All Figures

$\begin{figure} \par\includegraphics[width=6cm,clip]{3644fg1.ps}\end{figure}$ Figure 1: Synchrotron spectra emitted by an electron population with log-parabolic (dashed lines) and power-law log-parabolic energy distributions (Eq. (11)) (solid lines), computed for r values in the interval 0.50-1.20. Spectra were shifted on the vertical scale to avoidconfusion.
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In the text

$\begin{figure} \par\includegraphics[width=5.7cm,clip]{3644fg2.ps}\end{figure}$ Figure 2: The relation between the peak frequencies of the synchrotron SED and those of the energy spectrum of the emitting electrons computed using the SFD (Eq. (17)) for the LP and LPPL cases (see text). The abscissa is the inverse of the electron spectrum curvature to show the linear trend expected from Eq. (18). The dashed line is the best fit computed for 1/r >0.33. Note the small deviations of LPPL points from the best fit line at low values of 1/r.
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In the text

$\begin{figure} \par\includegraphics[width=5.75cm,clip]{3644fg3.ps}\end{figure}$ Figure 3: The relation between the log-parabolic curvature parameters of the electron energy distribution r and those of the synchrotron radiation computed applying the $\delta$ approximation (crosses) and the SFD. The two LP point sets correspond to log-parabolic electron spectra with b evaluated by a best fit around the SED peak (filled circle) and on the high frequency branch (diamonds). LPPL points (open squares) correspond to a combined log-parabolic power law distribution. Dashed lines are linear best fits used for the calculation of the b/r ratio.
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In the text

$\begin{figure} \par\includegraphics[width=6.9cm,clip]{3644fg4.ps}\end{figure}$ Figure 4: Time evolution of the SR spectrum ( upper panel) and of the corresponding spectrum of electrons, multiplied by the square of the Lorentz, under SR losses. The injection spectrum was a log-parabola with s=1.2 and r=0.7, corresponding to a peak energy of ${\sim } 10^5$ . Spectra are plotted for equal time steps of $\sim$ 0.4 cooling times. Note the decrease in the peak energy and the deviation from a log-parabola due to difference in cooling time with $\gamma$ .
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{3644fg5.ps}\end{figure}$ Figure 5: Time evolution of the log-parabolic curvature parameters r of the electron spectrum ( upper line) and b of the SR SED ( lower line) computed by means of a best fit around the peak. Solid lines are linear best fits to the computed values.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{3644fg6.ps}\end{figure}$ Figure 6: The relation between the peak frequency and the curvature parameter b of the SR spectra plotted in the upper panel of Fig. 4. The dashed line is the best fit to the computed values.
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In the text

$\begin{figure} \par\includegraphics[width=7.1cm,clip]{3644fg7.ps}\end{figure}$ Figure 7: The SR and SSC spectral energy distributions emitted by an electron population with power-law log-parabolic distributions (Eq. (11)), computed for r values in the interval 0.50-1.20. Upper panel: spectra for $\gamma _0=10^3$ ; lower panel: spectra for $\gamma _0=2\times 10^4$ .
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In the text

$\begin{figure} \par\includegraphics[width=5.9cm,clip]{3644fg8.ps}\end{figure}$ Figure 8: Dependence of the peak frequencies upon the particle characteristic energies in the SED of a single zone SSC model. Upper panel: frequency of SSC peak vs. electron Lorentz factors of the peaks for r values in the interval 0.50-1.90, the three curves correspond to $\gamma _0=10^3$ (filled circles), $5\times 10^3$ (open cicrcles), 10⁴ (crosses). Lower panel: ratio between the peak frequencies of IC and SR components for the same values of the spectral parameters.
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In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{3644fg9.ps}\end{figure}$ Figure 9: The curvature parameter b of the IC spectrum for a single zone SSC model plotted against the electron spectral curvature r. Dashed-dotted lines are the curvature parameters for the electrons and solid lines for SR component. Dashed lines correspond to IC curvatures evaluated in three adjacent frequency intervals with an amplitude of about a decade selected starting from $\nu _{\rm pC}$ : lowest lines correspond to the intervals closest to the peaks and the highest ones to those at the highest frequencies. The upper panel shows b values computed for $\gamma _0=10^3$ and lower panel those for $\gamma _0=2\times 10^4$ . Note that when the largest contribution to IC emission is from Thomson scatterings ( upper panel), curvatures are closer to those of SR, while in the Klein-Nishina regime ( lower panel) b values result very close to r.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{3644fg10.ps} \end{figure}$ Figure 10: Two spectral energy distributions of Mkn 501 during the low and high states observed on 7 and 16 April 1997, respectively. X-ray points are from Paper II, TeV points are simultaneous CAT data (Djannati-Atai et al. 1999) and soolid lines are the spectra computed in a 1-zone SSC model for the SR and IC components. In the upper panel IC, spectra have been absorbed (dashed lines) by interaction with infrared EBL photons according to the LLL model by Dwek & Krennich (2005). In the lower panel EBL absorption was neglected.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{3644fg11.ps} \end{figure}$ Figure 11: Two spectral energy distributions of Mkn 501 during the high states observed on 7, 11 April 1997 ( upper panel) and 7, 16 April 1997 ( lower panel). X-ray points are from Paper II, and TeV points are simultaneous CAT data (Djannati-Atai et al. 1999). Thin solid lines are the spectra computed in a 2-zone SSC model for the SR and IC components, dashed lines are the spectra of the high-energy flaring component, and the thick solid line is that of a slowly evolving component.
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{3644fg1.ps}\end{figure}$	Figure 1: Synchrotron spectra emitted by an electron population with log-parabolic (dashed lines) and power-law log-parabolic energy distributions (Eq. (11)) (solid lines), computed for r values in the interval 0.50-1.20. Spectra were shifted on the vertical scale to avoidconfusion.
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$\begin{figure} \par\includegraphics[width=7.2cm,clip]{3644fg5.ps}\end{figure}$	Figure 5: Time evolution of the log-parabolic curvature parameters r of the electron spectrum ( upper line) and b of the SR SED ( lower line) computed by means of a best fit around the peak. Solid lines are linear best fits to the computed values.
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{3644fg6.ps}\end{figure}$	Figure 6: The relation between the peak frequency and the curvature parameter b of the SR spectra plotted in the upper panel of Fig. 4. The dashed line is the best fit to the computed values.
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$\begin{figure} \par\includegraphics[width=7.1cm,clip]{3644fg7.ps}\end{figure}$	Figure 7: The SR and SSC spectral energy distributions emitted by an electron population with power-law log-parabolic distributions (Eq. (11)), computed for r values in the interval 0.50-1.20. Upper panel: spectra for $\gamma _0=10^3$ ; lower panel: spectra for $\gamma _0=2\times 10^4$ .
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