### Question --- Describe the following relations and what they are useful for: (i) Kennicutt-Schmidt; (ii) M-sigma relation; (iii) the Madau plot; (iv) the star-forming main sequence. ### Answer --- ##### (i) Kennicutt-Schmidt ![[Kennicutt-Schmidt.jpg|align:center|300]] The **Kennicutt-Schmidt** is an empirical relation between the local surface gas density ($\Sigma_{\rm gas}$) and star formation rate (SFR) surface density ($\Sigma_{\rm SFR}$) in a given region. $\Sigma_{\rm SFR} \propto (\Sigma_{\rm gas})^{n} \hspace{1cm} \text{where} \hspace{1cm} \left[ \Sigma_{\rm SFR} \right] \equiv \frac{({\rm mass} / {\rm time})}{{\rm area}} \hspace{0.5cm} , \hspace{0.5cm} \left[ \Sigma_{\rm gas} \right] \equiv \frac{\rm mass}{\rm area}$ The index was initially inferred to be $n \sim 2 \pm 1$ for the Milky Way (Schmitz, 1959), but has been since been narrowed to $n \sim 1.4 \pm 0.15$ by using a larger sample of spiral & starburst galaxies (Kennicutt, 1989). ##### (ii) M-Sigma Relation ![[Velocity Dispersion#M-Sigma Relation]] ##### (iii) Madau Plot ![[madau.jpg|align:center|450]] The **Madau Plot** describes the cosmic evolution of the average star formation rate. - Cosmic star formation peaks at around $z\simeq 2$. (Is this cosmic noon?) - This is also when the number density of [[Active Galactic Nuclei#Quasar / Quasi-Stellar Object (QSO)|quasars]] appears to peak - Infers a connection between galaxy and AGN evolution like [[Velocity dispersion#M-sigma relation|M-sigma]]. - Suggests that many metals formed early during the deaths of massive stars - Corroborated by [[Intracuster Medium|ICM]] measurements. ##### (iv) Star-Forming Main Sequence ![[sf_main_seq.png|align:center|500]] The **Star-Forming Main Sequence** correlates the star formation rate with the stellar mass of a galaxy (number of existing stars). - This suggests that galaxies spend much of their lifetime building up stars in a self-regulated way. - Seen across all broad classes of galaxy, including [[Galaxy Classification#Starburst Galaxy (SBG)|Starburst Galaxy (SBG)]]. > [!note] > The Milky Way forms about 7 new stars per year.