Issue 
A&A
Volume 520, SeptemberOctober 2010



Article Number  A83  
Number of page(s)  16  
Section  Extragalactic astronomy  
DOI  https://doi.org/10.1051/00046361/201014484  
Published online  07 October 2010 
VHE ray emission of PKS 2155304: spectral and temporal variability
HESS Collaboration  A. Abramowski^{4}  F. Acero^{15}  F. Aharonian^{1,13}  A. G. Akhperjanian^{2}  G. Anton^{16}  U. Barres de Almeida^{8,}^{}  A. R. BazerBachi^{3}  Y. Becherini^{12}  B. Behera^{14}  W. Benbow^{1}  K. Bernlöhr^{1,5}  A. Bochow^{1}  C. Boisson^{6}  J. Bolmont^{19}  V. Borrel^{3}  J. Brucker^{16}  F. Brun^{19}  P. Brun^{7}  R. Bühler^{1}  T. Bulik^{29}  I. Büsching^{9}  T. Boutelier^{17}  P. M. Chadwick^{8}  A. Charbonnier^{19}  R. C. G. Chaves^{1}  A. Cheesebrough^{8}  L.M. Chounet^{10}  A. C. Clapson^{1}  G. Coignet^{11}  J. Conrad^{31}  L. Costamante^{1,34}  M. Dalton^{5}  M. K. Daniel^{8}  I. D. Davids^{22,9}  B. Degrange^{10}  C. Deil^{1}  H. J. Dickinson^{8}  A. DjannatiAtaï^{12}  W. Domainko^{1}  L. O'C. Drury^{13}  F. Dubois^{11}  G. Dubus^{17}  J. Dyks^{24}  M. Dyrda^{28}  K. Egberts^{1,30}  P. Eger^{16}  P. Espigat^{12}  L. Fallon^{13}  C. Farnier^{15}  S. Fegan^{10}  F. Feinstein^{15}  M. V. Fernandes^{4}  A. Fiasson^{11}  A. Förster^{1}  G. Fontaine^{10}  M. Füßling^{5}  S. Gabici^{13}  Y. A. Gallant^{15}  L. Gérard^{12}  D. Gerbig^{21}  B. Giebels^{10}  J. F. Glicenstein^{7}  B. Glück^{16}  P. Goret^{7}  D. Göring^{16}  D. Hampf^{4}  M. Hauser^{14}  S. Heinz^{16}  G. Heinzelmann^{4}  G. Henri^{17}  G. Hermann^{1}  J. A. Hinton^{33}  A. Hoffmann^{18}  W. Hofmann^{1}  P. Hofverberg^{1}  M. Holleran^{9}  S. Hoppe^{1}  D. Horns^{4}  A. Jacholkowska^{19}  O. C. de Jager^{9}  C. Jahn^{16}  I. Jung^{16}  K. Katarzynski^{27}  U. Katz^{16}  S. Kaufmann^{14}  M. Kerschhaggl^{5}  D. Khangulyan^{1}  B. Khélifi^{10}  D. Keogh^{8}  D. Klochkov^{18}  W. Kluzniak^{24}  T. Kneiske^{4}  Nu. Komin^{7}  K. Kosack^{7}  R. Kossakowski^{11}  G. Lamanna^{11}  J.P. Lenain^{6}  T. Lohse^{5}  C.C. Lu^{1}  V. Marandon^{12}  A. Marcowith^{15}  J. Masbou^{11}  D. Maurin^{19}  T. J. L. McComb^{8}  M. C. Medina^{6}  J. Méhault^{15}  R. Moderski^{24}  E. Moulin^{7}  M. NaumannGodo^{10}  M. de Naurois^{19}  D. Nedbal^{20}  D. Nekrassov^{1}  N. Nguyen^{4}  B. Nicholas^{26}  J. Niemiec^{28}  S. J. Nolan^{8}  S. Ohm^{1}  J.F. Olive^{3}  E. de Oña Wilhelmi^{1}  B. Opitz ^{4}  K. J. Orford^{8}  M. Ostrowski^{23}  M. Panter^{1}  M. PazArribas^{5}  G. Pedaletti^{14}  G. Pelletier^{17}  P.O. Petrucci^{17}  S. Pita^{12}  G. Pühlhofer^{18}  M. Punch^{12}  A. Quirrenbach^{14}  B. C. Raubenheimer^{9}  M. Raue^{1,34}  S. M. Rayner^{8}  O. Reimer^{30}  M. Renaud^{12}  R. de los Reyes^{1}  F. Rieger^{1,34}  J. Ripken^{31}  L. Rob^{20}  S. RosierLees^{11}  G. Rowell^{26}  B. Rudak^{24}  C. B. Rulten^{8}  J. Ruppel^{21}  F. Ryde^{32}  V. Sahakian^{2}  A. Santangelo^{18}  R. Schlickeiser^{21}  F. M. Schöck^{16}  A. Schönwald^{5}  U. Schwanke^{5}  S. Schwarzburg^{18}  S. Schwemmer^{14}  A. Shalchi ^{21}  I. Sushch^{5}  M. Sikora^{24}  J. L. Skilton^{25}  H. Sol^{6}  . Stawarz^{23}  R. Steenkamp^{22}  C. Stegmann^{16}  F. Stinzing^{16}  G. Superina^{10}  A. Szostek^{23,17}  P. H. Tam^{14}  J.P. Tavernet^{19}  R. Terrier^{12}  O. Tibolla^{1}  M. Tluczykont^{4}  K. Valerius^{16}  C. van Eldik^{1}  G. Vasileiadis^{15}  C. Venter^{9}  L. Venter^{6}  J. P. Vialle^{11}  A. Viana^{7}  P. Vincent^{19}  M. Vivier^{7}  H. J. Völk^{1}  F. Volpe^{1,10}  S. Vorobiov^{15}  S. J. Wagner^{14}  M. Ward^{8}  A. A. Zdziarski^{24}  A. Zech^{6}  H.S. Zechlin^{4}
1  MaxPlanckInstitut für Kernphysik, PO Box 103980, 69029
Heidelberg, Germany
2  Yerevan Physics Institute, 2 Alikhanian Brothers St., 375036
Yerevan, Armenia
3  Centre d'Étude Spatiale des Rayonnements, CNRS/UPS, 9 Av. du
Colonel Roche, BP 4346, 31029 Toulouse Cedex 4, France
4  Universität Hamburg, Institut für Experimentalphysik, Luruper
Chaussee 149, 22761 Hamburg, Germany
5  Institut für Physik, HumboldtUniversität zu Berlin, Newtonstr. 15,
12489 Berlin, Germany
6  LUTH, Observatoire de Paris, CNRS, Université Paris Diderot,
5 place Jules Janssen, 92190 Meudon, France
7  CEA Saclay, DSM/IRFU, 91191 GifSurYvette Cedex, France
8  University of Durham, Department of Physics, South Road, Durham DH1
3LE, UK
9  Unit for Space Physics, NorthWest University, Potchefstroom 2520,
South Africa
10  Laboratoire LeprinceRinguet, École Polytechnique, CNRS/IN2P3,
91128 Palaiseau, France
11  Laboratoire d'AnnecyleVieux de Physique des Particules,
Université de Savoie, CNRS/IN2P3, 74941 AnnecyleVieux, France
12  Astroparticule et Cosmologie (APC), CNRS, Université Paris 7 Denis
Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13,
France
^{}
13  Dublin Institute for Advanced Studies, 5 Merrion Square, Dublin 2,
Ireland
14  Landessternwarte, Universität Heidelberg, Königstuhl, 69117
Heidelberg, Germany
15  Laboratoire de Physique Théorique et Astroparticules, Université
Montpellier 2, CNRS/IN2P3, CC 70, Place Eugène Bataillon, 34095
Montpellier Cedex 5, France
16  Universität ErlangenNürnberg, Physikalisches Institut,
ErwinRommelStr. 1, 91058 Erlangen, Germany
17  Laboratoire d'Astrophysique de Grenoble, INSU/CNRS, Université
Joseph Fourier, BP 53, 38041 Grenoble Cedex 9, France
18  Institut für Astronomie und Astrophysik, Universität Tübingen,
Sand 1, 72076 Tübingen, Germany
19  LPNHE, Université Pierre et Marie Curie Paris 6, Université Denis
Diderot Paris 7, CNRS/IN2P3, 4 place Jussieu, 75252 Paris
Cedex 5, France
20  Charles University, Faculty of Mathematics and Physics, Institute
of Particle and Nuclear Physics, V Holesovickách 2, 180 00 Prague 8,
Czech Republic
21  Institut für Theoretische Physik, Lehrstuhl IV: Weltraum und
Astrophysik, RuhrUniversität Bochum, 44780 Bochum, Germany
22  University of Namibia, Department of Physics, Private Bag 13301,
Windhoek, Namibia
23  Obserwatorium Astronomiczne, Uniwersytet Jagiellonski, ul. Orla
171, 30244 Kraków, Poland
24  Nicolaus Copernicus Astronomical Center, ul. Bartycka 18, 00716
Warsaw, Poland
25  School of Physics & Astronomy, University of Leeds, Leeds
LS2 9JT, UK
26  School of Chemistry & Physics, University of Adelaide,
Adelaide 5005, Australia
27  Torun Centre for Astronomy, Nicolaus Copernicus University,
ul. Gagarina 11, 87100 Torun, Poland
28  Instytut Fizyki Jadrowej PAN, ul. Radzikowskiego 152, 31342
Kraków, Poland
29  Astronomical Observatory, The University of Warsaw,
Al. Ujazdowskie 4, 00478 Warsaw, Poland
30  Institut für Astro und Teilchenphysik,
LeopoldFranzensUniversität Innsbruck, 6020 Innsbruck, Austria
31  Oskar Klein Centre, Department of Physics, Stockholm University,
Albanova University Center, 10691 Stockholm, Sweden
32  Oskar Klein Centre, Department of Physics, Royal Institute of
Technology (KTH), Albanova, 10691 Stockholm, Sweden
33  Department of Physics and Astronomy, The University of Leicester,
University Road, Leicester, LE1 7RH, UK
34  European Associated Laboratory for GammaRay Astronomy, jointly
supported by CNRS and MPG
Received 22 March 2010 / Accepted 14 May 2010
Abstract
Context. Observations of very highenergy rays from
blazars provide information about acceleration mechanisms occurring in
their innermost regions. Studies of variability in these objects lead
to a better understanding of the mechanisms in play.
Aims. To investigate the spectral and temporal
variability of VHE (
)
rays of the
wellknown highfrequencypeaked BL Lac object
PKS 2155304 with the HESS imaging atmospheric Cherenkov
telescopes over a wide range of flux states.
Methods. Data collected from 2005 to 2007 were
analyzed. Spectra were derived on time scales ranging from
3 years to 4 min. Light curve variability was studied
through doubling timescales and structure functions and compared with
red noise process simulations.
Results. The source was found to be in a low state
from 2005 to 2007, except for a set of exceptional flares that occurred
in July 2006. The quiescent state of the source is
characterized by an associated mean flux level of
above
,
or approximately
of the Crab Nebula, and a powerlaw photon index of .
During the flares of July 2006, doubling timescales of
are found. The spectral index variation is examined over two orders of
magnitude in flux, yielding different behavior at low and high fluxes,
which is a new phenomenon in VHE ray emitting blazars. The
variability amplitude characterized by the fractional rms
is strongly energydependent and is .
The light curve rms correlates with the flux. This is the signature of
a multiplicative process that can be accounted for as a red noise with
a Fourier index of .
Conclusions. This unique data set shows evidence of
a lowlevel ray
emission state from PKS 2155304 that possibly has a different
origin than the outbursts. The discovery of the light curve lognormal
behavior might be an indicator of the origin of aperiodic variability
in blazars.
Key words: gamma rays: general  galaxies: active  galaxies: jets  BL Lacertae objects: individual: PKS 2155304
1 Introduction
The BL Lacertae (BL Lac) category of active galactic nuclei (AGN) represents the vast majority of the population of energetic and extremely variable extragalactic very highenergy ray emitters. Their luminosity varies in unpredictable, highly irregular ways, by orders of magnitude and at all wavelengths across the electromagnetic spectrum. The very highenergy (VHE, ) ray fluxes vary often on the shortest timescales that can be seen in this type of object, with large amplitudes that can dominate the overall output. It thus indicates that the understanding of this energy domain is the most important one for understanding the underlying fundamental variability and emission mechanisms in play in high flux states.It has been difficult, however, to ascertain whether ray emission is present only during high flux states or also when the source is in a more stable or quiescent state but with a flux that is below the instrumental limits. The advent of the current generation of atmospheric Cherenkov telescopes with unprecedented sensitivity in the VHE regime gives new insight into these questions.
The highfrequencypeaked BL Lac object (HBL) PKS 2155304, located at redshift z=0.117, initially discovered as a VHE ray emitter by the Mark 6 telescope (Chadwick et al. 1999), has been detected by the first HESS telescope in 20022003 (Aharonian et al. 2005b). It has been frequently observed by the full array of four telescopes since 2004, either sparsely during the HESS monitoring program or intensely during dedicated campaigns, such as described in Aharonian et al. (2005c), showing mean flux levels of of the Crab Nebula flux for energies above . During the summer of 2006, PKS 2155304 exhibited unprecedented flux levels accompanied by strong variability (Aharonian et al. 2007a), making temporal and spectral variability studies possible on timescales on the order of a few minutes. The VHE ray emission is usually thought to originate from a relativistic jet, emanating from the vicinity of a supermassive black hole (SMBH). The physical processes in play are still poorly understood, but the analysis of the ray flux spectral and temporal characteristics is wellsuited to providing deeper insight.
For this goal, the data set of HESS observations of PKS 2155304 between 2005 and 2007 is used. After describing the observations and the analysis chain in Sect. 2, the emission from the ``quiescent'', i.e. nonflaring, state of the source is characterized in Sect. 3. Section 4 explains the spectral variability related to the source intensity. Section 5 describes the temporal variability during the highly active state of the source and its possible energy dependence. Section 6 illustrates the observed variability phenomenon by a random stationary process, characterized by a simple power density spectrum. Section 7 shows how limits on the characteristic time of the source can be derived. The multiwavelength aspects from the high flux state will be presented in a second paper.
2 Observations and analysis
HESS is an array of four imaging atmospheric Cherenkov telescopes situated in the Khomas Highland of Namibia ( South, East), at an elevation of 1800 m above sea level (see Aharonian et al. 2006). PKS 2155304 was observed by HESS each year after 2002; results of observations in 2002, 2003, and 2004 can be found in Aharonian et al. (2005b), Aharonian et al. (2005c) and Giebels et al. (2005). The data reported here were collected between 2005 and 2007. In 2005, 12.2 h of observations were taken. A similar observation time was scheduled in 2006, but following the strong flare of July 26 (Aharonian et al. 2007a), it was decided to increase this observation time significantly. Ultimately, from June to October 2006, this source was observed for 75.9 h, with a further 20.9 h in 2007.
Figure 1: Zenith angle distribution for the 202 4telescopes observation runs from 2005 to 2007. The inset shows, for each zenith angle, the energy threshold associated with the analysis presented in Sect. 2. 

