The effect of extreme ionisation rates during the initial collapse of a molecular cloud core
Abstract
What cosmic ray ionisation rate is required such that a non-ideal magnetohydrodynamics (MHD) simulation of a collapsing molecular cloud will follow the same evolutionary path as an ideal MHD simulation or as a purely hydrodynamics simulation? To investigate this question, we perform three-dimensional smoothed particle non-ideal magnetohydrodynamics simulations of the gravitational collapse of rotating, one solar mass, magnetised molecular cloud cores, that include Ohmic resistivity, ambipolar diffusion, and the Hall effect. We assume a uniform grain size of ag = 0.1μm, and our free parameter is the cosmic ray ionisation rate, ζcr. We evolve our models, where possible, until they have produced a first hydrostatic core. Models with ζcr10-13 s-1 are indistinguishable from ideal MHD models and the evolution of the model with ζcr=10-14 s-1 matches the evolution of the ideal MHD model within one per cent when considering maximum density, magnetic energy, and maximum magnetic field strength as a function of time; these results are independent of ag. Models with very low ionisation rates (ζcr10-24 s-1) are required to approach hydrodynamical collapse, and even lower ionisation rates may be required for larger ag. Thus, it is possible to reproduce ideal MHD and purely hydrodynamical collapses using non-ideal MHD given an appropriate cosmic ray ionisation rate. However, realistic cosmic ray ionisation rates approach neither limit, thus non-ideal MHD cannot be neglected in star formation simulations.