4 Observational consequences

4.1 Predicted contribution to the Galactic CR spectrum

Based on the picture laid out in Sect. 3, we can try to predict what might be observed in the CR spectrum due to the presence of Galactic microquasars.

First, it is obvious that close enough to a powerful relativistic jet source the locally observed CR spectrum will be completely dominated by the CRs produced in the terminal shock of the jet. However, it is clear that the powerlaw spectrum observed near earth is not dominated by a narrow component of microquasar origin - the current spectral limits rule out any contribution greater than a few percent.

In a simple isotropic diffusion picture, the CR energy density in the environment of a continuously active source will fall roughly like the inverse distance to the source r^-1 (see Eq. (8)) for large r much larger than a particle mean free path, $r \gg \kappa/c \sim 0.2~{\rm pc}\ H_{\rm kpc}^2/\tau_{15}$, and smaller than the Galactic disk height, $r \mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$<$ }}}H_{\rm disk} = 1~{\rm kpc}~H_{\rm kpc}$.

Given the observed CR energy density of $\sim$10 $^{-12}\ {\rm ergs\ cm^{-3}}$, we can estimate that the sphere of influence of a given source, defined as the region inside which the source contributes more than 30% of the total measured CR power (at which level it would enter the realm of detectability of by AMS 02) has a radius of order

$$R_{\rm 30\%} \sim 1\ {\rm kpc} \frac{L_{38.5}}{\kappa_{28.3}}\cdot$$ (5)

The time it takes the source to populate this sphere with CRs is roughly

$$\tau_{\rm 30\%} \sim 15\times 10^{6}\ {\rm yrs} \frac{L_{38.5}^2}{\kappa_{28.3}^3}\cdot$$ (6)

Particles that reach the edge of the Galactic disk will be siphoned off into the Galactic halo. Thus the CR flux will diminish rapidly, roughly exponentially, beyond a source distance of order the disc thickness, r > H. It would take source activity longer than $10^{8}~{\rm yrs}$ to fill the Galactic halo and the disk.

The well known microquasars mentioned above are all located much further from the solar system than this limit. However, if a source similar to, say, GRS 1915+105 had been active in the solar neighborhood (inside about 1 kpc) within the last $\sim$10⁷ yrs, our local CR flux should show a clear sign of the contribution from this source.

In this context it is important to mention that GRO J1655-40, V4641 Sgr, Cyg X-3 (and also SS433) are known to be in high-mass X-ray binaries. Their lifetimes are therefore expected to be short. If such a relativistic jet black hole binary was located in the Orion nebula region within the past 10⁶ yrs, we should be able to detect a strong signal in the low energy CR spectrum from this source alone.

Far enough away from any single source, an observer will measure the time averaged contribution from all Galactic sources, washed out by CR diffusion (similar to the situation described in Strong & Moskalenko 2001). Since sources will likely follow a distribution of Lorentz factors of width $\Delta \Gamma_{\rm jet}$, the observed signal will be smeared out over at least that width. Any intrinsic width of the produced CR spectrum will add to this effect, as well as broadening effects like solar modulation and scattering off of interstellar turbulence.

In Fig. 7 we have plotted possible contributions to the CR proton spectrum from a single Galactic jet source. Depending on how much we have underestimated the power in Galactic jets and how much adiabatic losses of particles trapped in adiabatically expanding shock will suffer, we might over or underestimate the contribution. Taking the figure at face value, however, it seems likely that a contribution at the few percent level can be expected in the energy region of a few GeV.

