ASTRONOMY AND The temporal characteristics of the TeV...

Astron. Astrophys. 342, 69–86 (1999) ASTRONOMYAND

ASTROPHYSICS

The temporal characteristics of the TeV gamma-radiationfrom Mkn 501 in 1997

I. Data from the stereoscopic imaging atmospheric Cherenkov telescope systemof HEGRA

F.A. Aharonian1, A.G. Akhperjanian 7, J.A. Barrio 2,3, K. Bernl öhr1,?, H. Bojahr6, J.L. Contreras3, J. Cortina3, A. Daum1,T. Deckers5, V. Fonseca3, J.C. Gonzalez3, G. Heinzelmann4, M. Hemberger1, G. Hermann1,??, M. Heß1, A. Heusler1,W. Hofmann1, H. Hohl6, D. Horns4, A. Ibarra 3, R. Kankanyan1,7, O. Kirstein5, C. Köhler1, A. Konopelko1,???,H. Kornmeyer2, D. Kranich2, H. Krawczynski1,4, H. Lampeitl1, A. Lindner 4, E. Lorenz2, N. Magnussen6, H. Meyer6,R. Mirzoyan2, A. Moralejo3, L. Padilla3, M. Panter1, D. Petry2,6,†, R. Plaga2, A. Plyasheshnikov1,†, J. Prahl4,G. Pühlhofer1, G. Rauterberg5, C. Renault1, W. Rhode6, V. Sahakian7, M. Samorski5, D. Schmele4, F. Schröder6,W. Stamm5, H.J. Völk1, B. Wiebel-Sooth6, C. Wiedner1, M. Willmer 5, and H. Wirth 1

1 Max-Planck-Institut f̈ur Kernphysik, Postfach 103980, D-69029 Heidelberg, Germany2 Max-Planck-Institut f̈ur Physik, F̈ohringer Ring 6, D-80805 M̈unchen, Germany3 Universidad Complutense, Facultad de Ciencias Fı́sicas, Ciudad Universitaria, E-28040 Madrid, Spain4 Universiẗat Hamburg, II. Institut fuer Experimentalphysik, Luruper Chausse 149, D-22761 Hamburg, Germany5 Universiẗat Kiel, Institut f̈ur Kernphysik, Olshausenstrasse 40, D-24118 Kiel, Germany6 Universiẗat Wuppertal, Fachbereich Physik, Gaußstrasse 20, D-42097 Wuppertal, Germany7 Yerevan Physics Institute, Alikhanian Br. 2, 375036 Yerevan, Armenia

Received 12 August 1998 / Accepted 21 October 1998

Abstract. During 1997, the BL Lac Object Mkn 501 was thebrightest known object in the TeVγ-ray sky. The emission wascharacterized by dramatic variations in intensity with a meanflux exceeding by a factor of three the steadyγ-ray flux ofthe Crab Nebula. The stereoscopic HEGRA system of 4 Imag-ing Atmospheric Cherenkov Telescopes, with an energy thresh-old of about 500 GeV, an angular resolution of 0.1◦, an en-ergy resolution of20%, and a flux sensitivityν Fν at 1 TeV of10−11 ergs/cm2sec ' 1/4 Crab for 1 hour of observation time(S/

√B=5σ), has been used in 1997 for a comprehensive study

of the spectral and temporal characteristics of the TeVγ-rayemission from Mkn 501 on time scales of several hours or less.In this paper (Part I) theγ-ray fluxes and spectra on a diurnalbasis during the period March to October 1997 are presented.Furthermore, the correlation of the TeV emission with the fluxmeasured by the RXTE All Sky Monitor in the energy rangefrom 2 to 12 keV are studied. Finally the implications of theseresults on the physics of relativistic jets in BL Lac objects are

Send offprint requests to: H. Krawczynski([email protected])

? Now at Forschungszentrum Karlsruhe, P.O. Box 3640, D-76021Karlsruhe, Germany?? Now at Enrico Fermi Institute, University of Chicago, 933 East

56th Street, Chicago, IL 60637, USA??? Permanent address:Altai State University, Dimitrov Street 66,656099 Barnaul, Russia

† Now at Universidad Aut́onoma de Barcelona, Institut de Fı́sicad’Altes Energies, E-08193 Bellaterra, Spain

briefly discussed. The companion paper (Part II) describes theresults from the stand alone telescopes CT1 and CT2.

Key words: gamma rays: observations – galaxies: BL Lacertaeobjects: individual: Mkn 501

1. Introduction

Mrk 501 was discovered as a source of TeV-γ-radiation in 1995by the Whipple group (Quinn et al. 1996). The observation wasconfirmed later by the HEGRA collaboration (Bradbury et al.1997). Together with two other extragalactic TeVγ-ray sourcesdetected so far, Mrk 421 (Punch et al. 1992; Petry et al. 1996)and 1ES 2344+514 (Catanese et al. 1998), Mrk 501 belongsto a sub-population of Active Galactic Nuclei (AGNs), the so-called BL Lac objects. Flux variability on various time scales,ranging from dramatic flares of Mrk 421 in May 1996 withdurations of about 1 h (Gaidos et al. 1996) to a state of highflaring activity of Mrk 501 which lasted several months (e.g.Protheroe et al. 1997), is a characteristic feature of the TeVemission observed from BL Lac objects. This agrees well withthe general properties of BL Lac objects – highly variable AGNswithout significant optical line emission, but showing a strongnonthermal (synchrotron) component of radiation from radio toX-ray wavelengths (e.g. Urry & Padovani 1995).

The correlated flares of BL Lac objects in the keV energyband and in the TeV energy band, discovered for the first time

70 F.A. Aharonian et al.: TeV Characteristics of Mkn 501. I

during simultaneous observations of Mrk 421 by the Whip-ple and ASCA detectors (Takahashi et al. 1996; Buckley et al.1996), strongly support the commonly accepted view that bothcomponents originate in a relativistic jet, with Doppler factorsδj ≥ 5, due to synchrotron and inverse Compton (IC) radiationof the same population of ultrarelativistic electrons (for a reviewsee e.g. Ulrich et al. 1997). Since in the Thomson regime theIC cooling timetIC = −Ee/(dEe/dt) is proportional to1/Ee,and since the Compton scattering boosts ambient photons withenergies�0 up toEγ ∝ �0 · E2e , the characteristic time ofγ-rayemission decreases with energy as∝ E−1/2γ . This explains ina natural way the less dramatic variations of the MeV/GeVγ-ray fluxes during the keV/TeV flares; the relatively low energyelectrons, responsible for the GeV IC photons as well as for theoptical/UV synchrotron radiation do not respond as rapidly tochanges of the physical conditions in the jets as the high en-ergy electrons do. In addition, the expected hard spectra of ICradiation below 100 GeV explain the low fluxes of GeVγ-raysfrom Mrk 421, and their non-detection by EGRET in the case ofMkn 501 and 1ES 2344+514. This implies that the VHEγ-rayregion, combined with X-ray observations, is likely to be themost important window of the electromagnetic spectrum to in-fer the highly non-stationary processes of particle accelerationand their radiation in BL Lac objects. Imaging AtmosphericCherenkov Telescope (IACT) detectors, characterized by largeeffective detection areas of∼ 105 m2 and an effective sup-pression of the background of cosmic rays, are well suited toaccess this very informative “TeV” channel. This was convinc-ingly demonstrated by the Mkn 501 observations with severalCherenkov telescopes located in the Northern Hemisphere dur-ing the extreme activity of the source in 1997 (Protheroe et al.1997).

During the first two years after its discovery as a TeVγ-raysource, Mkn 501 showed rather low fluxes at a level significantlybelow the Crab flux (Quinn et al. 1996; Bradbury et al. 1997).However, in March 1997 the source went into a state of highlyvariable and strong emission with maximum fluxes roughly 10times that of the Crab. According to the All Sky Monitor (ASM)on board theRossi X-Ray Timing Explorer(RXTE) (Remillard& Levine 1997), the high X-ray activity of the source startedin March 1997 and continued until October 1997. Apparentlythe period of high activity coincided with the period of the vis-ibility of the source by ground-based optical instruments. Thusit was possible to continuously monitor the source during thisextremely bright emission period with several IACTs, i.e. withCAT (Barrau et al. 1997), HEGRA (Aharonian et al. 1997a),TACTIC (Bhat et al. 1997), Whipple (Catanese et al. 1997), andthe Telescope Array (Hayashida et al. 1998).

The HEGRA experiment is located on the Roque de losMuchachos on the Canary Island of La Palma, (lat. 28.8◦ N,long. 17.9◦ W, 2200 m a.s.l.). The HEGRA collaboration oper-ates 6 Cherenkov telescopes. A system of at present four tele-scopes (telescopes CT3, CT4, CT5, and CT6) is used as a singledetector for stereoscopic air shower observations (Daum et al.1997). The two telescopes, CT1 (Mirzoyan et al. 1994; Rauter-

berg et al. 1995) and CT2 (Konopelko et al. 1996), are currentlyoperated each as independent detectors. The IACT system ischaracterized by a high sensitivity and excellent spectroscopiccapabilities. The stand alone telescopes CT1 and CT2 have beenused to considerably extend the Mkn 501 time coverage, in par-ticular during moonshine periods, when the stereoscopic systemwas not operated.

In this paper (Part I) the results obtained from the IACT sys-tem data are presented. The companion paper (Part II) describesin detail the results from CT1 and CT2 data.

The basic concept of the IACT array is thestereoscopicapproachbased on simultaneous detection of air showers by≥ 2 telescopes under widely differing viewing angles. Withthe stereoscopic technique an angular resolution of 0.1◦ perphoton, an energy resolution of20% per photon, and a sup-pression of the isotropic cosmic ray background on the triggerlevel and by image analysis by a factor of the order of 100 isachieved. Thusγ-ray observations with unprecedented signal tonoise ratio and excellent spectroscopic capabilities are possible.Furthermore, since a hardware trigger requiring the coincidentdetection of air showers by at least two telescopes strongly sup-presses triggers caused by the night sky background light or bylocal muons, the energy threshold of a stereoscopic telescopessystem is mainly limited by Cherenkov photon statistics. As aconsequence, the IACT system achieves an energy threshold aslow as 500 GeV despite the relatively small size of the telescopemirrors of8.5 m2 (the energy threshold is defined as the energyat which theγ-ray detection rate peaks for Crab type spectra withdifferential photon indices of∼ −2.5). The flux sensitivity ofthe IACT system for episodic TeVγ-ray phenomena with dura-tions of the order of 1 h isabout 1/4 Crab1 (for S/

√B=5σ), which

corresponds to aν Fν-flux at 1 TeV of∼ 10−11 erg/cm2s. Thisenergy flux sensitivity combines nicely with the comparableenergy flux sensitivities of the current X-ray instruments likeASCA, BeppoSAX and RXTE for the study of the high energyemission of BL Lacs, especially of Mkn 501 and of Mkn 421.These two sources proved to release a comparable amount ofnonthermal energy in X-rays and in TeVγ-rays, with an aver-age energy flux in both channels exceeding∼ 10−11 erg/cm2s.During strong flares of these sources with fluxes up to 10 Crab,a 2 minute exposure is sufficient for the IACT system to detect astatistically significantγ-ray signal, and a 1 h exposure sufficesfor a measurement of the differential energy spectrum.

