The effect of extreme ionization rates during the initial collapse of a molecular cloud core

What cosmic ray ionization 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 MHD simulations of the gravitational collapse of rotating, one solar mass, magnetized molecular cloud cores, which include Ohmic resistivity, ambipolar diffusion, and the Hall effect. We assume a uniform grain size of a_g = 0.1 μm, and our free parameter is the cosmic ray ionization rate, ζcr. We evolve our models, where possible, until they have produced a first hydrostatic core. Models with ζcr ≳ 10⁻¹³ s⁻¹ are indistinguishable from ideal MHD models, and the evolution of the model with ζcr = 10⁻¹⁴s⁻¹ matches the evolution of the ideal MHD model within 1 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 ionization rates (ζcr ≲ 10⁻²⁴ s⁻¹) are required to approach hydrodynamical collapse, and even lower ionization rates may be required for larger a_g. Thus, it is possible to reproduce ideal MHD and purely hydrodynamical collapses using non-ideal MHD given an appropriate cosmic ray ionization rate. However, realistic cosmic ray ionization rates approach neither limit; thus, non-ideal MHD cannot be neglected in star formation simulations.