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Table 1: Summary of observations for each year.
The data were recorded during runs of 28 min nominal duration, with the telescopes pointing at from the source position in the sky to enable a simultaneous estimate of the background. This offset was taken alternatively in both right ascension and declination (with both signs), in order to minimize systematics. Only the runs passing the HESS dataquality selection criteria were used for the analyses presented below. These criteria imply good atmospheric conditions and checks that the hardware state of the cameras is satisfactory. The number of runs thus selected is 22 for 2005, 153 for 2006, and 35 for 2007, corresponding to livetimes of 9.4, 66.1, and 13.8 h respectively. During these observations, zenith angles were between 7 and 60 degrees, resulting in large variations in the instrument energy threshold ( , see Fig. 1) and sensitivity. This variation has been accounted for in the spectral and temporal variability studies presented below.
Table 2: The various data sets used in the paper, referred to in the text by the labels presented in this table.
The data have been analyzed following the prescription presented in Aharonian et al. (2006), using the loose set of cuts that are well adapted for bright sources with moderately soft spectra, and the ReflectedRegion method for the definition of the onsource and offsource data regions. A yearwise summary of the observations and the resulting detections are shown in Table 1. A similar summary is given in Appendix A for the 67 nights of data taken, showing that the emission of PKS 2155304 is easily detected by HESS almost every night. For 66 nights out of 67, the significance per square root of the livetime ( , where T is the observation livetime) is at least equal to , the only night with a lower value  MJD 53705  corresponding to a very short exposure. In addition, for 61 nights out of 67 the source emission is high enough to enable a detection of the source with 5 significance in one hour or less, a level usually required in this domain to firmly claim a new source detection. In 2006 the source exhibits very strong activity (38 nights, between MJD 5391653999) with a nightly varying from 3.6 to 150, and being higher than for 19 nights. The activity of the source climaxes on MJD 53944 and 53946 with statistical significances that are unprecedented at these energies, the rate of detected rays corresponding to 2.5 and , with 150 and respectively.
For subsequent spectral analysis, an improved energy reconstruction method with respect to the one described in Aharonian et al. (2006) was applied. This method is based on a lookup table determined from MonteCarlo simulations, which contains the relation between an image's amplitude and its reconstructed impact parameter as a function of the true energy, the observation zenith angle, the position of the source in the camera, the optical efficiency of the telescopes (which tend to decrease due to the aging of the optical surfaces), the number of triggered telescopes and the reconstructed altitude of the shower maximum. Thus, for a given event, the reconstructed energy is determined by requiring the minimal between the image amplitudes and those expected from the lookup table corresponding to the same observation conditions. This method yields a slightly lower energy threshold (shown in Fig. 1 as a function of zenith angle), an energy resolution that varies from 15% to 20% over all the energy range, and biases in the energy reconstruction that are smaller than 5%, even close to the threshold. The systematic uncertainty in the normalization of the HESS energy scale is estimated to be as large as 15%, corresponding for such soft spectrum source to 40% in the overall flux normalization as quoted in Aharonian et al. (2009).
All the spectra presented in this paper have been obtained
using a forwardfolding maximum likelihood method based on the measured
energydependent onsource and offsource distributions. This method,
fully described in Piron et al. (2001), performs
a global deconvolution of the instrument functions (energy resolution,
collection area) and the parametrization of the spectral shape. Two
different sets of parameters, corresponding to a power law and
to a power law with an exponential cutoff, are used for the
spectral shape, with the following equations:
represents the differential flux at E_{0} (chosen to be 1 TeV), is the powerlaw index and the characteristic energy of the exponential cutoff. The maximum likelihood method provides the best set of parameters corresponding to the selected hypothesis, and the corresponding error matrix.
Finally, various data sets have been used for subsequent analyses. These are summarized in Table 2.
3 Characterization of the quiescent state
Figure 2: Monthly averaged integral flux of PKS 2155304 above obtained from data set D (see Table 2). The dotted line corresponds to 15% of the Crab Nebula emission level (see Sect. 3.2). 

