2 Outline of the model

In this section we will present a general description of the model proposed for CR production in microquasars.

As we will argue below, it is likely that the plasma traveling far downstream in the jet towards the working surface is cold (the mean particle velocity is $\langle v^2\rangle \ll c^2$ in the rest frame of the jet plasma), especially if microquasar jets are composed of electron-ion plasma. The same is, of course, also true for the undisturbed interstellar medium (ISM). Thus, the bulk of the plasma transported to the interface between the jet and the ISM (for simplicity we will call this interface the working surface of the jet, regardless of its detailed physical structure) is initially cold.

This conjecture is inspired by observations of the mildly relativistic jets in SS433 (the best studied relativistic Galactic jet to date, albeit mildly relativistic and not considered a microquasar). In this source, red- and blue-shifted Balmer H$\beta$ and other optical recombination lines, usually radiated by plasmas with temperatures of order $10^{4}~{\rm K}~\sim 1~{\rm eV}$, allow the determination of the bulk velocity of the flow: 0.26  c. This velocity is remarkably constant over the 20 years the source has been observed (Margon 1984; Milgrom et al. 1982). ASCA (Kotani et al. 1998) and recent Chandra (Marshall et al. 2002) observations of X-ray lines of hydrogen- and helium-like ions of iron, Argon, Sulfur, and Oxygen show that these ions are moving in the flow with the same velocity, 0.26  c. This X-ray emitting plasma at temperatures of $T \sim 10^{7}{-}10^{8}~{\rm K} \sim 10^{3}{-}10^{4}~{\rm eV}$ is observed at much smaller distances ($\sim$ $10^{11}~{\rm cm}$) from the central compact object than the optical line emission region ($\sim$ $10^{14}~{\rm cm}$). A striking feature of the SS433 jet is that the plasma is observed to be moving with relativistic velocities. Yet, at the same time the jet plasma itself shows very little line broadening (i.e., it is cold).

If microquasar jets are similar to the SS433 jets in composition and properties (i.e., cold electron-ion plasma at relativistic bulk speeds) the consequences for the interpretation of these jets will be far reaching, as we will argue below. Independent from this argument, the radio synchrotron emission detected from microquasar jets and several radio nebulae surrounding microquasar sources (see Sect. 3.1) is clear evidence for the presence of relativistic electrons, which, when released into the ISM, will act as cosmic ray electrons.

Figure 2: Cartoon of the standard picture of the interface between jet and ISM ( left panel), as envisaged to apply in FR II radio galaxies. The injection of relativistic particles can occur either in the reverse or forward shock. Right panel: cartoon of particle trajectories for particles crossing the shock only once (upper solid line) and particles participating in diffusive shock acceleration (lower solid line), particle scattering indicated as stars.

   
2.1 The standard picture for jet working surfaces

The standard picture for the interface between powerful radio galaxies and their environment is a strong double shock structure (forward shock into the ISM and reverse shock into the jet), shown in Fig. 2. The shocked jet material is shed at the head of the jet and inflates an enshrouding cocoon around the jet, filled with relativistic plasma, which has gone through the terminal shock. Such a scenario might also be relevant for the terminus of Galactic relativistic jets. A similar picture arises if the jets are composed of discrete ejections, propagating into an external medium at relativistic speeds, as sketched in Fig. 3.

Figure 3: Left: cartoon of a jet composed of discrete ejections with precession. In such a non-stationary picture, each ejection is slowed by its interaction with the ISM (which might be disturbed by previous ejections). This interaction will likely happen in the form of a forward shock (into the ISM). ISM particles will leave the shock with energies of order $\Gamma_{\rm jet}~m_{\rm p}~ c^2$ (here, $\Gamma _{\rm jet}$ is the Lorentz factor of the individual ejection, which decreases with time). Right: cartoon of particles crossing a relativistic forward shock, likely the appropriate scenario for a cold ejection running into the ISM. Same nomenclature as in Fig. 2.

