GALACTIC STRUCTURE, SPIRALS INTERSTELLAR GAS, THEORY WILLIAM W. ROBERTS, JR. Because of the winding dilemma associated with material arms, a wave interpretation of large-scale spiral structure is necessary for disk-shaped galaxies such as our own Milky Way. Such a wave interpretation was first provided in the linear density wave theory, initiated by C.C. Lin and F.H. Shu over 25 years ago. The present-day linear modal theory for spiral density waves, when merged with the theory for the nonlinear dynamics of the interstellar gas, not only makes strides in solving the dilemma of why spiral arms do not necessarily wind up but also supplies a mechanism for forming those stars which delineate spiral arms. In this theory, the luminosity of a spiral arm is believed to originate primarily from the very young, newly forming stars whose ages are only about 1/1000 of the age of the Galaxy and whose mass makes up only a small percentage of the bulk of the galactic mass, and the spiral arm itself is believed to be a spiral wave-a nonlinear galactic shock wave in the interstellar gas-that is capable of triggering from the gas the formation of the young stars selectively along the wave crest. What was thought of two decades ago as a fairly uniform galactic gaseous medium is now seen to be highly nonuniform, with numerous 1-20-pc-scale clumps or clouds of relatively cool, dense gas at one end of the spectrum, 20-100-pc-scale giant molecular clouds [GMCs] and diffuse atomic hydrogen clouds in the middle, and massive hundred parsec to several kiloparsec scale aggregations of GMCs and diffuse cloud complexes at the other, all embedded in a highly rarefied, partly ionized intercloud medium. Present-day high-resolution observations of the atomic and molecular gas components in global grand design spirals indicate that the largest of these local nonuniformities, the GMC complexes and aggregations, are almost exclusively located in spiral arms. The spiral arms often show a very high resolution into knots that comprise these aggregations and associations of clouds, active star formation regions of newly forming protostars, young luminous stars, and giant H II regions. Such concentrations of GMC complexes and aggregations in spiral arms may also be the case for our own Galaxy. However, their exact distances and their global distribution within our Milky Way system are known with less certainty because of the fact that the bird's eye view we enjoy of the spiral structure in extragalactic systems is largely lacking from the vantage point of our location within the disk of the Milky Way system. On the global scale in grand design spirals, the clumpy, cloudy gaseous interstellar medium is found to exhibit strong nonlinear contrasts in arm-to-interarm density with peak-to-mean values measured on the order of 2:1-4:1 and strong systematic velocity streaming motions with measured magnitudes on the order of 30-80 km s*** across the major spiral arms. Striking examples are the extragalactic systems: M31, M51, and M81. Prominent narrow dust lanes also delineate the striking nonlinear character of the atomic and molecular interstellar gas and provide excellent optical tracers of the major spiral arms. In view of the observed highly nonuniform and multiphase gaseous interstellar medium, a basic problem stands out; namely, what physical mechanisms and dynamical processes can organize the locally clumpy and cloudy interstellar gas into its strongly coherent nonlinear distribution on the global scale and can trigger star formation from the cloudy gas along a grand design of spiral structure in an orderly fashion and yet simultaneously provide for the formation of spurs, feathers, arm branchings, and secondary features on intermediate scales? DOMINANT PHYSICAL MECHANISMS AND DYNAMICAL PROCESSES The basic problem to be addressed spans the hierarchy of galactic scales: the locally clumpy, cloudy interstellar medium, giant molecular clouds, and star formation on local scales; spurs, feathers, arm branchings, and secondary features on intermediate scales; and the grand design of spiral structure on the global scale. Dominant physical mechanisms and dynamical processes are outlined in Table 1, with particular emphasis on the self-gravitational effects, dissipative effects, and collisional dynamics of cloudy gaseous galactic dish. The self-gravitational response of the gas driven by an underlying two-armed spiral density wave mode computed in the modal density wave theory is shown in Fig. 1 for one representative model galaxy with a 2% gas mass fraction. The cloudy gaseous galactic disk consists in part of a system of N finite-cross-section clouds (taken to be 10,000), initially distributed randomly over a two-dimensional disk-out to a maximum radius *** (taken as 12 kpc) and given local circular velocities plus small peculiar velocities (amounting to a one-dimensional dispersion, **, of 6 km s***) and in part of a system of young stellar associations that form from the clouds. The clouds and young stellar associations interact gravitationally with each other, and their motions are governed gravitationally by their own self-gravity as well as by the background modal-spiral-perturbed gravitational field which attains a