, the region size was roughly estimatedas R < 6  1015 cm (ı=10). These results are consistent with values previously reported. For the February flare, therise time, tr < 1.3  105 s, gives a loose upper limit on the size as R < 4  1016 cm .ı=10/, although the longer decay
time, td  1.4  105 s, indicates B  1.5  102 G (ı=10)1=3, which is weaker than the previous results. This could
be reconciled by invoking a scenario that this flare is a superposition of unresolved events with a shorter timescale.
Key words: BL Lacertae objects: individual (Markarian 421) — galaxies: active — radiation mechanisms:
non-thermal — X-rays: galaxies
1. Introduction
Blazars, including BL Lacertae (BL Lac) objects, are a classof active galactic nuclei (AGN), from which a relativistic
jet is emanating close to our line of sight. In addition totheir non-thermal radiation ranging from the radio to gammaray frequencies, and strong polarization at radio and opticalfrequencies, one of the most outstanding characteristics of
blazars is their rapid and high-amplitude intensity variations
or flares, which provide clues about the flow dynamics, as wellas to particle acceleration and cooling processes operating in
the jet. Since the Ginga (e.g., Sembay et al. 1993; Tashiro et al.

1995) and ASCA era (e.g., Takahashi et al. 2000; Tanihata et al.
2001), X-ray observations have been one of the most usefultools to study the variability of blazars. In addition, remarkable progress was successively accomplished by X-ray observations with RXTE and Swift observations (e.g., Kataoka et al.
2001; Tramacere et al. 2009).
Located at a redshift of z = 0.031, Mrk 421 is a high-energy
peaked BL Lac object (HBLs: Padovani & Giommi 1995).
The object is one of the brightest extragalactic sources at very
high energy (VHE) gamma-rays above 100 GeV (Punch et al.
1992). A number of studies (e.g., Kino et al. 2002) revealed
that the multi-frequency spectral energy distribution (SED)L56

N. Isobe et al.

of the source and its variation are basically well understoodwithin the framework of a simple one-zone synchrotron-selfCompton (SSC) model (Band & Grindlay 1985). For Mrk 421,
the X-ray and VHE gamma-ray bands correspond to, or are
located slightly above, the peak frequencies of the synchrotron
and inverse Compton (IC) spectral components, respectively.
As a result, Mrk 421 is one of the most extensively studied
blazars in the X-ray band (e.g., Takahashi et al. 2000; Tanihata
et al. 2004), and X-ray flares were frequently reported (e.g.,Tramacere et al. 2009; Donnarumma et al. 2009).
As the first astronomical mission on the Exposed Facilityof the Japanese Experiment Module “Kibo”, attached to theInternational Space Station (ISS), Monitor of All-sky X-ray
Image (MAXI: Matsuoka et al. 2009) started its operation in2009 August. Thanks to its unprecedentedly high sensitivity as
an all-sky X-ray monitor, and to its capability of real-time datatransfer, MAXI is able not only to make a continuous monitorof X-ray sources including AGN, but also to quickly alert us tovarious transient X-ray phenomena (Negoro et al. 2010), likeflares of blazars. Actually, in the 7-month MAXI observation,
we successfully alerted two strong X-ray flares from Mrk 421(Isobe et al. 2010a, 2010b); in one of these flares the object
exhibited the highest X-ray flux among those ever recorded. In
the present paper, we report on the X-ray features of Mrk 421
in these flares, and discuss their implication.

[Vol. 62,

Fig. 1. Daily lightcurve of Mrk 421. Panels (a) and (b) show
the normalized count rates in the 2–4 keV (F410 ) and 4–10 keV(F24 ) ranges, respectively, measured with the MAXI GSC from 2009
August 22 (MJD = 55062) to 2010 March 20 (MJD = 55275). For
MJD = 55197, 55243, and 55249, F410 and F24 are plotted ina time resolution of 6 hours, in order to resolve the peak. The Swift
BAT lightcurve in 15–50 keV, F1550 , is plotted in panel (c). All errors
represent the 1 statistical one. The dotted lines indicate the count rateof 100 mCrab in the individual energy ranges. The two arrows in thecenter panel define Epochs A and B.

