1 Introduction

Microquasars (Mirabel & Rodr $\acute{\rm {\i}}$guez 1999) are Galactic X-ray binaries where the three basic ingredients of quasars are found - a central black hole, an accretion disk and relativistic jets. Jets are thought to be driven by magnetohydrodynamic (MHD) mechanisms (Blandford & Payne 1982; Camenzind 1986) triggered by the interaction of those three components, although the jet formation process is not yet fully understood (e.g. Fendt 1997). Some microquasars are superluminal sources, e.g. GRS1915+105 at a distance of 7-12kpc (Fender et al. 1999) with a central mass of about $14\,{M}_{\odot}$ (Greiner et al. 2001).

Fendt & Greiner (2001, FG01) presented solutions of the MHD wind equation in Kerr metric with particular application to microquasars. These solutions provide the flow dynamics along a prescribed poloidal magnetic field line. FG01 found temperatures up to more than 10¹⁰K in the innermost part of the jet proposing that thermal X-rays might be emitted from this region. Here, we calculate the thermal spectrum of such an optically thin jet flow taking into account one of the solutions of FG01 and considering relativistic Doppler shifting and boosting as well as different inclinations of the jet axis to the line-of-sight (l.o.s.). A similar approach was undertaken by Brinkmann & Kawai (2000, BK00) who have been modeling the two dimensional hydrodynamic outflow of SS 433 applying various initial conditions. However, they do not consider relativistic effects such as Doppler boosting in their spectra.

Figure 1: Dynamical parameters of the MHD jet (see FG01). Shown is the radial dependence of the properly normalized poloidal velocities $u_{\rm p}(x) = \gamma v_{\rm p}/c$, particle densities $\rho (x)$, temperatures T(x) (in K), and size of the emitting volumes V(x) (from left to right) along the chosen magnetic field line. For the calculations in this paper we apply a central mass of $5\,{M}_{\odot }$ and a jet mass flow rate of $\dot{M}_{\rm jet} = 10^{-10}\,{M}_{\odot}\,{\rm yr}^{-1}$. The units are therefore $r_{\rm g} = 7.4 \times 10^5$cm for all length scales, $r_{\rm g}^3 = 4.1 \times 10^{17}$cm3 for the volumes, and $4.31 \times 10^{16}$cm-3 for the particle densities. Note that the jet injection point is located at $R_{\rm i} = 8.3\,r_{\rm g}$ with a gas temperature of $T_{\rm i} = 10^{10.2}$K. In this solution for the MHD wind equation, the poloidal velocity saturates to a value of $u_{\rm p} = 2.5$ beyond $x\simeq 10^8$. The flow is weakly collimated reaching a half opening angle of $70\hbox {$^\circ $ }$ at about x=250.