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Astron. Astrophys. 342, 69-86 (1999)

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7. Discussion

The observations of Mkn 501 during its remarkable state of flaring activity in 1997 with the HEGRA IACT system allowed us to study in detail the temporal and spectral characteristics of the source with, for gamma-ray astronomy, unprecedented photon statistics and precision. More than 38,000 TeV [FORMULA]-ray photons were detected during March 1997 until October 1997. These photons enabled the localization of the [FORMULA]-ray source with an accuracy of about 40 arc seconds.

The mean flux of [FORMULA]-rays averaged over the whole period of activity was as high as three times the flux of the Crab Nebula, the strongest persistent TeV source in the sky. For a source of this strength, even "loose" shape cuts result in an almost background free detection of [FORMULA]-rays: several 100 [FORMULA]-rays against 20 background events caused by cosmic rays. This implies the statistically significant detection of the source every few minutes 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 energy of individual [FORMULA]-rays with [FORMULA] resolution combined with high [FORMULA]-ray statistics makes it possible to measure the energy spectra of the radiation and their evolution in time on a night-by-night basis.

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

7.1. Spectral characteristics

Commonly it is believed that the study of the TeV [FORMULA]-ray spectra of BL Lac objects at different epochs of their activity provides key insights into the nature of the [FORMULA]-ray production processes in the relativistic jets. Generally, in these highly dynamical objects, when the flux could be changed by an order of magnitude within 1 day of observations, strong time-variation of the spectral shape of the radiation is expected as well. However, the average spectra of Mkn 501 in the energy range from 1 TeV to 10 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 be interpreted as result of (1) a time-independent spectrum of accelerated electrons, together with (2) a very fast radiative cooling of the electrons which establishes an equilibrium spectrum of electrons during the time required for the collection of sufficient photon statistics for proper spectral measurements (typically a few hours or less if the absolute [FORMULA]-ray flux exceeds the flux level of the Crab). At first glance, this contradicts the observed dramatic shift of the synchrotron peak in the Mkn 501 spectrum by 2 orders of magnitude in frequency, discovered with BeppoSAX during the April 1997 flaring phase (Pian et al. 1998). Formally speaking, the position of the synchrotron peak [FORMULA] is proportional to [FORMULA], henceforth its variation could be explained by the variation of any of the three appropriate parameters - magnetic field B, Doppler factor [FORMULA], and the maximum energy of accelerated electrons [FORMULA]. However as it was argued by Pian et al. (1998), the shift of the synchrotron peak during these specific observations could hardly be attributed to the variation of the Doppler factor and/or magnetic field, but is caused rather by an increase (by a factor of 10 or so) of the maximum energy of accelerated electrons. On these grounds we may expect a significant hardening of the TeV spectrum as well. However, due to the Klein-Nishina cross-section, the increase of [FORMULA] in the IC spectrum is expected to be substantially less pronounced.

It should be emphasized, that during the whole period of 1997 the source was in a "high" state with a TeV flux [FORMULA]. It will be of utmost interest to use the IACT system to study the Mkn 501 spectrum in a really low state, characterized by a TeV flux well below one Crab unit.

The second interesting feature of the flux-selected spectra averaged over almost 6 months of observations (Fig. 13) is their smooth shape with power-law photon index of about [FORMULA]2.25 ([FORMULA]) at energies between 1 TeV and several TeV, but with a gradual steepening at higher energies. We would like to make a comment concerning the implications of the steepening of the spectrum for the estimates of the diffuse extragalactic background radiation (DEBRA). If one interprets the lack of a cutoff in the [FORMULA]-ray spectra of both Mrk 421 (Zweerink et al. 1997) and Mrk 501 (Aharonian et al. 1997a) up to 10 TeV as an indication for the absence of absorption in the DEBRA, an upper limit on the energy density of DEBRA, [FORMULA] at [FORMULA] can be derived from the condition of the transparency of the intergalactic medium for 10 TeV [FORMULA]-rays (Weekes et al. 1997). The recent studies of the problem, based on different assumptions about the 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 et al. (1997), the lack of an apparent cutoff in [FORMULA]-ray spectra does not automatically imply negligible intergalactic absorption. Indeed, some infrared background models, like the cold+hot dark matter model of Macminn & Primack (1996), predict a modulation rather than cutoff in the spectra of Mrk 421 and Mrk 501. The absorption results in a steepening of the [FORMULA]-ray spectrum, but a power-law form could be conserved, at least up to 10 TeV. Also, the revised estimate of the effect of the intergalactic absorption by Stecker and De Jager (1998) based on an empirically derived flux of the DEBRA (Malkan & Stecker 1998), does not produce a cutoff until [FORMULA]15 TeV.

