Long-term monitoring of the TeV emission from Mrk 421 with the ARGO-YBJ experiment
ABSTRACT ARGO-YBJ is an air shower detector array with a fully covered layer of
resistive plate chambers. It is operated with a high duty cycle and a large
field of view. It continuously monitors the northern sky at energies above 0.3
TeV. In this paper, we report a long-term monitoring of Mrk 421 over the period
from 2007 November to 2010 February. This source was observed by the
satellite-borne experiments Rossi X-ray Timing Explorer and Swift in the X-ray
band. Mrk 421 was especially active in the first half of 2008. Many flares are
observed in both X-ray and gamma-ray bands simultaneously. The gamma-ray flux
observed by ARGO-YBJ has a clear correlation with the X-ray flux. No lag
between the X-ray and gamma-ray photons longer than 1 day is found. The
evolution of the spectral energy distribution is investigated by measuring
spectral indices at four different flux levels. Hardening of the spectra is
observed in both X-ray and gamma-ray bands. The gamma-ray flux increases
quadratically with the simultaneously measured X-ray flux. All these
observational results strongly favor the synchrotron self-Compton process as
the underlying radiative mechanism.
arXiv:1106.0896v1 [astro-ph.HE] 5 Jun 2011
Long-term monitoring of the TeV emission from Mrk 421 with
the ARGO-YBJ experiment
B. Bartoli1,2, P. Bernardini3,4, X.J. Bi5, C. Bleve3,4, I. Bolognino6,7, P. Branchini8,
A. Budano8, A.K. Calabrese Melcarne9, P. Camarri10,11, Z. Cao5, A. Cappa12,13,
R. Cardarelli11, S. Catalanotti1,2, C. Cattaneo7, P. Celio8,14, S.Z. Chen0,5,T.L. Chen15,
Y. Chen5, P. Creti4, S.W. Cui16, B.Z. Dai17, G. D’Al´ ı Staiti18,19, Danzengluobu15,
M. Dattoli12,13,20, I. De Mitri3,4, B. D’Ettorre Piazzoli1,2, T. Di Girolamo1,2, X.H. Ding15,
G. Di Sciascio11, C.F. Feng21, Zhaoyang Feng5, Zhenyong Feng22, F. Galeazzi8,
P. Galeotti13,20, E. Giroletti6,7, Q.B. Gou5, Y.Q. Guo5, H.H. He5, Haibing Hu15, Hongbo
Hu5, Q. Huang22, M. Iacovacci1,2, R. Iuppa10,11, I. James8,14, H.Y. Jia22, Labaciren15,
H.J. Li15, J.Y. Li21, X.X. Li5, G. Liguori6,7, C. Liu5, C.Q. Liu17, J. Liu17, M.Y. Liu15,
H. Lu5, X.H. Ma5, G. Mancarella3,4, S.M. Mari8,14, G. Marsella4,23, D. Martello3,4,
S. Mastroianni2, P. Montini8,14, C.C. Ning15, A. Pagliaro19,24, M. Panareo4,23,
B. Panico10,11, L. Perrone4,23, P. Pistilli8,14, X.B. Qu21, E. Rossi2, F. Ruggieri8, P. Salvini7,
R. Santonico10,11, P.R. Shen5, X.D. Sheng5, F. Shi5, C. Stanescu8, A. Surdo4, Y.H. Tan5,
P. Vallania12,13, S. Vernetto12,13, C. Vigorito13,20, B. Wang5, H. Wang5, C.Y. Wu5,
H.R. Wu5, B. Xu22, L. Xue21, Y.X. Yan17, Q.Y. Yang17, X.C. Yang17, Z.G. Yao5,
A.F. Yuan15, M. Zha5, H.M. Zhang5, Jilong Zhang5, Jianli Zhang5, L. Zhang17, P. Zhang17,
X.Y. Zhang21, Y. Zhang5, Zhaxiciren15, Zhaxisangzhu15, X.X. Zhou22, F.R. Zhu22,
Q.Q. Zhu5and G. Zizzi9
(The ARGO-YBJ Collaboration)
0Corresponding author: S.Z. Chen, email@example.com
– 2 –
1Dipartimento di Fisica dell’Universit` a di Napoli “Federico II”, Complesso Universitario
di Monte Sant’Angelo, via Cinthia, 80126 Napoli, Italy.
2Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di
Monte Sant’Angelo, via Cinthia, 80126 Napoli, Italy.
3Dipartimento di Fisica dell’Universit` a del Salento, via per Arnesano, 73100 Lecce, Italy.
4Istituto Nazionale di Fisica Nucleare, Sezione di Lecce, via per Arnesano, 73100 Lecce,
5Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese
Academy of Sciences, P.O. Box 918, 100049 Beijing, China.
6Dipartimento di Fisica Nucleare e Teorica dell’Universit` a di Pavia, via Bassi 6, 27100
7Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, via Bassi 6, 27100 Pavia, Italy.
8Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, via della Vasca Navale 84,
00146 Roma, Italy.
9Istituto Nazionale di Fisica Nucleare-CNAF, Viale Berti-Pichat 6/2, 40127 Bologna,
10Dipartimento di Fisica dell’Universit` a di Roma “Tor Vergata”, via della Ricerca Scien-
tifica 1, 00133 Roma, Italy.
11Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tor Vergata, via della Ricerca
Scientifica 1, 00133 Roma, Italy.
12Istituto di Fisica dello Spazio Interplanetario dell’Istituto Nazionale di Astrofisica, corso
Fiume 4 - 10133 Torino, Italy.
13Istituto Nazionale di Fisica Nucleare, Sezione di Torino, via P. Giuria 1 - 10125 Torino,
14Dipartimento di Fisica dell’Universit` a “Roma Tre”, via della Vasca Navale 84, 00146
– 3 –
Not to appear in Nonlearned J., 45.
15Tibet University, 850000 Lhasa, Xizang, China.
16Hebei Normal University, Shijiazhuang 050016, Hebei, China.
17Yunnan University, 2 North Cuihu Rd, 650091 Kunming, Yunnan, China.
18Universit` a degli Studi di Palermo, Dipartimento di Fisica e Tecnologie Relative, Viale
delle Scienze - Edificio 18 - 90128 Palermo, Italy.
19Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Viale A. Doria 6 - 95125
20Dipartimento di Fisica Generale dell’Universit` a di Torino, via P. Giuria 1 - 10125 Torino,
21Shandong University, 250100 Jinan - Shandong, China.
22Southwest Jiaotong University - 610031 Chengdu, Sichuan, China.
23Dipartimento di Ingegneria dell’Innovazione, Universit` a del Salento - 73100 Lecce, Italy.
24Istituto di Astrofisica Spaziale e Fisica Cosmica, Istituto Nazionale di Astrofisica, via
La Malfa 153 - 90146 Palermo, Italy.
– 4 –
ARGO-YBJ is an air shower detector array with a fully covered layer of
resistive plate chambers. It is operated with a high duty cycle and a large field
of view. It continuously monitors the northern sky at energies above 0.3 TeV. In
this paper, we report a long-term monitoring of Mrk 421 over the period from
2007 November to 2010 February. This source was observed by the satellite-borne
experiments Rossi X-ray Timing Explorer and Swift in the X-ray band. Mrk
421 was especially active in the first half of 2008. Many flares are observed in
both X-ray and γ-ray bands simultaneously. The γ-ray flux observed by ARGO-
YBJ has a clear correlation with the X-ray flux. No lag between the X-ray and
γ-ray photons longer than 1 day is found. The evolution of the spectral energy
distribution is investigated by measuring spectral indices at four different flux
levels. Hardening of the spectra is observed in both X-ray and γ-ray bands.
The γ-ray flux increases quadratically with the simultaneously measured X-ray
flux. All these observational results strongly favor the synchrotron self-Compton
process as the underlying radiative mechanism.