This paper is organized as follows: Hardware issues arebriefly summarized in Sect. 2. Analysis methods are presentedin Sect. 3. Subsequently, the results concerning the TeV-γ-rayemission from Mkn 501 in 1997 are discussed. In Sect. 4 the1997 light curve of Mkn 501 is presented and possible corre-lations between the flux amplitude and the spectral slope areexplored. The most rapid time scales of flux variability are dis-cussed in Sect. 5. The correlation of the TeV-fluxes with thekeV-fluxes as measured with the RXTE All Sky Monitor are

1 In the case of the Crab Nebula, the IACT system currently gives,after cuts,'50γ-rays per hour over a flat background of 6 events perhour.

F.A. Aharonian et al.: TeV Characteristics of Mkn 501. I 71

studied in Sect. 6. Implications on models of the non-thermalγ−radiation from BL Lac objects are discussed in Sect. 7.

2. The IACT system of HEGRA

The HEGRA telescope system consists presently of 4, in the nearfuture of 5, identical IACTs – one at the center and 3 (in future4) at the corners of a 100 m by 100 m square area. The multi-mirror reflector of each telescope has an area of 8.5 m2. Thirtyfront aluminized and quartz coated spherical mirrors of 60 cmdiameter and of 4.9 m focal length are independently mountedon an almost spherical frame of an alt-azimuth mount, follow-ing the design of Davies and Cotton. Each telescope is equippedwith a 271 channel camera of 0.25◦ pixel size resulting in an ef-fective field of view of 4.3◦. The PMT pulses are fed into triggerelectronics and into shapers followed by 120 MHz flash analog-to-digital converters (FADCs). A multilevel trigger demandsatleast two adjacent pixelsin each ofat least 2 telescopes(Bulianet al. 1998). The topological “next-neighbor” condition of twoadjacentpixels reduces the number of night sky backgroundtriggers. In the following analysis we use the software triggercondition of at least two telescopes with images with more than40 photoelectrons.

At the beginning of each night, the camera is flat-fieldedusing an UV laser at each telescope to illuminate a scintilla-tor via an optical cable. The scintillator emits a spectrum withpeak emission in the near-UV and blue, similar to atmosphericCherenkov light. An absolute calibration of the system has beenperformed with a direct laser measurement and a calibrated low-power photon detector (Fraß et al. 1997). This measurement hasdetermined the conversion factor from photons to FADC countswith an accuracy of 10%.

The pointing of the telescopes is checked on a regular basiswith so called “point runs” (P̈uhlhofer et al. 1997), where asection of the sky surrounding a bright star is scanned. Thepointing of each telescope is inferred from the currents measuredin the PMTs surrounding the image of the star. After applyingthe resulting pointing correction function, an effective pointingaccuracy of better than 0.01◦ is achieved. This accuracy hasbeen experimentally confirmed withγ-ray data from the CrabNebula and Mkn 501 (P̈uhlhofer et al. 1997).

The first system telescope, called CT3, was installed in De-cember 1995. Subsequently CT4 started operation in July 1996,CT5 in September 1996, and CT6 in November 1996. The ar-ray of 4 telescopes is operational since end of November 1996.Since then, minor changes of the hardware were carried out.These are summarized in Table 1. In the following, HEGRAdata from March 1997 to October 1997 are used. The relevanthardware changes are (i) a mirror adjustment of CT3 and CT4on May 12th, 1997 and (ii) the incorporation of the topologicalnext-neighbour trigger condition on hardware level for CT3 andCT6 as well, and a reduction of the single pixel trigger thresholdfor all IACTs from 10 to 8 photoelectrons on June 24th, 1997.CT4 and CT5 had been operated with the next-neighbour trig-ger condition from the very beginning. These changes dividethe Mkn 501 1997 data into 3 groups (period I - period III). In

Table 1. The IACT system of HEGRA - Hardware changes during1996 and 1997.

Date Hardware Changes Performed Data-period

27.11.1996 Start of 4-telescope system ICT3, CT6: 2 pixel trigger,CT4, CT5: 2 pixel topologicaltrigger, single pixelthreshold 10 p.e.for all CTs

12.05.1997 adjustment of telescope mirrors II

24.06.1997 2 pixel topological trigger and IIIsingle pixel threshold 8 p.e.for all CTs

16.10.1997– CT4 not operational due to fire IV15.11.1998

Table 2. Efficiencies averaged over the wavelength region from 300to 600 nm.

Reason Efficiency

Atmospheric transmission 0.84Mirror Reflectivity 0.88Plexiglas and Funnel transmission 0.81Quantum efficiency 0.18Total, Cherenkov Photons to FADC channels 0.10

the next subsection it will be shown how the data is corrected forthese changes by the use of detailed Monte Carlo simulations.

3. Analysis of the IACT system data

3.1. Monte Carlo simulations

The Monte Carlo simulation (Konopelko et al. 1998) is di-vided into two steps. First, the air showers are simulated andthe Cherenkov photons hitting one telescope are stored on massstorage devices. Thereafter the detector simulation is carriedout. This method has the advantage that it is possible to usethe same simulated showers with different detector setups. Theair shower simulation is based on the ALTAI code. The resultsof the code have been tested against results of the CORSIKAcode which gave for hadron induced air showers excellent agree-ment in all relevant observables, e.g., in the predicted detectionrates and in the distribution of the image parameters (Hemberger1998). The detector simulation (Hemberger 1998) accounts forthe absorption of Cherenkov photons in the atmosphere due toozone absorption, Rayleigh scattering and Mie scattering. Fur-thermore, the mirror reflectivity, the mirror point spread func-tion, and the acceptances of the plexiglass panels and the lightcollecting funnels in front of the cameras are taken into account.See Table 2 for a summary of the efficiencies which are relevantfor the simulations. In the table only the mean values averagedover the wavelength region from 300 to 600 nm are given, in thesimulations the efficiencies depend on the wavelength. The point


spread functions of the telescope mirrors are extracted from thepoint runs. The time-resolved photon to photoelectron conver-sion by the PMTs is modeled using a measured PMT pulseshape and a measured single photoelectron spectrum. Finally,the trigger processes and the digitization of the PMT pulses aresimulated in detail.

The simulated events are stored in the same format as theraw experimental data and are processed with the same eventreconstruction and analysis chain as the experimental data.Showers induced by photons as well as by hydrogen, helium,oxygen, and iron nuclei were simulated for the zenith anglesθMC = 0◦,20◦,30◦, and 45◦. For the purpose of comparing theexperimental data with the Monte Carlo predictions, the MonteCarlo events are weighted to generate the appropriate spectrum.The events induced by the proton, helium, oxygen, and iron nu-clei are weighted according to the cosmic ray abundances ofthe corresponding groups from (e.g. Wiebel et al. 1998). Foreach type of primary particle, and for each zenith angle approx-imately 2· 105 showers have been generated.

The excellent agreement of the observable quantities in theexperimental data and the Monte Carlo data for cosmic ray-induced showers as well as for photon-induced showers is de-scribed in detail in Konopelko et al. (1998) and in Aharonianet al. (1998). The comparisons between data and Monte Carlowhich are relevant for the analysis of the Mkn 501 data of thispaper are discussed in the following 4 subsections.

Three different Monte Carlo event-samples have been gen-erated, with different trigger settings and mirror point spreadfunctions, corresponding to the three data-taking periods.

3.2. Data sample and data cleaning

The analysis described in this paper is based on 110 hours ofMkn 501 data acquired between March 16th, 1997 and October1st, 1997 under optimal weather conditions (i.e. a clear sky anda humidity less than 90%), with the optimal detector perfor-mance, and with Mkn 501 being more than 45◦ above the hori-zon. Only data runs where all 4 IACTs were operational and inwhich not more than 20 pixel were defective in any IACT havebeen admitted to the analysis. Furthermore the data runs had tosatisfy the requirements of the mean cosmic ray rate deviatingby less than 15% from the zenith angle dependent expectationvalue, and the width parameter averaged over all events andall telescopes deviating by less than 6% from the zenith angledependent expectation value.

The Mkn 501 data were acquired in the so called “wob-ble mode” (Daum et al. 1997). In this mode the telescopes arepointed into a direction which is shifted by 0.5◦ in declinationwith respect to the source direction. The direction of the shift isreversed for each data run of 20 minutes duration. For each run,the solid-angle region located 1◦ from the Mkn 501 location onthe opposite side of the camera center is used as OFF region forestimates concerning the background contamination of the ONregion by cosmic ray-induced showers. The large angular dis-tance between the ON solid-angle region around the Mkn 501direction and the OFF solid-angle region assures a negligible

Zenith angle [ o ]

Rat

e [ H

z ]

0

2

4

6

8

10

12

14

0 10 20 30 40

Fig. 1. The cosmic ray detection rate of the IACT system (dots) as afunction of zenith angle (data from data-period I). Monte Carlo ratepredictions are superimposed (solid line). The measured and the MonteCarlo data agree with an accuracy of 10% (hardware threshold, no cuts).

contamination of the OFF data with Mkn 501γ-rays. The sym-metric location of the ON and the OFF region in the camerawith respect to the optical axis and the camera geometry as-sures almost equal background characteristics for both regions.The zenith angle dependence of the background rate is to first or-der compensated by using as many runs with lower-declinationOFF regions as with higher-declination OFF regions.

The overall stability of the detector and the understandingof the detector performance during the three data periods hasbeen tested by comparing several key Monte Carlo predictionsfor hadron-induced showers with the experimental results. Inthe following 3 subsections tests concerning photon-inducedshowers, based onγ-rays from Mkn 501, will be described.