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As can be seen in Fig. 2, with the exception of the high state of July 2006 PKS 2155304 was in a low state during the observations from 2005 to 2007. This section explores the variability of the source during these periods of lowlevel activity, based on the determination of the runwise integral fluxes for the data set , which excludes the flaring period of July 2006 and also those runs whose energy threshold is higher than (see 3.1 for justification). As for Sects. 5 and 6, the control of systematics in such a study is particularly important, especially because of the strong variations of the energy threshold throughout the observations.
3.1 Method and systematics
The integral flux for a given period of observations is determined in a
standard way. For subsequent discussion purposes, the formula
applied is given here:
where T represents the corresponding livetime, A(E) and R(E,E') are, respectively, the collection area at the true energy E and the energy resolution function between E and the measured energy E', and S(E) the shape of the differential energy spectrum as defined in Eqs. (1) and (2). Finally, is the number of measured events in the energy range [ , ].
Figure 3: Distributions of the logarithms of integral fluxes above in individual runs. Left: from 2005 to 2007 except the July 2006 period (data set ), fitted by a Gaussian. Right: all runs from 2005 to 2007 (data set D), where the solid line represents the result of a fit by the sum of 2 Gaussians (dashed lines). See Table 4 for details. 

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In the case that S(E) is a power law, an important source of systematic error in the determination of the integral flux variation with time comes from the value chosen for the index . The average 20052007 energy spectrum yields a very well determined powerlaw index^{}. However, in Sect. 4 it will be shown that this index varies depending on the flux level of the source. Moreover, in some cases the energy spectrum of the source shows some curvature in the TeV region, giving slight variations in the fitted powerlaw index depending on the energy range used.
For runs whose energy threshold is lower than , a simulation performed under the observation conditions corresponding to the data shows that an index variation of implies a flux error at the level of , this relation being quite linear up to . However, this relation no longer holds when the energy threshold is above , as the determination of becomes much more dependent on the choice of . For this reason, only runs whose energy threshold is lower than will be kept for the subsequent light curves. The value of is chosen as , which is a compromise between a low value which maximizes the excess numbers used for the flux determinations and a high value which maximizes the number of runs whose energy threshold is lower than .
3.2 Runwise distribution of the integral flux
From 2005 to 2007, PKS 2155304 is almost always detected when observed (except for two nights for which the exposure was very low), indicating the existence, at least during these observations, of a minimal level of activity of the source. Focussing on data set (which excludes the July 2006 data where the source is in a high state), the distribution of the integral fluxes of the individual runs above has been determined for the 115 runs, using a spectral index (the best value for this data set, as shown in 3.4). This distribution has an asymmetric shape, with mean value and root mean square (rms) , and is very well described with a lognormal function. Such a behavior implies that the logarithm of fluxes follows a normal distribution, centered on the logarithm of . This is shown in the left panel of Fig. 3, where the solid line represents the best fit obtained with a maximumlikelihood method, yielding results independent of the choice of the intervals in the histogram. It is interesting to note that this result can be compared to the fluxes measured by HESS from PKS 2155304 during its construction phase, in 2002 and 2003 (see Aharonian et al. 2005b,c). As shown in Table 3, these flux levels extrapolated down to were close to the value corresponding to the peak shown in the left panel of Fig. 3.
Table 3: Integral fluxes and their statistical errors from 2002 and 2003 observations of PKS 2155304 during the HESS construction phase.
The right panel of Fig. 3 shows how the flux distribution is modified when the July 2006 data are taken into account (data set D in Table 2): the histogram can be accounted for by the superposition of two Gaussian distributions (solid curve). The results, summarized in Table 4, are also independent of the choice of the intervals in the histogram. Remarkably enough, the characteristics of the first Gaussian obtained in the first step (left panel) remain quite stable in the double Gaussian fit.
Table 4: The distribution of the flux logarithm.
This leads to two conclusions. First, the flux distribution of PKS 2155304 is well described considering a low state and a high state, for each of which the distribution of the logarithms of the fluxes follows a Gaussian distribution. The characteristics of the lognormal flux distribution for the high state are given in Sects. 57. Secondly, PKS 2155304 has a level of minimal activity that seems to be stable on a severalyear timescale. This state will henceforth be referred to as the ``quiescent state'' of the source.
3.3 Width of the runwise flux distribution
In order to determine if the measured width of the flux distribution (left panel of Fig. 3) can be explained as statistical fluctuations from the measurement process a simulation has been carried out considering a source that emits an integral flux above of 4.32 with a powerlaw spectral index (as determined in the next section). For each run of the data set the number expected by convolving the assumed differential energy spectrum with the instrument response corresponding to the observation conditions is determined. A random smearing around this value allows statistical fluctuations to be taken into account. The number of events in the offsource region and also the number of background events in the source region are derived from the measured values in the data set. These are also smeared in order to take into account the expected statistical fluctuations.
10 000 such flux distributions have been simulated, and for each one its mean value and rms (which will be called below RMSD) are determined. The distribution of RMSD thus obtained, shown in Fig. 4, is well described by a Gaussian centred on 0.98 (which represents a relative flux dispersion of 23%) and with a of 0.07 .
It should be noted that here the effect of atmospheric fluctuations in the determination of the flux is only taken into account at the level of the offsource events, as these numbers are taken from the measured data. But the effect of the corresponding level of fluctuations on the source signal is very difficult to determine. If a conservative value of 20% is considered^{} that is added in the simulations as a supplementary fluctuation factor for the number of events expected from the source, a RMSD distribution centred on 1.30 with a of 0.09 is obtained. Even in this conservative case, the measured value for the flux distribution rms ( ) is very far (more than 8 standard deviations) from the simulated value. All these elements strongly suggest the existence of an intrinsic variability associated with the quiescent state of PKS 2155304.
Figure 4: Distribution of RMSD obtained when the instrument response to a fixed emission ( and ) is simulated 10 000 times with the same observation conditions as for the 115 runs of the left part of Fig. 3. 