Figure 7: Toy model of the microquasar contribution to the CR spectrum, for a single microquasar situated in a low mass X-ray binary, active for $\tau \mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$>$ }}}1.5\times\ 10^{7}\ {\rm yrs}$ on the level of $3\times 10^{38}\ {\rm ergs\ s^{-1}}$ (similar to GRS 1915+105), and at a distance of $1~{\rm kpc}$. For simplicity, we assumed the source was operating with uniform bulk Lorentz factor $\Gamma _{\rm jet}=5$ (top) and $\Gamma _{\rm jet} = 2.5$ (bottom). The curves are normalized relative to the measured differential Galactic CR background spectrum (thick grey dashed line). Shown are the same curves as in Fig. 5: narrow feature for upstream temperature of $T\sim 7\times10^{10}~{\rm K}$ (dotted line) and for $T \sim 7\times 10^{8}~{\rm K}$ (solid line), Maxwellian with $kT\sim \Gamma_{\rm jet}~m_{\rm p}~c^2/3$ (dashed line), multiply scattered component for efficient pitch angle scattering (dash-dotted line) and for inefficient pitch angle scattering (dash-triple-dotted line), and the relative contribution of heavy elements for metallicity 10 times the solar value (long-dashed grey curve), as seen in GRO J1655-40 and V4641 Sgr. Each spectral component has been steepened by E-1/2 to account for the energy dependence of the diffusion coefficient.

4.2 Detectability of narrow features in the CR spectrum

Detecting and positively identifying such a CR component will be a formidable challenge. The advent of the high sensitivity AMS 02 instrument and of the solar minimum might make it possible, however. Given the preliminary specifications of AMS 02, we can estimate the detectability of spectral features such as produced by microquasars. The rigidity resolution (i.e., energy resolution) of the instrument is expected to be around 2% in the crucial range from 1 to 10 GeV, which will easily be sufficient to identify and resolve even the narrowest feature in Fig. 7.

For an effective area of order $0.4~{\rm m^2~sr}$, the expected total CR proton count rate by AMS 02 in the energy range from 1 to 10 GeV should be of the order of $10^{3}~{\rm s^{-1}}$. At 2% energy resolution, this implies a detection rate of about $2\times 10^{8}~{\rm yr^{-1}~bin^{-1}}$, with a relative Poisson-noise level of order 10^-4. Calibration and other systematic errors will likely dominate the statistics, however, these numbers are encouraging, and we expect that a source at the few-percent level will be detectable with AMS 02.

The heavy element sensitivity of AMS 02 will share similar characteristics: for the same energy resolution and effective area, the detection rates of carbon and iron, for example, should be of order $4\times 10^{5}~{\rm s^{-1}~bin^{-1}}$ and $4\times 10^{4}~{\rm s^{-1}~bin^{-1}}$ respectively. Aside from AMS 02, signatures might be detected by other instruments, and even existing data sets might contain signals. Identification would require scanning these data with high spectral resolution. Note that the effects of solar modulation will broaden any narrow spectral component significantly. Results by Labrador & Mewaldt (1997) demonstrate that a line at $\sim$5 GeV will be broadened by $\sim$1 GeV, (less at higher energies) though this effect will be reduced at solar minimum.

4.3 Gamma-ray emission from pion decay

As the CRs produced in microquasars travel traverse the Galaxy, they will encounter the cold ISM. The interaction of a CR proton (by far the most abundant and thus most energetic component of the CR spectrum) with a cold ISM proton can lead to secondary particle production and to the emission of gamma rays via several channels, the most important of which is $\pi ^{0}$decay.

