Self‐similar Accretion Flows with Convection

Abstract

We consider height-integrated equations of an advection-dominated accretion flow (ADAF), assuming that there is no mass outflow. We include convection through a mixing length formalism. We seek self-similar solutions in which the rotational velocity and sound speed scale as R −1/2 , where R is the radius, and consider two limiting prescriptions for the transport of angular momentum by convection. In one limit, the transport occurs down the angular velocity gradient, so convection moves angular momentum outward. In the other, the transport is down the specific angular momentum gradient, so convection moves angular momentum inward. We also consider general prescriptions which lie in between the two limits.When convection moves angular momentum outward, we recover the usual self-similar solution for ADAFs in which the mass density scales as ρ ∝ R −3/2 . When convection moves angular momentum inward, the result depends on the viscosity coefficient α. If α > α crit1 ∼ 0.05, we once again find the standard ADAF solution. For α < α crit , however, we find a non-accreting solution in which ρ ∝ R −1/2 . We refer to this as a "convective envelope" solution or a "convectiondominated accretion flow." Two-dimensional numerical simulations of ADAFs with values of α < ∼ 0.03 have been reported by several authors. The simulated ADAFs exhibit convection. By virtue of their axisymmetry, convection in these simulations moves angular momentum inward, as we confirm by computing the Reynolds stress. The simulations give ρ ∝ R −1/2 , in good agreement with the convective envelope solution. The R −1/2 density profile is not a consequence of mass outflow. The relevance of these axisymmetric low-α simulations to real accretion flows is uncertain.

Two-dimensional inflow-wind solution of black hole accretion with an evenly symmetric magnetic field

“…These simulations found that in contrast to our original picture, the mass accretion rate decreases with decreasing radius (see review in Yuan et al 2012b). To explain such an astonishing result, two models have been proposed, namely convection-dominated accretion flow (CDAF; Narayan et al 2000;Quataert & Gruzinov 2000) and adiabatic inflow-outflow solution (ADIOS; Blandford & Begelman 1999). By comparing the properties of inflow and outflow and studying the convective stability of MHD accretion flow, Yuan et al (2012a; see also Li, Ostriker & Sunyaev 2013) show that strong wind must exist and it is the wind rather than convection that results in the inward decrease of accretion rate 1 .…”

Formation of supermassive black holes

“…The rate at which matter actually reaches the black hole is suppressed due to the back reaction of the energy flux inside the radius of influence (Gruzinov, 1998;Blandford and Begelman, 1999;Narayan et al, 2000;Quataert and Gruzinov, 2000). In the absence of a wind that removes energy and/or angular momentum, the accretion rate is reduced toṀ BH ∼ −1 (cs/c) 2Ṁ…”

Constraints on relativistic jets in quiescent black hole X-ray binaries from broad-band spectral modelling

“…8 Even without including an outflow, or with the benefit of radio constraints, McClintock et al (2003) conclude that the Xrays are emitted via SSC (at least for ∼ < 100 keV photons; see Esin, McClintock & Narayan 1997) by a population of hot electrons, and they speculate that a non-thermal electron component could also be relevant. Of course, a major difference between the ADAF model and our jet model is that the jet model explicitly attributes the X-ray emission 8 Note that ADAFs are prone to developing various types of instabilities (e.g., Narayan & Yi 1995), and other variants of RIAFs are also possible (one example is the convection-dominated accretion flow, CDAF; Narayan, Igumenshchev & Abramowicz 2000;Quataert & Gruzinov 2000). In particular, as illustrated by the adiabatic inflow-outflow solution (ADIOS; Blandford & Begelman 1999), it is very plausible that a significant fraction of the accretion energy is instead carried away as mechanical energy in the form of an outflow, and not advected directly into the black hole (also see e.g., Fender, Gallo & Jonker 2003, and references therein, for the role that an outflow may play).…”