5 Discussion

5.1 X-ray luminosities

We find a total rest-frame X-ray luminosity of the jet $L_{\rm X} = 3.8 \times 10^{31}$ $(\dot{M}_{\rm j}/10^{-8}\,{M}_{\odot}\,{\rm yr}^{-1})\,{\rm erg\,s^{-1}}$. The total kinematic luminosity for this jet mass flow rate is $L_{\rm k} = \gamma \dot{M}_{\rm j} c^2 \approx 10^{39}\,{\rm erg\,s^{-1}} \gg L_{\rm X}$. This proves a posteriori that the assumption of a polytropic gas law used to obtain the MHD wind solution is consistent with the amount of radiation losses.

Considering the Doppler factor $D_{\parallel }$, the total X-ray luminosity of the jet is $L_{\rm X} = 6.4 \times 10^{32}~(\dot{M}_{\rm j}/10^{-8}\,{M}_{\odot}\,{\rm yr}^{-1})\,{\rm erg\,s^{-1}}$. In the case of an inclined jet axis (D_-20, D₊₂₀) we have $L_{\rm X} = 1.4 \times 10^{33}~(\dot{M}_{\rm j}/10^{-8}\,{M}_{\odot}\,{\rm yr}^{-1})\,{\rm erg\,s^{-1}}$. For D_-40 and D₊₄₀ we obtain $L_{\rm X} = 1.1 \times 10^{33}~(\dot{M}_{\rm j}/10^{-8}\,{M}_{\odot}\,{\rm yr}^{-1})\,{\rm erg\,s^{-1}}$. These values can be increased by the contribution of bremsstrahlung from the high temperature ( $T \geq 10^9$K) volumes till about $L_{\rm X} \approx 10^{34}\,{\rm erg\,s^{-1}}$.

In comparison, the X-ray luminosity of GRS1915+105 is $10^{38}\,{\rm erg\,s^{-1}}$ in low-state and $10^{39}\,{\rm erg\,s^{-1}}$ in high-state (Greiner et al. 1996), and larger than the one we obtain. Such a luminosity might be obtained from the jet for an increased mass flow rate. The jet inclination of $70\hbox {$^\circ $ }$ implies a maximum boosting of about 20 for some volumes. Further, also the accretion disk contributes to the X-ray flux. In SS433 we have $L_{\rm X} > 10^{35}\,{\rm erg\,s^{-1}}$ (Brinkmann et al. 1996) but no broad Fe-lines are observed. This might be either due to a very low mass flow rate (low jet luminosity) or to a very high mass flow rate (self-absorption of the emission lines).

Higher jet velocities ($\gamma >2$) may increase the Doppler boosting. Such velocities can be easily obtained for a higher flow magnetization, i.e. for a stronger magnetic field strength or a lower jet mass flow rate (see FG01; Fendt & Camenzind 1996). However, for the same mass flow rate, a higher velocity implies a lower gas density, which may lead, instead, to a decrease of the luminosity. The interplay of these effects is rather complex. The rest frame emissivity depends on the density as $\sim$$\rho^2$ and is also proportional to the emitting volume. The maximum Doppler boosting increases with the Lorentz factor, $D^3 (\cos\theta = 1) \simeq (2\gamma^2\,(1 + \sqrt{1 - \gamma^{-2}}))^{3/2}$, whereas the real boosting parameter also depends on the inclination of the velocity vector to the l.o.s. Answering the question how these effects determine the observed X-ray luminosity, would require a detailed study of various MHD wind solutions and their derived spectra investigating different magnetic field geometries (degree of collimation), jet mass flow rates (the flow magnetization), and also possible masses of the central black hole. We will return to this important point in a future paper.

Markoff et al. (2001) have recently shown (for XTE J1118+480) that synchrotron emission from the jet may play a role also in the X-ray band. Their model differs from ours in some respects, especially the initial jet acceleration is not treated and the jet nozzle geometry is more concentrated along the axis with a jet radius of only 10 Schwarzschild radii (in our model the jet is much wider and collimates later). As a consequence, the densities become higher and it is questionable whether a more reasonable jet geometry will deliver the same amount of X-ray flux.

5.2 Jet plasma composition

At this point we should note that the fundamental question of the plasma composition in relativistic jets has not yet been answered. In the case of microquasars we do not really know whether the jet consists of a $\rm e^-p^+$ or a $\rm e^-e^+$ plasma (see e.g. Fender et al. 2000). It could be possible that these jets are "light'' jets, i.e. made of a pair plasma only, and we would not expect to observe an iron line emission from such jets. Instead, the iron line emission would then arise from processes connected to the accretion disk or an accretion column. Such models were discussed for example in the case of XTEJ1748-288 (Kotani et al. 2000; Miller et al. 2001).

On the other hand, the theoretical spectra derived in our paper provide an additional information needed in order to interpret the observed emission lines. A deeper understanding will, however, require a more detailed investigation of different jet geometries, viewing angles and mass flow rates. In the end, this might answer the question whether the line emission, or at least part of it, comes from the highly relativistic jet motion or from a rapidly rotating (i.e. also relativistic) accretion disk. For example, we expect the emission lines of a collimated jet being narrower, and probably shifted by a larger Doppler factor, due to the strong beaming. One should also keep in mind that the direction of motion of the jet material is inclined (if not perpendicular) to the disk rotation.

Evidently, if the observations would tell us that the Doppler shifted Fe lines which are visible in our theoretical spectra arise in the jet material, this would also prove the existence of a baryonic component in these jets.

Nevertheless, observations in the radio and shorter wavelengths give clear indication for synchrotron emission from highly relativistic electrons. Whether this non thermal particle population contributes to all of the observed emission is not clear, a hot thermal plasma may also exist besides the non thermal electrons.

A similar discussion concerning the plasma composition is present in the context of extragalactic jets (e.g. Mukherjee et al. 1997). The non thermal emission from blazars can be explained by inverse Compton scattering of low-energy photons by the relativistic electrons in the jet. However, two main issues remain unsolved: the source of the soft photons that are inverse Compton scattered, and the structure of the inner jet, which cannot be imaged directly. The soft photons can originate as synchrotron emission either within the jet (see e.g. Bloom & Marscher 1996) or nearby the accretion disk, or they can be disk radiation reprocessed in broad emission line clouds (see e.g. Ghisellini & Madau 1996). In contrast to these leptonic jet models, the proton-initiated cascade model (see e.g. Mannheim & Biermann 1989) predicts that the high-energy emission comes from knots in jets as a consequence of diffusive shock acceleration of protons to energies so high that the threshold of secondary particle production is exceeded.

Comparison of our calculated Fe emission lines to the observed ones potentially give some hints on the plasma composition ( $\rm e^-p^+$ or $\rm e^-e^+$) in relativistic jets.