Figure 8: Toy model for the gamma ray signature produced in a microquasar CR halo via pion decay (including $\pi ^{0}$ decay and bremsstrahlung from secondary electrons and positrons). Curves were calculated assuming a source active for over $\tau \mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$>$ }}}15\times 10^{6}~{\rm yrs}$ with an average power of $L_{\rm kin} = 3\times 10^{38}~{\rm ergs~s^{-1}}$, at a distance of 10 kpc, and for an ISM particle density of $1~{\rm cm^{-3}}$, assuming CRs are lost once they have reached the edge of the Galactic disk at about 1 kpc distance from the source. Labes according to Fig. 5. Dotted line: Gamma ray signature from narrow component of the microquasar halo; dashed line: from thermalized component; dash-dotted line: from "powerlaw type component'' in the case of efficient scattering; dash-triple-dotted line: from "powerlaw type component'' in the case of inefficient scattering. Thick grey line: EGRET diffuse gamma ray background at the position of GRS 1915+105 (Hunter et al. 1997), assuming the same solid angle as subtended by the source. Thick long dashed line: background gamma ray emission over the same solid angle modeled assuming the proton CR spectrum measured near earth and an average ISM density of $1~{\rm cm^{-3}}$. Hatched line: GLAST sensitivity. Models were computed using the GALPROP routines by Moskalenko & Strong (1998). Insert: Angular dependence of the source contribution to the gamma ray flux $F_{\nu }$, relative to the background flux $B_{\nu }$ at a photon energy of $1~{\rm GeV}$ (see Eq. (8)). The right Y-axis shows the source distance at which the GLAST sensitivity is reached for the value of $F_{\nu }/B_{\nu }$ shown in the curve, the top X-axis shows the angle $\theta = r/D$ in units of arcmin/D10 where D10 is the source distance in units of 10 kpc.

Using the toy model presented in Fig. 7, we can estimate how much gamma ray flux can be expected from the CR halo of a powerful microquasar and compare it to the background flux from the Galaxy. We assume that the CRs diffuse away from the source until they reach the Galactic halo, approximated as a zero pressure boundary condition at radius $R \sim H_{\rm disk} = 1~{\rm kpc}~H_{\rm kps}$ (assuming spherical symmetry for simplicity). The result is shown in Fig. 8.

Note that the gamma ray signal even for a source of average kinetic power of $L_{\rm kin} = 3\times 10^{38}~{\rm ergs~s^{-1}}$ is small compared to the background signal coming from the same solid angle ($\pi R^{2}$). However, because the CR density increases towards the center of the source, higher spatial resolution can improve the signal-to-noise ratio somewhat. For a spherically symmetric cloud of CRs with luminosity L and vanishing pressure at the boundary $R \sim H_{\rm disk}$, the density follows

 

$${n_{\rm CR}(r,\gamma) = \frac{f(\gamma)}{\int {\rm d}\gamma' \gamma' m c^2 f(\gamma')}\frac{L}{4\pi \kappa}\left(\frac{1}{r} - \frac{1}{R}\right)}$$

$$6 \times 10^{-11}~{\rm cm^{-3}}\frac{f(\gamma)}{\int {\rm d}\gamm... ...{L_{38.5}\tau_{15}}{H_{\rm kpc}^2~R_{\rm kpc}}\left(\frac{R}{r} - 1\right)\cdot$$ (7)

Obviously, then, the gamma ray surface brightness of such a source is centrally peaked and thus the best observing strategy is to try to resolve the source. The photon flux $F_{\nu }$ from within an angular distance $\theta \leq r/D$ from the source position (here, D is the physical source distance, while $\theta$ the on-sky angular distance from the source position) is then proportional to

 

$${F_{\nu}(\theta \leq \frac{r}{D})} \sim \frac{n_{\rm ISM}~c}{4\pi~D^2}\frac{L~R^2}{3~\kappa}\left(\frac{\... ...{\nu}(\gamma') f(\gamma')}{\int {\rm d}\gamma' \gamma' m c^2 f(\gamma')}\right)$$

$$\times \left\{1 + 3~r^2~\left[\ln{\left( 1 + \sqrt{1 - r^2}\right)} - \ln{\left(r\right)}\right]\right.$$

$$\ \ \ \left.-\left(1 + r^2\right)\sqrt{1 - r^2}\right\}$$ (8)

whereas the galactic background flux $F_{\nu,~{\rm back}}$ for the same solid angle in the small angle approximation is simply proportional to (r/D)². Thus, the source contribution relative to the background, measured as $F_{\nu,~{\rm source}}/F_{\nu~{\rm back}}$, rises towards lower r, which we have plotted in the insert in Fig. 8.