Subject headings: BL Lacertae objects: individual (Markarian 421) - gamma rays:
– 5 –
Mrk 421 (z = 0.031) is one of the brightest blazars known and is classified as a BL
Lac object, a subclass of active galactic nuclei (AGNs). Mrk 421 was the first BL Lac
source detected (by EGRET in 1991) at energies above 100 MeV (Lin et al. 1992), and
was also the first extragalactic object detected by a ground-based experiment (Whipple)
at energies around 1 TeV (Punch et al. 1992)(in the following we will refer to γ-rays as
those around 1 TeV). Its emission, like that of the other blazars, is generally dominated
by nonthermal radiation from a relativistic jet aligned along our line of sight. The
spectral energy distribution (SED) is double-humped at X-ray and γ-ray energies in
a plot of νFν versus ν (Fossati et al. 1998), where ν is the frequency and Fν the flux
density. The hump at low energies is usually interpreted as being due to synchrotron
radiation from relativistic electrons (and positrons) within the jet. The origin of the hump
at high energies is under debate. Many models attribute the high-energy emission to
the inverse Compton scattering of the synchrotron (synchrotron self-Compton, SSC) or
external photons (external Compton, EC) by the same population of relativistic electrons
(Ghisellini et al. 1998; Dermer et al. 1992), therefore an X-ray/γ-ray correlation would
naturally be expected. Other models invoke hadronic processes including proton-initiated
cascades and/or proton-synchrotron emission in a magnetic-field-dominated jet. Although
the hadronic models may also accommodate the observed SED and X-ray/γ-ray correlation
(Aharonian 2000; M¨ ucke et al. 2003), they are generally challenged by the most rapid flares
in the TeV region (Gaidos et al. 1996).
Mrk 421 is a very active blazar with major outbursts about once every two years
in both X-ray (Cui et al. 2004) and γ-ray (Tluczykont et al. 2010) bands. A major
outburst usually lasts several months and is accompanied by many rapid flares with
timescales from tens of minutes to several days. Its high variability and broadband emission
– 6 –
require long-term, well-sampled, multiwavelength observations in order to understand
the emission mechanisms of these outbursts. During the last decade, several coordinated
multiwavelength campaigns focusing on Mrk 421 have been conducted both in response
to strong outbursts and as part of dedicated observation campaigns (Rebillot et al. 2006;
Fossati et al. 2008; Acciari et al. 2009; Donnarumma et al. 2009; Horan et al. 2009). Some
important general features of the AGN flares have been obtained. Although X-rays and
γ-rays are found to be strongly correlated, neither type is evidently correlated with optical
and radio emissions. The spectral index becomes harder at higher fluxes in both X-ray and
γ-ray bands (Rebillot et al. 2006; Krennrich et al. 2002; Aielli et al. 2010). An intensive
multiwavelength monitoring campaign has recently been conducted with the Whipple
telescope and the Rossi X-Ray Timing Explorer (RXTE) (Blazejowski et al. 2005).
Similar features, including correlated variability at different energies, flaring and spectral
evolution are also observed. All these phenomena can be interpreted in the framework of the
SSC model. However, “orphan flares”, which have only γ-ray emission without low-energy
companions, and a lag of about two days between X-rays and γ-rays (Blazejowski et al.
2005) are usually recognized as major challenges to the model.
A long-term simultaneous X-ray/γ-ray observation is better performed by means
of a combination of satellite-borne X-ray experiments and wide field-of-view air shower
experiments, such as the Tibet AS-γ experiment (Amenomori et al. 2003) and ARGO-YBJ
experiment (Aielli et al. 2006), which are operated day and night with a duty cycle higher
than 85% and can observe any source with a zenith angle less than 50◦. This is essential in
order to investigate the temporal features of AGN emissions. The ARGO-YBJ experiment
has continuously monitored the northern sky for outbursts from all AGNs, such as Mrk 421,
since 2006 June. Meanwhile, these sources were also monitored by the satellite-borne X-ray
detectors All-Sky Monitor (ASM)/RXTE and Burst Alert Telescope (BAT)/Swift. In this
paper, we report on the long-term monitoring of Mrk 421 for γ-ray outbursts and on the
– 7 –
correlation between γ-rays and simultaneous X-rays over the period from 2007 November
to 2010 February. The paper is organized as follows: the ARGO-YBJ experiment is briefly
introduced in Section 2 and its long-term performance is shown in Section 3. A data
analysis method is described in Section 4. Observation findings are presented in Section 5.
