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Astron. Astrophys. 344, 105-110 (1999)

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1. Introduction

Angular momentum in accretion disks around black holes must deviate from a Keplerian distribution, since the presence of ion, radiation or inertial pressure gradient forces become as significant as the gravitational and centrifugal forces (see Chakrabarti 1996a; Chakrabarti 1996b and references therein). The inertial pressure close to a black hole is high, because, on the horizon, the inflow velocity must be equal to the velocity of light. For causality, the velocity of sound must be less than the velocity of light. In fact, in the extreme equation of state of [FORMULA] (where c is the velocity of light and P and [FORMULA] are the isotropic pressure and mass density respectively), the sound speed is only [FORMULA]. Thus, the flow must pass through a sonic point and become supersonic before entering into the horizon. A flow which must pass through a sonic point must also be sub-Keplerian (Chakrabarti 1996b and references therein), and this causes the deviation. If the accretion rate is low, the flow cools down only by inefficient bremsstrahlung and Comptonization processes, unless the magnetic field is very high (Shvartsman 1971; Rees 1984; Bisnovatyi-Kogan 1998). This hot flow can undergo significant nucleosynthesis depending on the inflow parameters. Earlier, in the context of thick accretion disks calculations of changes in composition inside an accretion disk were carried out (Chakrabarti et al. 1987; Hogan & Applegate 1987; Arai & Hashimoto 1992; Hashimoto et al. 1993), but the disk models used were not completely self-consistent, in that neither the radial motion, nor the cooling and heating processes were included fully self-consistently. Second, only high accretion rates were used. As a result, the viscosity parameter required for a significant nuclear burning was extremely low ([FORMULA]). In the present paper, we do the computation after including the radial velocity in the disk and the heating and cooling processes. We largely follow the solutions of Chakrabarti (1996b) to obtain the thermodynamic conditions along a flow.

Close to a black hole horizon, the viscous time scale is so large compared to the infall time scale that the specific angular momentum [FORMULA] of matter remains almost constant and sub-Keplerian independent of viscosity (Chakrabarti 1996a,b; Chakrabarti 1989). Because of this, as matter accretes, the centrifugal force [FORMULA] increases much faster compared to the gravitational force [FORMULA] (where G and M are the gravitational constant and the mass of the black hole respectively, [FORMULA] and x are the dimensionless angular momentum and the radial distance from the black hole). As a result, close to the black hole (at [FORMULA]) matter may even virtually stop to form standing shocks (Chakrabarti 1989). Shock or no-shock, as the flow slows down, the kinetic energy of matter is converted into thermal energy in the region where the centrifugal force dominates. Hard X-rays and [FORMULA]-rays are expected from here (Chakrabarti & Titarchuk, 1995). In this centrifugal pressure supported hot `boundary layer' (CENBOL) of the black hole (Chakrabarti et al. 1996) we find that for low accretion rates, [FORMULA] of the infalling matter is completely photo-dissociated and no [FORMULA] could be produced. In this region, about ten to twelve percent of matter is found to be made up of pure neutrons. These neutrons should not accrete very fast because of very low magnetic viscosity associated with neutral particles (Rees et al. 1982) while protons are dragged towards the central black hole along with the field lines. Of course, both the neutrons and protons would have `normal' ionic viscosity, and some slow accretion of protons (including those produced after neutron decay) would still be possible. In contrast to neutron stars, the neutron disks which we find are not dense. Nevertheless, they can participate in the formation of neutron rich isotopes and some amount of deuterium. They can be eventually dispersed into the galaxy through jets and outflows, which come out of CENBOL (Chakrabarti 1998; Das & Chakrabarti 1998) thereby possibly influencing the metallicity of the galaxy.

On the equatorial plane, where the viscosity is the highest, a Keplerian disk deviates to become sub-Keplerian very close to the black hole (Chakrabarti & Titarchuk 1995; Wiita 1982). Away from the equatorial plane, viscosity is lower and the flow deviates from a Keplerian disk farther out. This is because the angular momentum transport is achieved by viscous stresses. Weaker the viscosity, longer is the distance through which angular momentum goes to match with a Keplerian disk. When the viscosity of the disk is decreased on the whole, the Keplerian disk recedes from the black hole forming quiescence states when the objects become very faint in X-rays (Ebisawa et al. 1996). Soft photons from the Keplerian disk are intercepted by this sub-Keplerian boundary layer (CENBOL) and photons are energized through Compton scattering process. For higher Keplerian rates, electrons and protons cool down completely and the black hole is in a soft state (Tanaka & Lewin 1995). Here, bulk motion Comptonization produces the power-law tail of slope [FORMULA] (Chakrabarti & Titarchuk 1995; Titarchuk et al. 1997). For lower Keplerian rates, the Compton cooling is incomplete and the temperature of the boundary layer remains close to the virial value,


