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

TL;DR

This study investigates how cosmic ray ionisation rates influence the collapse of molecular cloud cores in star formation, showing that realistic rates necessitate non-ideal MHD modeling for accurate simulation of the process.

Contribution

It quantifies the cosmic ray ionisation rates at which non-ideal MHD simulations align with ideal MHD or hydrodynamical models in star formation.

Findings

Ionisation rates above 10^{-13} s^{-1} mimic ideal MHD behavior.

Rates below 10^{-14} s^{-1} approach hydrodynamical collapse.

Realistic cosmic ray ionisation rates require non-ideal MHD in simulations.

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 $\zeta_\text{cr}\gtrsim10^{-13}$ 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 ($\zeta_\text{cr}\lesssim10^{-24}$ 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.