A cold upstream particle crossing an ultra-relativistic shock into a downstream region with relative Lorentz factor $\Gamma_{\rm rel} \sim \Gamma_{\rm jet}$ will have an internal energy of $\gamma m c^2 \sim \Gamma_{\rm jet} m c^2$ in the downstream frame after the first shock crossing. Consequently, all initially cold particles will leave the shock with about the same specific energy $\Gamma_{\rm jet} c^2$. Particles can pick up additional energy if they cross the shock multiple times, which is the basis of diffusive shock acceleration schemes like Fermi acceleration, resulting in the formation of a powerlaw distribution. However, as has recently been shown by Achterberg et al. (2001), the bulk of the particles crossing a relativistic shock escape after the very first shock passage and will therefore not participate in diffusive shock acceleration. It is these particles that carry off the bulk of the dissipated jet energy.

As a result, the bulk of the particles might leave the shock with a narrow energy distribution, peaking at an energy close to the specific kinetic energy of the jet: $\langle \gamma m c^2\rangle \sim \Gamma_{\rm jet} m c^2$, with an energy width similar to or higher than the Lorentz transformed thermal velocity, $\Delta \gamma \sim 2~\gamma~c_{\rm s}$(i.e., very narrow, since the internal sound speed $c_{\rm s}$ is small: $c_{\rm s} \ll 1$).

Whether this narrow distribution will be preserved as the particles travel away from the shock, or whether it will be thermalized, depends on the efficiency of collective plasma effects and small angle scattering on magnetic field irregularities, which are also needed to isotropize the particle distribution. If collective effects are strong, the particle spectrum will be broadened into a relativistic Maxwell-Boltzmann distribution, with a temperature corresponding to the value given by the relativistic Rankine-Hugoniot jump conditions. In the case of a strong, ultra-relativistic shock, this is simply $kT \sim 1/3 \Gamma_{\rm jet} m c^2$, i.e., the mean particle energy is just $\Gamma_{\rm jet} m c^2$(e.g. Blandford & McKee 1976). In this case the relativistic proton plasma in the shocked ISM is equivalent to the X-ray emitting gas in SNR shocks. However, in microquasar shocks we have extremely rarefied, relativistic particles with a relatively narrow thermal (i.e., not powerlaw) energy distribution.

   
2.2 Termination without strong shocks?

However, the structure of relativistic shocks is still not well understood and it might be that this interface is not a simple double shock structure. It could be significantly different in nature. For example, the jet could be magnetically connected with the environment, i.e., if the flux tubes join smoothly with the large scale magnetic field of the ISM, as shown in the cartoon in Fig. 4 (note, however, that Lubow et al. 1994 showed that realizing such configuration is rather difficult).

Figure 4: Cartoon of particle injection by a jet without a strong shock at its interface with the ISM (e.g., if the magnetic structure of the jet is connected with the ISM and the jet is sub-Alfv $\acute{\rm e}$nic). Dots represent CRs transported by the jet and released into the ISM at the bulk speed of the jet, grey arrows represent magnetic flux tubes. The right flux tube representation depicts the case where adiabatic losses are important, the left shows a case where the field flux tube is smoothly fused with the stochastic interstellar field and adiabatic losses might not be dominant in particle transport.

In such a case the shock would be replaced by stochastic pitch angle scattering of the particle distribution (this can occur if the jet is moving sub-Alfv $\acute{\rm e}$nically, for example). Since the jet plasma is traveling relative to the ISM, such a scenario would excite strong two-stream instabilities at the interface between ISM and jet plasma, which would isotropize and possibly thermalize the particle distribution of the jet very quickly. The deposition of jet thrust would then imply that this interface is itself moving through space. Precession, as observed in SS433 (e.g., Milgrom 1979) and suggested to be present in GRO 1655-40 (Hjellming & Rupen 1995), will significantly alter the dynamical balance between ISM and jet plasma, as will the time dependent nature of the interface if the jets are composed of discrete ejections.

If furthermore the magnetic field is stochastically tangled on small scales, the detailed behavior of the plasma could be very complicated, with a gradual change from relativistic, ballistic motion to random propagation. Qualitatively, this would be comparable to extragalactic FR I sources (though the exact nature of the dynamics in FR I sources is not yet clear, either).

In such a case, the absence of a strong shock would preclude diffusive shock acceleration (though stochastic acceleration might still exist if particles scatter off of relativistic turbulence which might exist in the transition region between jet and ISM). Only the narrow or thermalized component with mean energy of $\Gamma_{\rm jet} m_{\rm p} c^2$ and strong cutoff at higher energies would exist.

