INTERSTELLAR MEDIUM, RADIO RECOMBINATION LINES PETER A. SHAVER Radio recombination lines provide a wide-ranging and versatile observational tool in astrophysics. Above principal quantum number n=27, recombination transitions between adjacent energy levels of hydrogen emit photons at wavelengths longward of one millimeter, and these radio-frequency recombination spectral lines are distributed over the entire radio spectrum. The largest bound orbit corresponds to n=1000-1500 for typical interstellar conditions, and the lowest frequency spectral line observed to date in astronomy is a recombination line at a wavelength of 20 meters (corresponding to n=768). Thus, there are a great many such lines, each one conveying slightly different information. As these "Rydberg" atoms are very large (0.1-mm diameter for n=1000), they are sensitive probes of their environments. Also, as these transitions occur at radio frequencies, they can be studied across the Galaxy and in regions of high obscuration. They are therefore highly accessible and important probes of ionized gas in a variety of physical conditions, from stellar winds to the diffuse interstellar medium. THEORETICAL CONSIDERATIONS The physics of radio recombination lines is well understood. The relevant process is that in which a free electron combines with an ion at some high energy level. In some cases involving elements other than hydrogen, dielectronic recombination can occur, which proceeds through doubly excited states and can populate the high levels faster than radiative recombination, resulting in large overpopulations of the high quantum levels. The recombination lines arise as the recombined electron works its way down the ladder of energy levels. The frequency of a transition between upper principal quantum level m and lower level n is given by the generalized Rydberg formula, ****************************, where R=R*(1-**/M) is the Rydberg constant for an excited atom or ion of mass M and effective nuclear charge Z. The individual recombination lines are identified by the lower principal quantum number and the order of the transition (*, *, *,... for m-n=1,2,3,...); thus, H83* is a transition in atomic hydrogen from level 84 to level 83, and C527* is a transition in carbon from level 529 to level 527. The energy level populations are computed by solving simultaneous equations that equate all populating and depopulating processes for each level. Although the ratio ** of these energy level populations to the values they would have under conditions of local thermodynamic equilibrium (LTE) is very close to unity, the radio-frequency line intensities can still be affected strongly by the small remaining differences. The ratio of the true absorption coefficient ** to its LTE value *** is ****************************, where T* is the electron temperature. Thus, although ****** is very small for these high-n transitions, so is h*, and the line intensities can be altered strongly. Usually, the result is enhancement due to stimulated emission. The excess brightness temperature at the line center *** can be computed from the equations of radiative transfer, ************************ where *** and ** are the LTE line and continuum optical depths and T* is the brightness temperature of the background continuum. From these equations one can get some idea of the global behavior of the recombination line intensities. At low energy levels, radiative effects (hence, downward transitions) dominate, and the corresponding high- frequency recombination lines appear in emission. At high n, however, collisions dominate and tend to thermalize the populations, and the corresponding low-frequency recombination lines will ultimately appear in absorption against a strong background continuum. The line shapes are typically Gaussian, due to Doppler broadening characterized by the electron temperature and turbulence in the ionized gas. However, these very high energy levels are easily perturbed by collisions with free electrons, and pressure broadening therefore results. Adjacent levels are similarly affected by such collisions, so the net effect on transitions between them is reduced, but pressure broadening ultimately dominates over Doppler broadening for high-n transitions. The ratio of pressure to Doppler broadening varies approximately as ***. Radiation broadening can also be important, and has a similarly strong dependence on n. Thus, at the lowest frequencies, the lines become broadened to the point where they merge with the continuum and each other, and are no longer detectable. The study of radio recombination lines involves the interplay between a few basic phenomena, particularly stimulated emission (which enhances the peak line intensities) and broadening mechanisms (which diminish them). The lines convey information about electron temperatures and densities, turbulence, radial velocities, and relative ionic abundances, and so are important probes of ionized gas in a wide range of astrophysical contexts, as summarized in the following sections. THE SUN, STELLAR WINDS, AND PLANETARY NEBULAE Radio recombination lines from various ions are, in principle, detectable in the solar atmosphere. They could be enhanced by dielectronic recombination, and may appear either in emission or absorption. None have yet been detected, possibly due to the combined effects of pressure broadening, radiation broadening, and Zeeman splitting. The