2. Observation and Results
Among the two X-ray instruments onboard MAXI, the Gas
Slit Camera (GSC) and the Solid-state Slit Camera (Tsunemi
et al. 2010), we analyze only the GSC data in the present
paper, because of its higher sensitivity and sky coverage( 97% per day). The GSC utilizes 12 position-sensitive
large-area proportional counters sensitive to X-ray photons in
2–20 keV, although 4 out of them were switched off, on 2009
September 22, due to unexpected discharge events.
The MAXI GSC signals from Mrk 421 were integrated orbit
by orbit within a 3ı  3ı square aligned to the scan direction centered on the source, while the background level was
evaluated from two squares with offsets of ˙3ı toward thescan direction on the sky, of which the size was same asthat of the source region. We normalized the backgroundsubtracted signal counts by a time-integrated effective areaof the collimator plus slits above the proportional counters.
In the following, the data from all the activated counters
are summed up.
As assistance for interpreting the MAXI GSC data, we
utilized hard X-ray data taken with the Burst Alert Telescope(BAT: Barthelmy et al. 2005) onboard Swift. Swift BAT iscomposed of a coded aperture mask and large area (5200 cm2 )CdZnTe detectors. Thanks to its wide field of view ( 1.4 str),
the typical sky coverage of the instrument exceeds  70%(Krimm 2006) in a one-day observation. The daily Swift BAT
lightcurves of Mrk 421 in the 15–50 keV range are available
from the Swift BAT transient monitor results1 , provided by
the Swift BAT team.
Figures 1a and 1b show the normalized signal count1

hhttp://heasarc.gsfc.nasa.gov/docs/swift/results/transients/i.

rates from Mrk 421 derived with the MAXI GSC in
2–4 keV and 4–10 keV, F24 and F410 , respectively, from2009 August 22 (MJD = 55065) to 2010 March 20(MJD = 55275). In the plot, 10% of the count rate fromthe Crab Nebula (100 mCrab, F24 = 0.13 counts cm2 s1and F410 = 0.125 counts cm2 s1 : Nakahira et al. 2010)is indicated by dotted lines. We have noticed some relatively long data gaps, such as on 2009 September 3–7(MJD = 55077–55081), November 12–16 (MJD = 55147–
55151), and 2010 January 19–26 (MJD = 55215–55222).
During these periods, Mrk 421 was located in the direction
toward the ISS orbital pole unobservable with the MAXI GSC.
The Swift BAT lightcurve in the 15–50 keV range F1550 iscompared in figure 1c.
The lightcurve reveals that Mrk 421 is highly variable inall of the energy ranges. The fractional root-mean-squarevariability parameters (e.g., Rodrı́guez-Pascual et al. 1997) inF24 , F410 , and F1550 were evaluated to be 0.52, 0.71, and0.70, respectively, from the daily averaged lightcurves. The
GSC has detected at least four flares with an X-ray flux of& 100 mCrab, on 2009 November 1 (MJD = 55136), 2009
November 11 (MJD = 55146), 2010 January 1 (MJD = 55197:
Isobe et al. 2010a), and February 16 (MJD = 55243: Isobeet al. 2010b). Unfortunately, the observational conditions
for the first and second flares were found to be relatively
bad, although the second flare appears to be concurrent withthe hard X-ray one, detected with the Swift BAT on 2009
November 10 (MJD = 55145: Krimm et al. 2009). Therefore,
we focus on the GSC data associated with the third and forthflares, which are indicated by two arrows, denoted as Epoch A
and Epoch B, respectively, in figure 1b. During Epoch A,

Bright X-Ray Flares from Mrk 421, Detected with MAXI

L57

Fig. 2. Lightcurve of Mrk 421 during Epochs A (panel a) and B (panel b). The GSC 2–10 keV count rate, F410 + F24 for a time resolution of 6 hours
is shown at the top. A time resolution of 1.5 hour is adopted when the 6 hour averaged flux is higher than the 100 mCrab level (the dotted line). The centerand bottom display the daily-averaged hardness ratios, defined as HR1 = F410 =F24 and HR2 = F1550 =F24 , respectively. For MJD = 55197 inpanel (a), HR1 is displayed every 6 hours. The hardness for the Crab-like spectrum with a photon index of Γ = 2.08 (Toor & Seward 1974) with a galactic
absorption column density of NH = 3.2  21 cm2 (Kalberla et al. 2005) is expressed by the dotted lines. The long and short arrows in the center ofpanel (b) define the phases before and after the decay of the Epoch B first peak (MJD = 55246), adopted in figures 3 and 4.