Conclusions are given in Section 6.
2.The ARGO-YBJ Experiment
The ARGO-YBJ experiment, located in Tibet, China at an altitude of 4300 m a.s.l., is
the result of a collaboration among Chinese and Italian institutions and is designed for very
high energy γ-ray astronomy and cosmic ray observations. The detector consists of a single
layer of resistive plate chambers (RPCs), which are organized with a modular configuration.
The basic module is a cluster (5.7 m × 7.6 m) composed of 12 RPCs (2.850 m × 1.225 m
each). The RPCs are equipped with pick-up strips (6.75 cm × 61.80 cm each), and the
logical OR of the signal from eight neighboring strips constitutes a logical pixel (called a
“pad”) for triggering and timing purposes. One hundred thirty clusters are installed to form
a carpet of about 5600 m2with an active area of ∼93%. This central carpet is surrounded
by 23 additional clusters (a “guard ring”) to improve the reconstruction of the shower core
location. The total area of the array is 110 m × 100 m. More details about the detector
and RPC performance can be found in, for example, Aielli et al. (2006).
The RPC carpet is connected to two independent data acquisition systems
corresponding to two different operation modes, referred to as the shower and the scaler
(Aielli et al. 2008) modes. Data used in this paper refer to the shower mode, in which
the ARGO-YBJ detector is triggered when at least 20 pads in the entire carpet detector
are registered within 420 ns. The high granularity of the apparatus permits a detailed
spatial−temporal reconstruction of the shower profile and therefore the incident direction
– 8 –
of the primary particle. The arrival time of the particles is measured by time to digital
converters (TDCs) with a resolution of approximately 1.8 ns. In order to calibrate the
18,360 TDC channels, an off-line method (He et al. 2007) has been developed using cosmic
ray showers. The calibration precision is 0.4 ns, and the procedure is applied every month
(Aielli et al. 2009a).
The central 130 clusters began taking data in 2006 June, and the “guard ring” was
merged into the DAQ stream in 2007 November. The trigger rate is ∼3.6 kHz with a dead
time of 4%, and the average duty cycle is higher than 85%.
For long-term monitoring campaigns, the stable operation of the equipment is very
important. In order to continuously monitor the performance of the RPCs, including
detection efficiency and time resolution, a cosmic ray muon telescope is set up near the
detector array. The RPC efficiency fluctuates by about 0.3% and the time resolution by
about 0.4 ns in a day, and these values become 1.5% and 1 ns in a year, respectively.
Detailed information about the performance monitored using this telescope can be found in
Aielli et al. (2009c).
To estimate the angular resolution and effective area, a full Monte Carlo simulation of
the RPC detector array is developed. In the code, the CORSIKA package (Heck et al. 1998)
is used to describe the air shower development. G4argo (Guo et al. 2010), a GEANT4-based
(Agostinelli et al. 2003) package, is used to simulate the response of the RPC array. For
events with a number of fired pads (Npad) greater than 100, the Point Spread Function
(PSF) has a single Gaussian functional form. For events at lower Npad, the best fit to the
PSF becomes a combination of two Gaussian distributions, the wider of which contains
– 9 –
20% of the events. To simplify the description of the PSF, a parameter ψ70is defined as
is the opening angle containing 71.5% of the events. When the PSF is a single Gaussian,
ψ70maximizes the signal-to-background ratio for a point source. For Npad> 1000, ψ70is
0.47◦, while at Npad∼ 20 ψ70becomes 2.8◦. The effective area of the detector for γ-induced
showers depends on the γ-ray energy and incident zenith angle, e.g., it is about 100 m2at
