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 $a_{\text{g}}=0.1\mu$m, and our free parameter is the cosmic ray ionisation rate, ${\zeta }_{\text{cr}}$. We evolve our models, where possible, until they have produced a first hydrostatic core. Models with ${\zeta }_{\text{cr}}\gtrsim 10^{-13}$ s${}^{-1}$ are indistinguishable from ideal MHD models and the evolution of the model with ${\zeta }_{\text{cr}}=10^{-14}$ 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 $a_{\text{g}}$. Models with very low ionisation rates (${\zeta }_{\text{cr}}\lesssim 10^{-24}$ s${}^{-1}$) are required to approach hydrodynamical collapse, and even lower ionisation rates may be required for larger $a_{\text{g}}$. 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.

13 pages, 15 figures, accepted for publication in MNRAS

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