When we observe a star-forming region we sometimes wonder how it got there, or why stars formed there, or anywhere for that matter. The average gas density in most galaxies is very low, close to the tidal limit of ρtidal = -1.5Ω R (dΩ / dR) / (π G) ~ 1 cm-3 for galactic rotation rate Ω and radius R. This is also about the gas surface density limit where Toomre Q = σgasκ / (π GΣgas) ~ 1 for velocity dispersion σgas, epicyclic frequency κ, and mass column density Σgas. Stellar explosions produce denser gas in supernova remnants, but this gas is usually too tenuous to be strongly self-gravitating, as in the Veil Nebula, and it is also too short-lived in that state for self-gravity to operate (Desai et al. 2010). The two-phase instability makes cool gas, but this operates only between temperatures of ~ 10,000K and ~ 100K, which is not cold enough to make stars. Star formation requires a thermal Jeans mass close to a solar mass. The thermal Jeans mass is MJ,th = ρ kJ-3 ~ 7(T / 10 K)1.5 n-0.5 M⊙ for thermal Jeans wavenumber kJ = (4π Gρ)1/2 / c and isothermal sound speed c = (kT / μ)1/2 with mean weight μ of atomic gas, and density n = ρ / μ. For the range of temperatures expected from the thermal instability and for the average density, MJ,th ~ 200M⊙, which is too large for a star. Star formation requires gas that is both cold and dense to bring MJ,th down. Processes that do this may be thought of as star-formation triggers.
A fair question is whether the ISM can make cold and dense gas on its own, without non-ISM processes, such as stellar density waves, galactic shear, superbubbles, etc.. If there were no stars to compress the gas or supplement its gravitational self-attraction with additional mass, would new stars form? The answer is probably yes because galaxies once had no stars, and the gas formed stars anyway. Still, galaxy collisions in the young universe could have triggered the star formation by forcing the gas to be dense in the shocked overlap region and in a central concentration that formed after angular momentum loss.
During the last few years, observations of very young galaxies seem to suggest that they can form giant clumps of star formation on their own, even with no observable underlying disk of older stars and no evidence for an interaction with another galaxy (Elmegreen et al. 2009a, Genzel et al. 2011). The only possible process for this seems to be a gravitational instability in the whole gas disk, with a resulting clump mass comparable to the turbulent Jeans mass, MJ,turb = Σgas kJ,2D-2 for kJ,2D = π G Σgas / σgas2. The clumps in young galaxies are large relative to the galaxy radii because the turbulent speeds are large relative to the rotation speeds vrot (Davies et al. 2011). This follows from R kJ,2D ~ GM / (R σgas2) ~ (vrot / σgas)2.
This process of gravitational collapse of the ISM is the most fundamental of triggering mechanisms. To carry the initial collapse all the way to stars in a young ISM may have also relied on the pervasive presence of CO molecules (Daddi et al. 2010, Tacconi et al. 2010), which allows for cooling to T < 100K, and on the extremely high Σgas, which lowers MJ,th by increasing the average midplane density. If we write the midplane pressure in a pure-gas disk as P = 0.5π GΣgas2 and the thermal Jeans mass as MJ,th = c4(4π G)-1.5 P-0.5, then
from which it can be seen that the observed ISM column densities in the clumps of young galaxies, Σgas> 100M⊙ pc-2 (Tacconi et al. 2010), raise the pressure so much that even temperatures of 100 K may be low enough for star formation. Collapse inside these clouds raises the pressure more because of the higher local column density in the resulting core, and it lowers the temperature more because of opacity.
When stars are present, gravitational instability in the ISM is augmented by stellar gravity. This happens most commonly in three ways: by a two-fluid swing-amplified instability (Toomre 1981), in the shocks of global spiral density waves (Roberts 1969), and in the dense central regions formed by gas accretion in a bar potential (Matsuda & Nelson 1977).
