Bondi/Hoyle and Shakura/Sunyaev - Max-Planck-Institut für ...

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The full system of equations Def. surface density Σ = 2hρ Mass conservation Angular momentum conservation M ˙ = 2πrΣvr 4πr2hfΦ = ˙ J + (r) − ˙ J − Energy conservation F = h ˙ Q(r, h) Vertical momentum conservation EOS h = cs(P, ρ)/Ω(r) P (ρ, T ) = 2ρkT/mp + aT 4 /3 Viscosity law Opacity <strong>and</strong> scattering fΦ = αP ¯κ −1 (ρ, T ) = ¯κ −1 Radiative transport abs (ρ, T ) + ¯κ−1 scatt F (r) = Λ(ρ, T ) h F (r) = F (r) = acT τ < 1 4 /τ(¯κ, Σ) τ ≥ 1 Parameters α, M, M˙ Known relations J ˙+ (r), J˙ − , Q(r, ˙ h), cs(P, ρ), ¯κabs(ρ, T ), ¯κscatt, Λ(ρ, T ), τ(¯κ, Σ) Solution vector ρ(r), h(r), Σ(r), vr(r), P (r), T (r), fΦ(r), ¯κ(r), F (r) 27
Structure of the solution • The solution in r can be divided into three regions: ⋆ Outer region: Gas pressure dominates radiation pressure, opacity is free-free absorption ⋆ Middle region: Gas pressure dominates radiation pressure, opacity is electron scattering ⋆ Inner region: Radiation pressure dominates gas pressure, opacity is electron scattering • Depending on the choice of parameters, not all regions will exist 28
Page 1 and 2: Accretion: Bondi/Hoyle and Shakura/
Page 3 and 4: Literature • This talk is based o
Page 5 and 6: Accretion onto compact objects •
Page 7 and 8: Models of accretion • Analytical
Page 9 and 10: 2. Spherical accretion 8
Page 11 and 12: Flow description • 1D radial flow
Page 13 and 14: • u(r) at small radii: free-fall
Page 15 and 16: 3. Disk accretion 14
Page 17 and 18: Disk accretion: General features
Page 19 and 20: Sketch of a thin accretion disk 18
Page 21 and 22: Angular momentum conservation • M
Page 23 and 24: Vertical momentum conservation •
Page 25 and 26: Viscosity law • Several physical
Page 27: Radiative transport • Transport f
Page 31 and 32: 4. General relativistic torus accre
Page 33 and 34: The torus (thick disk) model • As
Page 35: Summary • Accretion is inflow of

Bondi/Hoyle and Shakura/Sunyaev - Max-Planck-Institut für ...

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