The observed cosmic ray detection rates have been com-pared with the detection rates as inferred from the Monte Carlosimulations together with the cosmic ray fluxes from the lit-erature. In Fig. 1 the dependence of the cosmic ray detectionrate on the zenith angle is shown for the first data-period andthe corresponding Monte Carlo data-sample. The Monte Carlodescribes the dependence with an accuracy of 10%. In Fig. 2the measured and predicted rates are shown for the whole 1997data-base. The measured rates have been normalized to a zenithangle of 15◦ according to the empirical parameterization shownin Fig. 1. For all three data periods the Monte Carlo simula-tions predict the measured rates with an accuracy of 10%, andthey accurately describe the relative rate differences betweenthe data-taking periods. The measured rates within each data-period show a spread of4% FWHM, after correcting for thezenith angle dependence of the rate. The origin of this smallspread is still unclear. The rate deviations do not correlate withthe temperature, the pressure, or the humidity, as measured atthe Nordic Optical Telescope which is localized within severalhundred meters from the HEGRA site. Neither is a correlationfound with the V-band extinction measured with the CarlsbergMeridian Circle which is situated at a distance of∼500 m fromthe HEGRA site.

To summarize, the measurements of the cosmic-ray eventrate prove the stability of the IACT system at a level of 5%


Date [ MJD-50000 ]

Nor

mal

ized

Rat

e [ H

z ]

0

2

4

6

8

10

12

14

16

18

550 600 650 700

Fig. 2. The measured cosmic ray detection rate (dots) and the MonteCarlo based predictions (solid line) are shown for all the cosmic ray dataof the Mkn 501 runs of 1997. The measured rates have been normal-ized to a zenith angle of 15◦ using an empirical parameterization. TheMonte Carlo simulations for 0◦ zenith angle have been used (hardwarethreshold, no cuts).

and the event rate is correctly predicted by the Monte Carlosimulations using the cosmic ray abundances from the literaturewith an accuracy of 10%.

3.3. The stereoscopic reconstruction of the directionof primary particles

Based on the stereoscopic images of the shower, the shower axisis reconstructed accurately and unambiguously using a simplegeometric method (Aharonian et al. 1997b). The reconstruc-tion permits to determine the distances of the telescopes fromthe shower axis and consequently, to accurately reconstruct theshower energy and to efficiently suppress the background ofcosmic ray-induced showers.

The reconstruction method uses the standard second mo-ment parameterization (Hillas 1985; Fegan 1996) of the indi-vidual images. Each image is described by an ellipsoid of inertiacomputed from the measured Cherenkov light intensities in thecamera. The intersection of the major axes oftwo imagessuper-imposed in the “common focal plane”, i.e. in directional space,yields oneestimate of the shower direction. If more than twotelescopes observed a shower, the arrival directions computedfor all pairs of images are combined with a proper weightingfactor to yield the common estimate of the arrival direction.The weighting factor is chosen proportional tosin δ, whereδ isthe angle between the two major axes. Taking into account theshower direction, the shower core is reconstructed using a verysimilar geometric procedure. Note, that this method is basedexclusively on the geometry of the imaging systems and of theshower axis and does not rely on any Monte Carlo predictions.

The angular resolution achieved with this method has beendetermined using both Mkn 501γ-ray data and the Monte Carlosimulations. In the case of the Mkn 501 data this is done as fol-lows. The squares of the angular distancesΘof the reconstructedshower directions from the Mkn 501 position are histogrammed.The subtraction of the corresponding distribution of the ficti-tious OFF source yields the background-subtracted distribution

of theγ-ray events. In order to reduce the background-inducedfluctuations, the analysis is performed with theγ/h-separationcut w̄sc < 1.3 (see next subsection for the definition ofw̄sc).In the following, the Monte Carlo photon-induced showers areweighted according to a power law spectrum with differentialspectral index of−2.2.

On the left side of Fig. 3 theΘ2-distributions for the ONand the OFF regions are shown for the zenith angle interval 0◦-30◦. On the right side of Fig. 3 the distribution obtained afterbackground subtraction is compared to the distribution for the20◦ Monte Carlo showers. There is good agreement betweenthe data and the Monte Carlo. The projected angular resolutionis 0.1◦ for showers near the zenith and is slightly worse for the30◦- and the 45◦-showers i.e. 0.11◦ and 0.12◦ respectively. Inthe analysis presented in this paper, only a loose cut ofΘ <0.22◦ is used which accepts, after softwarethreshold, 85% ofthe photon induced showers and rejects 99% of the hadron-induced showers. By this loose cut the systematic uncertaintiescaused by the energy-dependentγ-ray acceptance of the cut areminimized.

In Fig. 4 theγ-ray acceptance (κγ,Θ) of the angular cut isshown as a function of the reconstructed shower energy, as de-termined both from the Mkn 501 and from Monte Carlo data. Inthe case of the Mkn 501 data the same background subtractiontechnique is used as described above. For the lowest energies(< 1 TeV) theγ-ray acceptance is slightly lower than for higherenergies, i.e. the angular resolution is slightly worse. This is aconsequence of the photon statistics per image and the corre-sponding uncertainty of the images’ major axes. At higher en-ergies the angular resolution improves less than expected fromthe increase in photon statistics. This is a consequence of anincreasing fraction of showers which at higher energies are stillable to fulfill the trigger criteria, albeit having impact points faraway from the telescope system. With increasing distance ofthe impact point from the telescope system, the accuracy of thedirection reconstruction decreases as a consequence of smallerangles between the image axes of the different telescopes.

3.4. Image analysis gamma/hadron separation

The IACT technique permits the suppression of the backgroundof cosmic ray-induced showers by the directional informationand, additionally, by analysis of the shapes of the shower images.In the case of stereoscopic IACT systems, the gamma/hadronseparation power of the parameterWIDTH of the standard sec-ond moment analysis, which describes the transverse extensionof the shower image in one camera, can be increased substan-tially, due to two facts: First, the location and the orientationof the shower axis is known from the three-dimensional eventreconstruction and cuts can be optimized accordingly. Second,a telescope system provides complementary information aboutthe transversal extension of the shower obtained from differentviewing angles.

The parameter “mean scaled width”w̄sc (Konopelko 1995;Daum et al. 1997) has been used for gamma/hadron-separation.It is defined according to:


Mkn 501 Data, ON-Region

Mkn 501 Data, OFF-Region

Θ2 [ degree 2 ]

Num

ber

of E

vent

s

0

2000

4000

6000

0 0.05 0.1 0.15

Mkn 501 Data ( γ)

Monte Carlo ( γ)

Θ2 [ degree 2 ]

Num

ber

of E

vent

s

0

2000

4000

6000

0 0.05 0.1 0.15

Fig. 3. On the left side, the squared angu-lar distancesΘ2 of the reconstructed eventdirections from the Mkn 501 direction (fullline) and from the OFF source direction (dot-ted line) are shown for zenith angles below30◦. On the right side, the measured back-ground subtractedΘ2-distribution (full cir-cles) is compared to the 20◦ zenith angleMonte Carlo simulations (open circles) Alldistributions have been computed using thesoftware threshold of at least 2 IACTs withsize > 40 and the looseγ/h-separation cutw̄sc < 1.3.

Mkn 501 Data ( γ)Monte Carlo ( γ)

Reconstructed Energy [ TeV ]

κ γ o

f ang

ular

cut

0

0.5

1

1.5

2

1 10

Fig. 4. Theγ-ray acceptance of the cutΘ < 0.22◦ as a function of thereconstructed primary energy, computed with the Mkn 501 gamma-rays (full circles) and with the Monte Carlo simulations (open circles).The computation of the cut acceptances is based on the number ofexcess events found in the ON region of angular radius of0.45◦ (cutsas in Fig. 3).

w̄sc =1

Ntel

∑i

WIDTH i〈WIDTH (ri, sizei, θ)〉γ

, (1)

where the sum runs over allNtel telescopes which triggered.WIDTH i is theWIDTH -parameter measured with telescopeiand〈WIDTH (ri, sizei, θ)〉γ is theWIDTH -value expected forphoton-induced showers, given the telescope distanceri fromthe shower axis, the total number of photoelectrons,sizei, ob-served in the telescope, and the zenith angleθ of observations.The〈WIDTH (ri, sizei, θ)〉γ-values are computed from a MonteCarlo table, using an empirical function for interpolation be-tween the simulated zenith angles. By using ascaledWIDTH -parameter, it is possible to take into account that on averagethe widths of the shower images widen with increasing tele-scope distance from the shower axis and with the total numberof photoelectrons recorded in a telescope. Byaveragingoverthe values computed for each telescope, the statistical accuracyof the parameter determination improvesand the informationabout the shower gained from different viewing angles is com-bined.

Fig. 5 shows the distribution of thēwsc parameter for theMkn 501γ-rays and for the Monte Carlo photon data-sample.The distribution for the Mkn 501γ-rays has been obtained as

follows. Thew̄sc-values of the events satisfying the loose cuton the angular distanceΘ from the Mkn 501 locationΘ < 0.3◦

are histogrammed. The subtraction of the corresponding OFFdistribution yields the background-free distribution of theγ-rayevents. As can be seen in Fig. 5 the experimental distributionand the Monte Carlo distribution are in excellent agreement.

In the analysis of this paper only a loose cut ofw̄sc < 1.2which accepts, after softwarethreshold, 96% of the photons andrejects 80% of the cosmic ray-induced air showers is used. Withthis loose cut the systematic uncertainties caused by the energydependentγ-ray acceptance of the cut are minimized. In Fig. 6the γ-ray acceptancesκγ,img of the shape cut as determinedfrom data and as determined from Monte Carlo as a function ofthe reconstructed energy are compared to each other. The resultsare in excellent agreement with each other. Due to backgroundfluctuations, the determination of the cut acceptance from ex-perimental data can yield values larger than one.

3.5. Reconstruction of the primary energy and determinationof differential spectra

The determination of a differentialγ-ray spectrum is performedin several steps. In the first step, for all events of the ON andthe OFF region the primary energyE is reconstructed underthe assumption that the primary particles are all photons. Thereconstruction is based on the fact that, for a certain type ofprimary particle and a certain zenith angleθ, the density of at-mospheric Cherenkov light created by the extensive air showerat a certain distance from the shower axis is to good approxima-tion proportional to the energy of the primary particle. Presentlytwo algorithms are used:

1. The first method is based on the functions〈size(r, E, θ)〉γand

σsize(r, E, θ)2 ≡〈(

size(r, E, θ) − 〈size(r, E, θ)〉γ)2〉

γ

which describe the expected sum of photoelectrons,size,and its variance as a function of the distancer of a telescopefrom the shower axis, the primary energyE of the photon,and the zenith angleθ. Both functions are computed fromthe Monte Carlo event-sample and are tabulated inr-, E-,andθ-bins. Given, for theith telescope, the shower axis dis-


Mkn 501 Data, ON

Mkn 501 Data, OFF

Mean Scaled Width [ degree ]

Num

ber

of E

vent

s

0

5000

10000

15000

0 1 2 3

Mkn 501 Data ( γ)

Monte Carlo ( γ)

Mean Scaled Width [ degree ]

Num

ber

of E

vent

s

0

5000

10000

15000

0 1 2 3

Fig. 5. On the left side, the mean scaledwidth distribution is shown for the ON re-gion (full line) and for the OFF region (dot-ted line). On the right side, the backgroundsubtracted distribution (full circles) is com-pared to the Monte Carlo distribution (opencircles). (all distributions: software thresh-old: at least 2 IACTs withsize > 40, and,cut: Θ < 0.3◦, data: all zenith angles,Monte Carlo: zenith angle = 20◦).

