On the detection of microwave spectral lines in radio astronomy.

Detection of spectral lines in radio astronomy is plagued by the unfortunately low cosmic abundances of constituents other than hydrogen in the interstellar medium. Thus no line has been detected other than the hyperfine transition in the ground state of Hi. The relative strength of an electric dipole- to a magnetic dipole-type transition is of the order i04 to I in favor of the electric dipole. The significant role of the electric dipole has led to predictions of favorable detection chances for such interstellar radicals as OH and CH, which have electric dipole-type microwave transitions (Townes and Schawlow 1955, Shklovskii 1953). It is the purpose of this note to call attention to other consequences of the electric dipole moment which may reduce the chances of detecting such lines in emission, but would correspondingly enhance the chances of detection in absorption-line studies. Detecting a microwave emission or absorption line depends on the state temperature, Ps, which characterizes the population distribution in the two states responsible for the line. There appear to be two dominant mechanisms which compete to establish the population distribution and thereby determine P5. The two processes are collisions and radiative de-excitation, both spontaneous and stimulated (Purcell and Field, in press). A kinetic temperature, Pk, characterizes the collisions, and the radiation density may be described in terms of a radiation temperature, Pr. The antenna temperature of an isotropic receiver, located typically in space, tuned to the frequency range of interest, would be equal to Pr. For the hydrogen case, P5 has been shown to correspond closely with the kinetic temperature, I200K, (Purcell and Field, in press). This is possible because the 21 cm transition is a magnetic dipole transition and the natural lifetime of the upper hyperfine level is very long compared to the time between collisions. Hence, collisions are primarily responsible for determining the population distribution. When considering other components of the interstellar medium it should be noted that P5 may not in general be equal to the kinetic temperature as has been implied (Shklovskii 1953). In particular the electric dipole-type transitions have natural radiative lifetimes shorter by a factor i ~ than similar magnetic dipole transitions. The radiative lifetime is further reduced by the background radiation field near the resonant frequency. All of this produces a stronger coupling to Pr and thus lowers P5. The three temperatures involved, P0, Pr, and Pk are related in the form P0 = Pk 0 $ Pr T0 y Pk' where P0 is a measure of the relative importance of collisional and radiative de-excitation mechanisms. The quantity P0 is given by _ hv R10 - T A10, where o' is the resonant frequency, R10 is the probability per second of a collisionally induced transition from the upper to the lower state and A10 is the spontaneous radiative transition probability. Clearly P0 and consequently P5 depend on the interstellar particle density, the effective collisional cross sections and whether the transition is of the electric dipole- or magnetic dipole-type. The effectiveness of the atomic hydrogen- hydrogen collisions has been demonstrated for the 21-cm line (Purcell and Field, in press), a large P0 results, and therefore P5 Pk. For electric dipole transitions, A10 is of the order i ~ larger than it is for the 21-cm case and consequently P0 may be considerably smaller, pulling P5 toward Pr. This decrease may be partially or completely counterbalanced by an increase in the effectiveness of the collisions. A radical such as CH or OH, possessing a permanent electric dipole moment, will interact with positive ions and electrons. According to a private communication by Townes the larger cross section for the infrequent radical-ion collisions may compete strongly with the more frequent radical-Hi atom collisions. This is due to the long-range interaction between a dipole and a charged particle (Massey 1932). However, in typical interstellar gas regions, the increase in A10 is a powerful influence, and P5 may approach Pr. This would make the transition very difficult to detect in emission since the maximum emission temperature would be P5 - Pr. Since the opacity of a fixed number of radicals varies as PEl there is an increase in the opacity as P5 is lowered. This suggests that the most favorable observational detection possibilities are absorption investigations using intense discrete sources such as Cassiopeia A, Cygnus A and Taurus A. Massey, H. S. W. 1932, Proc. Camb. Phil. Soc. 28, 99. Purcell, E. M. and Field, G. Ap. J., in press. Shklovskii, I. S. 1953, Doklady Akad. Nauk USSR 92 (1), 25. Townes, C. H. and Schawlow, A. L. 1955, Microwave Spectroscopy (New York: McGraw-Hill Book Co.). Naval Research Laboratory, Washington, D. C.