best prospects probably lie in the far-infrared and submillimeter wavelength ranges. Some ionized stellar winds are sufficiently massive to produce significant radio emission. High-frequency radio recombination lines have recently been detected in one stellar wind source, MWC 349. These lines are almost certainly dominated by strong maser action. The profiles vary from line to line, and they also vary with time on scales of months. They provide an important new probe of the physical conditions in these objects. The radio recombination line emission from planetary nebulae is relatively uncomplicated, as they are comparatively sharply defined objects. The derived electron temperatures and densities and helium abundances agree well with values obtained from optical studies. The optical data can be incomplete because of extinction, however, and the radio recombination line data give improved information on global properties such as the velocity structure. HII REGIONS AND THEIR ENVIRONS Embedded within many HII regions are compact cores with densities of up to 10*-10* cm** and sizes of 0.01-0.1 pc. The sites of recent star formation, these are usually obscured optically, and difficult to detect with large single radio telescopes. Radio interferometers, however, discriminate against the more extended surrounding HII region and make it possible to study the compact cores themselves. The high densities and relative homogeneity make it possible to observe extremes in the behavior of the radio recombination lines. Pressure broadening is often observed (directly or indirectly), there can be large systematic mass motions, the line intensities can be quite anomalous, and large variations are found in the ratios of the helium to hydrogen lines (from 1 to 40%, whereas the actual abundance ratio is about 10%). These latter variations can be due to a variety of causes. A low He*/H* ratio can be caused by incomplete ionization of helium as a result of excitation by a relatively cool star or can be caused by selective absorption of ionizing photons by dust. A high ratio can, in principle, be caused by an exceptionally hard ionizing radiation field or by genuine helium enrichment by stars. These extreme effects are generally masked when the HII region is observed at lower angular resolution with a single radio telescope. The overall density distribution is inhomogeneous with strong gradients. The observed line emission is a complicated average over several components; usually, the lower densities dominate and the resulting recombination line appears to be Gaussian with approximately normal intensity. The He*/H* ratio still varies significantly from one HII region to another, an effect probably due largely to variations in the ionizing radiation field. One of the important discoveries using radio recombination lines was that the electron temperatures of most HII regions are significantly lower than the canonical 10* K obtained for the brightest HII regions using optical spectral lines. Some of the radio recombination lines are so narrow that the widths alone give absolute upper limits of just 3000-4000 K on the electron temperature. It is now known that the temperatures range from a few thousand degrees for diffuse, low- brightness HII regions to 10* K for the brightest, densest HII regions, to which the optical observations are most sensitive. At low frequencies the outer, lowest-density components of HII regions dominate the recombination lines, as the line emission from more dense components is washed out by pressure broadening. In addition, recombination line emission from otherwise unknown diffuse HII regions along the galactic plane can be detected. The electron densities in these cases are low (*1-10 cm**) and the lines from these old, relaxed HII regions are often relatively narrow. In the presence of suitable background sources, significant stimulated emission can be observed. At the outer boundaries of the HII regions are zones of rapidly diminishing ionization. Narrow recombination lines of hydrogen are observed that come from a cool zone where the hydrogen is only partially ionized. Still further out, in zones where hydrogen is no longer ionized, recombination lines of carbon and other heavy elements are frequently detected. Carbon dominates, as it is the most abundant element with an ionization potential lower than that of hydrogen. These lines are thought to originate in thin (*0.01 pc), cold (20 K) layers, and are often enhanced by stimulated emission on the near sides of the HII regions. Beyond this transition zone, the recombination line emission falls off and HI and molecular line emission begins to dominate. In dark clouds, extended regions of carbon recombination line emission are sometimes seen, produced by embedded B stars. INTERSTELLAR CLOUDS AND THE DIFFUSE INTERSTELLAR MEDIUM Radio recombination lines are also emitted by cold interstellar HI clouds, which are partially ionized by cosmic rays, x-rays, and the ambient ultraviolet radiation field. They are most easily detected at low frequencies (<200-300 MHz) in the spectra of strong background sources of continuum radiation or in the general galactic nonthermal background itself. They can show up as emission features, due to stimulated emission, but at the lowest frequencies (<100 MHz) they must ultimately go into absorption. Very low frequency recombination lines in absorption appear to be ubiquitous