100 GeV and >10,000 m2above 1 TeV for a zenith angle of 20◦(Aielli et al. 2009b).
The angular resolution, pointing accuracy and stability of the ARGO-YBJ detector
array have been thoroughly tested by measuring the shadow of the Moon in cosmic rays
(Iuppa et al. 2009). The shadow is detected with a significance of 10 σ per month using
the ARGO-YBJ data. The position of the shadow allows the investigation of any pointing
bias. The east-west displacement is in good agreement with the expectation, while a 0.2◦
pointing error toward the north is observed and is under investigation.
For the analysis presented in this paper, only events with a zenith angle less than 45◦
are used, and the data set is divided into six groups according to Npad. The event selections
are listed in Table 1, where R is the distance between shower core position and the carpet
center, and TS is the time spread of the shower front in the conical fit defined in Eqation(1)
of Aielli et al. (2009a). With these selections, the angular resolution is improved, e.g., for
events with Npad> 60 and Npad> 100, the opening angle ψ70decreases from 1.68◦and
1.27◦to 1.36◦and 0.99◦. As a consequence, the significance of the Crab Nebula is increased
by about 10% and 25%, respectively.
In order to obtain a sky map using events in each Npadgroup, an area centered at the
source location in celestial coordinates (right ascension and declination) is divided into a
– 10 –
grid of 0.1◦× 0.1◦bins and filled with detected events according to their reconstructed
origin. The number of events in each grid bin is denoted as ni, where the subscript i denotes
the bin number. In order to extract an excess of γ-rays from the source, the direct integral
method (Fleysher et al. 2004) is applied to estimate the number of cosmic ray background
events in the bin, denoted as bi. An essential assumption in this estimation is that the
background must be uniform around the source. However, an anisotropy of the cosmic ray
flux is measured over spatial scales such as 10◦× 10◦and larger (Amenomori et al. 2006;
Zhang et al. 2009). This anisotropy as measured by the ni/biratio is stable; therefore, it
is possible to correct it with a long-term measurement for each grid bin. An average of
the ratio over the bins in a window 11◦× 11◦centered on the source bin is applied for
smoothing. In this procedure, in order to avoid any contamination of the excess in the
source bin and possible spread out due to the finite angular resolution, the contribution
from a 5◦× 5◦window around the source bin is excluded. Finally the correction factor,
denoted as βi, is calculated as follows:
where the subscript j is the index of the m = 12100 − 2500 = 9600 selected grid bins. The
corrected number of background events in each bin is b∗
i= βibi. The typical value of β
around Mrk 421 is approximately 0.9995. The value of β for each bin is calculated using
about two years of data and is stored in a database for routine analysis.
Taking into account the PSF of the ARGO-YBJ detector, the events in a circular area
centered on the bin with an angular radius of ψ70are summed together. Namely,
where k is the number of bins in the circular area, Nonis the total number of events, and
Nbis the number of background events. The Li−Ma formula (Li & Ma 1983) is used to
estimate the significance.
– 11 –
The data used in this paper were collected by the ARGO-YBJ experiment in the
period from 2007 November to 2010 February. The total lifetime is 676.0 days. The
numbers of events in different groups after the selections are listed in Table 1. A clear signal
from Mrk 421 with significance greater than 11σ is observed using events with Npad> 60
(see Figure 1). A signal at such a level of significance allows us to study flux variations,
correlations with the X-ray flux, and the evolution of the SED.
5.1. Temporal Analysis
In order to study the correlation between γ-rays and X-rays, the daily averaged light
curves of both the hard X-rays (15−50 keV) measured by BAT/Swift1and the soft X-rays
(2−12 keV) measured by ASM/RXTE2are used. The observations by RXTE and Swift
have a rather long exposure by orbiting the Earth every 1.5 hr. Since the fluctuation of the
X-ray flux is abnormally large in some days, in order to control the quality of the data, days
that have a very large error on the mean daily event rate are removed from the data set. For
ASM/RXTE, the distribution of the error indicates that a selection of the errors smaller
than 1 count s−1will cut everything beyond four standard deviations in the distribution.
