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Astron. Astrophys. 346, 713-720 (1999)

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1. Introduction

The Advection Dominated Accretion Flows (ADAFs) have been reviewed by a number of authors, most recently by Narayan et al. (1998), Kato et al. (1998), and Lasota (1998). The ADAFs represent a class of optically thin solutions of the accretion flow, which radiate so inefficiently, that almost all the heat dissipated inside the fluid is subsequently advected toward the black hole horizon. Since the cooling of matter is negligible, the equations of fluid dynamics are independent of the equations describing the emission, absorption and scattering of radiation. This allows one to address these two topics separately. In this paper we are concerned mostly with the radiation processes inside the flow.

The fully relativistic dynamics of ADAFs has been described and some solutions have been obtained in Lasota (1994), Abramowicz et al. (1996, hereafter ACGL), Abramowicz et al. (1997), Peitz & Appl (1997), Jaroszynski & Kurpiewski (1997, hereafter Paper I), Gammie & Popham (1998), and Popham & Gammie (1998). The most extensive survey of the parameter space is probably presented by Popham & Gammie (1998), where the dependence of the flow on the black hole spin a, the viscosity parameter [FORMULA], the gas adiabatic index and on the advection parameter f (where [FORMULA] means fully advective flow without any cooling) is investigated. This work shows rather strong dependence of the flow characteristics on parameters mentioned, especially on the black hole spin. The dependence on advection parameter is also substantial, but for a narrow range of f, which can represent flows with negligible cooling ([FORMULA]) one can use the [FORMULA] solutions. Similarly, the solutions depend strongly on the viscosity parameter [FORMULA], but for the limited range of this parameter ([FORMULA]), which is more physically relevant (Balbus et al. 1995), the differences between the solutions are not dramatic, in particular the topology of the isobars is the same.

In our calculations we use the solutions of the equations describing the flow dynamics presented in Paper I. All our models use [FORMULA] and [FORMULA]. Both values are representative of the physically relevant ADAFs. The black hole spin, we consider, is limited to the three values ([FORMULA], 0.5, and 0.9).

The main purpose of this paper is a self-consistent treatment of photon Comptonization in a two temperature plasma of an ADAF solution. To do so we need a 3D distribution of matter density, velocity and temperature, while the standard solutions give only the vertically averaged quantities as measured at the equator. At this point it is important to choose the relevant method of vertical averaging and we follow Abramowicz et al. (1997), Quataert & Narayan (1998) and Paper I in choosing averaging on spheres (and not on cylinders). In this approach the matter distribution in space is limited by the centrifugal forces barrier and does not resemble the infinite isothermal atmosphere, obtained in the alternative approach.

We calculate the spectrum of photons leaving the flow. The photons originate in bremsstrahlung and thermal synchrotron processes, which can be described locally. The scattering (if any) can take place at any point of the photon trajectory inside matter distribution and is nonlocal. We simulate this process using Monte Carlo approach. Our simulation of photon Comptonization is quite standard, but the flow, where the processes take place is rather complicated. Since the optical depth for scattering is low, a photon can travel to a distant part of the fluid before undergoing any interaction. The relative motion of the fluid elements, where consecutive interactions of photons with matter take place, can be substantial. Also, the photons traveling in the densest parts of the flow, near the horizon, can be deflected by the gravitational field. This and other relativistic effects in photon motion are included in our study.

The main aim of our investigation is the self-consistent treatment of Comptonization. Most non-analytical thermal Comptonization models use iterative methods of solving the kinetic equations (e.g. Poutanen & Svensson 1996). This method has been adopted by Narayan et al. (1997) to calculate the spectrum of soft X-ray transient source V404 Cyg in which, they believe, ADAF exists. In our calculations we use Monte Carlo method which has been described in most detail by Pozdnyakov et al. (1977) and Górecki & Wilczewski (1984). This method allows us to follow only one photon at a time and we are not able to take into account the creation of [FORMULA] pairs. However as Björnsson et al. (1996) and Kusunose & Mineshige (1996) showed, the role of [FORMULA] pairs in ADAFs is not significant.

In the next section we briefly characterize the model of ADAF. The method of Monte Carlo Comptonization is presented in Sect. 3. In Sect. 4 we present the results of calculations, showing the ADAFs spectra. The discussion and conclusions follow in the last section.

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© European Southern Observatory (ESO) 1999

Online publication: May 21, 1999