along the galactic plane. Carbon again appears to dominate, as in the partially ionized zones around HII regions. Analysis indicates electron densities of *0.1-1 cm**, low enough for the lines still to be observable at frequencies as low as 10-20 MHz. The 768* line observed at 14.7 MHz in the spectrum of Cassiopeia A is the lowest-frequency spectral line so far detected in astronomy. These very low frequency lines do, however, show clear evidence of pressure or radiation broadening and come close to the limits (n*1000) set by ionospheric opacity and by radiation damping due to the galactic nonthermal radiation field, which ultimately causes adjacent lines to merge. Upper limits on hydrogen recombination line emission from these clouds, combined with measurements of HI absorption, permit stringent limits to be set on the hydrogen ionization rate. low-frequency recombination lines can be used to set constraints on the filling factors of HII regions and partially ionized clouds, hence also on that of the hot intercloud medium. Radio recombination lines should also be emitted by the intercloud medium itself, perhaps enhanced by dielectronic recombination, but they must be very weak, and have yet to be detected. LARGE-SCALE PROPERTIES OF THE GALAXY Radio recombination lines play an important role in identifying the different types of discrete radio sources along the galactic plane, by discriminating between HII regions, which are strong line emitters, and nonthermal supernova remnants, which are not. The detected recombination lines can then be used, together with a model of galactic rotation, to map out the spiral structure of our galaxy. These lines, like those of HI and CO, are well suited to this task because the radio waves pass unimpeded across the Galaxy. With greater sensitivity, multiple components due to different HII complexes scattered along the line of sight are increasingly being found in individual spectra. The global distribution of ionized gas over the Galaxy, and its relation to the radial distributions of HI, CO, and far-infrared emission, can also be studied in this way. Furthermore, it has been found that there is a galactocentric gradient in the electron temperatures of HII regions, which is almost certainly due to a gradient in elemental abundances; these gradients give information about the chemical evolution of our galaxy. Searches for a systematic gradient in the He*/H* ratio with galactocentric radius have been inconclusive, due primarily to large variations in ionization. Radio recombination lines provide a unique probe of the galactic center. Interferometric observations reveal strong velocity gradients in the central few parsec, which are well matched by a solid body rotation model and give important information about the central mass concentration. A strong gradient in electron temperature is also found, possible evidence for a central source of ionizing radiation. Limits can be placed on magnetic fields in the vicinity of the galactic center from the absence of Zeeman splitting in the recombination lines. EXTRAGALACTIC RADIO RECOMBINATION LINES With distance from our galaxy, spontaneous radio recombination line emission becomes increasingly difficult to detect. Such lines have been detected from a few prominent HII regions in the nearby Magellanic Clouds and from the unusual radio galaxy M 82, at a distance of 3 Mpc. This spontaneous recombination line emission is useful in determining the total mass of ionized gas in these galaxies and the star formation rate, parameters that may otherwise be difficult to obtain due to obscuration. At much greater distances, spontaneous line emission becomes exceedingly weak, but radio recombination lines still can be detected due to stimulated emission or absorption in the spectra of distant continuum radio sources such as quasars. Stimulated emission of radio recombination lines has been detected clearly from the radio galaxies M 82 and NGC 253, establishing that such emission must in principle be detectable from much more distant sources. Promising possibilities are the narrow emission-line regions of radio-loud quasars, and the intervening galaxies and gas clouds that cause the optical absorption features in quasar spectra. Such lines could be used for a variety of purposes: obtaining redshifts of optically-unidentified radio sources, deriving absolute distances independent of redshifts, and setting limits on the variations of certain fundamental physical quantities over cosmic time scales. Still further possibilities include protogalaxies at very high redshifts and, perhaps, ultimately even the general intergalactic medium and the cosmic microwave background itself. Additional Reading Brown, R.L., Lockman, F.J., and Knapp, G.R.(1978). Radio recombination lines. Ann. Rev. Astron. Ap. 16 445. Dupree, A.K. and Goldberg L.(1970). Radiofrequency recombination lines. Ann. Rev. Astron. Ap. 8 231. Gordon, M.A.(1988). HII regions and radio recombination lines. In Galactic and Extragalactic Radio Astronomy, G.L. Verschuur and K.I. Kellermann, eds. Springer-Verlag Berlin, p. 37. Gordon, M.A. and Sorochenko, R.L., eds.(1990). Radio Recombination Lines: 25 Years of Investigation. Kluwer Academic Publishers, Dordrecht. Mezger, P.G. and Palmer, P.(1968). Radio recombination lines: A new observational tool in astrophysics. Science 160 29. Shaver, P.A., ed.(1980). Radio Recombination Lines. D. Reidel, Dordrecht.