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Ken-ya Watarai, New Analytical Formulae for Optically Thin Accretion Flows, Publications of the Astronomical Society of Japan, Volume 59, Issue 2, 25 April 2007, Pages 443–449, https://doi.org/10.1093/pasj/59.2.443
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Abstract
In a previous paper, we described new analytic formulae for optically thick supercritical accretion flows (Watarai 2006, hereafter paper 1). Here, we present analytic formulae for optically thin one-temperature accretion flows including the advection-dominated regime, using the “semi-iterative” method, described in paper 1. Our analytic formulae have two real solutions. The first solution corresponds to advection-dominated accretion flow (ADAF), and the second solution corresponds to radiation-dominated accretion flow, described by Shapiro, Lightman, and Eardley (the so-called SLE model). Both solutions are given by a cubic equation for the advection parameter, |$f$|, which is the ratio of the advection cooling rate, |$Q_{\rm adv}$|, to the viscous heating rate, |$Q_{\rm vis}$|, i.e., |$f=Q_{\rm adv}/Q_{\rm vis}$|. Most previous studies assumed that |$f$| is constant (|$f \sim 1$| for the ADAF). However, it is clear that |$f$| should be a function of the physical parameters of the radiative-cooling dominated regime. We found that the ratio |$f$| can be written as a function of the radius, mass-accretion rate, and viscous parameter, |$\alpha$|. Using this formula, we can estimate the transition radius from the inner optically thin ADAF to the outer optically thick standard disk, which can be measured using observations of the quiescent state in black hole X-ray binaries.