The first of these involves the simultaneous collapse of gas and stars, which produces a moderately dense clump of both components on a timescale (Gρtotal)-1/2 ~ κ-1 for Q ~ 1. The stellar part of this collapse bounces as the stars move away with enhanced energy in epicycles. Nearby stars form a spiral wake (Julian & Toomre 1966). The dissipative gas remains as a dense clump at the center of gravity of the instability, with a gas filament also forming in the wake. This is the two-fluid swing-amplified instability (Jog & Solomon 1984, Rafikov 2001, Romeo & Wiegert 2011, Elmegreen 2011). It appears to be common in galaxies, taking the form of multiple spiral arms that are long and irregular in the outer parts. Usually these arms are more regular in the inner regions, where multiple-arms often merge into symmetric two-arm structures midway in the disk (Elmegreen & Elmegreen 1995).
The second way in which stellar gravity augments the condensation of gas into star-forming clumps is through stellar density waves, which arise in the gas+star mixture as a result of perturbations from the outer disk, companion galaxies, or bars, and which may last for several rotations (Lin & Shu 1964) before moving to the center (Toomre 1969). These waves move through the gas and stars (unlike the swing amplifier instability which follows the gas+star mixture for a time κ-1) and they shock the gas as it passes through. The shock appears as a thin dust lane. If the shocked gas is dense enough, it can become gravitationally unstable and form giant clumps and star complexes. It can also form stars by cooling interarm gas and squeezing interarm clouds. Most star formation in the Milky Way is in giant molecular clouds (GMCs) that are parts of 107M⊙ HI+CO complexes in spiral arms (Grabelsky et al. 1987). Because shear is low in spiral density wave arms, the process of gas collapse can be augmented by magnetic tensional forces, which remove angular momentum (Elmegreen 1987, Kim et al. 2002).
Some galaxies have a stellar component that is either too warm or too rapidly rotating for its column density to form strong spiral arms, i.e., Qstars >> 1; then the gas+star mixture is not particularly unstable. The gas is dissipative, however, and can still collapse on its own, or with only a small contribution from underlying stars. The result is a network of thin and short gaseous arms that form stars, giving a flocculent appearance. These arms should be co-moving with the material close to the site of the initial collapse, although they can be wave-like far from this site, in the spiral wake.
Figure 1 shows a piece of the galaxy M51 from an image taken with the Hubble Space Telescope. There is a spiral density wave with two large concentrations of gas in the dust lane, 107 M⊙ each, and star formation in each concentration. When there are several of these concentrations along part of an arm, they look like "beads on a string". Efremov (2010) studied the relation between such regular patterns and the magnetic field. For several magnitudes of extinction, and for a thickness through the plane of ~ 100 pc, the average density in the dustlane is ~ 10 cm-3 (D. Elmegreen 1980) and so the average dynamical time is ~ (Gρ)-1/2 ~ 30 Myr. This average density is about what is expected for a density wave shock where the average incident density is the intercloud value ( ~ 0.3 cm-3) and the ratio of the shock velocity to the internal turbulent speed is ~ 5. The average dynamical time is too long for gravitational collapse to develop much while the gas is in the dust lane, but the interarm gas is clumpy and these clumps feel a pressure increase when they enter the arm, causing them to collapse. Kim & Ostriker (2002) showed the process of dustlane collapse starting with a smooth ISM. It took several rotations to build up enough density structure for a self-gravitating cloud to form in a spiral arm.
Figure 1. HST image of the southern arm in M51, showing large dark clouds, star formation in the clouds, and young stars downstream with shells and rings around them. The gas flows from the top left to the bottom right in the figure. The large dark clouds contain around 107 M⊙ of gas. The shells and rings appear to contain new star formation along the periphery.
