3 X-ray spectra in the rest frame of the volumes

The computation of the continuum spectrum and the emission lines of an optically thin plasma takes into account free-free, free-bound and two-photon processes (Mewe et al. 1985; Kotani et al. 1996; BK00). Cosmic abundances given by Allen (1973) are used for a plasma in equilibrium at the local temperature.

3.1 Luminosities of the fast flow ( $\mathsfsl{T = 10^{6.2}{-}10^9}$K)

Considering the size, density and temperature of each volume, the luminosities ( ${\rm erg\,s^{-1} (0.1\,keV)^{-1}}$) of the jet-tori have been calculated in the energy range 0.2-10.1keV (bin size 0.1keV). Examples are shown for four temperatures in Fig. 2 (see also Table 1). With the increase of the temperature the luminosity range is compressed, therefore those spectra are flatter and the strong cutoff seen for lower temperatures disappears. The luminosity of hot gas volume elements ( $T \simeq 10^9$K), located above the injection point, is higher (factor 100) than the one of the cooler, but faster volume elements. Note that the luminosities shown in Fig. 2 are calculated for $\dot{M}_{\rm j} = 10^{-10}\,{M}_{\odot}\,{\rm yr}^{-1}$. This quantity is hardly known from observations and, in turn, the calculated luminosities may constrain its value. A mass flow rate 100 times higher increases the luminosity by a factor of 10⁴, for the same magnetic field geometry.

For temperatures T = 10⁶-10⁹K many emission lines are present in the energy range 0.2-10.1keV (Mewe et al. 1985). The 0.5-0.9keV band contains O, N, Fe, Ne, S, Ca lines whereas lines of Ne, Fe, Mg, Ni, Si, S, Ar, Ca are found between 1.0-4.0keV. From 6.6-7.0keV mostly FeXXV (He-like) and FeXXVI (H-like) emission lines are present (BK00). For fully ionized plasma of $T \ge 10^9$K the bremsstrahlung continuum emission is dominant.

The total rest-frame spectrum (neglecting the velocity of the volumes) of a conical sheet of the jet is the integrated luminosity of the single volumes along the field, taking into account also the number of volumes along the jet-tori (Fig. 3c). The emission lines at 6.6 and 6.9keV can be identified as $K\alpha$ lines from He-like and H-like iron, while the one at 8.2keV could be the $K\beta$ from the He-like iron.

3.2 The hot flow close to the disk ( $\mathsfsl{T \geq 10^9}$K)

The thermal continuum of an optically thin fully ionized plasma follows from the formula of bremsstrahlung emission (Rybicki & Lightman 1979),

$$\varepsilon_\nu \equiv \frac{{\rm d}W}{{\rm d}V{\rm d}t~{\rm ... ...8} Z^2 n_{\rm e} n_{\rm i} T^{-1/2}{\rm e}^{-h\nu/kT} \bar{g},$$ (1)

(in ${\rm erg\,s^{-1}\,cm^{-3}\,Hz^{-1}}$), with the velocity averaged Gaunt factor $\bar{g}(T, \nu)$, the atomic number Z, the electron and ion number densities $n_{\rm e}$ and $n_{\rm i}$, the Planck constant h and the Boltzmann constant k. Considering the calculated volume parameters for temperatures below 10⁹K, we obtain a bremsstrahlung luminosity $L_{\rm br}$comparable to the results in Fig. 2 as expected, in fact, since bremsstrahlung is included in that calculation. Still considering $\dot{M}_{\rm j} = 10^{-10}\,{M}_{\odot}\,{\rm yr}^{-1}$, for $T \simeq 10^{10}$K we obtain $L_{\rm br} \approx 10^{25}\,{\rm erg\,s^{-1}(0.1\,keV)^{-1}}$, for $T \simeq 10^{11}$K we obtain $L_{\rm br} \approx 10^{27}\,{\rm erg\,s^{-1}(0.1\,keV)^{-1}}$, and when $T \simeq 10^{12}$K the luminosity is $L_{\rm br} \approx 10^{30}\,{\rm erg\,s^{-1}(0.1\,keV)^{-1}}$. Therefore, we expect an increase of the X-ray luminosity due to the bremsstrahlung contribution of the hottest regions in the jet-disk system, if the optically thin condition is still satisfied there.

Figure 3: Doppler shifted and boosted spectra. Spectra for a volume element with T = 107K a) and T = 109K b) for different jet inclinations. Doppler factor D-40 (triple dotted-dashed line, top), D-20 (dotted-dashed line, top), rest-frame (solid line), $D_{\parallel }$ (dotted line), D+20 (dotted-dashed line, bottom), D+40 (triple dotted-dashed line, bottom). c) Comparison of the total shifted/boosted spectrum $D_{\parallel }$ (thick dotted line) of a conical sheet with the rest-frame spectrum (thin solid line). d) Inclined jet, comparison of the boosted spectra D-20 (thick line top) and D+20 (thick line bottom) with the total spectrum (thick line middle) and the rest-frame spectrum (thin line middle).