A fast and robust recipe for modeling non-ideal MHD effects in star-formation simulations

Non-ideal MHD effects are thought to be a crucial component of the star-formation process. Numerically, several complications render the study of non-ideal MHD effects in 3D simulations extremely challenging and hinder our efforts of exploring a large parameter space. We aim to overcome such challenges by proposing a novel, physically-motivated empirical approximation to model non-ideal MHD effects. We perform a number of 2D axisymmetric 3-fluid non-ideal MHD simulations of collapsing prestellar cores and clouds with non-equilibrium chemistry and leverage upon previously-published results. We utilize these simulations to develop a multivariate interpolating function to predict the ionization fraction in each region of the cloud depending on the local physical conditions. We subsequently use analytically-derived, simplified expressions to calculate the resistivities of the cloud in each grid cell. Therefore, in our new approach the resistivities are calculated without the use of a chemical network. We benchmark our method against additional 2D axisymmetric non-ideal MHD simulations with random initial conditions and a 3D non-ideal MHD simulation with non-equilibrium chemistry. We find excellent quantitative and qualitative agreement between our approach and the "full" non-ideal MHD simulations both in terms of the spatial structure of the simulated clouds and regarding their time evolution. We achieve a factor of 100-1000 increase in computational speed. Given that we ignore the contribution of grains, our approximation is valid up to number densities of 10^6 cm^(-3) and is therefore suitable for pc-scale simulations of molecular clouds. The tabulated data required for integrating our method in hydrodynamical codes, along with a fortran implementation of the interpolating function are publicly available at https://github.com/manosagian/Non-Ideal-MHD-Approximate-Code.