Mkn 501 Data ( γ)Monte Carlo ( γ)


κ γ o

f im

age

cut

00.20.40.60.8

11.21.41.61.8

2

1 10

Fig. 6. Theγ-ray acceptance of the cut̄wsc < 1.2 as a function of thereconstructed primary energy, computed with the Mkn 501 gamma-rays (full circles) and with the Monte Carlo simulations (open circles)(cuts as in Fig. 5).

tanceri from the stereoscopic event analysis and the sumof recorded photoelectronssizei, an estimateEi of the pri-mary energy is made by numerical inversion of the function〈size(r, E, θ)〉γ . Subsequently the energy estimates from alltriggered telescopes are combined with a proper weightingfactor proportional to1/(σsize(ri, Ei, θ))2 to yield a com-mon energy value.

2. In a very similar approachE is estimated from thesizei andtheri using a Maximum Likelihood Method which takes thefull probability density functions (PDFs)p(size; r, E, θ) ofthesize-observable into account. The PDFs are determinedfrom the Monte Carlo-simulations for certain bins inr, E,andθ. The common estimate for the energyE maximizes thejoint a posteriori probability function

∏i p(sizei; ri, E, θ)

that thesizei-values have been observed at the zenith angleθ and at the distancesri.

Monte Carlo showers have been simulated for the 4 discretezenith angles0◦, 20◦, 30◦, and45◦. The energies for arbitraryθ-values between 0◦ and 45◦ are determined by interpolation ofthe two energy estimates computed with the Monte Carlo tablesof the adjacent zenith angle values below and aboveθ. Herebyan interpolation linear in cos(θ)−ζ is used, whereζ = 2.4 isderived as described below. Very small images withsize < 40

NTel ≥ 2NTel ≥ 3

∆E / E

Ent

ries

0

1000

2000

3000

-1 0 1 2

Fig. 7. The relative error of the energy reconstruction∆ E / E (with∆ E > 0 if the reconstructed energy is higher than the true energy),shown forγ-ray induced showers. The full line shows the distributionfor all showers with at least 2 telescopes withsize > 40 and the dottedline shows the distribution for all showers with at least 3 telescopes withsize > 40 (Monte Carlo, zenith angle 20◦, after looseγ/h-separationcuts, weighting according todNγ / dE ∝ E−2.2).

are excluded from the analysis. Both methods yield the sameenergy reconstruction accuracy of∆E/E ∼ 20% for photon-induced showers, almost independent of the primary energy. Inthe analysis presented below the Maximum Likelihood Methodis used. In Fig. 7 the relative reconstruction error∆ E / E isshown for the second method for all triggeredγ-ray showerswhich pass the looseγ/h separation cuts and which produceat least two or three images withsize > 40. Increasing therequirement on the minimum number of images improves theenergy resolution slightly but reduces theγ-ray statistics. Inthe following we are interested in one-day spectra with sparsephoton statistics; consequently we will use the weaker conditionof only two telescopes withsize > 40.

In the second step, the differential photon flux per energychannel is computed using the formula

dΦdE

(Ei) =1

∆t ∆Ei

non,i∑j=1

[κγ,Θ(Ej , θj) κγ,img(Ej , θj) A′eff(Ej , θj)]−1 −


noff,i∑j=1

[κγ,Θ(Ej , θj) κγ,img(Ej , θj) A′eff(Ej , θj)]−1

(2)

where∆t is the observation time and∆Ei is the width of theithenergy bin. The first sum runs over all ON events reconstructedin theith energy bin. The second sum runs over all OFF eventsreconstructed in theith energy bin.Ej is the reconstructed en-ergy of thejth event and the parameterθj is the zenith angleunder which the source was observed when thejth event wasrecorded. The second term subtracts on a statistical basis thebackground contamination of the ON region. The effective areaA′eff accounts for the acceptance of the detectorand its energyresolution. The factorsκγ,Θ andκγ,img account for theγ-rayacceptances of the angular cut and the image cut, respectively.Given the differentail flux, the integral flux can be computedeasily by integrating Eq. 2 over the relevant energy range.

Generally, the effective area is computed from

Aeff(E, θ) =Ntr(E, θ)NMC(E, θ)

AMC(E, θ) (3)

whereNMC is the number of Monte Carloγ-ray-induced show-ers generated for a certain energy and zenith angle bin,Ntr is thenumber of these showers which trigger the detector and pass theselection cuts, andAMC is the area over which the Monte Carloshowers were thrown. The areaAMC is chosen sufficiently large(depending on the primary energy and the simulated zenith an-gle between2 × 105 and6 × 105 m2), so that virtually noexterior events trigger the experiment.

The energy resolution of the detector is taken into account byusing a slightly modified effective areaA′eff,α which takes, for agiven power law spectrumΦ(E) ∝ Eα, the response functionof the energy reconstructionp(E, Ẽ) (properly normalized) intoaccount:

A′eff,α(Ẽ; θ) =∫

dE p(E, Ẽ; θ) Aeff(E, θ) Φ(E)Φ(Ẽ)

. (4)

In practice,A′eff,α is computed with Eq. 3, weighting the eventsaccording to an incident power law spectrum with differentialspectral indexα and using forE the reconstructed energy andnot the true energy. Hereby the cut on the distancer of theshower axis from the center of the telescope systemr < 195 mwhich is also used in the spectral analysis is taken into account.

Eq. 2 permits, by definition, to reconstruct accurately a dif-ferential power law spectrum with indexα. Due to the goodenergy resolution of 20% of the IACT system,A′eff,α dependsonly slightly onα. Monte Carlo studies prove that power lawspectra with spectral indices between−1.5 and−3 are recon-structed with a systematic error smaller than 0.1 usingA′eff, αwith a fixed value ofα = −2.2. Furthermore we have testedthis method with several other types of primary spectra, i.e. withbroken power law spectra and with power law spectra with ex-ponential cut-offs. The method, used withA′eff, −2.2, reproducesthe input-spectra with good accuracy.

Differential Mkn 501 spectra obtained with this method, aswell as the method for fitting model spectra to the data, will be

discussed below. Alternatively we have tested the standard for-ward folding technique and more sophisticated deconvolutionmethods. The deconvolution methods yield a slightly improvedeffective energy resolution at the expense of a heavier use ofdetailed Monte Carlo predictions and/or a larger statistical errorof the individual differential flux estimates.

On the left side of Fig. 8,Aeff(E, θ) and on the leftside of Fig. 9,A′eff(E, θ) are shown, computed forθMC =0◦, 20◦, 30◦, and45◦. The zenith angle dependence of theAeff -curves can be described with the following empirical formula:

Aeff(E, θ) =1

cosξ(θ)Aeff(cosζ(θ) · E, 0◦) (5)

with ξ = 1.7 andζ = 2.4 (see Fig. 8, right side). The sameformula with the exponentsξ = 0.4 andζ = 2.2 describes thezenith angle dependence of theA′eff -curves (see Fig. 9, rightside). This formula is used in the data analysis to interpolateAeff between the simulated zenith angles.

The Monte Carlo reproduces nicely the following propertiesof γ-ray-induced showers:

– the shape of the lateral Cherenkov light distribution as afunction of the primary energy (Aharonian et al. 1998),

– the single telescope trigger probability as function of showeraxis distance and primary energy, and

– the distribution of the shower cores,

all determined with the Mkn 501γ-ray data-sample. Hence,we are confident that the Monte Carlo correctly predicts theγ-ray effective areas, except for a possible scaling factora =1.00±0.15 in the energy which derives from the accuracies withwhich the atmospheric absorption and the Cherenkov photon toADC counts conversion factor are known. Note, that the possiblescaling factora introduces an uncertainty in the absolute fluxestimates, but not in the measured differential spectral indices.

The Crab Nebula is known to be a TeV source with an ap-proximately constant TeV emission (Buckley et al. 1996). Wehave tested the full analysis chain described above and the sta-bility of the IACT system directly withγ-rays from this source.Within statistical errors the Crab observations prove that theIACT system runs stably and that the analysis based on theMonte Carlo simulations accounts correctly for the hardwarechanges performed during 1997 as well as for the IACT system’szenith angle dependence of theγ-ray acceptance (Aharonian etal. 1999 in preparation).

4. The 1997 Mkn 501 light curve

Between March 16th and October 1st, 1997, 110 h of Mkn 501data, satisfying the conditions described above, were acquired.The excess of about38, 000 photons is shown in Fig. 10 in equa-torial coordinates (hardware threshold, no cuts). Note, that thefigure shows the number of excess events as function of dec-lination and right ascension and not a likelihood contour. Themean location of the excess photons coincides with the Mkn 501location with an accuracy of 0.01◦ (Pühlhofer et al. 1997), cor-responding to an angular resolution of the IACT system of better


θ = 0o

θ = 20o

θ = 30o

θ = 45o

Energy [ TeV ]

Aef

f(θ) [

m2

]

10 3

10 4

10 5

10 6

10-1

1 10

from θ = 0o

from θ = 20o

from θ = 30o

from θ = 45o

Energy [ TeV ]

Aef

f(θ=0

o ) [

m2

]

10 3

10 4

10 5

10 6

10-1

1 10

Fig. 8. On theleft sidethe effective areas ofthe HEGRA system of 4 IACTs forγ-raydetection as functions of the primary energyare shown for the 4 different zenith anglesθ = 0◦, 20◦, 30◦, and45◦ (Monte Carlo).The right sideshows the effective area forvertically incident showersθ = 0◦ calcu-lated with the effective areas at the zenithanglesθ = 20◦, 30◦, and45◦ according toEq. 5 (hardware threshold of at least 2 trig-gered telescopes, no cuts).

