Ambipolar Diffusion with a Polytropic Equation of State

Stars form when dense regions of molecular gas in our galaxy collapse due to their self-gravity. But for this to occur, the magnetic field supporting these regions must diffuse out through a process known as ambipolar diffusion. This mechanism has been studied extensively both semi-analytically and numerically. We build upon this work by considering a one-dimensional self-gravitating gas with a polytropic equation of state (P ∝ ρ^ε) and consider cases that range from softer (ϵ < 1) to stiffer (ϵ > 1) than isothermal. Our results indicate that the diffusion time is not very sensitive to the polytropic exponent ϵ when stiffer than isothermal but is sensitive to the exponent when softer than isothermal. Additionally, the presence of magnetic and density fluctuations causes the ambipolar diffusion process to speed up, with the shortest diffusion times obtained for gases with large initial magnetic to gas pressure ratios and fairly soft equations of state. However, the diffusion time starts to increase significantly for ϵ ≲ 0.5, indicating that such soft equations of state are inconsistent with observations.