The linear marginal instability of an axisymmetric magnetohydrodynamics Taylor-Couette flow of infinite vertical extension is considered. We are only interested in those vertical wave numbers for which the characteristic Reynolds number is minimum. For hydrodynamically unstable flows minimum Reynolds numbers exist even without a magnetic field, but there are also solutions with smaller characte...

Radiative efficiency, η ≡ L/Ṁc, of a slowly accreting black hole is estimated using a two-temperature model of accretion. The radiative efficiency depends on the magnetic field strength near the Schwarzschild radius. For weak magnetic fields, β ≡ B/8πp ∼< 10 , the low efficiency η ∼ 10 assumed in some theoretical models is achieved. For β > 10, a significant fraction of viscous heat is dissipat...

1 Chandrasekhar, S., "The Stability of Non-Dissipative Couette Flow in Hydromagnetics," these PROCEEDINGS, 46, 253-257 (1960); see also Velikhov, E. P., "Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic field," Soviet Phys.-JETP, 36, 995-998 (1959). 2 Reid, W. H., "Inviscid modes of instability in Couette flow," J. Math. Anal. and Applications (to appea...

We extend and reconcile recent work on turbulence and particle heating in advection-dominated accretion flows. For approximately equipartition magnetic fields, the turbulence primarily heats the electrons. For weaker magnetic fields, the protons are primarily heated. The division between electron and proton heating occurs between β ∼ 5 and β ∼ 100 (β ≡ ratio of gas to magnetic pressure), depend...

We extend and reconcile recent work on turbulence and particle heating in advection-dominated accretion flows. For approximately equipartition magnetic fields, the turbulence primarily heats the electrons. For weaker magnetic fields, the protons are primarily heated. The division between electron and proton heating occurs between β ∼ 5 and β ∼ 100 (β ≡ ratio of gas to magnetic pressure), depend...

Using mean field MHD, we discuss the energetics of optically thin, two temperature, advection-dominated accretion flows (ADAFs). If the magnetic field is tangled and roughly isotropic, flux freezing is insufficient to maintain the field in equipartition with the gas. In this case, we expect a fraction of the energy generated by shear in the flow to be used to build up the magnetic field strengt...