Ambipolar Diffusion with a Polytropic Equation of State

Ambipolar diffusion is the mechanism believed to be responsible for the loss of magnetic support in dense molecular cloud cores, and is therefore likely to play a key role in the star formation process. As such, this mechanism has been studied extensively both semianalytically and numerically. We build upon this existing body of work by considering a one-dimensional self-gravitating gas with a polytropic equation of state (P proportional to rho(epsilon)), and consider cases that range from softer (epsilon < 1) to stiffer (epsilon > 1) than isothermal. Our results indicate that the diffusion time is not very sensitive to the polytropic exponent epsilon 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 epsilon less than or similar to 0.5, indicating that such soft equations of state are inconsistent with observations.