Local Star Formation Rate

In Figure 3.2 (left), the correlation between star formation rate and gas density is plotted for specific galaxies (NGC 4254 and NGC 2841). This shows us that H$\alpha$ surface brightness (star formation rate) and the gas column density are well correlated each other. Figure 3.2 (left) also indicates that there seems a critical gas density below which star formation is not observed. The value of this threshold column density is approximately $\simeq 4M_\odot {\rm pc}^{-2}$ for both galaxies in Figure 3.2 (left). The same correlation is seen in other spiral galaxies [Fig.3.2(right)]. Fitting the correlation with a power-law, he obtained

$$\Sigma_{\rm SFR} \propto \Sigma_{\rm gas}^{1.3\pm 0.3},$$ (3.7)

for the region active in star formation. Take notice that this power is very close to that of the global Schmidt law [eq.(3.4)] The threshold surface gas density ranges from 1 $M_\odot{\rm pc}^{-2}$ to 10 $M_\odot{\rm pc}^{-2}$ ( $10^{20}-10^{21}{\rm H\,cm}^{-2}$). Therefore, theory of star formation must explain (1) the Schmidt law (clear correlation between star formation rate and the gas surface density) above the threshold column density and (2) the fact that there is no evidence for star formation in the gas deficient region below the threshold column density.

Figure 3.2: Distributions of $\Sigma_{\rm SF}$ and $\Sigma_{\rm gas}$. (Left:) Relation between $\Sigma_{\rm SF}$ and $\Sigma_{\rm gas}$ for an Sc galaxy NGC 4254 and an Sb galaxy NGC 2841. (Right:) Relation between $\Sigma_{\rm SF}$ and $\Sigma_{\rm gas}$ for various galaxies. These are taken from Figs.7 and 8 of Kennicutt (1989).