   
2.3 Spectral characteristics

Based on Sects. 2.1 and 2.2, we therefore predict that each Galactic microquasar produces a narrow component of CRs, which peaks at an energy $\Gamma_{\rm jet} m c^2$. For protons, this energy should fall into the range of $\Gamma_{\rm jet} m_{\rm p} c^2 \sim 3 {-} 10$ GeV. The superposition of these spectral signatures from several microquasars will appear as a broad feature in the energy range from 3 -10 GeV.

Even if most of the particles are thermalized downstream, the spectrum will still show a steep turnover beyond energies of order $3kT \sim \Gamma_{\rm jet}~ m_{\rm p}~ c^2$ (see the dashed curve in Fig. 5), which will appear as an edge-like feature in the overall CR spectrum.

Similarly, a number of other processes will tend to broaden any narrow component produced in the working surface, including adiabatic losses (competing with diffusion of particles out of the loss region, see Appendix B and the right panel in Fig. 5) and solar modulation. The effect of these processes will be to spread particles to lower energies, leaving the strong turnover/cutoff above energies of $\Gamma_{\rm jet}~m~c^2$ intact.

The only serious cooling these CR protons at energies of a few GeV might experience will be adiabatic losses, which will occur if the particles are confined to an expanding plasma volume (e.g., if it is overpressured with respect to the environment). However, since many processes can lead to increased diffusion of these particles, it appears plausible that a large fraction of the CRs might escape before they suffer strong adiabatic losses.

If a component of cold electrons is also present in the jets in addition to the observed powerlaw electrons, a similar, very low energy relativistic electron component (around 2-5 MeV) might appear. However, it would contain only a fraction $m_{\rm e}/m_{\rm p}$ of the energy in the proton component.

The remaining fraction of particles (both ions and electrons) which do not escape the shock after the first shock passage and thus perform multiple shock crossings will be accelerated diffusively to a powerlaw-like distribution. Only the high energy tail of this powerlaw-like electron component is directly observable via synchrotron radio emission.

Likening the acceleration of particles crossing a relativistic shock to the problem of Compton up-scattering of low energy photons on relativistic thermal electrons (see, for example, Pozdnyakov et al. 1983), we note that a particle scattered both up-stream and down-stream of the shock will experience an energy gain by a factor of order $\Gamma_{\rm rel}^2$ per crossing cycle, where $\Gamma_{\rm rel} \sim \Gamma_{\rm jet}$ is the relative Lorentz factor between upstream and downstream plasma. This was argued by Vietri (1995), applied to the acceleration of particles in gamma-ray burst shocks. This will lead to the production of several peaks in the spectrum. The input spectrum for this up-scattering process is the narrow particle population produced in the initial shock crossing (discussed above), and thus peaks will appear at energies $\sim$ $few\times{\Gamma_{\rm jet}}^{2i + 1}~ m_{\rm p}~ c^2$, where i is the number of shock crossing cycles performed by the particle. The normalization of each peak, and thus the approximate powerlaw index, is determined by the escape probability of the particles (similar to the optical depth in inverse Compton scattering). The resulting spectrum is sketched in Fig. 5.

Figure 5: Left panel: sketch of the predicted contribution from a microquasar to the Galactic CR spectrum for $\Gamma _{\rm jet}=5$. a) Dotted line: narrow component, corresponding to cold ( $T\sim 7\times10^{10}~{\rm K}$) upstream particles simply isotropized upon crossing the working surface (Lorentz transformed energy distribution), arbitrary normalization; b) dashed line: Maxwell-Boltzmann component from particles thermalized in the shock (normalized to contain the same power as component a); c) dash-dotted line: powerlaw-like component (escape probability 99%, normalized to contain 10% of component a) for the case of strong scattering. Note the similarity to Comptonization of low energy seed photons by a relativistic medium with low optical depth (i.e., high escape probability); d) dash-triple-dotted line: powerlaw spectrum for weak scattering case (Achterberg et al. 2001) for the same normalization as component c). Note the difference in the position of the first peak between c) and d), $\sim \Gamma _{\rm jet}^2$ vs. $\sim \Gamma _{\rm jet}^3$. Right panel: estimate of the effects of adiabatic losses on the particle distribution for different ratios of the adiabatic losses time  $\tau _{\rm ad}$ of the particles to the escape time $\tau _{\rm esc}$, compared to the injected particle distribution (solid) line for a pressure differential between shock and ISM of $p_{\rm shock}/p_{\rm ISM}=3\times 10^8$ (see Appendix B): strong adiabatic losses ( $\tau _{\rm ad}/\tau _{\rm esc} = 10^{-3}$, dashed line), intermediated losses ( $\tau _{\rm ad}=\tau _{\rm esc}$, dash-dotted line), and weak adiabatic losses ( $\tau _{\rm ad}/\tau _{\rm esc}=10^{3}$, dotted line).

