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Accretion disks

Lecture 4. AST3020. Accretion disks. Flaring shape jets. Outflows disappear before the disks do. High!. (on the other hand, in debris disks which don’t have a lot of gas and much less dust as well, both the opacity of dust and the

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Accretion disks

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  1. Lecture 4. AST3020 Accretion disks

  2. Flaring shape jets Outflows disappear before the disks do

  3. High! (on the other hand, in debris disks which don’t have a lot of gas and much less dust as well, both the opacity of dust and the surface density of matter are much lower, so that the optical depth is tau_0 << 1 in every direction.)

  4. [accretion heating active disks; illumination heating passive disks] Since the flux F also equals sigma * T^4, and c ~ T^(1/2), we have that in disks where Sigma*nu = const. (stationary thin disks far from the stellar surface) F ~ r^(-3) ~ T^4 ==> T ~ r^(-3/4) z/r ~ c / v_K ~ r^(+1/8), a slightly flaring disk.

  5. Diffusion equation for the viscous evolution of an accretion disk cf. Pringle (1981 in Ann Rev Astr Astoph) [accretion heating active disks; illumination heating passive disks]

  6. The ratio of viscous to dynamical time is called Reynolds number and denoted Re. It always is a very large number in astrophysics.

  7. The analytical solutions (Pringle 1981)

  8. *** *** - there is another solution…which??

  9. ANOMALOUS VISCOSITY IN DISKS

  10. Problem: convection transports angular momentum inwards

  11. - disks Shakhura-Sunyayev (1973) Non-dimensional parameter c = soundspeed z = disk scale height Idea: gather all uncertainties in alpha-parameter: l = Specific angular momentum because Reynolds number: (spiralling of gas very much slower than v_k, Keplerian vel.)

  12. Magneto-rotational instability (MRI) as a source of viscosity in astrophysical disks. Velikhov (1959), Chandrasekhar (1960), and re-discovered by Balbus and Hawley (1991). Disk conditions:gas ionized; magnetic field dragged with gas magnetic field energy and pressure << gas energy,pressure differential rotation (angular speed drops with distance) 2-D and 3-D simulations of Magnetic turbulence inside the disk

  13. Chris Reynolds et al. Results: alpha computed ab initio, sometimes not fully self-consistently often not in full 3-D disk: alpha ~ several * 1e-3 Charles Gammie et al.

  14. VISCOUS EVOLUTION SEEN IN DISKS

  15. PPIV = Protostars and Planets IV book (2000) Observations of dM/dt as a function oflog age [yr] M_sun/yr log age [yr]

  16. Observed dM/dt ~ 1e-6 M_sun/yr for ~0.1 Myr time ==> total amount accreted ~0.1 M_sun Observed dM/dt ~ 1e-7 M_sun/yr for ~Myr time ==> total amount accreted ~0.1 M_sun

  17. Mass of the dust in disks (around A-type and similar stars) Primordial solar nebulae Debris disks = beta Pic disks, zodiacal light disks Natta (2000, PPIV)

  18. gas (T Tau stars) dM/dt [M_sun/yr] log age [yr] PPIV = Protostars andPlanets IV book (2000)

  19. Observations Modeling of observations Compares OK Ab-initio calculations (numerical)

  20. Percentage of optically thick “outer disks” (at~3AU) From: M. Mayers, S. Beckwith et al. Conclusion: Major fraction of dust cleared out to several AU in 3-10 Myr 0.1 1 10 100 1000 Myr Age

  21. SED = Spectral En. Distrib. If part of the disk missing => SED may show a dip => possible diagnostic of planets. flux If this ring missing frequency

  22. Z0

  23. Summary of the most important facts about accretion disks: Found in: • quasars’ central engines, • active galactive nuclei (AGNs), galaxies, • around stars (Cataclysmic Var., Dwarf Novae, T Tauri, b Pic), • around planets. Drain matter inward, angular momentum outside. Release gravitational energy as radiation, or reprocess radiation. Easy-to-understand vertical structure with z/r ~ c/v_K Radial evolution due to some poorly known viscosity, parametrized by alpha <1. Best mechanism for viscosity is MRI (magneto-rotational instability), an MHD process of growth of tangled magnetic fields at the cost of mechanical energy of the disk. Simulations give alpha= a few * 1e-3

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