The Role of the Outer Boundary Condition in Accretion Disk Models: Theory and Application

Abstract

In a previous paper (Yuan 1999, hereafter Paper I), we find that the outer boundary conditions(OBCs) of an optically thin accretion flow play an important role in determining the structure of the flow. Here in this paper, we further investigate the influence of OBC on the dynamics and radiation of the accretion flow on a more detailed level. Bremsstrahlung and synchrotron radiations amplified by Comptonization are taken into account and two-temperature plasma assumption is adopted. The three OBCs we adopted are the temperatures of the electrons and ions and the specific angular momentum of the accretion flow at a certain outer boundary. We investigate the individual role of each of the three OBCs on the dynamical structure and the emergent spectrum. We find that when the general parameters such as the mass accretion rateṀ and the viscous parameter α are fixed, the peak flux at various bands such as radio, IR and X-ray, can differ by as large as several orders of magnitude under different OBCs in our example. Our results indicate that OBC is both dynamically and radiatively important therefore should be regarded as a new "parameter" in accretion disk models.As an illustrative example, we further apply the above results to the compact radio source Sgr A * located at the center of our Galaxy. Advection-dominated accretion flow (ADAF) model has been turned out to be a great success to explain its luminosity and spectrum. However, there exists a discrepancy between the mass accretion rate favored by ADAF models in the literature and that favored by the three dimensional hydrodynamical simulation, with the former being 10-20 times smaller than the latter.

Inner Boundary Conditions for Advection‐dominated Accretion onto Black Holes

“…Utilization of equation (1) is convenient because it facilitates a semiclassical approach to the problem that simplifies the analysis considerably, while maintaining good agreement with fully relativistic calculations. For this reason, the pseudo-Newtonian potential has been adopted by a number of authors in their investigations of accretion onto Schwarzschild black holes (e.g., Matsumoto et al 1984;Abramowicz et al 1988;Chen et al 1997;Narayan et al 1997;Hawley & Krolik 2001Yuan 1999;Yuan et al 2000;Reynolds & Armitage 2001). We show in the Appendix that the relativistically correct energy equation for a particle freely falling from rest at infinity in the Schwarzschild metric can be written as…”

“…The proposition that the viscous torque actually vanishes at some radius outside the horizon is inevitably model dependent. Following Narayan, Kato, & Honma (1997), Yuan (2001), and Yuan et al (2000), we shall therefore assume here that the torque vanishes at the horizon and ask whether self-consistent ADAF models with this property can be constructed based on the standard Shakura-Sunyaev viscosity prescription. Our basic approach is to explore the associated disk structure using rigorous asymptotic analysis.…”

On the Nature of the Variable Infrared Emission from Sagittarius A*

“…In this section we briefly summarize the ingredients in our models. The dynamical quantities describing the accreting plasma, such as the density and temperature, are obtained by solving a one-dimensional global model of the accretion flow (see, e.g., Yuan et al 2000). Motivated by theoretical calculations and numerical simulations, we assume that the accretion rate is a function of radius, withṀ ¼Ṁ 0 (R=R out ) s (e.g., Blandford & Begelman 1999;Stone, Pringle, & Begelman 1999;Hawley & Balbus 2002;Igumenshchev, Abramowicz, & Narayan 2000;Igumenshchev, Narayan, & Abramowicz 2003).…”

A Jet-ADAF model for Sgr A*

“…The modeling technique is described in detail in Yuan et al (2000;see also Nakamura et al 1997). We use the Paczyński & Wiita (1980) potential to mimic the geometry of the central black hole.…”