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Astron. Astrophys. 358, 57-64 (2000)

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7. The accretion emission

To this point the colliding star model does not take into account the fate of all matter ejected by star collisions into the region around the black hole. It is not our purpose to perform here a detailed physics of this matter evolution and emission. Nevertheless, it is important to test here if and how much this plasma can change the results of the previous section.

We can easily suppose that part of the plasma ejected into the interstellar medium can stream along different planes towards the central black hole and can be accreted. In this framework two different emission contributions would be present: the hot expanding shells of plasma caused by star collisions and the accretion of the same plasma on the central black hole.

The second emission process can be taken into account supposing that in each collision about ([FORMULA]) of plasma goes, once cooled, into accretion, producing energy with a conversion efficiency assumed to be about 0.05. Since the collision rate is [FORMULA], the overall emission due to accretion is:

[EQUATION]

This picture, although very simplified, can give an order of magnitude of this process even if the real accretion luminosity would be probably lower (since we have chosen an upper limit for the amount of accreting matter) and varying in time (since matter is discontinually injected into the interstellar medium).

It is important to take into account that this approximate treatment is self consistent only if the typical accretion time [FORMULA] is longer than the matter free fall time on the black hole, i.e. if holds

[EQUATION]

If the mean luminosity due to collisions is approximatively expressed as in Eq. (9) and expression (3) is taken into account, the above expression for [FORMULA] can be rewritten as

[EQUATION]

and the total observable luminosity results

[EQUATION]

With this new expression for the cluster emission we have performed the same computations as in the case without accretion. The same parameter sets have been used with the only exception that those pairs ([FORMULA]) which did not fulfill the upper limit for [FORMULA] of Eq. (10) have been rejected. So the reported results correspond to parameter values for which it results [FORMULA]. The results are shown in Fig. 5. In this case, because of noise, we cannot state the compatibility of luminosity versus variability values with a line of specific slope. However, it is important to note that the introduction of the accretion component (even if in an approximated form) does not prevent the possibility of the previous found compatibility with the line of slope (-0.08).

[FIGURE] Fig. 5. Variability as a function of [FORMULA] for [FORMULA], [FORMULA] and: a) all the pairs ([FORMULA]) shown in Figs. 2 and 3 [dots]; b) a series of pairs ([FORMULA]) corresponding to density configurations with [FORMULA] [asterisks]. Pairs ([FORMULA]) corresponding to density configurations with [FORMULA] have been rejected. The straight line has the same slope of that shown in Fig. 1 of Paltani & Courvoisier 1997

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© European Southern Observatory (ESO) 2000

Online publication: June 26, 2000
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