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Astron. Astrophys. 324, 395-409 (1997)

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8. Model fits to Mrk 421

We can now use our code and the results summarized in the last section to reproduce the broadband spectrum of the first extragalactic object significantly detected in TeV [FORMULA] -rays, Mrk 421. Mrk 421 is a BL Lac object at [FORMULA] which exhibited a prominent TeV flare in May 1994 (Kerrick et al., 1995). In this flaring phase, a flux of [FORMULA] photons cm-2 s-1 above 250 GeV has been found. We assume [FORMULA], account for absorption by the intergalactic infrared background radiation (IIBR) using the model fits by (Stecker & de Jager 1996) which do not differ very much from each other for photons of energies [FORMULA] TeV and neglect absorption by accretion disk radiation scattered back by surrounding clouds (Böttcher & Dermer 1995).

Our first example, shown in Figs. 7 and 8, demonstrates that jet parameters are possible where the [FORMULA] -ray emission from Mrk 421 in its quiescent state can emerge from a small region where light-travel time arguments allow for even more rapid flickering in [FORMULA] -rays than observed recently by Gaidos et al. (1996). As illustrated in Fig. 11, the synchrotron emission from this emission region is far below the observed radio to optical flux from Mrk 421.

A successful fit to the broadband spectrum of Mrk 421 in its quiescent state can be achieved with a very low density, as chosen for our second example, illustrated in Figs. 9 and 10. This is shown in Fig. 12.

[FIGURE] Fig. 9. Instantaneous [FORMULA] -ray spectra from the blob of simulation 2. Parameters: [FORMULA], [FORMULA], [FORMULA], [FORMULA] cm, [FORMULA] cm-3, [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA] pc, [FORMULA], [FORMULA]. Total emission: solid; IC scattering of accretion disk radiation: dashed; SSC radiation: dot-dashed; synchrotron radiation: long dashed. (all quantities in the observer's frame)
[FIGURE] Fig. 10. Time-integrated [FORMULA] -ray spectrum from the blob illustrated in Fig. 9 (total [FORMULA] -ray spectrum: solid; external IC: dashed; SSC: dot-dashed; synchrotron: long dashed)
[FIGURE] Fig. 11. Comparison of the time-averaged photon flux from simulation 1 (Figs. 7, 8) to the broadband spectrum of Mrk 421 in its quiescent state, indicated by squares (data from Macomb et al. [1996])
[FIGURE] Fig. 12. Comparison of the time-averaged photon flux from simulation 2 (Figs. 9, 10) to the broadband spectrum of Mrk 421 in its quiescent state

The flaring state of Mrk 421 can result from an increase of the maximum Lorentz factors of the pairs which could be related to some increase of energy input in hydromagnetic turbulences accelerating the primary particles which can plausibly also imply an increase in the magnetic field. Increasing the cut-off energies to [FORMULA], [FORMULA] and the magnetic field to [FORMULA] G while the other parameters remain the same is in our model calculation for the low state (see caption of Fig. 9) yields an acceptable fit to the flaring state of Mrk 421, as shown in Fig. 13. Here, we integrated over an observing time of [FORMULA] s, after which the the flux from this blob is far below the quiescent one.

[FIGURE] Fig. 13. Model fit to the broadband spectrum of Mrk 421 in its high state (stars); [FORMULA], [FORMULA], [FORMULA] G; other parameters as given in the caption of Fig. 9

Petry et al. (1996) found a spectral index of the differential spectrum of Mrk 421 above 1 TeV of [FORMULA] which translates to a spectral index of the integral spectrum of [FORMULA]. In Fig. 14 we demonstrate that our model fit to the low state of Mrk 421 is in agreement with this measurement. Above 1 TeV, absorption by the IIBR becomes important. In order to account for this, we used the model fits by Stecker & de Jager (1996). The figure demonstrates that both fits result in very similar absorbed spectra. The HEGRA flux value is obtained in averaging over long observing times compared to the variability of Mrk 421. It lies between the Whipple data points for quiescent and flaring state (included in Figs. 11 - 13) and is well in agreement with a duty cycle of 5 % between high and low TeV state (Petry, priv. comm.).

[FIGURE] Fig. 14. Integral photon flux resulting from simulation 2. The dotted and dot-dashed lines represent a power-law integral spectrum with spectral index 2.6 and 3.6, respectively. The solid and dashed lines are calculated describing absorption by the intergalactic infrared background radiation by Stecker & de Jager's (1996) model fit 1 and 2, respectively

It is remarkable that the broadband fits shown here imply an injection height of [FORMULA] pc which is far outside the [FORMULA] -ray photosphere for TeV photons. A high low-energy cutoff in the electron spectrum is required in order not to overproduce the X-ray flux. This, in turn, implies a very low particle density in order to recover the observed relative luminosity of the synchrotron to the SSC component.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998