Nonmagnetic and magnetized cooling flow models

We have numerically simulated nonmagnetic and magnetized cluster cooling flows in a cylindrical geometry. The cooling gas in the magnetized models was threaded initially by a weak toroidal (B-phi) or axial (B-z) magnetic field of 1 mu G. Most cooling flow models have been followed for 15 Gyr in two dimensions assuming azimuthal symmetry at all times. No global, exponential instabilities develop. Initial perturbations are carried into the central region by the cooling gas and produce some inhomogeneities within the inner 10-20 kpc. After similar to 4 Gyr, radiative cooling causes a catastrophic collapse of the gas in the inner core, irrespective of the presence of the magnetic field. In magnetized models, magnetic pressure builds up gradually in the inner region. In models with an unmagnetized core, the field is carried into the core from the exterior but does not become dynamically important for over 14 Gyr. If a weak field exists in the core initially, it begins to build up substantially at the center after the cooling catastrophe at 4 Gyr. Outside of the inner 50 kpc, the magnetic field quickly approaches the steady state profiles determined by the conservation laws of mass and magnetic flux, i.e., B-phi proportional to rho r and B-z proportional to rho, where r denotes the cylindrical radius and rho denotes the density. We have also studied linear and nonlinear m = 2 perturbations in three dimensions under the same initial conditions but at modest numerical resolution. No additional nonaxisymmetric structure develops during inflow. The original perturbations are carried homologously into the inner core without growing. These results do not support the presence of any kind of global nonaxisymmetric instability at long wavelengths.