Note, however, that Achterberg et al. (2001) argue that higher order shock crossings do not lead to energy gains of order $\Gamma_{\rm rel}^2$. In their treatment, scattering is limited to very small angles and the energy gain is only of order unity, and thus the position of the peaks would be much more closely spaced, resembling a powerlaw much more than in the Compton scattering analogy discussed in the previous paragraph. The low energy turnover (or cutoff) of this powerlaw distribution would then be located roughly at $\Gamma_{\rm jet}^2 \sim 10 {-} 100$ GeV. At higher energies, multiple scattering will form a powerlaw with index $s \sim 2.3$. According to this simple approach, the difference between these two pictures is therefore the energy of the second peak ( $\sim \Gamma _{\rm jet}^3$ vs. $\sim \Gamma _{\rm jet}^2$).

Since the structure of relativistic shocks, and their presence in the working surfaces of microquasar jets are subject to considerable uncertainty, the observational discovery of any of the features discussed in this paper (and in particular the second peak, which would help to distinguish between the two scenarios of diffusive acceleration mentioned in the previous paragraphs, see Fig. 5) or evidence of their absence would be important input into theories of relativistic shocks.

2.4 Comparison with the canonical CR powerlaw component

The CR components described above and shown in Fig. 5 should be compared to the well known powerlaw CR component observed near earth: CR protons and nuclei have a powerlaw spectrum with a uniform slope around $s \sim 2.5 {-} 2.7$ over an extremely broad energy range from 1 GeV up to 10¹⁵ eV. Locally, the CR energy density is of order $10^{-12}~{\rm ergs~cm^{-3}}$. Observations of the light elements produced by spallation reactions show that the lifetime $\tau_{\rm CR,~disk}$ of relativistic protons in the Galactic disk is of order $\tau_{\rm CR,~disk} \sim 1.5 \times 10^{7}~{\rm yrs}$ (Yanasak et al. 2001), while the lifetime in the Galactic halo $\tau_{\rm CR,~halo}$ is close to 10⁸ years (e.g., Ginzburg 1996). This enables us to estimate the CR luminosity of the Galaxy as $L_{\rm CR} \sim 4 \times 10^{40}~{\rm ergs\ s^{-1}}$, with a diffusion coefficient $\kappa$ inside the disk of

$$\kappa \sim \frac{H_{\rm disk^2}}{\tau_{\rm CR,~disk}} = 2\ti... ...tau_{15}} \sim 10^{28.3}~\frac{\rm cm^2}{\rm s}~\kappa_{28.3}$$ (1)

where $H_{\rm kpc}$ is the disk height in kpc, $\tau_{15}$ is the CR lifetime in the disk in units of 15 Myrs, and $\kappa_{28.3}$ is the ISM diffusion coefficient, normalized to a value of $2\times 10^{28}~{\rm cm^2~s^{-1}}$. The current paradigm for the bulk of the CRs observed in the vicinity of the earth is that they are produced by shock acceleration in the decelerating blast waves of SNRs (e.g. Blandford & Ostriker 1978). The usual assumption is that about 5% of the mechanical energy of the SNR are converted into CR energy.

There is no doubt that in the vicinity of an active microquasar the low energy part of the Galactic CR spectrum must be strongly distorted. As a result, smooth maxima or edge-like features should exist in the few GeV range of the CR spectrum. For a distant observer, the signals from several sources will be superimposed due to the long diffusion time through the galaxy. Integrally, though, deviations from the powerlaw spectrum expected in diffusive shock acceleration models should be observable.