A similar cut applies to the BAT/Swift data, in which a selection of the errors smaller
than 0.0035 counts cm−2s−1cuts everything beyond four standard deviations in the error
distribution. Approximately, 6.4% and 5.6% of events are removed from the RXTE and
Transientmonitorresultsprovided by theBAT/Swift team:
2Quick-look results providedbythe ASM/RXTE team:
– 12 –
Swift data sets, respectively. Whether it is day or night, ARGO-YBJ observes Mrk-421
while the AGN is in its field of view. A typical transit lasts usually 6 hr. An observational
time less than 5 hr day−1indicates some malfunctioning of the detector in that day, which
is thus removed from the data set. In total, 9.7% of data are removed in this way. Finally,
737, 728, and 712 days are selected from the ASM, BAT, and ARGO-YBJ reconstructed
data sets, respectively.
5.1.1. Light Curves
In 552 days all three experiments observed Mrk 421 simultaneously. In Figure 2, the
accumulation of event rates from the Mrk 421 direction is shown. The Swift event rate has
been normalized using the RXTE scale and the ARGO-YBJ curve is obtained using events
with Npad> 100, thus the median energy of the observed photons is 1.8 TeV, assuming a
spectral index −2.4. The fast increase in the three curves indicates that the source had a
long-term outburst at the beginning of 2008. The following quiet state lasted for about
200 days. Afterward Mrk 421 became increasingly more active. In fact, there were flares
in 2009 November ( Isobe et al. 2010). The duty cycle of ARGO-YBJ was low due to
detector maintenance, therefore it is not obvious in Figure 2. There was a large flare in
2010 February ( Isobe et al. 2010; Ong 2010).
Out of the long-term variation that is clearly revealed in the cumulative light curve
shown in Figure 2, Mrk 421 undergoes a large outburst during the period from 2008
February to June, indicated by the steepest part of the curves. In fact, it is a combination
of several large flares. A better view of these is shown in Figure 3, where a smoothing
analysis is applied for both γ-ray and X-ray curves, and each point is the event rate
averaged over five days. Four large flares are observed by all three detectors, and the peak
times are in good agreement with one another. The fourth flare has been reported by the
– 13 –
ARGO-YBJ experiment in Aielli et al. (2010). It gives an important observation when the
Cherenkov telescopes are hampered by the Moon. It can be concluded that there exists a
good long-term correlation between γ-rays and X-rays.
5.1.2. X-ray/TeV Correlation
The discrete correlation function (DCF) (Edelson & Krolik 1988) is used to quantify
the degree of correlation and the phase differences (lags) in the variations between γ-rays
and X-rays. The daily fluxes before smoothing are used for this analysis. The DCF (in
1 day bins) derived from RXTE and ARGO-YBJ data (with Npad> 100) is shown in
the left panel of Figure 4, where a positive value means that γ-rays lag X-rays. The peak
of the distribution is around zero and the correlation coefficient at zero is ≃ 0.77. The
result derived from Swift and ARGO-YBJ data is shown in the right panel of Figure 4
and the correlation coefficient at zero is ≃ 0.78. To estimate the lag and its uncertainty,
a data-based simulation suggested by Peterson et al. (1998) is applied and the correlation
coefficient between −10 and 10 days is fitted with a Gaussian function. The median
value and corresponding 68% confidence level errors are −0.14+0.86
for the correlations of ARGO-YBJ/RXTE and ARGO-YBJ/Swift data, respectively. No
significant lag longer than one day is found.