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3.4 Quiescentstate energy spectrum
The energy spectrum associated with the data set , shown in Fig. 5, is well described by a power law with a differential flux at 1 TeV of and an index of . The stability of these values for spectra measured separately for 2005, 2006 (excluding July), and 2007 is presented in Table 5. The corresponding average integral flux is , which is as expected in very good agreement with the mean value of the distribution shown in the left panel of Fig. 3.
Figure 5: Energy spectrum of the quiescent state for the period 20052007. The green band correponds to the 68% confidencelevel provided by the maximum likelihood method. Points are derived from the residuals in each energy bin, only for illustration purposes. See Sect. 3.4 for further details. 

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Table 5: Parametrization of the differential energy spectrum of the quiescent state of PKS 2155304, determined in the energy range 0.210 TeV, first for the 20052007 period and also separately for the 2005, 2006 (excluding July) and 2007 periods.
Bins above 2 TeV correspond to ray excesses lower than 20 and significances lower than . Above 5 TeV excesses are even less significant ( or less) and 99% upperlimits are used. There is no improvement of the fit when a curvature is taken into account.
4 Spectral variability
4.1 Variation of the spectral index for the whole data set 20052007
The spectral state of PKS 2155304 has been monitored since 2002. The first set of observations (Aharonian et al. 2005b), from July 2002 to September 2003, shows an average energy spectrum well described by a power law with an index of , for an integral flux (extrapolated down to ) of . No clear indication of spectral variability was seen. Consecutive observations in October and November 2003 (Aharonian et al. 2005c) gave a similar value for the index, , for a slightly higher flux of . Later, during HESS observations of the first (MJD 53944, Aharonian et al. 2007a) and second (MJD 53946, Aharonian et al. 2009) exceptional flares of July 2006, the source reached much higher average fluxes, corresponding to and ^{} respectively. In the first case, no strong indications for spectral variability were found and the average index was close to those associated with the 2002 and 2003 observations. In the second case, clear evidence of spectral hardening with increasing flux was found.
The observations of PKS 2155304 presented in this paper also include the subsequent flares of 2006 and the data of 2005 and 2007. Therefore, the evolution of the spectral index is studied for the first time for a flux level varying over two orders of magnitude. This spectral study has been carried out over the fixed energy range 0.21 TeV in order to minimize both systematic effects due to the energy threshold variation and the effect of the curvature observed at high energy in the flaring states. The maximal energy has been chosen to be at the limit where the spectral curvature seen in high flux states begins to render the power law or exponential curvature hypotheses distinguishable. As flux levels observed in July 2006 are significantly higher than in the rest of the data set (see Fig. 6), the fluxindex behavior is determined separately first for the July 2006 data set itself ( ) and secondly for the 20052007 data excluding this data set ( ).
Figure 6: Integral flux above measured each night during late July 2006 observations. The horizontal dashed line corresponds to the quiescent state emission level defined in Sect. 3.2. 

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On both data sets, the following method was applied. The integral flux was determined for each run assuming a power law shape with an index of (average spectral index for the whole data set), and runs were sorted by increasing flux. The set of ordered runs was then divided into subsets containing at least an excess of 1500 above and the energy spectrum of each subset was determined^{}.
The left panel of Fig. 7 shows the photon index versus integral flux for data sets (grey crosses) and (black points). Corresponding numbers are summarized in Appendix B. While a clear hardening is observed for integral fluxes above a few , a break in this behavior is observed for lower fluxes. Indeed, for the data set (black points) a linear fit yields a slope / , whereas the same fit for data set (grey crosses) yields a slope / . The latter corresponds to a probability ; a fit to a constant yields but with a constant fitted index incompatible with a linear extrapolation from higher flux states at a 3 level. This is compatible with conclusions obtained either with an independent analysis or when these spectra are processed following a different prescription. In this prescription the runs were sorted as a function of time in contiguous subsets with similar photon statistics, rather than as a function of increasing flux.
Figure 7: Evolution of the photon index with increasing flux in the 0.21 TeV energy range. The left panel shows the results for the July 2006 data (black points, data set ) and for the 20052007 period excluding July 2006 (grey points, data set ). The right panel shows the results for the four nights flaring period of July 2006 (black points, data set ) and one point corresponding to the quiescent state average spectrum (grey point, again data set ). See text in Sects. 4.1 ( left panel) and 4.2 ( right panel) for further details on the method. 

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Figure 8: Integrated flux versus time for PKS 2155304 on MJD 5394453947 for four energy bands and with a 4min binning. From top to bottom: , 0.2 , 0.35 and 0.6 . These light curves are obtained using a power law spectral shape with an index of , also used to derive the flux extrapolation down to when the threshold is above that energy in the top panel (grey points). Because of the high dispersion of the energy threshold of the instrument (see Sect. 2, Fig. 1), and following the prescription described in 3.1, the integral flux has been determined for a time bin only if the corresponding energy threshold is lower than . The fractional rms for the light curves are respectively, 0.86 , 0.79 , 0.89 and 1.01 . The last plot shows the variation of the photon index determined in the 0.21 TeV range. See Sect. 4.2 and Appendix B.4 for details. 

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The form of the relation between the index versus integral flux is unprecedented in the TeV regime. Prior to the results presented here, spectral variability has been detected only in two other blazars, Mrk 421 and Mrk 501. For Mrk 421, a clear hardening with increasing flux appeared during the 1999/2000 and 2000/2001 observations performed with HEGRA (Aharonian et al. 2002) and also during the 2004 observations performed with HESS (Aharonian et al. 2005a). In addition, the Mrk 501 observations carried out with CAT during the strong flares of 1997 (DjannatiAtaï et al. 1999) and also the recent observation performed by MAGIC in 2005 (Albert et al. 2007) have shown a similar hardening. In both studies, the VHE peak has been observed in the distributions of the flaring states of Mrk 501.
4.2 Variation of the spectral index for the four flaring nights of July 2006
In this section, the spectral variability during the flares of July 2006 is described in more detail. A zoom on the variation of the integral flux (4min binning) for the four nights containing the flares (nights MJD 53944, 53945, 53946, and 53947, called the ``flaring period'') is presented in the top panel of Fig. 8. This figure shows two exceptional peaks on MJD 53944 and MJD 53946 that climax respectively at fluxes higher than 2.5 and 3.5 ( and times the Crab Nebula level above the same energy), both about two orders of magnitude above the quiescent state level.
The variation with time of the photon index is shown in the bottom panel of Fig. 8. To obtain these values, the excess above has been determined for each 4min bin. Then, successive bins have been grouped in order to reach a global excess higher than 600 . Finally, the energy spectrum of each data set has been determined in the 0.21 TeV energy range, as before (corresponding numbers are summarized in Appendix Table B.4). There is no clear indication of spectral variability within each night, except for MJD 53946 as shown in Aharonian et al. (2009). However, a variability can be seen from night to night, and the spectral hardening with increasing flux level already shown in Fig. 7 is also seen very clearly in this manner.
It is certainly interesting to directly compare the spectral behavior seen during the flaring period with the hardness of the energy spectrum associated with the quiescent state. This is shown in the right panel of Fig. 7, where black points correspond to the four flaring nights; these were determined in the same manner as for the left panel (see 4.1 for details). A linear fit here yields a slope / . The grey cross corresponds to the integral flux and the photon index associated with the quiescent state (derived in a consistent way in the energy range from 0.21 TeV), showing a clear rupture with the tendancy at higher fluxes (typically above ).
These four nights were further examined to search for differences in the spectral behavior between periods in which the source flux was clearly increasing and periods in which it was decreasing. For this, the first 16 min of the first flare (MJD 53944) are of special interest because they present a very symmetric situation: the flux increases during the first half, and then decreases to its initial level. The averaged fluxes are similar in both parts ( ), and the observation conditions (and thus the instrument response) are almost constant  the mean zenith angle of each part being respectively 7.2 and 7.8 degrees. Again, the spectra have been determined in the 0.21 TeV energy range, giving indices of and respectively. To further investigate this question and avoid potential systematic errors from the spectral method determination, the hardness ratios were derived (defined as the ratio of the excesses in different energy bands), using for this the energy (TeV) bands [0.20.35], [0.350.6] and [0.65.0]. For any combination, no differences were found beyond the level between the increasing and decreasing parts. A similar approach has been applied  when possible  for the rest of the flaring period. No clear dependence has been found within the statistical error limit of the determined indices, which is distributed between 0.09 and 0.20.
Finally, the persistence of the energy cutoff in the differential energy spectrum along the flaring period has been examined. For this purpose, runs were sorted again by increasing flux and grouped into subsets containing at least an excess of 3000 above ^{}. For the seven subsets found, the energy spectrum has been determined in the 0.210 TeV energy range both for a simple power law and a power law with an exponential cutoff. This last hypothesis was found to be favoured systematically at a level varying from 1.8 to 4.6 compared to the simple power law and is always compatible with a cutoff in the 12 TeV range.
5 Light curve variability and correlation studies
This section is devoted to the characterization of the temporal variability of PKS 2155304, focusing on the flaring period observations. The high number of rays available not only enabled minutelevel time scale studies, such as those presented for MJD 53944 in Aharonian et al. (2007a), but also to derive detailed light curves for three energy bands (Fig. 8): 0.20.35 TeV, 0.350.6 TeV and 0.65 TeV.
The variability of the energydependent light curves of PKS 2155304 is in the following quantified through their fractional rms defined in Eq. (4) (Nandra et al. 1997; Edelson et al. 2002). In addition, possible time lags between light curves in two energy bands are investigated.
5.1 Fractional rms F_{var}
All fluxes in the energy bands of Fig. 8 show a
strong variability that is quantified through their fractional
rms
(which depends on observation durations and their sampling).
Measurement errors
on each of the N fluxes
of the light curve are taken into account in the definition
of
:
where S^{2} is the variance
and where is the mean square error and is the mean flux.
The energydependent variability has been calculated for the flaring period according to Eq. (4) in all three energy bands. The uncertainties on have been estimated according to the parametrization derived by Vaughan et al. (2003b), using a Monte Carlo approach which accounts for the measurement errors on the simulated light curves.
Figure 9 shows the energy dependence of over the four nights for a sampling of 4 min where only fluxes with a significance of at least 2 standard deviations were considered. There is a clear energydependence of the variability (a null probability of ). The points in Fig. 9 are fitted according to a power law showing that the variability follows .
Figure 9: Fractional rms versus energy for the observation period MJD 5394453947. The points are the mean value of the energy in the range represented by the horizontal bars. The line is the result of a power law fit where the errors on and on the mean energy are taken into account, yielding . 