no significant increase in F1550 was apparently found, while
the object brightened in all energy ranges during Epoch B. The
flare of Epoch A (MJD = 55197) was not covered with theSwift BAT, due to sparse sampling toward Mrk 421 during thisperiod. In addition, the hardness variation between Epoch A
and Epoch B (before the first peak) was found to be statistically insignificant, as we show below.
Figure 2 shows the 2–10 keV GSC lightcurve, F24 +F410 , during Epochs A and B, together with the hardness ratios, defined as HR1 = F410 =F24 and HR2 =F1550 =F24 . The lightcurve in Epoch A peaks at MJD =55197.4, with a 2–10 keV flux of 120 ˙10 mCrab, averaged
over 6 hours around the peak. Here and hereafter, the error
represents the 1  statistical one. The doubling time scales in
the rise and decay phases of this flare were estimated to be
tr . 2  104 s and td  2.5  104 s, respectively. During
Epoch B, the source activity continued for about one month,and we found several flares in the lightcurve. The peak
2–10 keV flux of the first flare in Epoch B was measured at
MJD = 55243.6 as 164 ˙ 17 mCrab on a 6-hour average. The
decay time of this flare is derived as td  1.4  105 s, a factor
of 5–6 longer than that of the Epoch A flare. Due to a data gap
with & 1 day just before the peak seen in figure 2, we put only
a loose upper limit on the rise time, as tr < 1.3  105 s. The
lightcurve exhibited the second peak at MJD = 55249.6 witha 2–10 keV flux of 108 ˙ 7 mCrab.
Utilising the daily averaged hardness ratio, we quantitatively
investigated the spectral variation of Mrk 421 during Epochs A
and B, as summarised in table 1. The hardness of the source
was found to stay unchanged during Epoch A within the statistical uncertainties (2 =dof = 7.3=18 and 14.9=15 for HR1 andHR2, respectively). The average and standard deviation of
HR1 were derived as HR1 = 0.74 and 1 = 0.10, respectively,

Table 1. Summary of spectral variation of Mrk 421.




Epoch

A

B

B

HR1
1 
2 =dofHR22 
2 =dof

0.74
0.10
7.3=185.3  102
2.3  102
14.9=15

0.73
0.13
6.6=11
6.2  102
1.1  102
7.4=9

0.90
0.15
42.1=27
10.0  102
2.7  102
73.8=27

 Before the first flare (MJD = 55232–55245).
 After the first flare (MJD = 55246–55275).
 Average of HR1 and HR2.

 Standard deviations of HR1 and HR2.

while those of HR2 were calculated as HR2 = 5.3  102 , and2 = 2.3  102 . Before the decay of the first flare in Epoch B(MJD = 55232–55245; corresponding to the arrows denoted as“Before” in figure 2), the object exhibited a hardness similar tothat in Epoch A. No statistically significant spectral variation
was observed during this phase (2 =dof = 6.6=11 and 7.4=9
for HR1 and HR2). After the decay of the Epoch B first flare(MJD = 55246–55275; indicated by the arrows with “After”
in figure 2), the spectrum of the source seems to have hardened into HR1 = 0.90 and HR2 = 10.0  102 , with a standard deviation of 1 = 0.15 and 2 = 2.7  102 , respectively.
In addition, the source hardness is found to have been variable (2 =dof = 42.1=27 and 73.8=27 for HR1 and HR2) during
this period. Toward the end of Epoch B (MJD & 55264), thesource appears to have recovered a hardness similar to those
before the first peak (and hence those in Epoch A). In order
to visualize these spectral variations associated with the flares,

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N. Isobe et al.

