Carbon Monoxide Nitrogen
A multilayered interstellar grain.
We can deduce the electric charge for grains from theoretical considerations. There are two ways for grains to acquire charge: (1) Charged particles (both positive and negative) from the gas can strike the grains and stick to the surface. (2) Photons striking the grain surface can eject electrons via the photoelectric effect. The grain is left with one unit of positive charge for every electron ejected. In an equilibrium situation the net charge on the grains must be constant.
We first consider the situation in which the photoelectric effect is not important. This would be the case in regions of high extinction. For particles striking the grains, the negative charges are mostly carried by electrons, and the positive charges are mostly carried by protons. At any given temperature the average speed of the electrons, which have lower mass, will be greater than that of the protons. Therefore, electrons will hit grains at a greater rate than protons or C+, ionized carbon. If the grains are initially neutral, this will tend to build up negative charge. However, once the grains have a small negative charge, the electrons will be slowed down as they approach the grains, while the positive charges will be accelerated. Therefore, if the grains have a net negative charge it is possible to have protons and electrons striking the grain at the same rate, keeping the charge on the grain constant. Note that, if the grains have a net negative charge, the gas must have a net positive charge if the interstellar medium as a whole is to be neutral.
Example 14.3 Charge on dust grains Estimate the electric charge (in multiples of e) required to keep the charge on dust grains constant. Take the radius of the grain to be 10— 5 cm and the gas kinetic temperature to be 100 K.
We estimate the grain charge for which the electric potential energy of an electron at the grain surface is equal in magnitude to the average kinetic energy of the electrons in the gas. If the net charge on the grain is — Ne, the potential energy for an electron on the surface, a distance r from the center, is
The average kinetic energy is (3/2)kT. Equating these and solving for N gives
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