The Importance of de Vaucouleurs Family and Variety Subdivisions

The long axis of de Vaucouleurs' revised Hubble classification volume was clearly considered by him to be the dimension most connected with the basic physics of galaxies. This is because a number of measured properties (total colors, mean surface brightnesses, HI mass-to-light ratios) correlate smoothly with the de Vaucouleurs T index, as shown in the figure below. The de Vaucouleurs T index is a numerical coding of the stage that he extensively used to investigate such correlations. The coding is such that T=-5 corresponds to E galaxies, T=0 to S0/a galaxies, T=3 to Sb galaxies, T=5 to Sc galaxies, T=10 to Im galaxies, and so on. The factors that might determine the stage include the initial angular momentum distribution, the initial density, the halo mass fraction, the total galaxy mass, and the initial velocity dispersion of the dark matter. References to these ideas are summarized in Table 1 below.

Correlations between measured colors, surface brightnesses, and HI mass-to-light ratios with de Vaucouleurs T index

The origins of bars and rings are perhaps more interesting. It is known that the integrated colors of galaxies do not really depend on the position of the galaxy within the cross section at a given stage (Buta 1989), so that bars and rings may not impact integral stellar populations very much at a given type. However, bars may impact the chemical enrichment history of galactic disks by weakening or eliminating chemical abundance gradients (Martin and Roy 1994). Bars and rings may have their greatest value for understanding how galaxies evolve after they have mostly formed their disk components. Bar instabilities (Hohl 1971; Miller and Smith 1979) or orbit trappings (Lynden-Bell 1979) may explain some bars, while others may be tidally-generated (Noguchi 1996). Sellwood (2000) favors that most real bars form by an episodic growth process that converts short, weaker bars into strong, longer bars. Bars may not be permanent features of galaxies but may dissolve in less than a Hubble time due to increasing central mass concentration (Hasan and Norman 1990). Thus, the apparent strength of a bar could be a transient property, an aspect connected to evolutionary state.

The de Vaucouleurs family is the only aspect of the classification that has been quantified directly. Buta and Block (2001) and Block et al. (2001) have used near-infrared images to infer gravitational force fields for 75 normal bright galaxies. Bar strength can be defined in terms of the maximum value of the ratio of the tangential force to the axisymmetric part of the radial force (Combes and Sanders 1981). Given the gravitational potential $\Phi(R,\theta)$ in the disk plane, these authors defined the bar strength at radius R as

$$Q_T(R) = {F_T^{max}(R) \over F_0(R)} = {{{1\over R}\bigl{(}{... ...er \partial\theta}\bigr{)}_{max}} \over {d\Phi_0(R)\over dR}}$$ (1)

where F_T^max(R) represents the maximum amplitude of the tangential force and F₀(R) is the mean axisymmetric radial force, inferred from the m=0 component of the gravitational potential. Under the assumptions of a constant mass-to-light ratio and an exponential vertical scale height, the near-infrared light distribution of a galaxy may be transformed into a gravitational potential (Quillen, Frogel, and González 1994). A tangential-to-radial force ratio map reveals a butterfly pattern that is the characteristic signature of a bar, as shown in the Figure here. The actual force ratio changes sign from quadrant to quadrant relative to the bar axis, because the total force in the plane is slightly offset towards the ends of the bar. In the case of perfect symmetry, |Q_T| would reach a maximum at the same radius and angle relative to the bar in each quadrant. However, slight asymmetries and/or noise can make these maxima different in each quadrant. If we let Q_bi = |Q_T|^maxin quadrant i, then the average of these four values can provide a single measure of bar strength for a whole galaxy, if the gravitational potential is known. This average is called the relative bar torque parameter, Q_b. The Q_bi are known as the ``maximum points.''

top left: tangential-to-radial force ratio map of NGC 1433; top middle: schematic showing how sign of tangential force changes with quadrant relative to the bar axis; top right: maximum points plotted on near-infrared (1.6micron) image of NGC 1433; remaining rows: near-infrared images of a sequence of 9 galaxies of increasing bar strength, with maximum points plotted in each case.

The figure below shows that de Vaucouleurs' view of bar strength as a continuous property is largely confirmed by the relative bar torque parameter. Q_b correlates well with de Vaucouleurs family, although the scatter is large in each category.

Plot of relative bar torque parameter Q_b versus de Vaucouleurs family classification The de Vaucouleurs family classifications discriminate true bar strength better than the Hubble classes S and SB, as shown in the following table, where the Hubble classes are from the revised Shapley-Ames catalogue (Sandage and Tammann 1981, 1987).

Classification	<Qb> $\pm$ $\sigma$	N	range
RSA S	0.11$\pm$0.08	32	0.01-0.33
RSA SB	0.28$\pm$0.13	32	0.07-0.63
deV SA	0.06$\pm$0.04	14	0.01-0.14
deV SAB	0.16$\pm$0.08	32	0.02-0.33
deV SB	0.33$\pm$0.13	23	0.16-0.63

The origin of rings is one of the best understood properties of barred galaxies. Numerous studies (see review by Buta and Combes 1996) have shown that inner, outer, and nuclear rings are often sites of enhanced blue colors, HII region concentration, and molecular and atomic gas, consistent with active star formation. This suggests that gas is at the heart of ring formation and, since most ringed galaxies are barred, a bar must also be an essential element in this process.