θ = 0o

θ = 20o

θ = 30o

θ = 45o


Aef

f‘(θ)

[ m

2 ]

10 3

10 4

10 5

10 6

10-1

1 10

from θ = 0o

from θ = 20o

from θ = 30o

from θ = 45o


Aef

f‘(θ=

0o) [

m2

]

10 3

10 4

10 5

10 6

10-1

1 10

Fig. 9. On the left sidethe effective areasas function of thereconstructedprimary en-ergy are shown for the 4 different zenith an-gles (Monte Carlo). The same cuts as in thespectral studies have been used, i.e. the soft-ware threshold of two telescopes with asize-value above 40 and a distance of the showeraxis from the center of the telescope systemsmaller than 195 m. On theright side it isshown, how the effective area for verticallyincident showers can be computed from theeffective areas computed for the other threezenith angles using Eq. 5.

Right Ascen

sion [ hours

]

Declination [ degree ]

Ent

ries

16.855

16.898

16.941

39.5

39.75

40

40.25

200

300

400

500

600

700

Fig. 10. All events reconstructed in the 1◦ × 1◦ solid-angle regioncentered on the Mkn 501 direction. The prominentγ-ray excess canbe seen above the approximately flat background (hardware threshold,no cuts).

than 40 arc sec when limited by systematic uncertainties and notby statistics.

Fig. 11 shows the differential spectra obtained for 8 ex-emplary individual nights. For each of the four data periodsMarch/April, April/May, May/June, and June/July 1997 a nightof weak emission and a night of strong emission has been cho-sen. As can be seen, the stereoscopic IACT system, due to itshigh signal to noise ratio and due to an energy resolution of20%, permits a detailed spectral analysis on a diurnal basis. Thespectra can approximately be described by power law models,although above 5 TeV the spectra apparently steepen (see alsoAharonian et al. 1997c; Samuelson et al. 1998).

In a first analysis, we fit the data with power laws in theenergy region from 1 to 5 TeV. The lower bound of the fit re-gion is determined by the requirement of the bound being higherthan the energy threshold of the IACT system in the zenith angleinterval from 0◦ to 45◦. The upper bound of 5 TeV has been cho-sen to minimize systematic correlations between the emissionintensity and the fitted spectral index which could be causedby the combined effect of a curvature of the Mkn 501 spec-trum and the effective maximum fit range. The latter actuallyis smaller for nights of low Mkn 501 activity, since for thesenights the higher energy channels above∼ 5 TeV are frequentlynot populated and do not contribute to the fit result.

In order to minimize the correlations between the fitted fluxamplitude and the spectral index due to the fitting procedure,the modeldΦ/dE = Φ2 TeV · (E / 2 TeV) α is used, whereΦ2 TeV is the differential flux at 2 TeV andα is the spectral index.


Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]

MJD 50625 / 50626

Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]

MJD 50635 / 50636

10-14

10-13

10-12

10-11

10-10

10-9

1 10

Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]

MJD 50606 / 50607

Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]

MJD 50600 / 50601

10-14

10-13

10-12

10-11

10-10

10-9

1 10

Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]

MJD 50582 / 50583

Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]MJD 50568 / 50569

10-14

10-13

10-12

10-11

10-10

10-9

1 10

Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]

MJD 50550 / 50551

Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]

MJD 50547 / 50548

10-14

10-13

10-12

10-11

10-10

10-9

1 10

Fig. 11. The differentialγ-ray spectra of eight individual nights. For each of the four data periods March/April, April/May, May/June, andJune/July, 1997 a night of weak emission and a night of strong emission has been chosen. Statistical errors only; see text for systematic errors;the upper limit has 2σ confidence level (MJD 50550 corresponds to April 12th, 1997).

Date [ MJD-50000 ]

Φ2

TeV

[cm

-2 s

-1 T

eV-1

]

Date [ MJD-50000 ]

Spe

ctra

l Ind

ex

0

0.2

0.4

x 10-10

525 550 575 600

-3

-2

-1

0

525 550 575 600

Date [ MJD-50000 ]

Φ2

TeV

[cm

-2 s

-1 T

eV-1

]

Date [ MJD-50000 ]

Spe

ctra

l Ind

ex

0

0.2

0.4

x 10-10

625 650 675 700 725

-3

-2

-1

0

625 650 675 700 725

Fig. 12. Daily flux amplitudesΦ2 TeV anddifferential spectral indices (1-5 TeV) for the1997 Mkn 501 data. For clearness, spectralindices are shown only for the days with suf-ficient statistics, i.e. with errors on the spec-tral index smaller than 0.5. Statistical errorsonly; see text for systematic errors (MJD50550 corresponds to April 12th, 1997).

The energy 2 TeV approximately equals the median energy ofthe Mkn 501γ-rays recorded with the IACT system.

We estimate the systematic error on the flux amplitude tobe '20%. This error is dominated by the 15% uncertainty ofthe energy scale. The systematic error on the spectral indexis currently estimated to be 0.1 and derives from the MonteCarlo-dependence of the results. The systematic errors as well

as more detailed studies of the differential Mkn 501 spectra,especially in the energy range below 1 TeV and above 10 TeV,will extensively be discussed in a forthcoming paper. Note, thatall errors shown in the following plots are statistical only.

The differential fluxes at 2 TeV and the spectral indices de-termined on a daily basis are shown in Fig. 12. In Table 3 theresults are summarized. The gaps in the light curve are caused


Table 3. Results on diurnal basis. Statistical Errors only; see text forsystematic errors.

Starta ∆t b dΦ/dE (2TeV)c Spectral indexd Φ(> 1TeV)e

50523.1266 2.42 10.22 +0.96−0.88 −2.13 +0.18−0.19 35.55± 3.7450526.1791 1.35 10.01 +1.05−1.13 −2.40 +0.25−0.26 36.73± 4.1450527.2305 0.32 − − 5.96± 8.0950539.0783 0.32 7.21 +5.63−5.65 −3.48 +3.13−1.52 13.41± 10.0250540.0758 1.21 6.79 +1.33−1.28 −2.14 +0.30−0.33 24.39± 5.1950545.2038 0.56 5.51 +1.56−1.58 −2.52 +0.98−0.68 19.21± 5.4050546.0839 2.16 6.53 +0.83−0.85 −2.17 +0.26−0.27 22.21± 3.1650547.0566 2.68 3.16 +0.73−0.70 −2.10 +0.41−0.46 11.06± 2.6350548.0537 2.63 8.71 +0.91−0.83 −1.95 +0.21−0.22 32.79± 3.3150549.0512 2.88 8.89 +0.93−0.84 −2.34 +0.24−0.25 34.55± 3.8950550.0561 1.75 6.66 +1.00−1.04 −2.26 +0.34−0.36 24.07± 3.8050551.0671 1.30 31.76 +1.95−1.84 −1.87 +0.13−0.14 111.99± 7.2250552.0751 2.27 20.30 +1.04−1.18 −2.35 +0.13−0.13 73.99± 4.1650566.0047 0.16 − − 6.47± 15.7550567.0018 1.05 − − 16.14± 5.0750568.0608 0.40 − − 15.20± 7.2650569.0386 1.62 6.79 +0.94−0.94 −2.55 +0.29−0.30 25.38± 3.6550569.9936 3.17 3.49 +0.64−0.63 −1.87 +0.32−0.39 11.94± 2.7350570.9909 4.08 7.89 +0.65−0.60 −2.35 +0.19−0.19 27.88± 2.4750571.9882 4.65 16.15 +0.66−0.63 −2.16 +0.10−0.11 57.39± 2.8050572.9855 3.68 7.89 +0.65−0.68 −2.24 +0.18−0.18 27.42± 2.5650573.9829 4.84 8.29 +0.51−0.56 −2.45 +0.15−0.14 31.70± 2.2050575.0000 4.53 15.21 +0.78−0.59 −2.12 +0.11−0.10 54.08± 2.7050576.0015 2.59 30.52 +1.24−1.19 −2.28 +0.09−0.09 109.59± 4.7850576.9745 4.80 26.03 +0.79−0.77 −2.18 +0.07−0.07 92.66± 3.3450577.9720 4.00 20.71 +0.63−1.00 −2.25 +0.10−0.10 74.21± 3.3650578.9799 3.57 26.82 +0.81−1.05 −2.16 +0.08−0.08 95.76± 3.9650580.0128 2.24 21.12 +1.08−1.22 −2.43 +0.12−0.13 78.77± 4.4550582.0693 0.65 14.47 +1.67−1.88 −2.09 +0.28−0.29 51.45± 6.6450583.0979 0.79 21.33 +1.77−1.63 −2.15 +0.16−0.16 79.02± 6.1650601.0393 1.30 11.51 +1.08−1.09 −2.64 +0.26−0.24 42.92± 4.1750601.9731 2.96 15.52 +0.79−0.75 −2.47 +0.11−0.11 57.10± 2.9150603.9630 2.01 24.04 +1.23−0.94 −2.25 +0.10−0.11 87.11± 4.1650604.9625 2.60 20.30 +0.82−0.99 −2.37 +0.10−0.10 74.36± 3.6150606.0659 0.67 28.19 +2.03−2.16 −1.95 +0.17−0.17 96.24± 7.7650606.9592 2.30 34.39 +1.04−1.34 −2.38 +0.08−0.08 126.10± 4.5950610.0151 1.34 16.31 +1.18−1.25 −2.57 +0.15−0.15 60.63± 4.5250623.9119 0.98 18.38 +1.33−1.57 −2.37 +0.19−0.19 63.91± 5.4050625.9323 0.62 50.20 +3.09−2.91 −2.06 +0.13−0.13 178.07± 10.1250626.9801 0.87 44.99 +2.30−2.18 −2.19 +0.11−0.12 159.90± 8.5450628.0342 0.65 33.72 +2.43−2.27 −2.24 +0.15−0.14 123.09± 8.5150628.9089 0.95 10.53 +1.22−1.18 −2.61 +0.27−0.26 38.95± 4.4350631.9110 0.94 − − 11.83± 3.1650632.9106 0.98 5.68 +1.05−1.12 −2.24 +0.56−0.45 15.15± 3.1050633.9104 0.95 3.93 +0.91−0.93 −2.94 +0.69−0.52 17.37± 3.5450634.9107 2.03 8.37 +0.78−0.72 −2.05 +0.20−0.21 28.83± 2.7950635.9088 2.09 2.54 +0.50−0.52 −3.06 +0.50−0.42 11.19± 2.0650636.9242 0.71 3.74 +0.96−0.99 −3.28 +0.75−0.54 16.29± 4.0850637.9472 0.65 3.89 +0.95−0.95 −3.27 +0.56−0.43 19.87± 4.1050638.9759 0.89 29.62 +1.82−1.72 −2.45 +0.14−0.13 106.12± 6.6850639.9962 0.80 24.77 +1.79−1.90 −2.31 +0.17−0.16 89.15± 6.6650641.0329 0.64 19.70 +1.85−2.04 −2.25 +0.25−0.26 72.00± 7.5250642.0453 1.06 15.06 +1.58−1.69 −2.23 +0.24−0.25 52.92± 6.7550643.0700 0.48 34.39 +3.60−3.87 −2.27 +0.29−0.28 117.60± 14.8650657.9012 1.55 13.91 +1.00−1.06 −2.24 +0.17−0.18 50.27± 3.8750661.0177 0.55 − − 25.66± 6.7350662.9027 0.83 7.21 +1.33−1.42 −1.14 +0.41−0.45 23.05± 4.4250664.8955 0.82 10.95 +1.39−1.42 −2.07 +0.34−0.33 38.63± 4.8550666.9129 0.85 13.36 +1.69−1.74 −2.22 +0.26−0.28 45.21± 6.3550691.8717 1.89 9.62 +1.01−1.00 −2.15 +0.25−0.26 34.64± 3.7650693.8690 0.95 3.25 +1.26−1.24 −2.73 +0.93−0.76 13.01± 4.3650694.9192 0.67 6.53 +1.28−1.28 −1.05 +0.30−0.38 22.03± 6.4750696.8962 1.05 3.29 +1.01−1.03 −1.70 +0.51−0.62 12.50± 4.3550712.8598 0.65 6.53 +1.76−1.78 −2.37 +0.74−0.73 24.38± 7.2250713.8566 0.90 2.89 +1.37−1.38 −2.56 +1.11−0.90 9.76± 4.8750716.8668 0.50 0.51 +2.71−2.70 −1.78 +2.27−3.22 1.76± 6.4850719.8476 0.33 20.91 +3.37−3.43 −1.95 +0.31−0.32 64.65± 10.4050720.8479 0.65 30.83 +2.55−2.92 −2.30 +0.16−0.17 110.59± 11.0550722.8444 0.64 12.84 +2.07−2.11 −2.15 +0.42−0.42 48.89± 8.37