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This energy dependence of is also perceptible within each individual night. In Table 6 the values of , the relative mean flux and the observation duration, are reported night by night for the flaring period. Because of the steeply falling spectra, the lowenergy events dominate in the light curves. This lack of statistics for high energy prevents to have a high fraction of points with a significance more than 2 standard deviation in light curves night by night for the three energy bands previously considered. On the other hand, the error contribution dominates, preventing the estimation of the in all these three energy bands. Therefore, only two energy bands were considered: low (0.20.5 TeV) and high (0.55 TeV). As can be seen in Table 6 also night by night the highenergy fluxes seem to be more variable than those at lower energies.
Table 6: Mean Flux and the fractional rms night by night for MJD 5394453947.
5.2 Doubling/halving timescale
While characterizes the mean variability of a source, the shortest doubling/halving time (Zhang et al. 1999) is an important parameter in view of finding an upper limit on a possible physical shortest time scale of the blazar.
If represents the light curve flux at a time T_{i}, for each pair of one may calculate , where = T_{j}T_{i}, = and . Two possible definitions of the doubling/halving are proposed by Zhang et al. (1999): the smallest doubling time of all data pairs in a light curve (T_{2}), or the mean of the 5 smallest T_{2}^{i,j} (in the following indicated as ). One should keep in mind that, according to Zhang et al. (1999), these quantities are ill defined and strongly depend on the length of the sampling intervals and on the signaltonoise ratio in the observation.
This quantity was calculated for the two nights with the highest fluxes, MJD 53944 and MJD 53946, considering light curves with two different binnings (1 and 2 min). Bins with flux significances more than and flux ratios with an uncertainty smaller than 30% were required to estimate the doubling time scale. The uncertainty on T_{2} was estimated by propagating the errors on the , and a dispersion of the 5 smallest values was included in the error for .
In Table 7, the values of T_{2} and for the two nights are shown. The dependence with respect to the binning is clearly visible for both observables. In this table, the last column shows that the fraction of pairs in the light curves that are kept in order to estimate the doubling times is on average 45%. Moreover, doubling times T_{2} and have been estimated for two sets of pairs in the light curves where = is increasing or decreasing respectively. The values of the doubling time for the two cases are compatible within , therefore no significant asymmetry has been found.
Table 7: Doubling/Halving times for the high intensity nights MJD 53944 and MJD 53946 estimated with two different samplings, using the two definitions explained in the text.
It should be noted that these values are strongly dependent on the time binning and on the experiment's sensitivity, so that the typical fastest doubling timescale should be conservatively estimated as being less than , which is compatible with the values reported in Aharonian et al. (2007a) and in Albert et al. (2007), the latter concerning the blazar Mrk 501.
5.3 Crosscorrelation analysis as a function of energy
Time lags between light curves at different energies can provide insight into acceleration, cooling and propagation effects of the radiative particles.
The discrete correlation function (DCF) as a function of the delay (White & Peterson 1984; Edelson & Krolik 1988) is used here to search for possible time lags between the energyresolved light curves. The uncertainty on the DCF has been estimated using simulations. For each delay, 10^{5} light curves (in both energy bands) have been generated within their errors, assuming a Gaussian probability distribution. A probability distribution function (PDF) of the correlation coefficients between the two energy bands has been estimated for each set of simulated light curves. The rms of these PDF are the errors related to the DCF at each delay. Figure 10 shows the DCF between the high and lowenergy bands for the fournight flaring period (with 4 min bins) and for the second flaring night (with 2 min bins). The gaps between each 28 min run have been taken into account in the DCF estimation.
The position of the maximum of the DCF has been estimated by a Gaussian fit that shows no time lag between low and high energies for either the 4 or 2 min binned light curves. This sets a limit of 14 from the observation of MJD 53946. A detailed study on the limit on the energy scale on which quantum gravity effects could become important, using the same data set, are reported in Aharonian et al. (2008a).
Figure 10: DCF between the light curves in the energy ranges 0.20.5 TeV and 0.55 TeV and Gaussian fits around the peak. Full circles represent the DCF for MJD 5394453947 4min light curve and the solid line is the Gaussian fit around the peak with mean value of 43 . Crosses represent the DCF for MJD 53946 with a 2min light curve binning, and the dashed line in the Gaussian fit with a peak centred at 14 . 

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5.4 Excess rmsflux correlation
Having defined the shortest variability time scales, the nature of the
process that generates the fluctuations is investigated, using another
estimator: the excess rms. It is defined as the variance of a
light curve (Eq. (5))
after subtracting the measurement error:
Figure 11 shows the correlation between the excess rms of the light curve and the flux, where the flux here considered are selected with an energy threshold of . The excess variance is estimated for 1 and 4min binned light curves, using 20 consecutive flux points that are at least at the significance level (81% of the 1 min binned sample). The correlation factors are r_{1}=0.60^{+0.21}_{0.25} and r_{4}=0.87^{+0.10}_{0.24}for the 1 and 4 min binning, excluding an absence of correlation at the and levels respectively, implying that fluctuations in the flux are probably proportional to the flux itself, which is a characteristic of lognormal distributions (Aitchinson & Brown 1963). This correlation has also been investigated extending the analysis to a statistically more significant data set including observations with a higher energy threshold in which the determination of the flux above requires an extrapolation (grey points in the top panel in Fig. 8). In this case the correlations found are compatible ( and for the 1 and 4 min binning, respectively) and also exclude an absence of correlation with a higher significance ( and , respectively).
Such a correlation has already been observed for Xrays in the Seyfert class AGN (Edelson et al. 2002; Vaughan et al. 2003a,b; MHardy et al. 2004) and in Xray binaries (Uttley & MHardy 2001; Uttley 2004; Gleissner et al. 2004), where it is considered as evidence for an underlying stochastic multiplicative process (Uttley et al. 2005), as opposed to an additive process. In additive processes, light curves are considered as the sum of individual flares ``shots'' contributing from several zones (multizone models) and the relevant variable that has a Gaussian distribution (namely Gaussian variable) is the flux. For multiplicative (or cascade) models the Gaussian variable is the logarithm of the flux. Therefore, this first observation of a strong rmsflux correlation in the VHE domain fully confirms the lognormality of the flux distribution presented in Sect. 3.2.
Figure 11: The excess rms vs. mean flux for the observation in MJD 5394453947 (Full circles). The open circles are the additional points obtained when also including the extrapolated flux points  see text). Top: estimated with 20 min time intervals and a 1 min binned light curve. Bottom: estimated with 80 min time intervals and a 4 min binned light curve. The dotted lines are a linear fit to the points, where for the 1 min binning and for the 4 min binning. Fits to the open circles yield similar results. 

