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Shoji Kato, Kenji E. Nakamura, Transition Radius from Cooling-Dominated to Advection-Dominated Regimes in Two Temperature Disks, Publications of the Astronomical Society of Japan, Volume 50, Issue 6, 1 December 1998, Pages 559–566, https://doi.org/10.1093/pasj/50.6.559
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Optically thin advection-dominated flows are known to be unable to extend outward beyond a certain critical (transition) radius in disk accretion. Outside of the radius, the disks are cooling-dominated. The advection-dominated self-similar steady flows cannot join thermally to the cooling-dominated steady standard disks, unless there is some external heating at the transition zone. We examine, under the condition of no such heating, the radius rtr of the transition analytically when the advection-dominated inner flows are two-temperature ones. The results are almost the same as those obtained by Honma (1996, AAA 65.067.241) to a one-temperature disk: i.e., rtr/rg ∼ 5.5 × 102(α4/ṁ2), where α is the viscosity parameter and ṁ is the mass accretion rate normalized by the critical accretion rate defined by the Eddington luminosity. This coincidence with the one-temperature case comes from the fact that the transition occurs after the ion temperature in the advection-dominated region decreases sharply outwards.
