The transport of angular momentum by gravitational instabilities and Rossby vortices in accretion disks

We propose a model for the birth of spiral galaxies and the supermassive black holes (SMBHs) at their centers. It all starts when a galaxy-mass gas condensation collapses to ∼ 200x the background density. It experiences weak tidal torques from similar condensations, which establish its spin parameter lambda. It forms a Lyman-alpha (Lyalpha) cloud, then undergoes an inviscid, angular-momentum-preserving collapse to a Mestel disk with a flat rotation curve (FRCD). A FRCD has v ∼ const, M<r alpha r and a column density Sigma alpha = 1/r. Observations and simulations of damped Lyalpha clouds provide the cloud's radius, mass and lambda. Upon collapse, these variables uniquely determine the mass, size, rotational velocities, and SMBH masses of spiral galaxies. We predict infant galaxy FRCs go all the way to the center. Following the FRCD, the black hole's mass ( MBH ≃ 3 x 107 M⊙ ) comes from the galaxy's innermost 3 pc, which is the radius where gas retains heat long enough to form an accretion disk instead of stars. We invoke two mechanisms to drive accretion: The self-gravity instability (SGI) and the Rossby vortex instability (RVI). Both mechanisms transport angular momentum coherently, so they easily dominate turbulent mechanisms wherever the disk is thin. The popular magneto-rotational instability (MRI) is semi-coherent, but it's not required for our model, so we leave it for further study. We use a 2-D Eulerian hydro code to simulate the SGI and RVI in both FRCDs and Keplerian disks. We explore the triggers of these instabilities, namely, the Toomre parameter Q in SGI-unstable FRCDs and pressure jumps in RVI-unstable Keplerian disks. We confirm that Q ≲ 1 triggers the SGI in FRCDs and that DeltaP/P ≳ 5 generates robust Rossby vortices in Keplerian disks. We also find that these instabilities interact in the transition region between these two types of disks. We relate all this to our self-consistent model which predicts the properties of galaxies, accretion disks, and SMBHs. The model might also predict the stellar initial mass function (IMF).