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6 Characterization of the lognormal process during the flaring period
This section investigates whether the variability of PKS 2155304 in the flaring period can be described by a random stationary process, where, as shown in Sect. 5.4, the Gaussian variable is the logarithm of the flux. In this case the variability can be characterized through its Power Spectral Density (PSD) (van der Klis 1997), which indicates the density of variance as function of the frequency . The PSD is an intrinsic indicator of the variability, usually represented in large frequency intervals by power laws ( ) and is often used to define different ``states'' of variable objects (see e.g., Paltani et al. 1997; and Zhang et al. 1999, for the PSD of PKS 2155304 in the optical and Xrays). The PSD of the light curve of one single night (MJD 53944) was given in Aharonian et al. (2007a) between 10^{4} and , and was found to be compatible with a red noise process ( ) with times more power as in archival Xray data (Zhang et al. 1999), but with a similar index. This study implicitely assumed the ray flux to be the Gaussian variable. In the present paper, the PSD is determined using data from 4 consecutive nights (MJD 5394453947) and assuming a lognormal process. Since direct Fourier analysis is not well adapted to light curves extending over multiple days and affected by uneven sampling and uneven flux errors, the PSD will be further determined on the basis of parametric estimation and simulations.
In the hypothesis where the process is stationary, i.e., the PSD is timeindependent, a powerlaw shape of the PSD was assumed, as for Xray emitting blazars. The PSD was defined as depending on two parameters and as follows: , where is the variability spectral index and K denotes the ``power'' (i.e., the variance density) at a reference frequency . This latter was conventionally chosen to be , where the two parameters and K are found to be decorrelated. Since a lognormal process is considered, is the density of variance of the Gaussian variable . The natural logarithm of the flux is conveniently used here, since its variance over a given frequency interval^{} is close to the corresponding value of , at least for small fluctuations. For a given set of and K, it is possible to simulate many long time series and to modify them according to experimental effects, namely those of background events and of flux measurement errors. Light curve segments are further extracted from this simulation, with exactly the same time structure (observation and nonobservation intervals) and the same sampling rates as those of real data. The distributions of several observables obtained from simulations for different values of and K will be compared to those determined from observations, thus allowing these parameters to be determined from a maximumlikelihood fit.
The simulation characteristics will be described in Sect. 6.1. Sections 6.26.4 will be devoted to the determination of and K by three methods, each of them based on an experimental result: the excess rmsflux correlation, the Kolmogorov firstorder structure function (Rutman 1978; Simonetti et al. 1985) and doublingtime measurements.
6.1 Simulation of realistic timeseries
For practical reasons, simulated values of
were calculated from Fourier series, thus with a discrete PSD. The
fundamental frequency
that corresponds to an elementary bin
in frequency, must be much lower than 1/T
if T is the duration of the observation.
The ratio T_{0}/T
was chosen to be of the order of 100, in such a way that the
influence of a finite value of T_{0}
on the average variance of a light curve of duration T
would be less than about 2%. Taking T_{0}
= 9
,
this condition is fulfilled for the following studies. With this
approximation, the simulated flux logarithms are given by:
(7) 
where is chosen in such a way that is less than the time interval between consecutive measurements (i.e., the sampling interval). According to the definition of a Gaussian random process, the phases are uniformly distributed between 0 and 2 and the Fourier coefficients a_{n} are normally distributed with mean 0 and variances given by with .
From the long simulated timeseries, light curve segments were extracted with the same durations as the periods of continuous data taking and with the same gaps between them. The simulated fluxes were further smeared according to measurement errors, according to the observing conditions (essentially zenith angle and background rate effects) in the corresponding data set.
6.2 Characterization of the lognormal process by the excess rmsflux relation
For a fixed PSD, characterized by a set of parameters , 500 light curves were simulated, reproducing the observing conditions of the flaring period (MJD 5394453947), according to the procedure explained in Sect. 6.1.
For each set of simulated light curves, segments of 20 min duration sampled every minute (and alternatively segments of 80 min duration sampled every 4 min) were extracted and, for each of them, the excess rms and the mean flux were calculated as explained in Sect. 5.4. For a wide range of values of and K, simulated light curves reproduce well the high level of correlation found in the measured light curves. On the other hand, the fractional variability and are essentially uncorrelated and will be used in the following. A likelihood function of and K was obtained by comparing the simulated distributions of and to the experimental ones. An additional observable that is sensitive to and K is the fraction of those light curve segments for which cannot be calculated because large measurement errors lead to a negative value for the excess variance. The comparison between the measured value of this fraction and those obtained from simulations is also taken into account in the likelihood function. The confidence contours for the two parameters and K obtained from the maximum likelihood method are shown in Fig. 12 for both kinds of light curve segments. The two selected domains in the plane have a large overlap which restricts the values of to the interval (1.9, 2.4).
Figure 12: 95% confidence domains for and K at obtained by a maximumlikelihood method based on the flux correlation from 500 simulated light curves. The dashed contour refers to light curve segments of 20 min duration, sampled every minute. The solid contour refers to light curve segments of 80 min duration, sampled every 4 min. The dotted contour refers to the method based on the structure function, as explained in Sect. 6.3. 

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6.3 Characterization of the lognormal process by the structure function analysis
Another method for determining
and K is based on Kolmogorov structure
functions (SF). For a signal X(t),
measured at N pairs of times separated by a
delay ,
(i=1,...,N), the firstorder
structure function is defined as (Simonetti et al. 1985):
In the present analysis, X(t) represents the variable whose PSD is being estimated, namely . The structure function is a powerful tool for studying aperiodic signals (Rutman 1978; Simonetti et al. 1985), such as the luminosity of blazars at various wavelengths. Compared to the direct Fourier analysis, the SF has the advantage of being less affected by ``windowing effects'' caused by large gaps between short observation periods in VHE observations. The firstorder structure function is adapted to those PSDs whose variability spectral index is less than 3 (Rutman 1978), which is the case here, according to the results of the preceding section.
Figure 13 shows the firstorder SF estimated for the flaring period (circles) for h. At fixed , the distribution of expected for a given set of parameters is obtained from 500 simulated light curves. As an example, taking and , values of are found to lie at 68% confidence level within the shaded region in Fig. 13.
Figure 13: First order structure function SF for the observations carried out in the period MJD 5394453947 (circles). The shaded area corresponds to the 68% confidence limits obtained from simulations for the lognormal stationary process characterized by and . The superimposed horizontal band represents the allowed range for the asymptotic value of the SF as obtained in Sect. 7. 

