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Astron. Astrophys. 356, 975-988 (2000)

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8. Observational tests of the model

8.1. Emission lines

In our model the jet flow initially consists of non-relativistic hot plasma. Due to adiabatic expansion losses of thermal energy during the propagation of this material along the conical jet with given opening angle, the temperature of the plasma decreases. Internal shocks as envisioned above lead to local heating and acceleration of relativistic particles but do not change this general picture. In reality the situation is very similar to that in the well-known source SS433. In SS433 we observe bright optical recombination Balmer, Paschen and Brackett lines of hydrogen which are blue-shifted in the approaching jet and red-shifted in the receding jet. The velocity of the jet flow in SS433 is equal to 0.26 c. Due to the precession of the jet the observed red and blue shifts are strong functions of time (Margon 1984). In our case the inclination angle of the jets of GRS 1915+105 is known from the observations by Mirabel & Rodríguez (1994). This angle, [FORMULA], and the bulk velocity of 0.6 c of the jet material found in our fiducial model permits us to estimate the red and blue line shifts of the emitting jet material:


Note that any line emission coming from the jet approaching the observer is hardly shifted in wavelength at all. Assuming that the bulk velocity of the jet material in the jets of GRO J1655-40 is also close to 0.6 c, we find for this source that the emission lines are redshifted for the approaching jet ([FORMULA]) as well as for the receding jet ([FORMULA]). This is caused by the large viewing angle, [FORMULA], of the jets in this object (Hjellming & Rupen 1995). In both cases the very large inclination angles result in a strong predicted asymmetry in the line shifts for the two jets. Measuring these shifts will permit us to estimate both the velocity of the jet bulk flow and the viewing angle [FORMULA]. Furthermore, any jet precession as in the case of SS433 could be detected.

Measuring the predicted line shifts is complicated by the low density of the material in the jet flow of SS433 and GRS 1915+105 which prevents the production of bright recombination lines. However, we know that in the case of SS433 there is a strong thermal instability in the flow which leads to the formation of small, dense cloudlets (Panferov & Fabrika 1997). This increases the recombination rate and effective emission measure of the plasma in the flow. If there is a similar instability in the jets of GRS 1915+105 and GRO J1655-40 we have a good chance to observe recombination lines from both of these sources. Another problem is the strong obscuration of GRS 1915+105 by interstellar dust. Therefore, it is only possible to look for recombination lines of hydrogen in the K-band. In the case of GRO J1655-40 obscuration is low and there is a chance to detect Lyman and Balmer lines. Unfortunately, the mechanical power of the jet in GRO J1655-40 is smaller than in GRS 1915+105 or SS433. This will lead to a smaller density and emission measure of the jet material and therefore also a smaller intensity of the lines. It is important to bear in mind that in SS433 the emission lines are extraordinarily bright but modern observational techniques permit us to look for blue and red-shifted lines which are weaker by many orders of magnitude.

In SS433 ASCA discovered red and blue-shifted X-ray K-lines of iron with a rest energy of roughly 6.7 keV and similar lines of hydrogen- and helium-like sulphur and argon (Kotani et al. 1997). In our case the cooling jet flow with an initially very high temperature must lead to the emission in similar lines of recombining high-Z ions. Again, the mechanical energy of the flows in GRS 1915+105 and GRO J1655-40 is smaller than in SS433 and, therefore, the lines should be weaker in these objects. However, the new X-ray spacecraft, XMM, CHANDRA, ASTRO-E, Constellation-X and XEUS, may be able to detect such emission in red and blue-shifted X-ray lines. Note in this respect the detection of shifted iron lines in GRO J1655-40 reported by Balucinska-Church & Church (2000) with RXTE which the authors attribute to the accretion disk but may very well originate in the continuous jets of this source.

All predictions for the production of line emission in the jets are based on the assumption that the jet flow consists of matter with a high but non-relativistic temperature moving as a whole with relativistic bulk velocities. There are two other obvious possibilities: (i) The jet matter consists of a pair plasma and (ii) the jets consist only of ultra-relativistic plasma with no cold electrons present. In case (i) we have to consider the possibility of a bubble around an X-ray source filled with a huge amount of positrons. If these positrons become non-relativistic due to adiabatic or other energy losses inside the jets and they cool down to sufficiently low temperatures, we may observe a blue and red-shifted recombination line of positronium in the optical and UV wavebands. This line has a wavelength twice that of the Ly-[FORMULA] line of hydrogen. Much more important in this case, annihilation lines could be observed again red and blue-shifted relative to the rest energy of 511 keV. The strong red-shift but weak blue-shift of this line predicted by our model leaves a unique signature which will be observable with INTEGRAL. A luminosity only a few times smaller than the mechanical power of the jets will be emitted in the electron-positron annihilation line in this case. This large luminosity should make the annihilation lines observable despite the unfavorable angle of the jets to our line of sight. In the case of only ultra-relativistic plasma in the jets, case (ii), no recombination or annihilation lines should be observable.