The general tendency of gradual steepening of the spectra of Mrk 501 obtained in this paper could be formally interpreted as a result of absorption in the intergalactic background radiation, which would allow to estimate the density of the DEBRA. Obviously this number could not be far from the above upper limit estimate. However, care should be taken in the interpretation of these results, since the intrinsic spectra of the source are not properly understood and probably several effects combine to steepen the TeV spectra of BL Lac objects.

7.2. Temporal characteristics

Our observations revealed flux variability on time scales [FORMULA] of between 5 and 15 h. Due to causality and light travel time arguments the size of the [FORMULA]-ray production region cannot exceed


with [FORMULA]/10 h and where [FORMULA] is the Doppler factor of the jet. The condition that the source is optically thin with respect to photon-photon pair production, [FORMULA], results in a lower limit on the Doppler factor of the jet [FORMULA], assuming that the low-frequency photons are produced co-spatially in the quasi-isotropically emitting cloud (blob): [FORMULA] (see e.g. Celotti et al. 1998), where [FORMULA] [FORMULA] is the observed energy flux of the optical and the infrared photons at the observed energy [FORMULA] with width [FORMULA]; [FORMULA] is the energy of detected [FORMULA]-ray photon. The characteristic fluxes of the optical and the infrared radiation from Mkn 501 of about [FORMULA] (see e.g. Pian et al. 1998), and the time variability of the 1-10 TeV [FORMULA]-rays within 5 to 15 h obtained above, require a minimum Doppler factor in the order of 5. Due to the weak dependence of [FORMULA] on [FORMULA] and [FORMULA], we can not expect a further significant strengthening of this lower limit on [FORMULA].

On the other hand, if the TeV [FORMULA]-rays are produced by relativistic electrons which up-scatter their low-frequency synchrotron radiation (the so-called Synchrotron Self Compton (SSC) scenario, see e.g. Ghisellini et al. 1996; Bloom & Marscher 1996; Inoue & Takahara 1996; Mastichiadis & Kirk 1997; Bednarek & Protheroe 1997), the observed time variability of TeV [FORMULA]-rays sets also a strong upper limit on the Doppler factor, if one requires that the synchrotron and Compton cooling time of the electrons is smaller than the flux variability time. Indeed, the energy density of the low-frequency target photons in this model is estimated as [FORMULA], where d is the distance to the source ([FORMULA] for [FORMULA]), R is the size of the [FORMULA]-ray production region which is limited by Eq. 10, but most probably cannot be significantly less than [FORMULA]. Assuming that the synchrotron and Compton cooling time of electrons [FORMULA] [FORMULA][FORMULA], where B is the magnetic field in the jet, does not exceed the flux variability time (in the frame of the jet) [FORMULA], we find


where [FORMULA] is the ratio of the energy flux emitted in the X-ray band and in the TeV band. For characteristic values of [FORMULA], [FORMULA], [FORMULA], [FORMULA] TeV, and [FORMULA] (Pian et al. 1998) one obtains [FORMULA].

In their different modifications, the inverse Compton (IC) models of TeV radiation of BL Lac objects predict the correlation between the X-ray- and TeV-regimes which is indicated in Figs. 21 and 22. Albeit a correlation X/TeV is a strong argument in favor of the common electronic origin of the parent particles which produce synchrotron X-rays and IC [FORMULA]-rays, the fact of the correlation alone does not decide definitively between the electronic and hadronic nature of the primary (accelerated) particles. For example in Proton Blazar type models (Mannheim 1993), the bulk of the nonthermal emission is produced at later stages of the proton-induced-cascade through the same synchrotron and IC radiation of the secondary (cascade) electrons.

In fact, the short time variability of the keV/TeV-radiation strongly argues in favor of electronic models. Whereas the fast radiative (synchrotron and IC) cooling time of the electrons in the jet readily match the observed time-variability on a time scale of some hours, the inelastic hadron interactions, both with ambient gas or photon fields are rather slow processes and only become effective at very high target gas densities and/or photon densities, exceeding significantly the typical values characterizing the [FORMULA]-ray emitting jets in BL Lac objects (Schlickeiser 1996; Sikora 1997). Nevertheless, presently the hadronic models cannot be ruled out unambiguously on the basis of arguments concerning the time variability of the TeV-flux. The rapid variability can be explained by geometrical effects, e.g., by anisotropies in the comoving frame of the jet (Salvati et al. 1998), or in models where the flares occur due to fast moving targets (gas clouds) which cross the beam of relativistic particles (Dar & Laor 1997).

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Online publication: December 22, 1998