[Vol. 62,

Fig. 3. HR1 (a) and HR2 (b) plotted against F24 + F410 , in a time resolution of a day. Only the data with F24 + F410 > 0.05 counts cm2 s1are displayed. The error bars indicate the 1  statistical errors. The circles show the data during Epoch A, while the triangle and crosses represent the
Epoch B data before and after MJD = 55246, respectively (indicated the ranges with the two arrows in figure 2). The data points covering the peaks ofthe Epoch A flare, the first and second flares of Epoch B are respectively indicated with A1, B1, and B2, respectively.

3. Discussion

Fig. 4. Color–color plot between HR1 and HR2, averaged over 3 days.
The symbol notation same as figure 3 is adopted for the individual
phases. Those covering the peaks of the Epoch A flare, the first andsecond flares of Epoch B are indicated by A1, B1, and B2, respectively.
The error bars indicate the 1  statistical errors. The dashed lines show
the values of HR1 and HR2, for the photon index of Γ = 2.0, 2.5, and3.0, assuming that the galactic absorption column density of NH = 1.9
 20 cm2 toward Mrk 421 (Kalberla et al. 2005). If the spectrum isa straight PL in the 2–50 keV range, the data points lie on the solid line.

HR1 and HR2 are plotted against the source X-ray intensity,
F24 + F410 , in figure 3.
Figure 4 shows a color–color plot between HR1 and HR2
with a time resolution of 3 days. From this figure, we roughly
evaluated the shape of the X-ray spectrum of Mrk 421. Whena simple power-law (PL) model was assumed, the observed
values of HR1 corresponded to a 2–10 keV photon index ofΓ = 2–2.5, as shown by the vertical dashed lines in figure 4.
The systematic uncertainty in the photon index due to thecurrent GSC response was estimated to be ΔΓ = 0.1 (Nakahira
et al. 2010). The figure also indicates a spectral softening from
the MAXI GSC to the Swift BAT energy ranges.

As shown in figures 1 and 2, at least the two active
phases of Mrk 421 in 2010 January (Epoch A) and February(Epoch B) were extensively monitored with the MAXI GSC.
The maximum 2–10 keV flux of the flare in Epoch A wasderived as 120 ˙10 mCrab at MJD = 55197.4. During
Epoch B, the MAXI GSC revealed a significant long-term
activity of the source for nearly one month with a 2–10 keV fluxof & 50 mCrab, exhibiting multiple flares. This demonstrates
a great advantage of the MAXI GSC for monitoring long-term
variations of blazars. Especially, the first flare of Epoch B,of which the peak flux was measured as 164 ˙ 17 mCrab(MJD = 55243.6), is probably associated with a strong andvariable activity in the VHE gamma-rays with the maximum
VHE flux exceeding the 10 Crab level, detected on 2010
February 17 (MJD = 55244) by the VERITAS Observatory(Ong et al. 2010).
Since it was identified as the first extragalactic VHE  -raysource in 1990s (Punch et al. 1992), Mrk 421 has been one of
the most extensively studied blazars. As a result, a numberof X-ray observations of the object were conducted withvarious X-ray observatories, including Ginga (Makino et al.
1992), ASCA (Takahashi et al. 1996, 2000; Tanihata et al.
2001, RXTE (e.g., Kataoka et al. 2001), XMM-Newton (e.g.,Tramacere et al. 2007), Suzaku (Ushio et al. 2009), and soforth. Except for in significant X-ray flares, its 2–10 keV X-ray
flux was reported to be typically below  50 mCrab. Thanks
to recent X-ray monitoring observations with Swift and the All
Sky Monitor on board RXTE, strong X-ray flares were successively reported from the object; these include the flare in 2006
June with the 2–10 keV flux of  85 mCrab (Tramacere et al.
2009), the flare in 2008 June with 130 mCrab (Donnarumma
et al. 2009) and the flare in 2009 December with  100 mCrab(D’Ammando et al. 2009). It is important to note that the
maximum X-ray flux in the first flare of Epoch B, measured
with the MAXI GSC, is higher than any other previous results.