a MJDb duration of measurement in hoursc in (10−12cm−1 s−1 TeV−1)d fitted from 1 to 5 TeVe in (10−12cm−1 s−1)

Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]

Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]

Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]

Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]

Energy [ TeV ]

dΦ

/dE

[ cm

-2 s

-1 T

eV-1

]

10-13

10-12

10-11

10-10

1 10

Fig. 13. The Mkn 501 data has been divided into 5 groups accord-ing to the activity of the source as determined on a night to nightbasis. For each of the 5 groups a time averaged spectrum has beendetermined. The five groups have (from bottom to upwards)Φ2 TeV[10−12 cm−2 s−1 TeV−1

]of below 7, 7–10, 10–20, 20–30, and above

30, respectively. Statistical errors only; see text for systematic errors.

by the moon, since the IACT system is only operated duringnights without moon. The emission amplitude is dramaticallyvariable, the measured daily averages range from a fraction ofthe Crab emission to∼ 10 Crab, the average flux being 3 Crab.The largest flare was observed in June 1997 and peaked at June26th/27th.

In contrast, the spectral indices are rather constant. A con-stant model ofα = −2.25 fits all spectral indices with a chanceprobability for a largerχ2 of 11%. The largest deviations havebeen found for the nights MJD 50550/50551 where the spectralindex of−1.87 +0.13−0.14 deviates by 2.7σ from the meanvalue and for MJD 50694/50695 where the spectral index−1.05+0.30−0.38 deviates by 3.2σ from the mean value. Henceforth,although the IACT system makes it possible to determine thedaily spectral indexα with an accuracy of∆α ≤ 0.1 for 15% ofthe nights, with an accuracy of∆α ≤ 0.2 for 45% of the nights,and with an accuracy of∆α ≤ 0.35 for 75% of the nights theevidence for a change in the spectrum is marginal.

In order to study the correlation between flux intensity anddifferential spectrum, we divided the IACT system data intofive groups according to the diurnal emission intensity, i.e. aΦ2 TeV-value in units of

[10−12 cm−2 s−1 TeV−1

]of below7

(group i), 7–10 (group ii), 10–20 (group iii), 20–30 (group iv),and above 30 (group v), respectively. In Fig. 13 the differen-tial spectra determined with the data of each group are shown.Within statistical errors the shapes of the five spectra are thesame. This is exemplified in Fig. 14, where the four lower fluxdifferential spectra (group i - iv) havebeen divided by the high-est flux differential spectrum (group v). For all four cases the


Energy [ TeV ]

Flu

x R

atio

d

0

0.25

0.5

0.75

1

1 10

Energy [ TeV ]

Flu

x R

atio

c

0

0.25

0.5

0.75

1

1 10

Energy [ TeV ]

Flu

x R

atio

b

0

0.25

0.5

0.75

1

1 10

Energy [ TeV ]

Flu

x R

atio

a

0

0.25

0.5

0.75

1

1 10

Fig. 14a–d. The results of dividing the differential spectra of the four lower flux intensity groups (a–d corresponding to group i-iv) by thedifferential spectrum of the highest flux intensity group (group v). The lines show the results of constant model fits to the ratio spectra.

ratio of the differential fluxes as a function of primary energycan be described by a constant model. The largest reducedχ2-values of a constant fit is 1.21 for 9 degrees of freedom, whichcorresponds to a chance probability for larger deviation fromthe hypothesis of a constant ratio spectrum of 28%. In Table 4the power law spectral indices (1 to 5 TeV) of the five groupsare listed. Within the statistical errors the first five indices areconsistent with the mean value of−2.25.

We studied whether the TeV spectra during the rising epochsof the light curves systematically differ from the TeV spectraduring the falling epochs of the light curves. For this purpose weselected two subsets of the data, consisting of the accumulateddata where the flux increased (group vi) or decreased (groupvii) by at least 25% in comparison to the preceding night. Alsoin this case, the ratio spectrum can well be fitted with a constantmodel. The reducedχ2-value of the constant model fit is 0.72for 9 degrees of freedom, corresponding to a chance probabilityfor largerχ2-values of 69%.

In Table 4 the power law spectral indices (1 to 5 TeV) ofthese two groups are given. There is only a weak indication thatgroup vi (“rising” days) with a spectral index of−2.19±0.03might have a flatter spectrum than group vii (“falling” days)with a spectral index of−2.29±0.05.

5. Study of the shortest time scales of variability

The time scales of the Mkn 501 TeV flux variability have beenstudied in two ways. First, the time gradients of the daily fluxamplitudesΦ2 TeV have been analyzed. The analysis uses theexponential increase/decay-constantτ , as computed for eachpair of two daily flux amplitudes according to:

τ ≡ ∆ t∆ ln Φ2 TeV

, (6)

where∆ t is the time difference between the two measure-ments and∆ ln Φ2 TeV is the difference between the logarithmsof the differential fluxes at 2 TeV. This formula has been de-rived by assuming a time dependence ofΦ2 TeV according toΦ2 TeV ∝ et/τ . In the case of small changes in the flux ampli-tude∆ Φ2 TeV � Φ̄2 TeV, whereΦ̄2 TeV is the time averagedflux amplitude, the “doubling time” is commonly used to char-acterize the variability time scale. It is defined as the time in

Table 4. Fit parameters of differential spectra of 7 data groups. Sta-tistical Errors only; see text for systematic errors.

Group dΦ/dE (2TeV) Observation Spectral index[10−12/cm2 s TeV

]time [h] (1-5 TeV)

i < 7 26.3 −2.31 +0.10−0.11ii 7–10 23.6 −2.22 +0.06−0.07iii 10–20 26.7 −2.27 +0.04−0.05iv 20–30 25.0 −2.24 +0.03−0.03v > 30 9.5 −2.22 +0.04−0.04vi “rising” 34.6 −2.19 +0.03−0.03vii “falling” 27.4 −2.29 +0.05−0.05

which the flux would have increased or decreased by 100%,assuming a linear increase or decrease of the flux:

tdouble ≡ ∆ t Φ̄2 TeV∆ Φ2 TeV . (7)

For small changes in the flux amplitude the increase/decay-constantτ computed with Eq. 6 equalstdouble computed withEq. 7.

In Fig. 15 theτ -values computed for adjacent nights areshown. The most rapidτ -values are in the order of 15 h. InTable 5 theτ -values more rapid than 24 h are listed. The distri-bution of theτ -values is to first order approximation symmetricunder time reversal (see Fig. 16), i.e. the daily data does not giveobvious evidence for a different rising and falling behavior.

In a second approach a dedicated search for variability onsub-day time scales has been performed. In order to search ontime scales well below one hour, where the determination of adifferential spectrum is plagued by large statistical uncertainties,the search directly uses theγ-ray excess rates. Using only datataken under zenith angles below 30◦ and applying a cut on thedistancer of the shower axis from the center of the telescopearrayr < 200 m, the zenith angle dependence of theγ-ray rateis negligible, i.e. less than25% for γ-ray spectra with differentialspectral indices between−2.5 and−1.

In Fig. 17 the excess-rate histories computed with 10 minutetemporal bins are shown for two typical nights, i.e. May 6th/7thand May 9th/10th. Here, as well as in the analysis below, thecutsΘ < 0.13◦ andw̄sc < 1.2 have been applied. No strong


date [ MJD-50000 ]

τ [ h

]

-100

-75

-50

-25

0

25

50

75

100

550 600 650 700

Fig. 15. The increase/decay constantsτ computed for the flux ampli-tudesΦ2 TeV of adjacent nights plotted against the mean MJD of thetwo nights (MJD 50550 corresponds to April 12th, 1997).

τ [ h ]

Ent

ries

0

1

2

3

4

5

-200 -100 0 100 200

Fig. 16. The distribution of increase/decay constantsτ computed forthe flux amplitudesΦ2 TeV of adjacent nights. Onlyτ -values between−250 h and +250 h are shown.

Table 5.The most rapid increase- and decay-times.

Night 1 [ MJD ] Night 2 [ MJD ] τ [ h ]

50547.1 50548.1 23.6± 5.850550.1 50551.1 15.4± 1.650628.0 50628.9 −18.2± 2.150635.0 50636.0 −20.1± 3.650638.0 50639.0 12.2± 1.5

variability can be seen and a method is needed to decide on thestatistical significance of the observed rate variations.

