Annu. Rev. Astron. Astrophys. 1998. 36: 189-231
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3.2. Dependence of Star Formation Rates on Gas Content

The strong trends in disk SFRs that characterize the Hubble sequence presumably arise from more fundamental relationships between the global SFR and other physical properties of galaxies, such as their gas contents or dynamical structure. The physical regulation of the SFR is a mature subject in its own right, and a full discussion is beyond the scope of this review. However, it is very instructive to examine the global relationships between the disk-averaged SFRs and gas densities of galaxies, as they reveal important insights into the physical nature of the star formation sequence and serve to quantify the range of physical conditions and evolutionary properties of disks.

Comparisons of the large-scale SFRs and gas contents of galaxies have been carried out by several authors, most recently Buat et al (1989), Kennicutt (1989, 1998), Buat (1992), Boselli (1994), Deharveng et al (1994), Boselli et al (1995). Figure 5 shows the relationship between the disk-averaged SFR surface density SigmaSFR and average total (atomic plus molecular) gas density Sigmagas, for a sample of 61 normal spiral galaxies with Halpha, HI, and CO observations (Kennicutt 1998). The SFRs were derived from extinction-corrected Halpha fluxes, using the SFR calibration in Equation 2. The surface densities were averaged within the corrected optical radius Ro, as taken from the Second Reference Catalog of Bright Galaxies (de Vaucouleurs et al 1976).

Figure 5

Figure 5. Correlation between disk-averaged SFR per unit area and average gas surface density, for 61 normal disk galaxies. Symbols are coded by Hubble type: Sa-Sab (open triangles); Sb-Sbc (open circles); Sc-Sd (solid points); Irr (cross). The dashed and dotted lines show lines of constant global star formation efficiency. The error bars indicate the typical uncertainties for a given galaxy, including systematic errors.

Figure 5 shows that disks possess large ranges in both the mean gas density (factor of 20-30) and mean SFR surface density (factor of 100). The data points are coded by galaxy type, and they show that both the gas and SFR densities are correlated with Hubble type on average, but with large variations among galaxies of a given type. In addition, there is an underlying correlation between SFR and gas density that is largely independent of galaxy type. This shows that much of the scatter in SFRs among galaxies of the same type can be attributed to an underlying dispersion in gas contents. The data can be fitted to a Schmidt (1959) law of the form SigmaSFR = A SigmagasN. The best-fitting slope N ranges from 1.4 for a conventional least squares fit (minimizing errors in SFRs only) to N = 2.4 for a bivariate regression, as shown by the solid lines in Figure 5. Values of N in the range 0.9-1.7 have been derived by previous workers, based on SFRs derived from Halpha, UV, and FIR data (Buat et al 1989, Kennicutt 1989, Buat 1992, Deharveng et al 1994). The scatter in SFRs at a given gas density is large, and most of this dispersion is probably introduced by averaging the SFRs and gas densities over a large dynamic range of local densities within the individual disks (Kennicutt 1989, 1998).

Figure 5 also contains information on the typical global efficiencies of star formation and gas consumption time scales in disks. The dashed and dotted lines indicate constant, disk-averaged efficiencies of 1, 10, and 100% per 108 years. The average value for these galaxies is 4.8%, meaning that the average disk converts 4.8% of its gas (within the radius of the optical disk) every 108 years. Since the typical gas mass fraction in these disks is about 20%, this implies that stellar mass of a disk grows by about 1% per 108 years, i.e. the time scale for building the disk (at the present rate) is comparable to the Hubble time. The efficiencies can also be expressed in terms of the average gas depletion time scale, which for this sample is 2.1 Gyr. Recycling of interstellar gas from stars extends the actual time scale for gas depletion by factors of 2-3 (Ostriker & Thuan 1975, Kennicutt et al 1994).

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