Bright X-Ray Flares from Mrk 421, Detected with MAXI

Therefore, we have concluded that MAXI GSC discovered thestrongest X-rays from Mrk 421.
The color–color plot in figure 4 suggests that the MAXI GSC
spectrum of Mrk 421 is roughly approximated by a PL witha photon index of Γ = 2–2.5. A convex curvature in the MAXI
GSC and Swift BAT energy range, inferred from a comparisonof HR1 to HR2 in figure 4, together with the previous determination of the synchrotron peak energy in Mrk 421 around theobserved photon energies of Ep = 0.3–5 keV (e.g., Tanihata
et al. 2004; Tramacere et al. 2007; Ushio et al. 2009), implies
a smoothly curved X-ray spectrum of the source.
In the case of HBLs, where the synchrotron peak frequency
is located at the X-ray band, the timescale of the X-ray
flux variation is thought to be controlled mainly by interplay
between the following timescales (Kataoka 2000): the acceleration timescale of high-energy electrons, acc ; the radiative
cooling time, cool ; and the light crossing time of the emission region, crs . We, here describe all of the timescales in theobserver’s frame, after having converted those in the source
rest frame,  0 , as  =  0 =ı, in order to relate them directly tothe observed timescales. For a significant flare to take place,the condition acc < cool is required. Assuming that a flare isa single event, the rise timescale, tr , is expected to be determined by the longer of acc and crs , while the longer of cooland crs is thought to dominate the decay timescale, td . The
soft X-ray lag, discovered with ASCA from Mrk 421 in the
decay phase of an X-ray flare (Takahashi et al. 1996), wasregarded to be produced by the energy dependence of tcool . In
contrast, symmetric X-ray lightcurves with tr  td , observedin day-scale flares from several HBLs, were interpreted to be
shaped by crs (Tanihata et al. 2001).
Because the 2–10 keV MAXI GSC spectrum around the
maximum of the flares was found to be consistent with Γ  2,
we regard that MAXI GSC observed the spectrum near thesynchrotron peak frequencies. Therefore, we adopt the above
argument about the flare timescale to evaluate the physicalparameters of Mrk 421 in these flares. In the flare of Epoch A
and the first flare of Epoch B, td was measured to be longer
than tr . This indicates that tr and td are dominated by different
timescales with each other. As a result, we speculate the condition cool & crs & acc or cool & acc & crs in these flares,
corresponding to td  cool and tr & crs .
The synchrotron radiation usually dominates other coolingprocess in HBLs, including Mrk 421 (e.g., Kataoka 2000).
Assuming isotropically distributed electrons in a randomly
oriented magnetic field, the synchrotron cooling time scale1=2
is expressed as cool  1.5  103 B 3=2 EkeV ı 1=2 s (reevaluated from Takahashi et al. 1996), with B, EkeV , and ı
being the magnetic field in G, the synchrotron photon energy
in keV, and the beaming factor of the jet, respectively. We
roughly evaluated a time-averaged magnetic field of B  4.5
 102 (ı=10)1=3 G in the flare of Epoch A, from the relation td  cool . Here, we assume the typical synchrotron
photon energy of EkeV  4 keV, by averaging the X-ray spectrum of Γ  2 in the MAXI GSC energy range (2–10 keV).
This is barely consistent with the value determined fromone-zone SSC modeling to the observed SED of Mrk 421
in previous observations within the systematic uncertainty