It is the star-forming character of resonance rings that makes them important to galactic evolution. In some galaxies, for example, a resonance ring is the only place where significant star formation is taking place. The key to understanding the processes involved is the nature of a bar and the periodic orbits associated with it. A bar is a self-gravitating pattern that rotates with a pattern angular velocity $\Omega_p$ (units usually km s^-1 kpc^-1). In linear theory, every star or gas cloud moving in the disk plane has two natural frequencies of orbital motion: the angular frequency $\Omega$ of circular rotation, and the radial epicyclic frequency $\kappa$. Orbital resonances occur at the locations in the disk where

$$\Omega_p = \Omega \pm {\kappa\over m}$$

where m is an integer. The major resonances relevant to ring formation are:

Outer Lindblad Resonance (OLR), where $\Omega_p = \Omega + \kappa/2$
Inner Lindblad Resonance (ILR), where $\Omega_p = \Omega - \kappa/2$
Inner 4:1 Ultraharmonic Resonance (UHR), where $\Omega_p = \Omega - \kappa/4$
Other important resonances are corotation (CR), where $\Omega_p=\Omega$, and the outer 4:1 resonance, where $\Omega_p = \Omega + \kappa/4$.

Periodic orbits are the building blocks of a barred galaxy. In an axisymmetric galaxy, periodic orbits are circles, but in a barred galaxy, these orbits are deformed into more complex shapes that depend mostly on the symmetry of the potential. Of critical importance to ring formation are that periodic orbits in a bar potential tend to (1) be elongated parallel or perpendicular to the bar; (2) become more elongated near a resonance than they are away from a resonance; and (3) change orientation by 90$^{\circ}$ across a resonance (Contopoulos and Grosbol 1989).

The principal theory is that rings form by gas accumulation at resonances, under the continuous action of gravity torques from the bar pattern. This has been revealed most clearly by ``sticky particle'' models of barred galaxies, which model the evolution of a cloud-particle disk over many bar revolutions. Gas plays an essential role in the process because of its dissipative character. In a nonaxisymmetric potential such as that due to a bar, tangential forces act on orbiting gas clouds. Because periodic orbits change orientation by 90$^{\circ}$ across a major resonance, and because these orbits achieve their maximum elongations near a resonance, it is possible for different periodic orbit families to intersect in a major resonance region. Gas clouds cannot follow intersecting orbits without colliding, so the gas follows a spiral where orbits are inclined to the symmetry axis of the bar. The bar can therefore exert a net torque on the gas, leading to a transfer of angular momentum. The torque changes sign at each major resonance: it is negative between CR and ILR, and positive between CR and OLR. This has the effect of depopulating the CR region, with gas moving either inward to the ILR or outward to the OLR. The net effect is that gas accumulates into ringlike patterns at these Lindblad resonances. It is possible also for some gas to accumulate at the UHR. Eventually, gaseous rings which form at each of these resonances align with the symmetry axes of the bar. In this circumstance, no net torque can act on them.

Schwarz (1981, 1984a) first demonstrated the efficiency of this process. Other papers confirmed or extended this work (e.g. Combes and Gerin 1985; Byrd et al. 1994; Piner, Stone, and Teuben 1995; Salo et al. 1999; Buta and Combes 1999). These studies have linked nuclear rings to the region between two ILRs in barred galaxies, inner rings to the UHR, and outer rings to the OLR. In general, however, it must be understood that the existence of these resonances is necessary but not completely sufficient for ring formation. Many galaxies may be affected by these resonances but no rings trace these locations, either because of a lack of sufficient gas (as in S0's) or because the mechanism of ring formation is not efficient (as in nonbarred spirals with strong stellar spiral density waves).

The different resonance rings are different kinds of star formation laboratories. In particular, nuclear rings are prone to massive starbursts and represent an unusual environment in a normal galaxy where ``super star clusters'' can form. The dynamics of the rings is elegantly described by Elmegreen (1994). The idea is that galactic bars exert a strong negative torque on gas located inside CR, causing gas to accrete near an ILR. The accretion is not necessarily allowed to continue to the center, but stalls at the ILR, forming a gas ring or spiral where the torques are in equilibrium. A starburst can occur in a nuclear ring when the gas density exceeds a critical value depending on the square of the epicyclic frequency in the region of ILR. Once the critical density is exceeded, the ring can become gravitationally unstable to fragmentation, and several large star-forming clouds can develop along its circumference. Once the gas forms stars, the star formation can cease for a period until the density once again exceeds the critical value, and a new star-forming episode can ensue.

Although gravity torques can also collect gas at the UHR and OLR of a barred galaxy, starbursts are less likely in these regions because the required critical gas density is not as high as in ILR rings. Indeed, the star formation in resonance rings should reflect the dynamics to a great extent. For example, star formation in inner and outer rings can show well-defined azimuthal and width variations (Crocker, Baugus, and Buta 1996; Buta and Purcell 1998; Ousley and Byrd 1998). The preferred alignments between different resonance rings and bars means that different resonant orbits are involved. The properties of these orbits will determine where star formation is most favored along a ring, and also what happens to aging clusters originally born in these regions. The degree of coupling between the stellar and gaseous disks is particularly evident in the existence of old-population resonance rings that may underlie a star-forming ring. In classic resonance ring galaxies like NGC 1433 (Buta and Combes 1999) and 3081 (Buta and Purcell 1998), the inner rings in the H-band are morphologically similar to their appearances in the B-band, only smoother, indicating the existence of a significant stellar component. Many classical outer rings are dominated by an old population (e.g., Gallagher and Wirth 1980), and even in inner rings star formation can clearly ``turn off'' leaving behind only these older components (e.g., NGC 7702, Buta 1991). Resonance rings form stars only so long as gas is available, and do not necessarily completely disappear even if the gas runs out.