The structure of gas in the interarms is a remnant of the structure it had leaving the previous arm, which can also be seen in Figure 1. As the ISM moves through the arm, star formation pressures from HII regions, winds, and multiple supernovae make superbubbles and super-rings. The figure shows many rings of dust. The small rings can be three-dimensional shells seen with enhanced absorption along the lines of sight through the edges, but the large rings are much bigger than the ISM scale height and have to be two-dimensional. All of these structures seem to contain active star formation in the peripheral dense gas, in addition to OB associations and star complexes inside the cleared regions. Some of the active star formation is lingering in the dense clouds, which means that it follows the dense gas as it moves. Other active star formation on the periphery is probably triggered by the high pressures that made the cavities. This is a second type of triggering for star formation: sequential triggering by previous generations of stars. We review this in the next section.
Figures 2 and 3 show a multiple-arm galaxy, M101, and a flocculent galaxy, NGC 5055. The spiral structure in M101 is more irregular than in the grand design galaxy M51, but there are still long spiral arms and each arm has several regularly-spaced giant star complexes in it, in various stages of collapse. The right-hand side of Figure 2 highlights the western arm in M101, suggesting that the giant dust cloud toward the bottom is in a younger stage than the two other star complexes toward the west. Unlike in M51, the star formation in M101 seems to be centered on the arms with no rings offset to one side. This is expected when the whole arm is the result of a gravitational instability, because it all twists around with local shear and has little relative motion between the pattern speed and the gas. Figure 3 shows numerous long and thin spiral arms with more of the "beads on a string" pattern. These arms are so thin and irregular that they should be mostly gas. They shear around, stretch out, and disperse over time, most likely forming stars by gravitational collapse along their length. Rings and shells are not visible in this image. It would be interesting to observe further whether flocculent galaxies produce the same type of ring pattern as observed down stream from the spiral arms in M51.
Figure 2. (Left) GALEX image in the uv of M101 from Gil de Paz et al. (2007). (Right) HST image of the western part of M101, showing two giant star complexes (A and B) and a dark cloud without much star formation yet (C). Young stars are centered in the spiral arms of M101, suggesting these arms are material patterns made from local gravitational collapse.
Figure 3. (top) Spitzer 3.6μ image from Elmegreen et al.(2011) showing weak and irregular underlying stellar waves. (bottom) Hα image from Dale et al. (2009) showing numerous beads on a string of star formation.
The third common way in which stars in a galaxy promote gravitational collapse in the gas is through bar-driven inflows. Bars exert strong negative torques inside their corotation radii, which are typically at 1.2 to 1.4 bar radii. Inside this, the gas hits the bar from behind and shocks, forming a dustlane (Athanassoula 1992). The shock strips angular momentum and orbital energy from the gas, which then falls along the bar to the region of the inner Lindblad resonance (ILR). After sufficient accumulation, the gas becomes unstable and form stars. Often it does this in a ring or tight two-arm spiral. There may be a second, smaller bar inside the ILR which affects the orbits there and brings the gas in further.
Figure 4 shows how the gas flows to the center of NGC 1672. Dust streamers plunge from near the end of the bar into the bar itself, and then directly to the center. This direct path means that gas inflow is rapid. A comparison of the inflow rate to the gas reservoir gives the timescale for accretion. In a study of NGC 1365 (Elmegreen et al. 2009c), which looks like NGC 1672, the timescale for gas exhaustion is only ~ 0.5 Gyr. If the initial reservoir of gas was comparable to what is there today, then this short time is also comparable to the age of the bar. That is, bars like these have to be fairly young, ~ 1 Gyr, or the gas would have been cleared out by now.
Figure 4. Barred galaxy NGC 1672 from the Hubble Heritage Team. Dust lanes suggest the gas flow pattern toward the center (arrows), where star formation is very active.
NGC 1365 and many other barred galaxies have massive clusters in their ILR regions – much more massive than typical disk clusters or clusters forming in spiral density wave arms. Perhaps this difference is only a size-of-sample effect if the ILR regions of bars have higher overall star formation rates. Or, star formation in bar ILRs may differ from that in main disks.