maximum amplitude of 12% that of the central axisymmetric force field. Displayed in Fig. 1 through a photographic intensity map at the sample time epoch of 480 million years (Myr) during the computations are the computed global distributions of the system of gas clouds (represented by patches) and the system of young to middle-aged stellar associations active with supernova events during the past 60 Myr (represented by white dots). Most striking is the strongly peaked gas density distribution that traces global gaseous spiral arms. A galactic shock formed within the gaseous component imparts distinctly nonlinear characteristics to these global gaseous spiral-wave arms. The regions of most active star formation lie along the ridge of the gas density distribution tracing the galactic shock. Consequently, the systems of gas clouds and young stellar associations triggered from the clouds both exhibit aggregations of giant complexes along the galactic shock and global spiral-wave arm structure. The most prominent aggregations of young stellar associations are strongly correlated with the regions of highest gas density adjacent to the galactic shock, with few associations which are not adjacent to clouds. During the short periods of time (*20 Myr) corresponding to their active star formation stages, the young stellar associations assume the mass of those clouds from which they form; after this active phase, the associations redeposit their mass back into clouds through supernova events. Consequently, the total mass attributed to and interchanged between these two "mobile" systems-gas clouds and young stellar associations-is taken together in the definition of total gas mass, and both systems are taken to constitute the total mobile, self-gravitating, gaseous component. The ratio of total gas mass (for these mobile systems) to underlying basic state mass (prescribed as a fixed background component) is defined as the gas mass fraction and is one of the constants by which this cloudy galactic disk model is characterized. Self-gravitational effects of the gaseous component (both the gas clouds and young stellar associations) play an important multifold role. On the large scale (e.g., 10-50 kpc) gaseous self-gravity acts to enhance the overall collective gravitational field driving the gaseous response and thus helps enhance and maintain the global spiral structure. On local scales, (e.g., up to hundreds of parsecs) gaseous self-gravity aids the gathering and assembling of clouds into the massive complexes and aggregations. Striking is the local raggedness and patchiness of the computed distributions of gas clouds and young stellar associations formed from the gas. On intermediate scales (e.g., hundreds of parsecs to several kiloparsecs) gaseous self-gravity helps in the formation of spurs, feathers, arm branchings, and secondary features. These intermediate-scale features continually break apart and reform as the loosely associated aggregations, and giant complexes of clouds continually disassemble and reassemble over time. Such transient features on these local and intermediate scales give rise to disorder and chaotic activity within the global spiral structure and tend to blur the global coherence. NONLINEAR GAS DYNAMICAL EFFECTS Nonlinear gas dynamical effects dominate the cold gaseous component in galactic disks. Nonlinear characteristics of the gas, including the galactic shock formed in the gas, are evident in Fig. 2. Displayed are the computed variations of selected physical quantities at the sample time epoch 500-520 Myr in the gaseous self-gravitating modal-spiral-galaxy model (of Fig. 1). Plotted with respect to spiral phase around a representative half-annulus (at 10 kpc) in the model galactic disk are cloud number density, components of velocity perpendicular and parallel to spiral equipotential loci, computed velocity dispersion among gas clouds, and the computed distribution of young stellar associations currently active with supernova events (SN Rate). First and foremost is the strong gaseous galactic shock that has developed and is being maintained on the global scale, despite local stochastic variations and perturbations. This is evidenced in part by the strong, persistent cloud-density and SN-density enhancements just downstream of 180ø spiral phase (i.e, at the potential minimum of the modal spiral) and in part by the corresponding large-scale systematic motions exhibited by the cloud system with magnitudes of 40-60 km s*** (bottom two panels), representing strong systematic perturbations from purely circular rotation. The density distribution of this self- gravitating cloud system (middle panel) is seen to be strongly peaked with peak-to-mean values on the order of 3:1-4:1 and arm-to-interarm contrasts typically 6:1-8:1, with arm thicknesses on the order of 1-2 kpc. The sharp deceleration of gas from supersonic to subsonic speeds, reflected in the *** velocity component just preceding 180ø spiral phase with much more gradual characteristic rise downstream (bottom panel) appears as a striking galactic shock manifestation in these self-gravitational computations. The characteristic skewness in the in **** velocity component as well as the characteristic asymmetry in