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The Nonthermal Rotational Distribution of H3+

Although H is nonpolar in the equilateral triangle equilibrium structure, symmetry breakdown due to centrifugal distortion causes a small dipole moment and hence rotational transitions. The spontaneous emission times are on the order of a few weeks for low rotational levels and are comparable to collision intervals in interstellar space. Moreover, there are metastable rotational levels such as J = K = 3, from which spontaneous emissions are rigorously forbidden. A very nonthermal rotational distribution is produced. We present a model calculation simulating the thermalization of H. Since the lifetime of H in interstellar space is orders of magnitude longer than the spontaneous emission time and collision intervals, a steady state approximation is assumed. Accurate theoretical values by ab initio theory are used for spontaneous emission rates. The rates of collision-induced transitions between rotational levels are calculated on the assumption of completely random selection rules using an approximate formula that satisfies the principle of detailed balancing. The results indicate that the observed high population of H in the (3, 3) metastable level toward the Galactic center (M. Goto and coworkers) signifies the presence of very large high-temperature (T ≥ 300 K) and low-density [n(H2) ≤ 70 cm-3] clouds. It is shown that other higher metastable levels may accommodate observable H in such clouds and that the excitation temperature determined from the observed relative populations of (1, 0) and (1, 1) should provide crucial information on the condition of such clouds.