GALAXIES, BARRED SPIRAL STEPHEN T. GOTTESMAN AND JAMES H. HUNTER, JR. EARLY OBSERVATIONS Nonstellar nebulous objects, some of which are visible to the naked eye in the night sky, have been recorded for several centuries. In the 1840s and 1850s the Earl of Rosse, using his great 6-ft telescope, found that several had a spiral form. In 1918 Heber D. Curtis drew attention to a second type of spiral: "its main characteristic is a band of matter extending diametrically across the nucleus and inner parts of the spiral." Owing to their shape, he called these *-type spirals. Edwin P. Hubble, in his 1926 study of the properties of galaxies, called these systems barred spirals, which he described as having the form of a *. He found that these were less abundant than normal spirals, but (with the exception of their bar) they appeared to have similar properties of the normal systems, a view supported by the photometric studies of Erick B. Holmberg some 30 years later. Initially, Hubble saw these as distinct but parallel families with a thin population of mixed types lying between the two. Barred spirals are observed to possess two main forms: those in which the arms are tangent to an external ring (r) at which the bar ends, and those for which the arms begin directly from the ends of the bar(s). The same phenomena are present, though less obvious, in normal spirals. Thus, by the late 1950s it was clear that Hubbles ordering was too coarse and that instead one should consider a classification volume incorporating the main families, transition groups, and the r and s varieties. Gerard de Vaucouleurs' synthesis accomplished this end. In Fig. 1, a cross section of this volume is shown, illustrating the transition between the normal (A) and the barred (B) families, and encompassing the r and s varieties. Owing to the continuum of forms, de Vaucouleurs suggested there was nothing abnormal about the barred species and proposed that A-type systems be called ordinary spirals. Furthermore, de Vaucouleurs found that ordinary and barred systems were about equally abundant and accounted for almost 50% of the easily classifiable (bright) systems. However, if one adds to the barred family systems with oval distortions, barred galaxies are the dominant shape. Indeed, it has been suggested that the bar-forming tendency is a more significant characteristic of disk systems than the tendency to form spirals. PHYSICAL DESCRIPTION Allan Sandage and others characterize several zones when describing barred spirals: (1) the nuclear bulge, (2) a region concentric with the nucleus that has the shape of a convex lens seen in projection (located between the bulge and disk; it is most prominent in the early-type barred systems), (3) a luminous ring of matter that, when present, lies at the outer edge of the lens and, as the r subvariety progresses, develops into the spiral arms (in some cases an outer ring is seen as well, aligned either perpendicular or parallel to the bar axis), and (4) the outer envelope of the galaxy. In addition, there is always present the defining characteristic, a bar that extends across the center and the lens (if present) terminating at its edge or at the innermost regions of the spiral arms. The bar phenomenon is associated with disk systems; barred elliptical galaxies do not exist. Bars are associated with high-angular-momentum structures and rotate much faster than do ellipticals. Furthermore, bars appear to rotate in the plane of the disk, in the same sense as galactic rotation, and as rigid bodies. However, the rate at which they tumble (the pattern speed) is uncertain. The existence of bars correlates strongly with the presence of grand design spiral structure in disk systems. Bars, as they are not axially symmetric, appear to be an extremely effective mechanism for driving density waves (both gaseous and stellar), particularly if the luminosity profile of the bar is flat rather than exponential. Several high-resolution studies of barred systems, which are rich in atomic hydrogen, have been made in order to investigate the dynamics of these galaxies. Hydrogen is a ubiquitous component of the interstellar medium and its distribution correlates well with spiral arms. Therefore, it is a medium that reveals the structure and kinematics of disk systems against which dynamical models can be tested. In the inner parts of these galaxies, the isopleths of radial velocity are twisted and skew the apparent line of nodes. In these regions, the bar effects the gas orbits most strongly. Streaming motions also are seen in association with the spiral arms. It is assumed that the arms are driven by the bars, and the direction of radial motions is sensitive to the radius at which the pattern corotates with the disk. Inside the corotation radius radial motions will be inwards, whereas beyond this critical radius the gas gains momentum at the expense of the pattern. Structural features may help locate this domain; many bars show narrow and strategically located dust lanes, frequently along their leading edges. Often at or near the bar-spiral-arm transition region these dust lanes abruptly shift to the trailing edge of the arm. The dust lanes appear to delineate shock regions and the abrupt change from leading to trailing phenomena may indicate passage across a resonance, such as corotation. Also, the location of inner rings may indicate the radius of corotation; for they too are expected to occur at or near resonances. Therefore, there is observational evidence that corotation happens at or just beyond the end of the bar. Unlike other triaxial phenomena in galaxies, bars have very large axial ratios, which can approach 5:1. However, the luminosity of the bar is typically