For the systematic search, a method introduced in (Col-lura & Rosner 1987) has been used. It is based on theχ2-fitting technique and permits a search on multiple time scales.It provides easy and straightforward computation of the signif-icances of the detected variabilities. For each night a variabilityis searched for, using different time bin sizes, by computing theχ2-value of a constant model fit to the data, and performingan averaging procedure over the relative location of the datapoints within these binning schemes. We use time bins withdurations∆T between 10 minutes and 2.24 hours, i.e. with∆T = (2n/4 × 10 minutes) forn = 1 to 15. The lowerlimit on the bin duration is given by the requirement of an ex-

MJD 50575

UTC [ h ]

dete

ctio

n ra

te [

γ / m

in ]

0

1

2

3

4

5

1 2 3 4 5

MJD 50578

UTC [ h ]

dete

ctio

n ra

te [

γ / m

in ]

0

1

2

3

4

5

1 2 3

Fig. 17. The γ-ray detection rate of two individual nights: MJD= 50574/50575 (May 6th/7th), and 50577/50578 (May 9th/10th). A10 minutes binning has been used.

pected number of recorded events per bin>∼ 5. The upper limitis determined by the maximum duration of the Mkn 501 obser-vations per night which is in the order of 4 h. For each night thebin duration which yields the most significant variability detec-tion is determined and the chance probabilitypc for a constantflux to yield a more significant variability is computed using ananalytic approximation.

The chance probabilities, actually the−log10(pc)- values,for the 51 nights for which sufficient data with zenith anglessmaller than 30◦ is available, are shown in Fig. 18 togetherwith the distribution of large−log10(pc)-values expected in theabsence of flux variability. The−log10(pc)-values distribute asexpected in the absence of any variability, except for valuesnear 0 (chance probabilities near 1) and except for values largerthan 3 (chance probabilities smaller than 1 per mill). The de-viation at small values derives from the analytical computationof the chance probabilities, and is thus a pure artifact of themethod (see also Collura & Rosner 1987). The deviation atlarge values correspond to two nights, the night of May 8th/9th(MJD 50576/50577) and the night of June 7th/8th, 1997 (MJD50606/50607), for which sub-day variability is indicated.

In the case of the first night, the most significant variabilityhas been found with 20 minute bins; in the case of the secondnight with 67 min bins. The excess rates during the two nightsare shown in Fig. 19. In the night from May 8th to May 9th,1997, theγ−ray rate oscillated between 3γ/min and 5.4γ/minon a time scale of 1.5 hours. In the night from June 7th to June8th, 1997, theγ−ray rate continuously increased from 4.9γ/minto 7γ/min within 2.6 h. The chance probability for a more sig-nificant apparent variability at constant flux is computed to be0.8 × 10−4 for the first night and2.0 × 10−4 for the secondnight. Taking into account that 51 nights have been searched forvariability, the chance probabilities increase to 0.4% for the firstnight and to 1% for the second night. The variability detectedin these two nights corresponds to an increase/decay constantof about 3 h for the first night and 7 h for the second night.

To summarize, the study of the time gradients of the diurnalfluxes yields smallest increase/decay times of the order of 15 h.The dedicated search for flux variability within individual nightson time scales between 10 minutes and several hours yieldedweak evidence for variability on time scales of around 5 hours.


-log 10(pc)

Ent

ries

10-3

10-2

10-1

1

10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Fig. 18. The results of the search for sub-day variability. For each night,the chance probabilitypc, computed with an analytic approximation,with which a constant signal would yield a more significant variabilityas the observed one has been computed. Shown is the distribution ofthe−log10(pc)-values (histogram) together with distribution expectedfor small chance probabilities in the absence of variability (dotted line).

MJD 50577

UTC [ h ]

dete

ctio

n ra

te [

γ / m

in ]

0

2

4

6

8

1 2 3 4

MJD 50606/50607

UTC [ h ]

dete

ctio

n ra

te [

γ / m

in ]

0

2

4

6

8

-1 0 1 223

Fig. 19.Theγ-ray detection rate of the two nights: MJD = 50576/50577(May 8th/9th) and 50606/50607 (June 7th/8th). For the first night, a20 minutes binning and for the second night, a 67 minutes binning hasbeen used.

6. Correlation of the TeV emission with the X-ray emission

A correlation of X-ray and TeV fluxes would give clues regard-ing the emission mechanism. The All Sky Monitor on boardtheRossi X-Ray Timing Explorerhas been regularly observingbright X-ray sources in the energy range from 2 - 12 keVsinceJanuary 5th, 1996. It observed mainly X-ray binaries and a list ofinitially 10, and since May 1997 a list of 74 bright active galac-tic nuclei. Each object is monitored roughly 5 times a day, eachtime for 90 seconds. The detection threshold per 90 second ob-servation is 30 mCrab. The ASM data is publicly available overthe Internet.

The ASM monitors Mkn 501 since January 5th, 1996. InFig. 20 the time histories of the ASM flux and the hardnessratio counts(5-12.1 keV) /counts(1.3-3.0 keV), both computedwith bins of 1 week duration, are compared to the light curve ofthe HEGRA IACT-system. We derived the ASM count ratesrXfrom the “definitive” ASM products satisfying the requirementof a dwell duration larger than 30 s and a flux fit with a reducedχ2-value smaller than 1.25. We excluded days with poor sam-pling (less than 25% of the data), by using only the diurnal ratesvalues which have an error smaller than 0.375 counts/sec. The

binned light curves, hardness ratios, and correlation coefficients(“slow” method with error propagation) have been obtained us-ing the “ftools 4.0” package.

The count rate increases from 0.4/sec in February, 1996,slowly to 1 counts/sec in January, 1997, and then dramatically to2 counts/sec in June/July 1997. After reaching its maximum of3.1±0.4 on June 24th, 1997, the count rates returned to around1 counts/sec until April 1998. During the major flaring phasein 1997, the X-ray spectrum hardens, i.e. the hardness ratioincreases from 0.8 in January 1997 to 1.5 in July 1997 anddecreases again to 1 until April 1998.

A correlation between the X-ray activity and the TeV-activity can be recognized in the sense that the X-ray activ-ity peaked in June/July when the amplitudes of the TeV flaresreached their maximum.

In Fig. 21 the correlation between the daily differential fluxat 2 TeV,Φ2 TeV, and the count raterX is shown. Hereby, for eachdaily Φ2 TeV-value, the ASM rate has been averaged over all90 second measurements within the 24 h time interval centeredclose to 0:00 UT. One sees indications of a correlation betweenthe emission in the two energy bands. A fit to the data gives thecorrelation:

rX [counts/sec] = 0.94+0.05−0.06 + (2.7 ± 0.3)× Φ2 TeV

10−10 cm−2 s−1 TeV−1. (8)

A possible time shift∆t between the TeV- and X-ray vari-ability has been searched for by computing the discrete corre-lation function, DCF, (Edelson & Krolik 1988)

ξ (∆t) =∑i (Φ2 TeV(ti) − Φ2 TeV)(rX(ti + ∆t) − rX)√∑

i (Φ2 TeV(ti) − Φ2 TeV)2∑

i (rX(ti + ∆t) − rX)2(9)

as function of∆t. The indexi runs over all nights with TeV-measurements, theΦ2 TeV(ti) are the daily TeV flux amplitudes,and therX(ti) are the ASM count rates averaged over 24 h,centered close to 0:00 UT. In Fig. 22 the results are presented.The DCF shows a positive peak reaching from∆t = −1 (TeVvariability follows X-ray variability after 1 day) to∆t = 1(TeV variability precedes X-ray variability by one day).

The data indicates a correlation of the TeV- and X-Ray emis-sion with a time lag of one day or less. For∆t = 0, 50 pairsof TeV and X-ray data enter the calculation and give a DCFof 0.37±0.03. Even completely uncorrelated time series are ex-pected to produce non-zero values of the DCF (Edelson & Krolik1988). The probability distribution of the DCF depends on thenumber of pairs used for its calculation and on the temporal au-tocorrelation characteristics of the TeV emission and the X-rayemission. Assuming 50 statistically independent flux measure-ments in two energy bands which follow Gaussian distributionsaround their mean values, the chance probability for DCF-valuesexceeding 0.37±0.03 is 0.43%. Reducing the number of statisti-cally independent flux pairs from 50 to 15, increases this chanceprobability to 8%. The true chance probability of the correla-tion indicated in Figs. 21 and 22 will lie between these two


Fig. 20. The ASM count ratesrX (2-12 keV), the ASM hardness ratioscounts(5-12.1 keV) /counts(1.3-3.0 keV), and the dailyHEGRA differential fluxes at 2 TeV againsttime, for the time period from January 1997until February 1998.

HEGRA dΦ/dE (2 TeV) [ 10 -10 cm-2 s-1 TeV-1 ]

AS

M R

ate

[ cou

nts/

sec

]

0

1

2

3

0 0.1 0.2 0.3 0.4 0.5

Fig. 21. The correlation of the one-day ASM count ratesrX (2-12 keV)with the daily HEGRA differential fluxes at 2 TeV. Superimposed is astraight line fit to the data.

extremes. Note, that the same correlation is found in the CT1data and in the CT2 data (see Part II).

We interpret the structure of the DCF which can be recog-nized in Fig. 22 as to arise from the periodic gaps in the HEGRAobservation time, paired with the spiky structure of the Mkn 501light curve in both energy bands.

7. Discussion

The observations of Mkn 501 during its remarkable state offlaring activity in 1997 with the HEGRA IACT system allowedus to study in detail the temporal and spectral characteristicsof the source with, for gamma-ray astronomy, unprecedentedphoton statistics and precision. More than 38,000 TeVγ-rayphotons were detected during March 1997 until October 1997.

Fig. 22. The correlation coefficient of the daily HEGRA differentialfluxes at 2 TeV and the one-day ASM count ratesrX (2-12 keV) as afunction of the time shift∆t between the considered TeV and X-rayfluxes. Positive∆t-values correspond to the TeV variability precedingthe X-ray variability.

These photons enabled the localization of theγ-ray source withan accuracy of about 40 arc seconds.

The mean flux ofγ-rays averaged over the whole period ofactivity was as high as three times the flux of the Crab Neb-ula, the strongest persistent TeV source in the sky. For a sourceof this strength, even “loose” shape cuts result in an almostbackground free detection ofγ-rays: several 100γ-rays against20 background events caused by cosmic rays. This implies thestatistically significant detection of the source every few min-utes during the whole 6 months of observations and makes it


possible to study the flux variability on sub-hour time scales.Furthermore, the good precision of reconstruction of the energyof individual γ-rays with20% resolution combined with highγ-ray statistics makes it possible to measure the energy spectraof the radiation and their evolution in time on a night-by-nightbasis.