L59(B = 0.036–0.44 G: Kino et al. 2002). A spectral softening orsoft lag, due to the energy dependence of cool , was unobservable within the MAXI GSC signal statistics. On the other hand,
we can put an upper limit on the size R of the emission region
as being R  ccrs ı=(1 + z), where c is the speed of light.
The condition tr & crs gives R . 6  1015 (ı=10) cm. This
upper limit appears to be consistent with the values reported inprevious strong X-ray flares (e.g., Donnarumma et al. 2009).
In a similar manner, we put a loose upper limit from tr on theregion size of the Epoch B first flare as R . 4  1016 (ı=10) cm.
The magnetic field, B  1.5  102 (ı=10)1=3 G, is found tobe weaker by a factor of  3 than that in the Epoch A flaredue to td being longer by a factor of 5–6, while the spectral
softening [from HR2 = (7.6 ˙ 0.9)  102 at MJD = 55243 to(5.1˙0.7)  102 at MJD = 55245], suggested in figures 2 and3 during the decay phase of the Epoch B first flare, appears to
be related to the cooling process. We cannot deny a simple
explanation for the possible weak magnetic field, that thisflare was produced in a part of the jet different from that of
the Epoch A flare with slightly different physical parameters
and/or conditions, from the MAXI data alone. However, we
regard that td is not actually determined by cool in the case ofthis flare, because the derived magnetic field is found to be outof the range of the typical value of Mrk 421 in previous studies(e.g., Kino et al. 2002). Based on a close examination of the
X-ray lightcurve of HBLs obtained in the long-look ASCA andRXTE observations with a duration of &1 week, Tanihata et al.
(2001) proposed a possibility that day-scale flares of HBLs arecomposed of short events with a timescale of 104 s. A similar
scenario is possible to account for the duration of the first flareof Epoch B (td  1:6 day), longer by a factor of 5–6 than thatof the Epoch A flare. It is important to note that in order tovalidate the physical quantities estimated here, the examinationof a multi-wavelength SED of Mrk 421, widely covering thesynchrotron and IC components, and its variation are required,although it is beyond the scope of the present paper.
Within the framework of a simple one-zone SSC
model, the peak energy and luminosity of the synchrotron
component is thought to scale as Ep / Bp2 ı and Lp /2.2Γ /p
B 2 pı 2+Γp Ne V , where p , Γp (< 2), Np , and V are
the maximum Lorentz factor of the radiating electrons, thesynchrotron photon index below Ep (assuming a simple PL
spectrum), the normalization of the electron number density
spectrum, and the volume of the emission region, respectively.
From these scaling relations, a change in B, p , or ı is expected
to be observed as a positive correlation between Ep and Lp ,while only Lp is anticipated to increase when Ne or V (corresponding to the total electron number) increase. The clear
positive Ep –Lp correlation, widely reported from Mrk 421 inprevious observations (e.g., Tanihata et al. 2004; Tramacere
et al. 2007), is thought to suggest a change in B, p , or ı.
The rise of Ep is thought to be recognised as rises in
HR1 and HR2. The hardness–intensity relation, shown infigure 3, suggests a slightly complicated spectral variation,
which appears not necessarily to follow the Ep –Lp positive correlation, especially in Epoch B. We notice that HR2
becomes larger after the end of the first flare in Epoch B, as
clearly shown in figure 2 and table 1. Although at the second

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N. Isobe et al.

flare of Epoch B the source is fainter by  30% than at the firstone, its hardness [HR2 = (10.3˙1.5)  102 at MJD = 55249]
is higher than that at the first flare [HR2 = (7.6 ˙ 1.5)  102
at MJD = 55243]. In addition, the hardest X-ray spectrum
was realized, when the source flux was about one third of the
maximum at the first peak [HR2 = (17.4 ˙ 2.5)  102 at
MJD = 55262]. In order to interpret such a spectral behavior
within a simple one-zone SSC framework, fine tuning of thephysical parameters is required (e.g., a combination of theincrease in B, p , or ı and the decrease in Ne or V ). Otherwise,a multiple-zone/component SSC model (e.g., Ushio et al. 2009)
could be preferred. For a detailed examination, it is necessary
to investigate the multi-frequency SED and its variation.

Thanks to valuable comments from an anonymous referee,
the present paper has been significantly improved. This
research has made use of the MAXI data,2 provided by the
RIKEN, JAXA, and MAXI teams. We acknowledge support
from the Ministry of Education, Culture, Sports, Scienceand Technology (MEXT) of Japan, by the Grant-in-Aid for
the Global COE Programs “The Next Generation of Physics,
Spun from Universality and Emergence” and “Nanoscienceand Quantum Physics”. This research was also supported
by MEXT through Grant-in-Aids (19047001, 20041008,
20540230, 20244015, 21340043, 21740140, 22740120). We
are grateful to Dr. M. Kino and Dr. M. Hayashida for theiradvice and assistance.

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