only a few percent of the luminosity of the disk, though it can be as large as 20%. Nonetheless, the distribution of light is not smooth. As we have noted, dust is seen often in the form of narrow lanes; in other cases it may be seen as patches symmetrically located at the ends of the bars. Also, the cusp region, at the ends of the bar, is often the locus of significant activity, ionized hydrogen or, particularly for early-type systems, lobes in the optical (stellar) emission. Qualitatively, these phenomena can be understood in terms of the prominent families of stellar orbits (and, by association, gas streamlines); where they cross, shocks will be generated in the gas. These appear to be regions of observed dust and/or enhanced star formation. In gas-free systems, the density of stellar orbits generates the luminosity distribution. Below, we will enlarge upon these points. Many, but not all, of the observed galaxies show either an absence of HI in the bar region, or a very severe reduction in the surface density of the gas. Also, many barred systems show abnormal amounts of stellar activity in their nuclei. A natural interpretation is that the gas in the central regions has lost angular momentum to the bar (the bar is inside corotation) and has been swept into the nucleus, where bursts of star formation occur. Often, CO emission is observed, confirming the association of a dense interstellar component with star formation. However, other galaxies that are centrally evacuated do not show these phenomena; perhaps nuclear star bursts are episodic. In contrast, some of these galaxies have gaseous bars. The critical difference appears to be revealed by dynamical models. If models can be constructed successfully employing a material bar, evacuation occurs. If an oval distortion of the disk will suffice, gaseous bars are formed. Therefore, it is extremely important that multicolor photometry be used to place constraints upon the mass distribution of the bar. ORBITAL CONSIDERATIONS: PARTICLE DYNAMICS The morphology of barred galaxies can be understood qualitatively from the (linear) theory of small oscillations, superimposed upon circular orbits (their guiding centers). Because most of the mass of a galactic disk resides in its stars, the disk consists principally of stars, orbiting about its center. In most respects, the ubiquitous interstellar gas is not of great dynamical importance, because it contributes but a small fraction of the global gravitational potential. In the absence of a bar, small disturbances of a star, moving initially in a circular orbit, oscillate about its circular-orbit guiding center at the epicyclic frequency in the plane of the disk, and with a more rapid frequency normal to the plane. Both frequencies can be calculated at each radial location in the disk plane from the (known) gravitational disk potential. The epicyclic frequency distribution is an important parameter in determining the morphology of barred spiral galaxies. If the angular velocity of stars orbiting at radius r in the plane of the background and axisymmetric disk is defined by *(r), the epicyclic frequency is defined as ***************************** For a Keplerian potential, in which *******************. In disk galaxies, * usually does not diminish this steeply with radius; hence, usually *(r)***(r). (For the Sun, *******, meaning that a star undergoes **1.3 radial oscillations per orbital period about the galactic center.) Bar formation occurs naturally in rotating systems undergoing gravitational collapse. This prediction, initially made from linear theory, has been confirmed by a wide range of numerical experiments. An intriguing characteristic of the numerical bars is that, in addition to their being very robust figures (difficult to destroy), the individual stellar orbits behave collectively, so that each bar rotates at a particular angular rate. Therefore, not surprisingly, a second quantity of fundamental importance to the morphology of barred galaxies is the angular velocity, or pattern speed ***, of the bar figure as it rotates rigidly in the central portion of the disk, thereby disturbing the nearly circular orbits of the stars. Of particular interest are those radial distances from the center of a disk where resonances occur between integer multiples n of the angular velocities of stars relative to the bar pattern speed and the epicyclic frequency at that radius, namely, ****************************** The values of r where these resonances occur are called Lindblad Radii, in honor of the Swedish astronomer Bertil Lindblad (1895-1965). The (+) sign denotes an inner resonance of order n, while the corresponding outer resonances bears the (-) sign. Stars orbiting near the inner resonances move more rapidly than (and therefore overtake) the bar potential, whereas those near outer resonances orbit more slowly than the bar pattern. The most important of the resonances occur when n=2 (because most galaxies are two-armed systems), whence ****************. These particular resonances conventionally are called the inner and outer Lindblad resonances, or ILR and OLR. Higher-order resonances usually are designated as inner (+) and outer (-) n/1 resonances. In addition to the ILR and OLR, a third resonance of fundamental importance in barred galaxies is the corotation resonance, defined by ***************************** Stars orbiting at the corotation radius have the same angular velocity as the bar. Among the important predictions of linear theory are that the departures from circular motions become greatest near the principal resonances, and that orbits change their alignments by 90ø at the ILR, the OLP, and at the corotation resonance. An interesting