Frozen condition for the charged particles in molecular clouds

How the ambipolar diffusion prior to star formation proceeds in molecular clouds is often discussed. At that time, it is fundamental to determine its timescale, which depends on the abundance of various charged particles. Interestingly, when the grains become dominant negatively charged particles instead of electrons, the diffusion timescale lengthens if they attach to the magnetic field. This attachment occurs even when the charged grains are not frozen into the field directly since they are attracted by the frozen ions via the electrostatic force. In other words, even when omega (g),- tau (g)-(n)/C(g) much less than 1, the charged grains can be frozen into the field. Here omega (g)- and tau (g)-(n) are the gyrofrequency and the friction timescale caused by the neutral of negatively charged grains, and C(g) is a correction factor caused by the charge state exchange of grains. This paper investigates the diffusion processes of various charged particles, including charged grains. We present the mobility parameters of charged grains, Theta (g-), and ions, Theta (i), relative to electrons, which are frozen into the magnetic fields very tightly at the density range considered here. Thus, when Theta (g)- > 1, the charged grains are frozen into the magnetic field. Moreover, even when omega (i)tau (in) much greater than1, it is possible that, becomes smaller than unity, and ions are never frozen into the field as far as Theta (i) < 1. Here (omega)(i) is the gyrofrequency of ions and tau (in) is the friction timescale of ions caused by neutrals. These effects may affect the drift velocities of various particles, hence, the metal abundance of the protostellar cores. The efficiency of the effects stated above depends strongly on the size distribution of grains. Being conscious of the effect of the grain size, we evaluate the drift velocities of the magnetic fields and various charged particles for typical clouds also. If there exist abundant small grains, the typical radius of which is 0.01 mum, electrostatic interaction between ions and negatively charged grains becomes important at a middle density range. Conversely, in the case that the typical grain radius is 0.1 mum, electrostatic interaction plays almost no role and, hence, the naive estimate of frozen conditions, omega (i) tau (in) > 1 for ions and omega (g)-tau (g)-n > 1 for negatively charged grains becomes the good approximation It seems that when the electrostatic interaction between ions and negatively charged grains is not so effective, the naive criterion for the frozen conditions is always reasonable.