4. Concluding remarks
Although outflows are common in many astrophysical systems which include compact objects such as black holes and neutron stars, it was difficult to compute the outflow rates since these objects do not have any intrinsic atmospheres and outflowing matter has to come out from the inflow only. We showed in the present paper that, assuming the formation of a dense region around these objects (as provided by a centrifugal barrier, for instance), it is possible to obtain the outflow rate in a compact form with an assumption of isothermality of the outflow at least up to the sonic point and the ratio thus obtained seems to be quite reasonable. Computation of the outflow rate with a non-isothermal outflow explicitly depends on several flow parameters. Our primary goal in this paper was to obtain the rate as a function of the compression ratio of the gas and the geometric quantities. We show that for a given inflow/outflow configuration, the outflow rate shows a peak as the shock-compression is increased. We do not concern ourselves with the collimation mechanism. Since observed jets are generally hollow, they must be externally supported (either by ambient medium pressure or by magnetic hoop stress). This is assumed here for simplicity. Our assumption of isothermality of the wind till the sonic point is based on `experience' borrowed from stellar physics. Momentum deposition from the hot photons from the dense cloud, or magnetic heating may or may not isothermalize the expanding outflow, depending on accretion rates and covering factors. However, it is clear that since the solid angle at which photons shine on electrons is close to (as in a narrow funnel wall), and since the number of electrons per photon is much smaller in a compact region, it may be easier to maintain the isothermality close to a black hole than near a stellar surface.
The centrifugal-pressure-supported region that may be present was found to be very useful in explaining the soft and the hard states (CT95), rough agreement with power-law slopes in soft states (CT95) as well as the amplitude and frequency of QPO (C96) in black hole candidates. Therefore, our reasonable estimate of the outflow rate from these considerations further supports the view that such regions may be common around compact objects. Particularly interesting is the fact that since the wind here is thermally driven, the outflow ratio is higher for hotter gas, that is, for a low accretion rate. It is obvious that the non-magnetized neutron stars should also have the same dense region we discussed here and all the considerations mentioned here would be equally applicable.
It is to be noted that although the existence of outflows is well known, their rates are not. The only definite candidate whose outflow rate is known with any certainty is probably SS433 whose mass outflow rate was estimated to be yr-1 (Watson et al. 1986), where f is the volume filling factor, is the electron density in units of cm-3, is the distance of SS433 in units of 5kpc. Considering a central black hole of mass , the Eddington rate is yr-1 and assuming an efficiency of conversion of rest mass into gravitational energy , the critical rate would be roughly yr-1. Thus, in order to produce the outflow rate mentioned above even with our highest possible estimated (see Fig. 2a), one must have which is very high indeed. One possible reason why the above rate might have been over-estimated would be that below cm from the central mass (Watson et al. 1986), because of the existence of the dense region at the base of the outflow.
We also discussed the effect of outflows on the spectral states and QPO properties of black hole candidates, such as GRS1915+105. The presence of QPO in the hard state, and periodic outbursts in intermediate state, generally absence of QPO in soft states, switching of states from hard to soft states in few seconds (free fall time rather than infall time) due to the presence of sub-Keplerian matter are generally understood in this scenario. Since the processes are highly non-linear, more detailed studies are necessary, but we believe that outflows play a major role in explaining these properties. In any case, qualitative agreement of the time scales decidedly prove that sub-Keplerian flows exist in a black hole accretion. Similar formation of outflows in neutron stars also should explain QPOs, especially that in neutron stars there could be two shocks (one near the hard surface and the other at a similar distance as the shock around a black hole; C90, C96). The only difference is that in neutron stars, the magnetic axis could be non-aligned with respect to the spin axis, and the outflows on either side of the disk would have an opposite effect in splitting the QPO frequency due to the Coriolis force as suggested in other contexts (Titarchuk et al. 1998).
In numerical simulations the ratio of the outflow and inflow has been computed on several occasions (Eggum et al. 1985; Molteni et al. 1994). Eggum et al. (1985) found the ratio to be for a radiation pressure dominated flow. This is generally comparable with what we found above (Eq. (19a)). In Molteni et al. (1994) the centrifugally driven outflowing wind generated a ratio of . Here, the angular momentum was present in both inflow as well as outflow, and the shock was not very strong. Thus, the result is again comparable with what we find here. On the other hand, when the angular momentum is very high, it was seen that the outflow rate becomes comparable to the inflow rate. In these simulations, it was seen that the disk mass changes dramatically, and occasionally evacuating the disk also. This is possible if is very large as in our present model.
© European Southern Observatory (ESO) 1999
Online publication: November 2, 1999