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2. What Regulates Star Formation on Global and Local Scales in Irregular Galaxies?

Or, to put it another way, what distinguishes an Im galaxy with a high star formation rate, but not a starburst, from a galaxy with a low rate. Detailed studies of the stellar populations of irregulars have shown that most irregular galaxies evolve at more or less constant star formation rates with variations of factors of 2-3 in the amplitude of the rate at least over the past few Gyrs (Tolstoy 1996, Tosi et al. 1991, Greggio et al. 1993, Marconi et al. 1995). Therefore, galaxies with relatively high rates today have most likely had relatively high rates for most of their lifetime, and similarly for those forming stars at low rates (but this remains controversial). Plots of star formation rates against other global properties do not yield correlations except for those properties that would be expected to be a consequence of the level of star formation. An example of the latter is surface brightness; the higher the star formation rate per unit area, the higher the surface brightness would be expected to be. This general lack of correlations suggests that local rather than global conditions are important in setting the star formation rate.

In 1984 I came to the USNO in Flagstaff to give a talk about star formation in irregular galaxies. The next day, my host, Dave Monet, and I hiked up to the top of a local mountain. There we chatted with a national forest service employee who was scanning the surrounding region for fires and who was interested to hear that we were astronomers. Dave told him about the talk I had just given and I told him that irregulars were useful laboratories for studying star formation because they were different from spiral galaxies. The fire look-out, who apparently is an avid reader of astronomy, responded, ``But, star formation is a local process, so why would you expect star formation to be different in different galaxies?'' There are two parts to the fire look-out's question, and we will come back to the second part in a later section. But, the first premise, that ``star formation is a local process,'' does indeed seem to be borne out as the following illustrates.

Hodge & Kennicutt (1983) found that the radial profile of H II regions and stars was approximately the same in a sample of spiral galaxies and concluded that there was radial ``continuity'' between current and past star formation. Ryder & Dopita (1994) come to a similar conclusion from a comparison of Halpha and I-band images of spirals. This relationship has been shown to carry over to irregular galaxies as well. Hunter & Gallagher (1985b) plotted the radial brightness in B against that in Halpha for the irregular galaxy NGC 4449. They found that the Halpha and B-band tracked each other with radius very well. The Halpha luminosity shows the current star formation activity and that in a broad-band filter such as B is related to the star formation activity integrated over something like a Gyr timescale (Gallagher et al. 1984). So, the conclusion was that star formation in irregular galaxies is a local process.

Now ``local'' can have several meanings. By ``local'' one can mean what goes on inside of a gas cloud once it forms, but here I am using ``local'' to mean a region of a galaxy, something one to a few kpc in size. We have now extended this to a longer look-back time for the star formation activity in NGC 4449 using J and H images. These near-IR images are sensitive to the star formation activity integrated over the galaxy's lifetime and show the same general correspondence with Halpha. In other words, the current star formation activity throughout NGC 4449 is in keeping with the past activity at that radius. In other irregulars that are not as busy as NGC 4449 in terms of star formation activity, the correspondence between Halpha and optical starlight is noisier. In these galaxies single star-forming regions coming and going have a larger impact on what is observed globally and so the statistics are poorer. Nevertheless, it seems to be true for a larger sample of irregulars that within the statistics the time-averaged level of past star formation activity is in keeping with the current level at that radius (Hunter, Elmegreen, & Baker 1997; also true for Sc spirals [Kennicutt 1989]) even though the current sites of active star formation move around within a galaxy over time (Hodge 1969, Payne-Gaposchkin 1974, Hunter et al. 1982).

There are still global aspects to the star formation process in the sense that large-scale processes determined the formation of irregular galaxies and the initial conditions within them that result in their slow evolution. But, given those initial global conditions, including the rotation curve and three-dimensional distribution of the gas, the star formation process responds to local conditions within the galaxy. What then might be the mechanisms that control star formation? The local equilibrium rules out processes such as infall of gas as major drivers of star formation in irregulars (Hunter & Gallagher 1985b), and we also suspect that the star formation process is not entirely stochastic and that gas distributions and velocity fields will play important roles.

There are several basic models currently in the literature that offer some insight.One is that of gravitational stability of gas in a thin rotating disk (Toomre 1964, Quirk 1972). This model defines a critical gas density Sigmac above which the gas is unstable and will form clouds that then can form stars and below which the gas is stable against the formation of clouds. This critical gas density depends on the velocity dispersion and the epicyclic frequency of the gas. Kennicutt (1989) applied this model to Sc spiral galaxies. He plotted the ratio of the observed gas density Sigmag to the model critical gas density Sigmac as a function of radius within the galaxies. Generally this ratio decreased with radius. Then he determined the radius at which he could no longer detect H II regions in these galaxies. The idea is that beyond that radius the gas is too stable to form clouds and interior to that the gas is unstable. For his sample of Sc spirals this ratio alpha = Sigmag / Sigmac was about 0.7 ± 0.2 at the radius where the last H II regions were seen. So, gas at densities lower than roughly 0.7 times the critical density was too stable to form the clouds needed for star formation (see also Larson 1992).