5.2.Spectral Energy Distribution
To study the SED at different flux levels, the data simultaneously observed in γ-ray
and X-ray bands are divided into four groups according to the observational time periods
in which the ASM/RXTE counting rate is 0 − 2, 2 − 3, 3 − 5 or > 5 cm−2s−1. For each
group, a flux-averaged SED is constructed both at γ-ray and X-ray energies.
– 14 –
5.2.1. X-ray Spectra
ASM/RXTE monitors the X-ray emission from Mrk 421 at three energy bands, i.e.,
1.5 − 3, 3 − 5 and 5 − 12 keV (Levine et al. 1996). In the flux estimation, the hydrogen
column density 1.38 × 1020cm−2(Dickey & Lockman 1990) and a power law spectrum are
assumed. The best-fit spectral indices for the four flux levels are −2.43±0.04, −2.15±0.03,
−2.05 ± 0.03, and −2.02 ± 0.08, respectively, in which only statistical errors are taken
into account. The spectral indices versus the corresponding fluences at 10 keV are shown
in Figure 5. This result is consistent with the analysis of Rebillot et al. (2006), in which
a spectral hardening toward high fluxes is also reported based on a shorter timescale
observation. This indicates that this correlation is independent of the timescale.
To estimate the spectrum of γ-rays with a distribution of the number of events in
excess as a function of Npad, we follow a widely used method that is described in detail
elsewhere (Amenomori et al. 2009; Aielli et al. 2010). In this procedure, we assume for the
spectrum of Mrk 421 a power law with a cutoff factor e−τ(E), which takes into account the
absorption of γ-rays in the extragalactic background light. We adopt the optical depth τ(E)
estimated by Franceschini et al. (2008). The ARGO-YBJ detector response is also taken
into account. The simulated events are sampled in the energy range from 10 GeV to 100
To test this method, the same analysis is performed with the data in the direction
of the Crab Nebula, the standard candle in the γ-ray sky. The resulting spectrum is
(4.2 ± 0.4stat) × 10−11(E/TeV)−2.57±0.09statphotons TeV−1cm−2s−1, which is in agreement
with our previous measurement (Aielli et al. 2010) and observations by other detectors,
– 15 –
such as H.E.S.S. (Aharonian et al. 2006), MAGIC (Albert et al. 2008), and Tibet AS-γ
(Amenomori et al. 2009).
Applying this procedure to Mrk 421, we obtain the spectra for the four event groups
with different flux levels. The spectral indices in the energy range from 300 GeV to 10 TeV
are −2.48±0.22, −2.53±0.21, −2.15±0.18, and −1.87±0.21, respectively. Only statistical
error is quoted. The corresponding flux above 1 TeV ranges from 0.8 to 6 times that of the
Crab Nebula unit, i.e., 2.67 × 10−11photons cm−2s−1. The spectra seem to become harder
with increasing flux, as indicated in Figure 6, in agreement with the function obtained
by the Whipple experiment (Krennrich et al. 2002). A similar result has been reported
elsewhere (Aielli et al. 2010) using the three-day flare data in 2008 June. The quoted errors
in Figure 6 are statistical. The systematic error is estimated to be ?30% in the flux level
determination (Aielli et al. 2010).
5.2.3.Correlation Between γ-ray and X-ray Fluxes
Using the spectra described above, we investigate the correlation between γ-ray and
X-ray fluxes. Figure 7 shows the integral γ-ray flux above 1 TeV as a function of the
integral X-ray flux from 2 keV to 12 keV; a positive correlation is observed. A quadratic
fit (with the function y = ax2+ b ) to the data points yields χ2/dof= 1.9/2, while a linear
fit yields χ2/dof= 7.7/2, where dof refers to degrees of freedom. The observation favors a
quadratic correlation between γ-ray and X-ray fluxes. A similar quadratic correlation has
been reported by Fossati et al. (2008). In contrast, an observation with linear correlation is
obtained by Amenomori et al. (2003). According to Katarzy´ nski et al. (2005), changes of
the magnetic field, electron density, and adiabatic cooling may be associated with different
correlations between γ-ray and X-ray fluxes.