Kennicutt-Schmidt Relation

From Tauwiki

The volume density of young stars formed per unit time in the Galactic disk is proportional to some power of the local gas volume density (Schmidt 1959). The same parametrization is usually assumed to apply to the observed surface densities in nearby galaxies (Kennicutt 1989).

a) Correlation between average observed 21-cm line surface brightness (converted to “HI mass surface density”) on the X-axis and the Far-UV surface brightness (taken as a measure of the formation rate of massive stars) on the Y-axis, from Deharveng et al. (1994). “Schmidt Law” fits are shown, with indexes of 1 (dashed line) and 0.6 (solid line). b) The data plotted with axes inverted so as to emphasize the explanation in terms of photodissociation.

From Gnedin & Kravtsov 2010

Observations show that star formation in galaxies correlates strongly with the molecular gas (e.g., Wong & Blitz 2002). Star formation rate (SFR) has only weak or no correlation with the density of atomic gas (Wong & Blitz 2002; Kennicutt et al. 2007; Bigiel et al. 2008). It is thus expected that ΣSFR relation with ΣH = ΣH2 + ΣHI will depend on the molecular fraction of the gas fH2 ≡ ΣH2/ΣH. The molecular fraction in observed galaxies is controlled by the gas density, FUV flux, and pressure (e.g., Blitz & Rosolowsky 2006), consistent with theoretical expectations (Elmegreen 1993; Elmegreen & Parravano 1994; Robertson & Kravtsov 2008), but is also expected to be sensitive to the dust content (and thus metallicity) of the gas because dust plays an important role both in shielding molecular gas from UV radiation and in catalyzing production of H2 (e.g., Stahler & Palla 2005).

Tracers of Star Formation

UV flux (unobscured star formation)

H-alpha flux

FIR flux (obscured star formation)

CO and HI flux (molecular & atomic gas)

Figure from Kennicutt 1998 (ARA&A)

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 correlation between SFR and gas density 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 law of the form ΣSFR = A Σ_gas^N (1 < N < 2; Schmidt 1959).

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.