In this paper we presented the results obtained from IACTsystem data. The data of CT1 and CT2 are described in Part II.The IACT system data has not given any evidence for a cor-relation between the emission intensity at 2 TeV and the spec-tral index, determined between 1 and 5 TeV. The study of thetime gradient of the diurnal flux at 2 TeV yielded shortest in-crease/decay times of the order of 15 h. A dedicated search forshort time variability within individual nights yielded evidencefor a variability with a corresponding increase/decay time of theorder of 5 h. The data indicated a weak correlation between theTeV-flux amplitudes and the 2 to 12 keV X-ray flux, fovouringa time lag between the TeV- and the X-ray variability of one dayor less. In the following we will briefly discuss these results.

7.1. Spectral characteristics

Commonly it is believed that the study of the TeVγ-ray spectraof BL Lac objects at different epochs of their activity provideskey insights into the nature of theγ-ray production processesin the relativistic jets. Generally, in these highly dynamical ob-jects, when the flux could be changed by an order of magnitudewithin 1 day of observations, strong time-variation of the spec-tral shape of the radiation is expected as well. However, theaverage spectra of Mkn 501 in the energy range from 1 TeV to10 TeV corresponding to largely different absolute flux levels,appear to be very similar as discussed in Sect. 4 (see Fig. 13).

In the framework of Inverse Compton models this could beinterpreted as result of (1) a time-independent spectrum of accel-erated electrons, together with (2) a very fast radiative coolingof the electrons which establishes an equilibrium spectrum ofelectrons during the time required for the collection of sufficientphoton statistics for proper spectral measurements (typically afew hours or less if the absoluteγ-ray flux exceeds the flux levelof the Crab). At first glance, this contradicts the observed dra-matic shift of the synchrotron peak in the Mkn 501 spectrum by2 orders of magnitude in frequency, discovered with BeppoSAXduring the April 1997 flaring phase (Pian et al. 1998). Formallyspeaking, the position of the synchrotron peakνs is proportionalto B δj E2max, henceforth its variation could be explained by thevariation of any of the three appropriate parameters - magneticfield B, Doppler factorδj, and the maximum energy of accel-erated electronsEmax. However as it was argued by Pian et al.(1998), the shift of the synchrotron peak during these specificobservations could hardly be attributed to the variation of theDoppler factor and/or magnetic field, but is caused rather by anincrease (by a factor of 10 or so) of the maximum energy ofaccelerated electrons. On these grounds we may expect a sig-nificant hardening of the TeV spectrum as well. However, dueto the Klein-Nishina cross-section, the increase ofEmax in theIC spectrum is expected to be substantially less pronounced.

It should be emphasized, that during the whole period of1997 the source was in a “high” state with a TeV flux≥ 1 Crab.It will be of utmost interest to use the IACT system to study theMkn 501 spectrum in a really low state, characterized by a TeVflux well below one Crab unit.

The second interesting feature of theflux-selectedspec-tra averaged over almost 6 months of observations (Fig. 13)is their smooth shape with power-law photon index of aboutα = −2.25 (dNγ / dE ∝ Eα) at energies between 1 TeVand several TeV,but with a gradual steepening at higher en-ergies. We would like to make a comment concerning the im-plications of the steepening of the spectrum for the estimatesof the diffuse extragalactic background radiation (DEBRA). Ifone interprets the lack of a cutoff in theγ-ray spectra of bothMrk 421 (Zweerink et al. 1997) and Mrk 501 (Aharonian et al.1997a) up to 10 TeV as an indication for the absence of ab-sorption in the DEBRA, an upper limit on the energy density ofDEBRA, u� = �2n(�) ' 10−3 eV/cm3 at λ ∼ 10 µm can bederived from the condition of the transparency of the intergalac-tic medium for 10 TeVγ-rays (Weekes et al. 1997). The recentstudies of the problem, based on different assumptions aboutthe spectral shape of the DEBRA, give similar results (Stanev&Franceschini 1997; Funk et al. 1998; Biller et al. 1998; Stecker& De Jager 1998). However, as it was emphasized by Weekes etal. (1997), the lack of an apparent cutoff inγ-ray spectra does notautomatically imply negligible intergalactic absorption. Indeed,some infrared background models, like thecold+hot dark mat-ter model of Macminn & Primack (1996), predict amodulationrather thancutoff in the spectra of Mrk 421 and Mrk 501. Theabsorption results in a steepening of theγ-ray spectrum, but apower-law form could be conserved, at least up to 10 TeV. Also,the revised estimate of the effect of the intergalactic absorptionby Stecker and De Jager (1998) based on an empirically derivedflux of the DEBRA (Malkan & Stecker 1998), does not producea cutoff until'15 TeV.

The general tendency of gradual steepening of the spectraof Mrk 501 obtained in this paper could be formally interpretedas a result of absorption in the intergalactic background radia-tion, which would allow to estimate the density of the DEBRA.Obviously this number could not be far from the above upperlimit estimate. However, care should be taken in the interpreta-tion of these results, since the intrinsic spectra of the source arenot properly understood and probably several effects combineto steepen the TeV spectra of BL Lac objects.

7.2. Temporal characteristics

Our observations revealed flux variability on time scales∆tobsof between 5 and 15 h. Due to causality and light travel timearguments the size of theγ-ray production region cannot exceed

R = ∆tobsc δj ' 3 · 1015 ∆t10 δj cm, (10)with ∆t10 = ∆tobs/10 h and whereδj is the Doppler fac-tor of the jet. The condition that the source is optically thinwith respect to photon-photon pair production,τγγ ≤ 1, re-sults in alower limit on the Doppler factor of the jetδj, assum-


ing that the low-frequency photons are produced co-spatially inthe quasi-isotropically emitting cloud (blob):δj,min ' 6F−10-(�)1/6 ∆t−1/610 (see e.g. Celotti et al. 1998), whereF−10(�) =Fobs(�)/ 10−10 erg/cm2s is the observed energy flux ofthe optical and the infrared photons at the observed energy� = 2m2e c

4 δ2j,min/Eγ ' 5 (δj/10)2 (Eγ/10 TeV)−1 eV withwidth ∆� ' �; Eγ is the energy of detectedγ-ray photon. Thecharacteristic fluxes of the optical and the infrared radiationfrom Mkn 501 of about0.5 · 10−10 erg/cm2s (see e.g. Pian etal. 1998), and the time variability of the 1-10 TeVγ-rays within5 to 15 h obtained above, require a minimum Doppler factor inthe order of 5. Due to the weak dependence ofδj,min on Fobsand∆tobs, we can not expect a further significant strengtheningof this lower limit onδj.

On the other hand, if the TeVγ-rays are produced by rel-ativistic electrons which up-scatter their low-frequency syn-chrotron radiation (the so-called Synchrotron Self Compton(SSC) scenario, see e.g. Ghisellini et al. 1996; Bloom &Marscher 1996; Inoue & Takahara 1996; Mastichiadis & Kirk1997; Bednarek & Protheroe 1997), the observed time variabil-ity of TeV γ-rays sets also a strongupper limiton the Dopplerfactor, if one requires that the synchrotron and Compton coolingtime of the electrons is smaller than the flux variability time. In-deed, the energy density of the low-frequency target photons inthis model is estimated aswr ' (d/R)2Fobsc−1δ−4j , whered isthe distance to the source (' 170 Mpc for H0 = 60 km/s Mpc),R is the size of theγ-ray production region which is lim-ited by Eq. 10, but most probably cannot be significantly lessthanR15 = R/1015 cm. Assuming that the synchrotron andCompton cooling time of electronst = [(4/3)σT(wr +B2/8π)Ee/m2ec

4]−1 ' 15 ((wr + B2/8π)/1 erg/cm3)−1(Ee/1 TeV)−1 s, whereB is the magnetic field in the jet, doesnot exceed the flux variability time (in the frame of the jet)∆t′ = ∆tobs δj, we find

δj,max ' 75 F 1/310 R−2/3min,15 ∆t1/310(

Ee1 TeV

)1/3(FX

FTeV

)1/3(11)

whereFX/FTeV is the ratio of the energy flux emitted in the X-ray band and in the TeV band. For characteristic values ofF10 '0.5, Rmin,15 ' 3, ∆t10 ' 1, Ee ' 1 TeV, andFX/FTeV ' 5(Pian et al. 1998) one obtainsδj,max ' 50.

In their different modifications, the inverse Compton (IC)models of TeV radiation of BL Lac objects predict the correla-tion between the X-ray- and TeV-regimes which is indicated inFigs. 21 and 22. Albeit a correlation X/TeV is a strong argumentin favor of the commonelectronicorigin of the parent particleswhich produce synchrotron X-rays and ICγ-rays, the fact of thecorrelation alone does not decide definitively between the elec-tronic and hadronic nature of the primary (accelerated) particles.For example inProton Blazartype models (Mannheim 1993),the bulk of the nonthermal emission is produced at later stagesof the proton-induced-cascade through the same synchrotronand IC radiation of the secondary (cascade) electrons.

In fact, the short time variability of the keV/TeV-radiationstrongly argues in favor of electronic models. Whereas the fastradiative (synchrotron and IC) cooling time of the electrons in

the jet readily match the observed time-variability on a timescale of some hours, the inelastic hadron interactions, both withambient gas or photon fields are rather slow processes and onlybecome effective at very high target gas densities and/or photondensities, exceeding significantly the typical values characteriz-ing theγ-ray emitting jets in BL Lac objects (Schlickeiser 1996;Sikora 1997). Nevertheless, presently the hadronic models can-not be ruled out unambiguously on the basis of arguments con-cerning the time variability of the TeV-flux. The rapid variabilitycan be explained by geometrical effects, e.g., by anisotropies inthe comoving frame of the jet (Salvati et al. 1998), or in modelswhere the flares occur due to fast moving targets (gas clouds)which cross the beam of relativistic particles (Dar & Laor 1997).

Acknowledgements.We thank the Instituto de Astrofı́sica de Canarias(IAC) for supplying excellent working conditions at La Palma. Wegratefully acknowledge the work of the technical support staff of Hei-delberg, Kiel, Munich and Yerevan. HEGRA is supported by the BMBF(Germany) and CYCIT (Spain). The correlation analysis of the TeVflux and the RXTE ASM X-ray flux has used data obtained throughthe High Energy Astrophysics Science Archive Research Center On-line Service, provided by the NASA/Goddard Space Flight Center.

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ASTRONOMY AND The temporal characteristics of the TeV...

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