Figure 9
Figure 9. Radially averaged ratio Sigmag / Sigmac of observed gas (H I + He + H2) density to critical gas density for the thin rotating disk model. Results for two representative irregulars are taken from Hunter & Plummer (1996) and Baker (1997); based on H I data taken from Skillman et al. (1988) for Sextans A and from Lake & Skillman (1989) for IC 1613. Also plotted are the radially averaged Halpha surface brightness which is proportional to the amount of current star formation. The dashed line denotes the median alpha, the ratio Sigmag / Sigmac at the radius of the furthest detected H II region, in a sample of 7 irregular galaxies, and the solid line is the average for spiral galaxies (Kennicutt 1989).

Hunter & Plummer (1996) and Baker (1997) have applied this model to several irregular galaxies for which azimuthally averaged H I column densities and rotation curves were available in the literature. They found that generally this ratio Sigmag / Sigmac in irregulars is everywhere less than the ratio found by Kennicutt for spirals, and typically alpha is 0.3-0.5 although there are a few exceptions (see also van Zee et al. 1996). This is illustrated for two irregulars in Figure 9. We have also extended this to a sample of more distant Im and Sm galaxies found in surveys by Schombert and collaborators (1988, 1992; see also, Bothun, Impey, & McGaugh 1997). Again, this ratio is low in these systems although not more so than in other irregulars. At face value, this low ratio of observed to critical gas density implies that irregulars have a much harder time forming clouds than spirals. In fact, Larson (1988) suggests that galaxies like irregulars that do not have the benefit of ``swing amplification'' (a mode of gravitational instability in differentially rotating disks [Goldreich & Lynden-Bell 1965]) will require even higher values of Sigmag / Sigmac to form stars. However, since stars are being formed in irregulars, this suggests that other processes in addition to gravity are important in facilitating cloud formation in irregulars (for example, feedback from massive stars, random gas motions).

Comparisons of the azimuthally-averaged ratio of observed to critical gas densities as a function of radius with the distribution of current star formation (Halpha surface brightness profiles) often show star formation occurring in the regions of higher Sigmag / Sigmac (see also van der Hulst et al. [1993] for low surface brightness spirals, Taylor et al. [1994] for H II galaxies, and van Zee et al. [1996] for another Im galaxy) although exceptions are seen. However, usually star formation ends long before the gas densities would suggest that it should even when the destabilization due to the two-fluid nature of galaxies (that is, stars as well as gas) is taken into account (Elmegreen 1995a; Hunter, Elmegreen, & Baker 1997). Furthermore, there does not seem to be any trend of average gas densities relative to the critical values with globally integrated star formation rates (but see Buat et al. [1989]).

A second model is that presented by Parravano (1989) and Elmegreen & Parravano (1994) in which they explore the pressure in a galactic disk and what is necessary for the formation of cold, dense clouds. They have suggested that low surface brightness galaxies have reduced star formation rates because the pressure in their disks is below the minimum pressure needed to enable the formation of dense molecular clouds that form stars. Hunter & Plummer (1996) have compared this model to the irregular Sextans A. The model is put in terms of the thermal pressure in the galactic disk and the stellar radiation field in the disk, quantitites whose observational determinations are fraught with difficulties, and agreement of the model with what is observed in Sextans A is mixed. The inner part of the galaxy that is forming stars lies just above the pressure threshold, but then so does a portion of the outer part of the galaxy which is not forming stars. Similar results are found for a larger sample of irregulars by Hunter, Elmegreen, & Baker (1997) although Young & Lo (1996) find that star-forming regions in Leo A are only associated with a cold component of the H I gas in that galaxy.

Neither of these two models is entirely satisfactory, however. For a rotating gas disk, for example, complications such as the presence of dark matter (Elmegreen et al. 1996) and the extra thickness of disks (Romeo 1992) have not been adequately explored. The thicker disks of irregulars (Hodge & Hitchcock 1966, van den Bergh 1988, see also Puche et al. 1992) should serve to stabilize the gas, lowering alpha. In addition the lack of shear in the ISM to aid in disrupting clouds could make star formation easier for a given alpha relative to the situation in spirals (Kenny, Carlstrom, & Young 1993). Furthermore, kinematics in Im systems are often dominated by random gas motions which can contribute significantly to the pressure (for example, Gottesman & Weliachew 1977, Tully et al. 1978, Huchtmeier et al. 1981, Sargent et al. 1983, Lo et al. 1993, Feitzinger et al. 1981), and in some cases rotation can be insignificant compared to random motions (Young & Lo 1996). In addition in physically small galaxies like these, single giant star-forming regions can dominate and it seems likely that the modifications of the ISM by concentrations of massive stars are likely to play a large role in feedback processes including facilitating further cloud formation. Thus, multiple factors are likely to be important in regulating cloud/star formation, and current models do not include this complexity.

In summary, it seems that star formation is largely a local (that is, regional) process in the sense that it is radially the same today as it has been historically over large time-scales. In irregulars star formation is likely to be regulated by a combination of processes including gravitational instabilities due to the gas density, thermal pressure within the disk, and modifications of the ISM by massive stars. In irregular galaxies, perhaps more so than in other larger systems, random gas motions and feedback from massive stars may play large roles.

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