the **** velocity component together delineate the galactic shock structure that is formed. Such skewness is less apparent in the density distribution, with the density rise occurring over the broad shock width of a number of collisional mean free paths. It is the dissipative character of the cold, cloudy gaseous component that makes possible these strong nonlinear effects, which largely distinguish the interstellar gas from the stellar component. First, dissipative cloud-cloud collisions serve to maintain a low-velocity- dispersion gaseous component. Only such a cold component is able to respond with sharp nonlinear characteristics. The presence of a cold, cloudy, dissipative gaseous component can also promote the physical regimes necessary for unstable, growing global density spiral modes. Indeed, in real galaxies, it is likely to be the balance achieved between such moderately to rapidly growing global modes on the one hand and the dissipative nonlinear gaseous response on the other that allows the emergence of finely tuned, coherent grand designs of global spiral structures. Without the presence of a cold and dissipative gaseous component, real galactic disks would be hard pressed to produce and exhibit any such sharp, clear-cut structures on global scales. Likewise, on local and intermediate scales, the presence of a cold, dissipative gaseous component is essential for the formation of giant aggregations of cloud complexes, corresponding active star formation regions, prominent spurs, feathers, arm branchings, and secondary features. Only such a cold, dissipative component can provide the appropriate environment for the effective assembling of the giant massive cloud complexes (GMCs) and thereby produce the fertile beds for star formation activity. COMPARISONS WITH OBSERVATIONS These theoretical-computational results appear to be in good agreement with recent high-resolution observational studies of measured observational tracers along and across the spiral arms in several selected grand design spirals. For example, Very Large Array observations of the ratio continuum emission in M81 show nonthermal radio emission spiral arms that are patchy and well resolved, with widths of 1-2 kpc. The HI gas, the nonthermal radio emission from the arms, the dust and narrow dust filaments, the young stars, and the set of giant radio HII regions are each distributed across a broad spiral compression zone that starts near the measured position of the spiral velocity shock front in the HI gas and extends 1-2 kpc downstream from the shock. These features are in good agreement with the theory presented herein, which places important emphasis on the cloudy nature of the interstellar medium. There also appears to be good agreement with the results of recent observations of CO emission from M51 that reveal density wave-galactic shock streaming motions with magnitudes on the order of 60-80 km s*** in the molecular gas which are coincident with the prominent dust lanes along the major spiral arms. These results appear as strong evidence that the spiral density wave-galactic shock in M51 assembles preexisting molecular clouds into giant associations and triggers the collapse of suitably primed clouds, leading to the formation of stars. On the basis of the theory, we would expect the GMCs in grand design spiral galaxies to be strongly concentrated in the spiral arms. For M51, the CO emission is found to be strongly peaked in the global spiral arms, with average arm-to-interarm integrated CO brightness ratios of 2.4 for a selected inner arm and 3.0 for a selected outer arm. A narrow dust lane traces closely the inner CO arm, with the dust lane and the CO arm having similar widths of about 300 pc. For M31, the CO distribution is also found to be strongly concentrated to the spiral arms. High-resolution CO observations reveal GMCs in M31 similar in size and molecular hydrogen mass to those in the solar neighborhood of our Milky Way system. These clouds are found to be closely associated with HII regions and are active sites of star formation, in, good agreement with the theory. Additional Reading Bertin, G., Lin, C.C., Lowe, S.A., and Thurstans, R.P.(1989). Modal approach to the morphology of spiral galaxies: I. Basic structure and astrophysical viability. Ap. J. 338 78, and Modal approach to the morphology of spiral galaxies: II. Dynamical mechanisms. Ap. J. 338 104. Kaufman, M., Bash, F.N., Hine, B., Rots, A.H., Elmegreen, D.M., and Hodge, P.W.(1989). A comparison of spiral tracers in M81. Ap. J 345 674. Lada, C.J., Margulis, M., Sofue, Y., Nakai, N., and Handa, T. (1988). Observations of molecular and atomic clouds in M31. Ap. J. 328 143. Miller, R.H.(1976). Validity of disk galaxy simulations. J. Comput. Phys. 21 (4) 400. Roberts, W.W., Lowe, S.A., and Adler, D.S.(1990). Simulations of cloudy, gaseous galactic dish. In Galactic Models, J.R. Buchler, S.T. Gottesman and J.H. Hunter, eds. Ann. N.Y. Acad. Sci. 596 130. Vogel, S.N., Kulkarni, S.R., and Scoville, N.Z.(1988). Star formation in giant molecular associations synchronized by a spiral density wave. Nature 334 402. See also Galactic Structure, Interstellar Clouds; Galactic Structure, Large Scale; Interstellar Medium, Galactic Atomic Hydrogen.