11.3. Bars in Early and Late-type Galaxies
Elmegreen & Elmegreen (1985, 1989) have shown that the nature of bars changes along the Hubble sequence. First, spiral galaxies with early Hubble types tend to have bars that are longer relative to the size of the optical disk and the turnover radius of the rotation curve, compared to late-type barred galaxies; second, early-type bars are more uniform in intensity relative to the outer disk light profile, compared to bars in later Hubble types. The spirals surrounding these bars also differ, with a tendency toward grand design two-armed spirals occurring for the early types, while the later types have a more multiple-armed or flocculent structure, as in nonbarred galaxies. The bar and spiral-arm amplitudes differ along the Hubble sequence too, with stronger bars and radially decreasing spiral-arm amplitudes in early type SB or SAB galaxies, and weaker bars with radially increasing spiral-arm amplitudes in late types.
These observations suggest that bars in early-type galaxies extend to corotation, where they drive two-armed spirals at the same pattern speed out to the outer Lindblad resonance, and that bars in late-type galaxies could end well inside CR, possibly as far in as the inner Lindblad resonance for the outer spiral pattern, and that these outer spirals are not always driven by bar.
The problem of the extent of bars has long been debated in the literature. Contopoulos (1980) has argued that bars should extend up to their corotation, or slightly inside, up to the 4 / 1 resonance: inside CR, the main stable periodic orbits are parallel to the bar, and bars are composed of slightly elongated orbits trapped around periodic orbits. Periodic orbits are perpendicular to the bar outside CR. Weak bars could still form by crowding effects in that case, but in the case of strong bars, orbits become stochastic outside corotation, which supports the bar confinement inside CR. In N-body simulations, no bar has been seen outside its corotation.
In the point of view developed by Lynden-Bell (1979), and further by Pasha & Polyachenko (1994) and Polyachenko (1994; see also Polyachenko 1996 and Polyachenko & Polyachenko 1996), bars are made of near-resonant orbits at the inner Lindblad resonance. The predicted pattern speed is then always below the maximum of - / 2, since the precessing rate of an elongated orbit is lower than the nearly axisymmetric one, and the pattern speed is now an average of all precessing rates of the orbits in the bar. The bar is also predicted to end near ILR, far before the corotation radius. This scenario has not yet found support from N-body simulations.
Petrou & Papayannopoulos (1986) have also proposed that bars are shorter than their corotation. This was meant essentially to resolve the problem of the position of dust lanes in the concave side of the arms, in strongly barred galaxies. If dust lanes trace shocks experienced by the gas as it enters the arms, their position in the concave side means that the arms are inside corotation. Since they are outside the bar, the latter must end well inside its CR. They claim that in very strong bars, there can exist a 1 / 1 resonance, and that orbits become stochastic outside the 1 / 1 radius. The bar will then end at this radius, well inside CR. Other solutions have been proposed to solve the same problem; one of them is the existence of two different pattern speeds for the bar and the spiral (Sellwood & Sparke 1988).
Combes & Elmegreen (1993) have studied by N-body simulations the properties of bars along the Hubble sequence. Basically, two models of galaxies were used, differing by their bulge-to-disk mass ratio (less than 10% for late-types, and equal to 2 for early-types). In any case, the bar pattern speed adjusts as a compromise of the precession rates of all trapped orbits. It is always very near the maximum of the - / 2 curve, slightly higher at the beginning, and lower at the end of bar formation, when the bar reaches a steady-state (Figure 63).
For early-type galaxies, the bar ends slightly inside corotation, as was frequently observed in N-body simulations. The bar is strong, non-linear, and ergodicity outside CR prevents the bar extension. The bar saturates inside, trapping all possible orbits, which explains the flat-topped profile. Bar growth is slow, however, due to the massive bulge and its stabilizing effect.
For late-types, the bar ends far inside CR, at about the inner Lindblad resonance. The pattern speed is so slow (corresponding to the low precessing rates - / 2) that corotation is pushed outside of the optical disk. The bar stops growing because of a lack of particles outside corotation which can receive angular momentum (cutting the bar amplification mechanism). The bar has a radial exponential profile, following the optical disk profile, since its growth has prematurely ended (cf. Figure 64).
The shape of the bar for late-types is also found to be more squarish (m = 4 term larger than in early-types). This can be understood in terms of orbits, since the x1 orbits supporting the bar are rounder when the axisymmetric background is stronger (Contopoulos 1988).