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6). 6). There is then enough time for a local balance to hold between viscous dissipation and radiative cooling. For the accretion rates implied in observed systems, the disk is then rather cool, which then justiﬁes the starting assumption H/r 1. This argument is somewhat circular, of course, because the accretion time is long enough for eﬀective cooling only if the disk is assumed to be thin to begin with. Other forms of accretion disks may exist, even at the same accretion rates, in which the cooling is ineﬀective compared with that of standard (geometrically thin, optically thick) disks.
1). ” If your career depends on being friends with this community, it would be wise to avoid discussions about accretion disks or Couette experiments. 5 Thin disks: equations Consider a thin (= cool, nearly Keplerian, cf. 2) disk, axisymmetric but not stationary. 39) where ρ0 and H0 are the density and scale height at the midplane, respectively. The approximate sign is used to indicate that the coeﬃcient in front of H in the last expression actually depends on details of the vertical structure of the disk.
49) where ri is the inner radius of the disk and β is a parameter appearing through the integration constant. 50) where Ωi is the Kepler rotation rate at the inner edge of the disk. If the disk accretes onto an object with a rotation rate Ω∗ less than Ωi , the rotation rate Ω(r) as a function of distance r jumps from Ω∗ close to the star to the Kepler rate ΩK (r) in the disk. It then has a maximum at some distance close to the star (distance of the order of the disk thickness H). At this point the viscous stress (proportional to ∂r Ω) vanishes and the angular momentum ﬂux is just the amount carried by the accretion ﬂow.