The Source of Turbulence in Astrophysical Disks An Ill-posed Problem..pdfVIP

The Source of Turbulence in Astrophysical Disks: An Ill-posed Problem. Denis Richard, NASA Ames Research Center UCSC-Ames Planet and Star Formation Meeting March 29, 2007 Astrophysical Disks Disks are ubiquitous in Astrophysics : * Planetary disks * Circumstellar Disks (around young stars) * Binary systems * Active Galactic Nuclei (around black holes) Therefore, understanding disks is fundamental to understand planetary and stellar formation and evolution. Wide range of sizes : From Saturns rings ( ~ 107 km) to AGN disks (~ parsec = 3.1 10 13 km) Wide variety of complex physical processes, one of them being the transport of angular momentum. Astrophysical Disks (Artist view) Astrophysical Disks (HST) Turbulence in Disks * Accretion Disk : gas and “dust” falling inward, toward the central object. * Thin disk = H/R 1 → Keplerian rotation : Ω ~ r -3/2 (no radial or vertical velocity in first approximation) * To maintain stationary rotation, angular momentum needs to be transported outward. * Need for an adequate transport mechanism. * Molecular viscosity is too small. * Turbulence : instability mechanism ? Transport properties ? * Early models : Shakura Sunyaev 1973 : * Turbulence most likely generated by differential rotation (shear flow). * Ad hoc model for transport : turbulent viscosity based on smallest constraints : ν t = α . Cs . H A Short History of Turbulence Models for Accretion Disks * 1973 – 1991 : Shakura Sunyaev era : - Source of turbulence unknown (shear flow assumption ?) - Work on turbulence, in order to improve transport model. - meanwhile, transport model : ν t = α . Cs . H * 1991 : Magneto Rotational Instability rediscovered Weak magnetic field coupled to shear flow gives rise to a linear instability. (Chandrasekhar 1960, Balbus Hawley 1991) * 1991 – present : MRI era : - Source of turbulence : MRI - Turbulent model : ν t = α . Cs . H Turbulent Viscosity Model What is it ? * Analytically : A description of tu