4.3.1 Sub-cosmic rays from sub-relativistic sources like SS433

Objects like SS433 might be important sources of sub-cosmic rays in the Galaxy: the cold thermal ions carried in the jet at 0.26 c will be accelerated to energies of order $E_{\rm ion} \equiv E_{30}\times 30~{\rm MeV}/{\rm nucleon}$. These particles will suffer severe ionization and Coulomb losses which will prevent them from traveling further than about 250 pc from the source.

However, they could act as a significant ionization source for the surrounding medium: the ionization loss timescale for a particle with energy $E = 30~{\rm MeV}~E_{30}$ is of order (Ginzburg 1979)

$$\tau_{\rm ion} \sim 2\times 10^{6}~{\rm yrs}~\frac{E_{30}^{3/2}}{n_{\rm ISM}},$$ (9)

much shorter than the expected lifetime of the particles inside the Galactic disk, i.e., the particles will deposit their energy in the vicinity of the source, especially if the source is located within a molecular cloud.

Furthermore, the excitation of nuclear $\gamma$-ray emission lines by interaction of these sub-cosmic rays with interstellar heavy ions of C, O, Fe, and other elements might be detectable by INTEGRAL.

4.4 Cold electron-positron jets

If the jet consists chiefly of relatively cold electron-positron plasma, and if dissipation occurs mostly in the reverse shock, then the jet terminus will produce relativistic electrons and positrons with energies of the order of $\Gamma_{\rm jet}~m_{\rm e}~c^2 \sim 2.5~{\rm MeV}$, which will then begin to diffuse into the ISM. Such positrons and electrons could produce additional bremsstrahlung radiation at energies of a few hundreds of keVs up to 2.5 MeV. Much like mildly relativistic protons, these electrons will contribute to the heating of the ISM due to the ionization losses, but much more important for future observations might be the electron-positron annihilation line at 511 keV.

For an integrated mechanical luminosity of $L_{\rm kin} = 3 \times 10^{38}~ {\rm ergs~s^{-1}} ~L_{38.5}$ of the entire ensemble of Galactic relativistic jets, the flux of positrons carried by jets is

$$\dot{N}_{\rm e^{+}} = \frac{L_{\rm kin}}{2~\langle \gamma \r... ...m s^{-1}}~\frac{L_{38.5}}{\Gamma_{5}~\langle \gamma \rangle},$$ (10)

where $\langle \gamma \rangle$ is the mean random Lorentz factor of the electrons/positrons in the jet plasma. Note that this estimate will be independent of whether dissipation occurs mostly in the forward or reverse shock. Assuming that these positrons can diffuse out of the radio plasma they are originally confined in, the estimated luminosity of the annihilation line will be of the order of $L_{\rm ann} \sim L_{\rm jet}/\langle \gamma \rangle$.

This is actually comparable to the total amount of positrons annihilating in the Galaxy according to the observations of the e⁺/e^-annihilation line from OSSE/GRO, $\dot{N}_{\rm e^{+}, Gal} \sim 3\times 10^{43}~{\rm s^{-1}}$ (Purcell et al. 1997). If Galactic jets are in fact composed of electron-positron plasma, this measurement immediately implies one of the following conclusions: a) either the mechanical luminosity of these jets is not far above our relatively conservative estimate of $3\times 10^{38}~{\rm ergs~s^{-1}}$, or b) the pair plasma is not cold, i.e., $\langle \gamma \rangle \gg 1$, or c) diffusion of particles across the magnetic boundary of the remnant jet plasma is very inefficient, in which case many Galactic "radio relics'' should exist, not unlike in the case of radio relics from radio loud AGNs in the intracluster medium (e.g., Ensslin et al. 1998).

The Integral SPI spectrometer and the IBIS imager would be able to measure the increase in the annihilation line flux towards microquasars located away from the Galactic center (where the background is highest) like GRS1915+105, and to measure the line width if it could be detected. These measurements could be very helpful in constraining the particle content of relativistic Galactic jets.