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

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6. Properties of GRS 1915+105

6.1. Energetics

Using the model parameters of our fiducial model we now derive some of the physical properties of the jets of GRS 1915+105 during the outburst of March 19. The rate at which energy is transfered by the jet shock to the relativistic particle population at time [FORMULA] is

[EQUATION]

where we have assumed that only electrons and/or positrons are accelerated and that the initial energy spectrum of the relativistic particles extends down to [FORMULA].

The rate at which energy is transported in the form of magnetic fields can be estimated by

[EQUATION]

where [FORMULA] is the opening angle of the conical jet and [FORMULA] is the speed of the shock in the frame of the shocked jet material. For our fiducial model [FORMULA] c. Fender et al. (1999) find that during another outburst of GRS 1915+105 in 1997 [FORMULA] was smaller than [FORMULA]. This would then imply an upper limit to [FORMULA] of [FORMULA] W. Note that the strength of the magnetic field in the jet after the passage of the shock is used here. This estimate does not imply that the unshocked jet material carries a magnetic field of this strength. Some or all of the magnetic field may be generated in the shock itself.

Finally, we can derive a lower limit for the bulk kinetic energy transported by the jet material. We know the number of relativistic light particles in the jet and so

[EQUATION]

This is only a strict lower limit, since we do not know whether the jets also contain thermal material and/or protons. In the case that there is one proton for each relativistic electron we find that the numerical constant in Eq. (19) increases to [FORMULA]. Note that this then is identical to the energy carried in the form of magnetic fields for [FORMULA].

The estimates for the energy transported along the jet in various forms presented above are lower by about a factor 10 than the estimates of Fender et al. (1999) for the weaker outburst in 1997. However, it should be noted that their estimates are based on the assumption that the radio emission is caused by two `blobs' of relativistic plasma which were ejected by the central source within about 12 hours. The continuous jet model presented here requires that the estimated energy supply to the jet is sustained by the central source for at least 42 days; the length of the first observing campaign. This means that the total amount of energy produced by GRS 1915+105 is predicted by our model to be at least an order of magnitude greater during the March 1994 outburst than it was in the case of discrete ejections assumed for the September 1997 event.

These estimates illustrate that a continuous jet model cannot decrease the total amount of energy needed for a given radio outburst but the rate at which this energy is produced is much lower than in a model assuming discrete ejection events. This is the case because much, if not most, of the energy needed to produce the radio emission observed is `stored' in the material of the continuous jet. This material was ejected by the central source during comparatively long period well before the process which led to the formation of the jet shock took place. Only the acceleration of relativistic particles at the jet shock then `lights up' the jet and we are able to detect it.

6.2. Self-absorption

Since all jet properties are assumed to scale with distance from the source centre in our conical jet, it is clear that at some early time in the outburst the jet material was opaque for radio emission because of synchrotron self-absorption. The absorption coefficient in the rest frame of the emitting gas is given by (e.g. Longair 1981)

[EQUATION]

where in our notation

[EQUATION]

and [FORMULA] is of order unity. We only consider the region just behind the jet shock where the energy distribution of the relativistic particles is completely described by a power law of exponent p. For a photon emitted at the centre of the jet the optical depth in the radial direction is then [FORMULA]. For our fiducial model we then find that the jet material becomes transparent at 8.4 GHz roughly 2 hours after the start of the outburst when the shock has reached a distance of [FORMULA] m from the source centre.

Mirabel et al. (1998) find that for the much weaker `mini-bursts' of GRS 1915+105 the jets become transparent about 30 minutes after the start of the burst. Bearing in mind that the mini-bursts may be quite different in their properties compared to the major outburst considered here, our value is therefore in good agreement with their findings.

6.3. Infrared emission

Several groups have reported the detection of infrared emission from GRS 1915+105 (i.e. Sams et al. 1996, Mirabel et al. 1996, 1998). In the case of the mini-bursts simultaneous flux measurements at radio frequencies and in the K-band are available at times of about 10 to 20 minutes after the start of the bursts (Mirabel et al. 1996). Because of the uncertainties in the dust corrections in the K-band towards GRS 1915+105 it is difficult to estimate the spectral behaviour from radio to infrared wavelengths. However, for the mini-bursts flat spectra, [FORMULA], regardless of the exact magnitude of extinction are observed very early during the bursts (Mirabel et al. 1996). The slope of the initial energy distribution of the relativistic particles in combination with the rather low high-energy cut-off of this distribution we found for our fiducial model is inconsistent with such flat emission spectra. However, this model does predict an unobscured, optically thin infrared flux of about 14 mJy in the K-band for a time about 15 minutes after the start of the burst. This may be enough to be detected in future observations of large outbursts. The timing requirements for such an observations are however difficult to meet, since the predicted infrared flux very quickly becomes undetectable at only slightly later times.

More puzzling is the detection of a resolved jet component with K-band flux of at least 1.8 mJy about 0.3" away from the centre of GRS 1915+105 by Sams et al. (1996). The shock on the approaching side of our jet model would need 24 days to reach such a large distance from the source centre. By this time our fiducial model predicts no synchrotron emission in the K-band at all. We have estimated whether this infrared emission may be caused by radio photons which are inverse Compton scattered to such high frequencies within the jet plasma. However, we find that this cannot explain the observations since the density of the relativistic particles in the jet in our model is orders of magnitude too low.

The observation of K-band emission far away from the core of GRS 1915+105 and the flat spectral indices of the mini-bursts suggest that two different types of outbursts may occur in the jets of this source. The strong radio bursts like the one of March 1994 are caused by jet shocks which produce large numbers of relativistic particles with a steep energy distribution. The weaker mini-bursts involve shocks which accelerate less particles but produce a flatter energy distribution which may also extend to higher energies than in the stronger bursts. The `mini-burst mode' may correspond to a phase of relative stable jet production with only small variations in the bulk velocity of the jet material. Such flat spectra extending to millimeter wavelengths, possibly coupled with the continuous ejection of a jet, have been observed in Cygnus X-1 (Fender et al. 2000). The strong radio outbursts then probably mark phases of more violent changes in the central jet production mechanisms. Fender (1999) points out that this proposed behaviour may also be reflected in the X-ray signature of the accretion disk. In any case, other sources of infrared emission in the close vicinity of the jets like dust illuminated by the disk and/or the jet may further complicate the situation (Mirabel et al. 1996). To test the validity of the proposed scenario resolved observations of outbursts of GRS 1915+105 and other galactic jet sources from radio to infrared frequencies would be necessary.

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© European Southern Observatory (ESO) 2000

Online publication: April 17, 2000
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