class of models is one in which no ILRs exist. (The shape of rotation curves, derived from high-resolution radio observations of neutral hydrogen in selected barred spiral galaxies, show that no ILRs exist in these galaxies if their corotation radii are ****** bar radii.) In the absence of ILRs, linear theory shows that the stellar orbits are aligned parallel to, and therefore reinforce, the bar within the corotation radius, and that the orbits are elongated perpendicular to the bar between corotation and the OLR. Thus, the latter class of orbits are aligned in a sense that would reinforce spiral structure between corotation and the OLR The gravitational potentials of generic bars often are represented by expansions of the form **************, where * is an angular coordinate in the disk plane, n is an even integer, and the coefficients A* (r) are the multipole amplitudes, which diminish rapidly with r. Usually only a few of the lowest-order terms are included (e.g., n=2 and n=4), with the 2* component being the dominant one. In addition to the bar, a spiral potential may be included between corotation and the OLR. Extensive numerical calculations have been carried out on two-dimensional models in which the motions are restricted to the disk plane. Particular generic characteristics that have been unveiled by these nonlinear studies are as follows. (1) When a strong bar is present, there are two main families of stable orbits elongated along the bar that have quite different shapes. The inner family of orbits, which are oval shaped and sometimes have loops at their ends, are found between the central region and the inner 4/1 resonance. However, between the inner 4/1 resonance and corotation, the orbits are shaped like parallelograms, with the longer sides parallel to the bar. In some models, the 4/1 family of parallelogram-like orbits is dominant, and gives a boxy appearance to the bar, whereas this family is of little importance in other models. (2) Orbits between the outer 4/1 resonance and the OLR support a strong, imposed spiral potential. Between corotation and the outer 4/1 resonance, the orbits support the spiral only if it is weak. However, in strong bars and spirals, most orbits are stochastic in this region. Consequently, a strong spiral cannot be reinforced by stellar orbits between corotation and the outer 4/1 resonance. As illustrated in Fig.2, barred spiral galaxies are observed to have both oval-and parallelogram-shaped bars. Thus, it seems clear that each of the principal families of stable, periodic orbits within corotation can dictate the appearances of bars in real galaxies. Patches of dust, ionized gas and stars, situated at the ends of some bars, plausibly may be associated with loops at the ends of certain oval orbits. Self-consistent model bars, as well as nearly self-consistent, two-dimensional models of barred spiral galaxies, have been constructed from orbit theory. Families of stable, periodic orbits form the backbone structures of these models. (3) For systems with very strong bars, stochastic orbits may become important. Stars on such orbits fill a zone which closely resembles the lenses that are seen in many early-type galaxies. GAS DYNAMICS Gas flows in barred spiral galaxies have been studied extensively, and many gaseous features observed in barred galaxies are replicated by theoretical models. For example, the dust lanes observed on the leading edges of the bars in galaxies such as NGC 1300 may be associated with shock fronts, which appear at those locations in gas dynamical models with strong bars. However, bars alone cannot excite the tightly wound, spiral gaseous arms that are observed in many barred galaxies. Thus, it is necessary to invoke an additional, nonaxisymmetric forcing mechanism, such as an imposed stellar spiral potential, to explain the gas morphology in these systems. Models of the gas flows in selected barred spirals, which have been observed in neutral hydrogen at high resolution, show that their bars must have pattern speeds which place corotation only slightly beyond the ends of the bars. Although it is a minor mass component, interstellar gas may play an important role in the structure of strongly barred galaxies. Since gas streams cannot cross, gas flows may smoothly connect the stellar spiral structure in the stochastic region between corotation and the outer 4/1 resonance. This conjecture has been borne out by preliminary calculations. Although much progress has been made in modeling barred spiral galaxies, fundamental questions about these systems remain unanswered. In particular, we do not yet understand in detail how collapsing rotating systems of gas and stars evolve into the configurations that we observe, which include both disk and bars. Additional Reading Contopoulos, G. and Grosbol, P.(1989). Orbits in barred galaxies. Astron. Ap. Rev. 1 261. Hunter, J.H., Jr.(1990). Model gas flows in selected barred spiral galaxies. In Galactic Models (Proceedings of the Fourth Florida Workshop in Nonlinear Astronomy), J.R. Buchler, S.T. Gottesman, and J.H. Hunter, Jr., eds. Ann. N.Y. Acad. Sci. 596 174. Kormandy, J.(1982). Observations of galaxy structure and dynamics. In Morphology and Dynamics of Galaxies, L. Martinet and M. Mayor, eds. Geneva Observatory, Sauverny, Switzerland, p. 115. Sandage, A.(1961). The Hubble Atlas of Galaxies. Carnegie Institution of Washington, Washington, DC. Sandage, A.(1975). Classification and stellar content of galaxies obtained from direct photography. In Galaxies and the Universe, A. Sandage, M. Sandage, and J. Kristian, eds. University of Chicago Press, Chicago, p. 1. See also Galaxies, Disk Evolution; Galaxies, Spiral, Structure; Stellar Orbits, Galactic.