Energy estimates which we present below show that this CR component produced in microquasars might contribute measurably to the spectrum of the CR protons in the energy band mentioned above. We will argue that, globally, microquasars should contribute upward of 0.1% of the total Galactic CR power. However, the locally measured (i.e., near earth) relative strength of the proposed CR components produced in microquasars compared to the canonical CR powerlaw distribution is highly uncertain, as it depends on the history of microquasar activity in our Galactic neighborhood.

Given these uncertainties, it might be rather difficult to detect the tiny deviations in the CR spectrum caused by distant microquasars (further complicated by the strong effects of solar modulation at and below the predicted energy range). However, they might be measurable by the upcoming AMS 02 experiment (e.g. Barrau 2001), which will offer unprecedented sensitivity and will be launched during the upcoming solar minimum (reducing the effects of solar modulation significantly). Traces of such a component might also be present in already existing high quality data sets from past or ongoing experiments, such as IMAX (Menn et al. 2000) or CAPRICE (Boezio et al. 1999).

Absence of any traces of spectral deviations in the upcoming AMS 02 experiment might become a strong argument in favor of electron-positron jets in Galactic superluminal radio sources or, alternatively, it would demonstrate that there is an unknown acceleration mechanism with 100% efficiency of transforming of the mechanical beam energy into a relativistic powerlaw distribution. Given these premises, we can state that one of the following two statements must hold: 1) either an additional hadronic CR component exists (though it may be so weak that detection inside the solar system is impossible) or 2) all jets are electron-positron dominated (in which case an additional CR electron-positron component should exist).

2.5 Peculiar abundances

Recent studies of the chemical composition of Galactic transients indicate that the binary companions of several microquasar sources are metal enriched: the heavy element abundances (e.g., N, O, Ca, Mg) in the optical counterparts of the X-ray sources GRO J1655-40 (Israelian et al. 1999) and V4641 Sgr (Orosz et al. 2001) exceed solar abundances by about an order of magnitude, much more so than the observed overabundance of the same elements in CRs (Zombeck 1990). Furthermore, the relative abundances between these elements are unusual compared to either solar abundances or the abundance pattern observed in the bulk of the CR spectrum.

These abundance anomalies in GRO J1655-40 and V4641 Sgr could be the result of mass exchange between two rapidly evolving massive stars or enrichment of the normal stellar atmosphere during the supernova explosion of the primary predecessor. Accretion brings these abundance anomalies into the jet creation region in the inner disk, from where they could be transported out by the jet, eventually producing CRs by the mechanism outlined above. Similarly, Cyg X-3 is known to have an extremely hydrogen deficient Wolf-Rayet companion (van Kerkwijk et al. 1992; van Kerkwijk et al. 1996; Fender et al. 1999b), which could also lead to a large overabundance in helium and heavier elements relative to hydrogen in the produced CR spectrum.

Therefore, Galactic jets might be responsible for part of the observed CR abundance anomalies. Moreover, the CR component produced in relativistic jet sources inside the Galaxy might show rather unusual chemical abundances, in comparison with the bulk of the CRs in the powerlaw population. This would immediately distinguish Galactic jets from other CR creation mechanisms. The comparison between the measured abundances in the energy range where we expect Galactic jet sources to contribute (of order a few GeV) with those measured in the pure powerlaw regime will thus be an important probe to search for the proposed CR component. Note that the CRs produced in SNRs originate in the external shock of the swept up ISM, thus the abundances of the produced CR spectrum reflect the ISM, which might have been enriched by a pre-collapse wind, but will not show the peculiar abundance of the SN ejecta. Because all the spectral components accelerated in microquasars originate from the same plasma, they should all show the same abundance pattern. This could be a way to associate spectral features at different CR energies with a microquasar origin.

A second way to distinguish particles accelerated in the relativistic shocks of Galactic microquasars from those accelerated in non-relativistic SNR shocks is the different energy-particle mass relation: All particles in relativistic cold jets have the same Lorentz factors. Since single-pass shock acceleration will accelerate all particles to roughly the same random Lorentz factor, the peak energy for different species will be proportional to their rest mass (i.e., a fixed energy per nucleon). Electromagnetic acceleration processes would instead produce particle energies proportional to Z/A. This difference might again be measurable by AMS 02, and might already be present in CR data on heavy nuclei from experiments like HEAO-3 (Engelmann et al. 1990) or ACE (Binns et al. 2001).