A fast and robust recipe for modeling nonideal magnetohydrodynamic effects in star formation simulations

Context. Nonideal magnetohydrodynamic (MHD) effects are thought to be a crucial component of the star formation process. Numerically, several complications render the study of nonideal MHD effects in 3D simulations extremely challenging and hinder efforts to explore a large parameter space. Aims. Here, we aim to overcome such challenges by proposing a novel physically motivated empirical approximation to model nonideal MHD effects. Methods. We performed a number of 2D axisymmetric three-fluid nonideal MHD simulations of collapsing prestellar cores and clouds with non-equilibrium chemistry and leveraged previously published results from similar simulations with different physical conditions. We utilized these simulations to develop a multivariate interpolating function that predicts the ionization fraction in each region of the cloud depending on the local physical conditions. We subsequently used 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 benchmarked our method against additional 2D axisymmetric nonideal MHD simulations with random initial conditions and a 3D nonideal MHD simulation with non-equilibrium chemistry. Results. We find excellent quantitative and qualitative agreement between our approach and the "full" nonideal MHD simulations both in terms of the spatial structure of the simulated clouds and regarding their time evolution. At the same time, we achieved a factor of similar to 10(2)-10(3) increase in computational speed. Given that we ignored the contribution of grains to the resistivities our approximation is valid up to number densities of similar to 106 cm(-3) and is therefore suitable for parsec-scale simulations of molecular clouds and/or simulations of stratified boxes.