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In the case of a power law PSD with index ,
the SF averaged over an ensemble of light curves is expected show a
variation as
(Kataoka et al. 2001).
However, this property does not take into account the effect of
measurement errors, nor of the limited sensitivity of Cherenkov
telescopes at lower fluxes. For the present study, it was
preferable to use the distributions of
obtained from realistic simulations including all experimental
effects. Using such distributions expected for a given set of
parameters
,
a likelihood function can be obtained from the experimental SF
and further maximized with respect to these two parameters.
Furthermore, the likelihood fit was restricted to values of
lower than ,
for which the expected fluctuations are not too large and are
wellcontrolled. The 95% confidence region in the plane
thus obtained is indicated by the dotted line in Fig. 12.
It is in very good agreement with those based on the excess
rmsflux correlation and give the best values for
and K:
The variability index at VHE energies is found to be remarkably close to those measured in the Xray domain on PKS 2155304, Mrk 421, and Mrk 501 (Kataoka et al. 2001).
6.4 Characterization of the lognormal process by doubling times
Simulations were also used to investigate if the estimator T_{2} can be used to constrain the values of and K. However, for less than 2, no significant constraints on those parameters are obtained from the values of T_{2}. For higher values of , doubling times only provide loose confidence intervals on K that are compatible with the values reported above. This can be seen in Table 8, showing the 68% confidence intervals predicted for T_{2} and for a lognormal process with and , as obtained from simulation. Therefore, the variability of PKS 2155304 during the flaring period can be consistently described by the lognormal random process whose PSD is characterized by the parameters given by Eq. (9).
Table 8: Confidence interval at 68% c.l. for T_{2} and predicted by simulations for = 2 and for the two highintensity nights MJD 53944 and MJD 53946, with two different sampling intervals (1 and 2 min).
7 Limits on characteristic time of PKS 2155304
In Sect. 5.2 the shortest variability time scale of PKS 2155304 using estimators like doubling times have been estimated. This corresponds to exploring the highfrequency behavior of the PSD. In this section the lower ( ) frequency part of the PSD will be considered, aiming to set a limit on the timescale above which the PSD, characterized in Sect. 6, starts to steepen to > 2. A break in the PSD is expected to avoid infrared divergences and the time at which this break occurs can be considered as a characteristic time, from which physical mechanisms occurring in AGN could be inferred.
Clearly the description of the source variability during the
flaring period by a stationary lognormal random process is in good
agreement with the flux distributions shown in Fig. 3.
Considering the second Gaussian fit in the right panel of Fig. 3, the
excess variance in the flaring regime reported in Table 9, although
affected by a large error, is an estimator of the intrinsic
variance of the stationary process. It has been demonstrated
that
represents the asymptotic value of the firstorder structure function
for large values of the delay
(Simonetti et al. 1985).
On the other hand, as already mentioned, a PSD
proportional to
with
cannot be extrapolated to arbitrary low frequencies; equivalently, the
average structure function cannot rise as
for arbitrarily long times. Therefore, by setting
a 95% confidence interval on
of
from Table 9,
it is possible to evaluate a confidence interval on a
timescale above which the average value of the
structure function cannot be described by a power law. Taking
account of the uncertainties on
and K given by Eq. (9), leads to the
95% confidence interval for this
characteristic time
of the blazar in the flaring regime:
This is compatible with the behavior of the experimental structure function at times s (Fig. 13), although the large fluctuations expected in this region do not allow a more accurate estimation. In the Xray domain, characteristic times of the order of one day or less have been found for several blazars including PKS 2155304 (Kataoka et al. 2001). The results presented here suggest a strong similarity between the PSDs for Xrays and VHE rays during flaring periods.
8 Discussion and conclusions
This data set, which exhibits unique features and results, is the outcome of a longterm monitoring program and dedicated, dense, observations. One of the main results here is the evidence for a VHE ray quiescentstate emission, where the variations in the flux are found to have a lognormal distribution. The existence of such a state was postulated by Stecker & Salamon (1996) in order to explain the extragalactic ray background at 0.03 detected by EGRET (Fichtel 1996; Sreekumar et al. 1998) as coming from quiescentstate unresolved blazars. Such a background has not yet been detected in the VHE range, as it is technically difficult with the atmospheric Cherenkov technique to find an isotropic extragalactic emission and even more to distinguish it from the cosmicray electron flux (Aharonian et al. 2008b). In addition, the EBL attenuation limits the distance from which TeV rays can propagate to (Aharonian et al. 2007b). As pointed out by Cheng et al. (2000), emission mechanisms might be simpler to understand during quiescent states in blazars, and they are also the most likely state to be found observationally. In the Xray band, the existence of a steady underlying emission has also been invoked for two other VHE emitting blazars (Mrk 421, Fossati et al. 2000; and 1ES 1959+650, Giebels et al. 2002). Being able to separate, and detect, flaring and nonflaring states in VHE rays is thus important for such studies.
Table 9: Variability estimators (definitions in Sect. 5.1) relative to both for the ``quiescent'' and flaring regime, as defined in Sect. 3.2.
The observation of the spectacular outbursts of PKS 2155304 in July 2006 represents one of the most extreme examples of AGN variability in the TeV domain, and allows spectral and timing properties to be probed over two orders of magnitude in flux. For the flaring states a clear hardening of the spectrum with increasing flux above a few is observed, as was seen for the blazars Mrk 421 and Mrk 501. In contrast, for the quiescent state of PKS 2155304 an indication of a softening is noted. If confirmed, this is a new and intruiging observation in the VHE regime of blazars. The blazar PKS 0208512 (of the FSRQ class) also shows such initial softening and subsequent hardening with flux in the MeV range, but no general trend could be found for ray blazars (Nandikotkur et al. 2007). In the framework of synchrotron selfCompton scenarios, VHE spectral softening with increasing flux can be associated with, for example, an increase in magnetic field intensity, emission region size, or the power law index of the underlying electron distribution, keeping all other parameters constant. A spectral hardening can equally be obtained by increasing the maximal Lorentz factor of the electron distribution or the Doppler factor (see e.g. Fig. 11.7 in Kataoka 1999). A better understanding of the mechanisms in play would require multiwavelength observations to be taken over a similar time span and with similar sampling density as the data set presented here.
It is shown that the variability time scale of a few minutes are only upper limits for the intrinsic lowest characteristic time scale. Doppler factors of of the emission region are derived by Aharonian et al. (2007a) using the black hole (BH) Schwarzschild radius light crossing time as a limit, while Begelman et al. (2008) argue that such fast time scales cannot be linked to the size of the BH and must occur in regions of smaller scales, such as ``needles'' of matter moving faster than average within a larger jet (Ghisellini & Tavecchio 2008), small components in the jet dominating at TeV energies (Katarzynski et al. 2008), or jet ``stratification'' (Boutelier et al. 2008). Levinson (2007) attributes the variability to dissipation in the jet coming from radiative deceleration of shells with high Lorentz factors.
The flaring period allowed the study of light curves in separated energy bands and the derivation of a power law dependence of with the energy ( ). This dependence is comparable to that reported in Giebels et al. (2007), Lichti et al. (2008), Maraschi et al. (2002), where between the optical and Xray energy bands was found for Mrk 421 and PKS 2155304, respectively. An increase with the energy of the flux variability has been found for Mrk 501 (Albert et al. 2007) in VHE rays on timescales comparable to those observed here.
The flaring period showed for the first time that the intrinsic variability of PKS 2155304 increases with the flux, which can itself be described by a lognormal process, indicating that the aperiodic variability of PKS 2155304 could be produced by a multiplicative process. The flux in the ``quiescent regime'', which is on average 50 times lower than in the flaring period and has a 3 times lower , also follows a lognormal distribution, suggesting similarities between these two regimes.
It has been possible to characterize a power spectral density of the flaring period in the frequency range 10^{4} , resulting in a power law of index 0.21 valid for frequencies down to . The description of the rapid variability of a TeV blazar as a random stationary process must be taken into account by timedependent blazar models. For PKS 2155304 the evidence of this lognormality has been found very recently in Xrays (Giebels & Degrange 2009) and as previously mentioned, Xray binaries and Seyfert galaxies also show lognormal variability, which is thought to originate from the accretion disk (MHardy et al. 2004; Lyubarskii et al. 1997; Arévalo & Uttley 2006), suggesting a connection between the disk and the jet. This variability behavior should therefore be searched for in existing blazar light curves, independently of the observed wavelength.
AcknowledgementsThe support of the Namibian authorities and of the University of Namibia in facilitating the construction and operation of HESS is gratefully acknowledged, as is the support by the German Ministry for Education and Research (BMBF), the Max Planck Society, the French Ministry for Research, the CNRSIN2P3 and the Astroparticle Interdisciplinary Programme of the CNRS, the UK Science and Technology Facilities Council (STFC), the IPNP of the Charles University, the Polish Ministry of Science and Higher Education, the South African Department of Science and Technology and National Research Foundation, and by the University of Namibia. We appreciate the excellent work of the technical support staff in Berlin, Durham, Hamburg, Heidelberg, Palaiseau, Paris, Saclay, and in Namibia in the construction and operation of the equipment.
Appendix A: Observations summary
The journal of observations for the 20052007 is presented in Table A.1.Table A.1: Summary of the 2005 to 2007 observations.
Appendix B: Spectral variability
The numerical information associated with Fig. 7 is given in Tables B.1 (left panel, grey points), B.2 (left panel, black points) and B.3 (right panel). In addition, numerical information associated with Fig. 8 is given in Table B.4.Table B.1: Integral flux ( ) in the 0.21 TeV energy range versus photon index corresponding to grey points in the left panel of Fig. 7.
Table B.2:
Integral flux (
)
in the 0.21 TeV energy range versus photon index
corresponding to black points in the left panel of Fig. 7.
Table B.3: Integral flux ( ) in the 0.21 TeV energy range versus photon index corresponding to the right panel of Fig. 7.
Table B.4: MJD, integral flux ( ) in the 0.21 TeV energy range, and photon index corresponding to the entries of Fig. 8.
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Footnotes
 ...^{}
 Supported by CAPES Foundation, Ministry of Education of Brazil.
 ... France^{}
 UMR 7164 (CNRS, Université Paris VII, CEA, Observatoire de Paris)
 ... index^{}
 The resulting spectral index is . The alternative hypothesis with a curvature in the spectrum (Eq. (2)) is favored at , yelding a harder index ( ) with an exponential cutoff at . As the integral flux is dominated by the lowenergy part of the spectrum, the choice of the model has a little effect on the integral flux values above .
 ... considered^{}
 A similar procedure has been carried out on the Crab Nebula observations. Assuming this source is perfectly stable, it allows the derivation of an upper limit to the fluctuations of the Crab signal due to the atmosphere. Nonetheless, this value, , is linked to the observations' epoch and zenith angles, and to the source spectral shape.
 ...^{}
 Corresponding to data set T200 in Aharonian et al. (2009).
 ... determined^{}
 Even for lower fluxes, the significance associated with each subset is always higher than 20 standard deviations.
 ...^{}
 To be significant, the determination of an energy cutoff needs a higher number of than for a powerlaw fit.
 ... interval^{}
 If is the variance of , .
All Tables
Table 1: Summary of observations for each year.
Table 2: The various data sets used in the paper, referred to in the text by the labels presented in this table.
Table 3: Integral fluxes and their statistical errors from 2002 and 2003 observations of PKS 2155304 during the HESS construction phase.
Table 4: The distribution of the flux logarithm.
Table 5: Parametrization of the differential energy spectrum of the quiescent state of PKS 2155304, determined in the energy range 0.210 TeV, first for the 20052007 period and also separately for the 2005, 2006 (excluding July) and 2007 periods.
Table 6: Mean Flux and the fractional rms night by night for MJD 5394453947.
Table 7: Doubling/Halving times for the high intensity nights MJD 53944 and MJD 53946 estimated with two different samplings, using the two definitions explained in the text.
Table 8: Confidence interval at 68% c.l. for T_{2} and predicted by simulations for = 2 and for the two highintensity nights MJD 53944 and MJD 53946, with two different sampling intervals (1 and 2 min).
Table 9: Variability estimators (definitions in Sect. 5.1) relative to both for the ``quiescent'' and flaring regime, as defined in Sect. 3.2.
Table A.1: Summary of the 2005 to 2007 observations.
Table B.1: Integral flux ( ) in the 0.21 TeV energy range versus photon index corresponding to grey points in the left panel of Fig. 7.
Table B.2:
Integral flux (
)
in the 0.21 TeV energy range versus photon index
corresponding to black points in the left panel of Fig. 7.
Table B.3: Integral flux ( ) in the 0.21 TeV energy range versus photon index corresponding to the right panel of Fig. 7.
Table B.4: MJD, integral flux ( ) in the 0.21 TeV energy range, and photon index corresponding to the entries of Fig. 8.
All Figures
Figure 1: Zenith angle distribution for the 202 4telescopes observation runs from 2005 to 2007. The inset shows, for each zenith angle, the energy threshold associated with the analysis presented in Sect. 2. 

