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Astron. Astrophys. 351, 185-191 (1999)

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3. Effects of outflows from shocked compressed accretion

One can discuss the effects of outflows of a stellar black candidate such as GRS 1915+105. Particularly interesting is that it shows QPO of around 1-15Hz and sometimes flares at around 0.01Hz (Paul et al. 1998). An interesting property of our solution (Fig. 2a) is that the outflow rate is peaked at around [FORMULA] ([FORMULA]), when the shock is of `average' strength. On either side, the outflow rate falls off very rapidly and this may have significant observational effects. As Eq. (16) is independent of shock location, shocks oscillating with time period similar to the infall time in [FORMULA] region (causing a 1-10Hz QPO in the hard state (CT95, C96)) will continue to have outflows and gradually fill the relatively slowly moving (sonic) sphere of radius [FORMULA] till [FORMULA] when this region would be cooled down catastrophically by inverse Comptonization. (In general, spectra may soften in the presence of outflows even in the hard state, see Chakrabarti, 1998) At this stage: (a) the [FORMULA] region would be drained to the hole in [FORMULA] seconds. This is typically what is observed for GRS1915+105. (Yadav et al. 1999). (b) The shock will disappear, and a smaller compression ratio ([FORMULA]) would stop the outflow (Fig. 2a). In other words, during burst/quiescence QPO phase, the outflow would be blobby. This is also reported (Mirabel & Rodriguez 1998). (c) The black hole will go to a soft state during a short period. If the angular momentum is high enough, so that the outflow rate is really high, this brief period of soft state may be prolonged to a longer period of tens of seconds depending on how the centrifugal barrier is removed by viscosity generated during shock oscillations. The fact that shock oscillation causes the 1-15Hz QPO is clearly demonstrated by the fact there is more power at high energy (Fig. 3 of Paul et al. 1998) and most of the high energy X-ray radiation is emitted in the post-shock region.

Using our solution, it is easy to compute the interval between two bursts during which the object is in QPO phase with [FORMULA] Hz. The sonic sphere becomes ready for catastrophic cooling in


Here, [FORMULA] is the average density of the sonic sphere and [FORMULA], [FORMULA] is the Thomson scattering cross-section. For an average shock R around 2.5, [FORMULA] stays close to 4, and with outflow and inflow of roughly equal angular dimension ([FORMULA]), [FORMULA] and [FORMULA] (using peak value in Fig. 3b). Putting typical values of a hard state [FORMULA], and [FORMULA], [FORMULA] in the above equation, we obtain


Our choice of [FORMULA] is not arbitrary. If the viscosity is low, the angular momentum could be high enough to have a shock at a larger distance (C90) and the oscillation frequency of QPO for [FORMULA] is around 6Hz as seen in GRS1915+105 (public RXTE archival data of May 26th, 1997). Our [FORMULA]s is encouraging, since on that day, bursts did repeat with [FORMULA]Hz. However, the system need not remain steady at these frequencies due to non-linear processes such as recycling a part of the wind back to the accretion disk. Systematic feeding of matter would raise the accretion rate, decreasing the cooling time and increasing the QPO frequency. Similarly, if the specific angular momentum remains higher, cool flow may take longer time to be drained, to the extent that the flow may like to stay for a long time in the burst phase in a soft state. When the Keplerian rate is actually increased in the inflow (due to a rise in viscosity at the outer edge of the disk, say), shocks would permanently cool down and outflows would be gradually turned off.

If the shock strength is on the higher side ([FORMULA]), [FORMULA], the location of the sonic point [FORMULA] increases linearly with [FORMULA], but the average density [FORMULA] decreases exponentially (Eq. (13)). So, [FORMULA] and the object will remain in the hard state. In this phase, hydrodynamic outflow may form continuously as the rate [FORMULA] does not go to zero. The QPO frequency [FORMULA] is still determined by the infall time scale from the shock location. (This is true if the cooling time and the infall time become comparable so that QPO forms in the first place.) Only when the Keplerian rate is intrinsically increased due to, say, a rise of viscosity at the outer boundary of the disk, does the shock get softened and the [FORMULA] starts getting smaller within observable resolution. Thus, in this scenario, in the pure soft state, [FORMULA] and in the pure hard state (with possible QPO) [FORMULA]. In between there is a possibility of having both soft (flaring) and hard states (including QPO) switching in tens to hundreds of seconds with periodicity of [FORMULA].

Since [FORMULA] and [FORMULA] (Molteni et al. 1996), it is expected that [FORMULA] and since [FORMULA], it is expected that [FORMULA]. Details are presented in Chakrabarti (1990).

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© European Southern Observatory (ESO) 1999

Online publication: November 2, 1999