8.2. Radio continuum

The internal shock models of GRBs (Rees & Meszaros 1994) attribute the formation of the shock traveling along the jet to the collision of shells of jet material with different bulk velocities. In the non-relativistic limit the velocity of the resulting shock is governed by the same momentum balance, Eq. (22), as the velocity of the termination surface of the jet. All quantities in that equation with subscript `c' now refer to the slower jet material in front of the jet shock while those with subscript `j' denote properties of the faster jet material driving the shock. The density ratio [FORMULA] is now simply given by the densities of the faster jet material driving the shock, [FORMULA], and that of the slower gas in front of the shock, [FORMULA]. We already pointed out in Sect. 7.1 that the jet shock is likely to be strong and so both Mach numbers in Eq. 22 are significantly greater than unity. Therefore [FORMULA]. Since in our model all material is assumed to be part of the conical jet structure, we find [FORMULA] and therefore [FORMULA]. This implies that within the limitations of the model presented here the velocity of the shock is constant as well which is confirmed by the observations (e.g. Mirabel & Rodríguez 1999 and references therein).

Once the energy of the shell collision is spent, the shock emission fades rapidly. It is therefore possible that we can observe the shock reaching the end of the jet only in special cases (XTE J1748-288, Hjellming et al. 1999; see above). We would then expect that the superluminal component should brighten, as well as decelerate rather abruptly. In the plasmon model the observed constant superluminal motion is taken to indicate a large mass and consequently large kinetic energy of the plasmon. If a plasmon is observed to slow down because of the growing mass of ISM it sweeps up, then this deceleration should be rather gradual unless the plasmon encounters a local overdensity in the ISM. The observed deceleration of the superluminal component in XTE J1748-288 occurred rather rapidly at a distance of about 1" from the core after a phase of expansion with practically constant velocity. Furthermore, the emission region is still detected in recent observations; 15 months after the start of the burst (Rupen, private communication). During this time it appears to have advanced only slowly at a velocity of about 0.01" per month or roughly 5000 km s-1. This slow motion and persistent radio emission may be interpreted as arising from the shock at the end of a continuous jet (see the previous section).

Some interesting predictions can be made from the model for future radio observations in the case that these can resolve the approaching and receding jet components along the jet axis. Because of the way in which the rate of acceleration of relativistic particles in the jet by the shock varies with time, the peak of the radio emission is not coincident with the position of the shock. This off-set depends on the observing frequency in the sense that the lower this frequency the more the emission peak lags behind the leading shock. This is illustrated in Fig. 4 where we plot the distance of the emission peak on the approaching jet side as a function of time for two different frequencies. Note also that this effect predicts that we should measure slightly different advance velocities of the emission peaks at different frequencies. This will not be observed in the case of discrete plasmon ejections.

[FIGURE] Fig. 4. Position of the radio emission peak in the fiducial model as a function of time after the start of the outburst. Solid line: Velocity of the jet shock derived from the 8.4 GHz observations, dashed line: Model prediction at 1.4 GHz and long dashed line: Model prediction at 8.4 GHz. Only the approaching jet component is plotted.

The steepening of the radio spectrum of the jets in microquasars in this model is explained by the superposition of the contribution to the total emission from various regions within the jet. In resolved radio maps of the jet components this should be visible because the model predicts the radio spectral index to change along the jet axis. This behaviour is shown in Fig. 5 for the approaching jet. Fig. 5 also shows the distribution of the flux along the jet axis. The relatively uniform distribution is caused by the decrease of the magnetic field strength further out along the jet counteracting the injection of newly accelerated particles by the shock. The jet region over which the spectrum steepens is small and the emission originating in this region also weakens considerably in the direction away from the jet shock. This may make a detection of the spectral steepening along the jet difficult. However, the apparent shortening of the emission region along the jet at higher observing frequencies may be detectable. The decrease in the strength of the magnetic field combined with the high energy cut-off of the energy spectrum of the relativistic particles leads to an overall steepening with time of the radio spectrum along the jet axis. This is also shown in Fig. 5 and should be observable if the jet components can be resolved at more than one frequency.

[FIGURE] Fig. 5. Predicted variation of the radio spectral index between 1.4 GHz and 8.4 GHz and flux along the jet axis. The length scale on the x-axis is normalised to the distance of the jet shock from the source centre at the respective observing time. Solid line: At the time of the first VLA observations, i.e. 4.8 days after the start of the outburst. Short-dashed line: At a time of 40 days after the start of the outburst. Dot-dashed line: Flux per relative distance in arbitrary units at 8.4 GHz at the time of the first VLA observations, corresponding to solid line. Long-dashed line: Flux per relative distance 40 days after the start of the outburst, corresponding to short-dashed line.

Note also that the length of the region along the jet axis which is emitting radiation at a given frequency increases with time. Although the fraction of the distance of the shock from the source centre subtended by the emitting region shrinks for later times (see Fig. 5), the absolute extent of this region will grow. This may also be detectable in future radio observations of sufficient surface brightness sensitivity.

Another prediction of the model is that the lightcurves of radio outbursts in microquasars at a given observing frequency should have a fairly constant slope for a few tens of days. After that they steepen rapidly once the critical frequency of the most energetic relativistic particles moves below the observing frequency. This steepening occurs earlier at higher frequencies. At the same time that the steepening of the lightcurves occurs, the flux ratio of the approaching and receding jet components should decrease. This effect is seen in Fig. 1. The jet components of the second outburst of April 21 observed during the second observing campaign with the VLA (Rodríguez & Mirabel 1999) show a much steeper lightcurve than those of the first outburst and, at the same time, a smaller flux ratio. Since these components were observed later in their evolution than those of the first outburst, this is in agreement with the predictions of the model.

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Online publication: April 17, 2000