Open with DEXTER  
In the text 
Figure 2: Monthly averaged integral flux of PKS 2155304 above obtained from data set D (see Table 2). The dotted line corresponds to 15% of the Crab Nebula emission level (see Sect. 3.2). 

Open with DEXTER  
In the text 
Figure 3: Distributions of the logarithms of integral fluxes above in individual runs. Left: from 2005 to 2007 except the July 2006 period (data set ), fitted by a Gaussian. Right: all runs from 2005 to 2007 (data set D), where the solid line represents the result of a fit by the sum of 2 Gaussians (dashed lines). See Table 4 for details. 

Open with DEXTER  
In the text 
Figure 4: Distribution of RMSD obtained when the instrument response to a fixed emission ( and ) is simulated 10 000 times with the same observation conditions as for the 115 runs of the left part of Fig. 3. 

Open with DEXTER  
In the text 
Figure 5: Energy spectrum of the quiescent state for the period 20052007. The green band correponds to the 68% confidencelevel provided by the maximum likelihood method. Points are derived from the residuals in each energy bin, only for illustration purposes. See Sect. 3.4 for further details. 

Open with DEXTER  
In the text 
Figure 6: Integral flux above measured each night during late July 2006 observations. The horizontal dashed line corresponds to the quiescent state emission level defined in Sect. 3.2. 

Open with DEXTER  
In the text 
Figure 7: Evolution of the photon index with increasing flux in the 0.21 TeV energy range. The left panel shows the results for the July 2006 data (black points, data set ) and for the 20052007 period excluding July 2006 (grey points, data set ). The right panel shows the results for the four nights flaring period of July 2006 (black points, data set ) and one point corresponding to the quiescent state average spectrum (grey point, again data set ). See text in Sects. 4.1 ( left panel) and 4.2 ( right panel) for further details on the method. 

Open with DEXTER  
In the text 
Figure 8: Integrated flux versus time for PKS 2155304 on MJD 5394453947 for four energy bands and with a 4min binning. From top to bottom: , 0.2 , 0.35 and 0.6 . These light curves are obtained using a power law spectral shape with an index of , also used to derive the flux extrapolation down to when the threshold is above that energy in the top panel (grey points). Because of the high dispersion of the energy threshold of the instrument (see Sect. 2, Fig. 1), and following the prescription described in 3.1, the integral flux has been determined for a time bin only if the corresponding energy threshold is lower than . The fractional rms for the light curves are respectively, 0.86 , 0.79 , 0.89 and 1.01 . The last plot shows the variation of the photon index determined in the 0.21 TeV range. See Sect. 4.2 and Appendix B.4 for details. 

Open with DEXTER  
In the text 
Figure 9: Fractional rms versus energy for the observation period MJD 5394453947. The points are the mean value of the energy in the range represented by the horizontal bars. The line is the result of a power law fit where the errors on and on the mean energy are taken into account, yielding . 

Open with DEXTER  
In the text 
Figure 10: DCF between the light curves in the energy ranges 0.20.5 TeV and 0.55 TeV and Gaussian fits around the peak. Full circles represent the DCF for MJD 5394453947 4min light curve and the solid line is the Gaussian fit around the peak with mean value of 43 . Crosses represent the DCF for MJD 53946 with a 2min light curve binning, and the dashed line in the Gaussian fit with a peak centred at 14 . 

Open with DEXTER  
In the text 
Figure 11: The excess rms vs. mean flux for the observation in MJD 5394453947 (Full circles). The open circles are the additional points obtained when also including the extrapolated flux points  see text). Top: estimated with 20 min time intervals and a 1 min binned light curve. Bottom: estimated with 80 min time intervals and a 4 min binned light curve. The dotted lines are a linear fit to the points, where for the 1 min binning and for the 4 min binning. Fits to the open circles yield similar results. 

Open with DEXTER  
In the text 
Figure 12: 95% confidence domains for and K at obtained by a maximumlikelihood method based on the flux correlation from 500 simulated light curves. The dashed contour refers to light curve segments of 20 min duration, sampled every minute. The solid contour refers to light curve segments of 80 min duration, sampled every 4 min. The dotted contour refers to the method based on the structure function, as explained in Sect. 6.3. 

Open with DEXTER  
In the text 
Figure 13: First order structure function SF for the observations carried out in the period MJD 5394453947 (circles). The shaded area corresponds to the 68% confidence limits obtained from simulations for the lognormal stationary process characterized by and . The superimposed horizontal band represents the allowed range for the asymptotic value of the SF as obtained in Sect. 7. 

Open with DEXTER  
In the text 
Copyright ESO 2010
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