11.7.5. Rate of Star Formation
The rate of star formation is presumed to depend on the gas density. Attempts to find a relationship of the form
[where * is the star (or HII region), and g the gas density] have yielded different values for the exponent n. Comparisons of HII region and bright star counts with HI surface densities have been made for the SMC, M31, and M33. For bright stars in the SMC Sanduleak (1969) obtained a value of n = 1.84 ± 0.14. In M31 Hartwick (1971) obtained a value of n = 3.50 ± 0.12 by comparing HII region counts with Roberts' (1966) HI density.
A comparison of the HI surface density in M33 (Wright et al., 1972) with HII region and star counts in M33 (Madore, 1971) finds a value of n = 1.72 ± 0.01 for stars and n = 3.15 ± 0.18 for HII regions. Most of the stars counted in M33 are the less massive O and B stars, whilst only large HII regions (excited by massive O stars) are included. The different values of n obtained in M33 tend to support the suggestion by Schmidt (1963) that n is the largest for the most massive stars. The values of n obtained for HII regions are in good agreement in M31 and M33.