In this case, bremsstrahlung is also important and the black hole is said to be in a hard state with energy spectral index [FORMULA] ([FORMULA], where [FORMULA] is the frequency of the photon) close to 0.5. In Eq. (1), [FORMULA] is the mass of the proton, [FORMULA] is the Schwarzschild radius of the black hole, and c is the velocity of light. (In future, we measure the distances and velocities in units of [FORMULA] and c.) In this low Keplerian rate, electrons are cooler typically by a factor of [FORMULA] unless the magnetic field is very high. Present high energy observations seem to support the apparently intriguing aspects of black hole accretion mentioned above. For instance, the constancy of (separate) spectral slopes in soft and hard states has been observed by many (Ebisawa et al. 1994; Miyamoto et al. 1991; Ramos et al. 1997; Grove et al. 1998; Vargas et al. 1997). ASCA observations of Cygnus X-1 seem to indicate that the inner edge of the Keplerian component is located at around [FORMULA] (instead of [FORMULA]) (Gilfanov et al. 1997). HST FOS observations of the black hole candidate A0620-00 in quiescent state seems to have very faint Keplerian features (McClintock et al. 1995) indicating the Keplerian component to be farther out at low accretion rates. Bulk motion Comptonization close to the horizon has been considered to be a possible cause of the power-law tail in very soft states (Crary et al. 1996; Ling et al. 1997; Cui et al. 1997). However, some alternative modes may not be ruled out to explain some of these features.

This observed and predicted dichotomy of states of black hole spectra motivated us to investigate the nuclear reactions thoroughly for both the states, but we report here the results obtained in the more important case, namely, when the flow is hotter, i.e., for hard states. We use 255 nuclear elements in the thermo-nuclear network starting from protons, neutrons, deuterium etc. till [FORMULA] and the nuclear reaction rates valid for high temperatures. We assume that accretion on the galactic black hole is taking place from a disk where matter is supplied from a normal main sequence star. That is, we choose the abundance of the injected matter to be that of the sun. Because of very high temperature, the result is nearly independent of the initial composition, as long as reasonable choices are made. When accretion rates are higher, the advective region becomes cooler and very little nucleosynthesis takes place, the results are presented elsewhere (Mukhopadhyay 1998; Mukhopadhyay & Chakrabarti 1998).

As hot matter approaches a black hole, photons originated by the bremsstrahlung process, as well as those intercepted from the Keplerian disk, start to photo-dissociate deuterium and helium in the advective region. There are two challenging issues at this stage which we address first: (a) Thermodynamic quantities such as density and temperature inside a disk are computed using a thin disk approximation, i.e., the vertical height [FORMULA] at a radial distance x very small compared to x ([FORMULA]), and assuming the flow to be instantaneously in vertical equilibrium. However, at a low rate, it is easy to show that the disk is optically thin in the vertical direction [FORMULA] ([FORMULA] is the Thomson scattering cross-section). However, soft photons from the Keplerian disk enter radially and [FORMULA], generally. In fact, this latter possibility changes the soft photons of a few keV from a Keplerian disk to energies up to [FORMULA]MeV by repeated Compton scattering (Sunyaev & Titarchuk 1980; Chakrabarti & Titarchuk 1995) while keeping the photon number strictly constant. The spectrum of the resultant photons emitted to distant observers becomes a power law [FORMULA] instead of a blackbody, where [FORMULA] for hard state and [FORMULA] for soft states of a black hole. (b) Now that the spectrum is not a blackbody, strictly speaking, the computation of photo-disintegration rate that is standard in the literature (which utilizes a Planckian spectrum) cannot be followed. Fortunately, this may not pose a major problem. As we shall show, the standard photo-disintegration rate yields a lower limit of the actual rate that takes place in the presence of power-law photon spectra. Thus, usage of the correct rate obtainable from a power-law spectrum would, if anything, strengthen our assertion about the photo-disintegration around a black hole. After photo-disintegration by these hard photons, all that are left are protons and neutrons. The exact location where the dissociation actually starts may depend on the detailed photon spectrum, i.e., optical depth of this boundary layer and the electron temperature.

The plan of the present paper is the following: in the next section, we present briefly the hydrodynamical model using which the thermodynamic quantities such as the density and temperature inside the inner accretion disk are computed. We also present the model parameters we employ. In Sect. 3, we present results of nucleosynthesis inside a disk. Finally, in Sect. 4, we present out concluding remarks.

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© European Southern Observatory (ESO) 1999

Online publication: March 10, 1999