In this 1998 paper, Kennicutt aimed to comprehensively examine the correlation between the SFR and gas density across a large dynamic range of star-forming galaxies. His sample included 61 “normal” spiral galaxies as well as 36 additional galaxies in which a very active episode of star formation – a starburst – was occurring in their centers (see Figure 1). For the normal spirals (which are disk galaxies roughly similar to the Milky Way), he compiled Hα (to trace the SFR) and H I + CO (to trace the atomic + molecular gas) measurements of galaxies from the literature. For each galaxy, the total integrated measurements were converted to surface densities by dividing by the galaxy’s area (after correcting for the inclination). For the starbursts, he instead used infrared data to calculate SFRs, as these engines of star formation are teeming with visible/ultraviolet-absorbing dust. Since the dust absorbs almost all the energy emitted by the starburst and then radiates it at its own blackbody temperature (or more accurately, temperatures, as there are likely multiple dust populations within a galaxy), the total infrared luminosity becomes a very reasonable tracer of the SFR in these systems. As the gas in starbursts is predominately molecular, Kennicutt used only CO (and not H I) measurements to estimate their gas densities. He converted integrated measurements to surface densities by dividing by the size of the starburst region, which is typically about a square kiloparsec.A strong correlation with lots of scatter
Plotting the results for all 61 spirals alongside the 36 starbursts, Kennicutt showed that a superlinear (slope N≈1.4) power law is an excellent empirical description of the relation between the star formation rate and gas surface densities across more than six orders of magnitude in SFR in galaxies. Figure 2 shows the original “Kennicutt-Schmidt” diagram that is now almost ubiquitously seen in talks about star formation in galaxies, either observational or theoretical. Let’s deconstruct this plot just a bit more.First, while the correlation is quite remarkable, there is still significant scatter present. Amongst the disk galaxies (the black circles), up to a factor of 30 difference in SFR is seen at a fixed gas density. Part of this may be due to how Kennicutt corrected for extinction in his Hα data: lacking any more robust means to determine how much of the Hα emission in the galaxy was being absorbed by dust, he simply assumed an extinction of 1.1 magnitude (a factor of 2.8 change in flux) for all galaxies. There is also some variation in how well CO traces H2 (the infamous “X-factor”) as a function of the physical conditions of the gas. While the actual amount of extinction and the value of the X-factor most certainly vary between (and within) galaxies, it is still unlikely that differences in these two factors alone could explain the full factor of 30 difference in SFRs across the sample. This suggests that much of the scatter actually represents real variations in the star formation efficiency (how long it takes the gas to turn into stars globally).Second, the correlation for the spirals alone is much less robust than the combined correlation. It is the addition of the starbursts that provides the lever arm to achieve the high dynamic range that makes the correlation robust. (To see this, place your hand over the right half of the plot and try to draw a line through the remaining points).Third, since the relation is superlinear, the efficiency of star formation – the SFR divided by gas density – seems to increase with increasing gas density. What does this mean? Kennicutt offers a theoretical argument for why this might be the case. If self-gravity in a gaseous spiral disk controls the formation of stars, the SFR volume density should scale as the gas volume density ρgas divided by the timescale for the growth of gravitational perturbations in the disk. Since the latter goes as the free-fall time tff~(Gρgas)-1/2 this suggests that the SFR should scale as the gas density to the 1.5 power – very similar to the value of 1.4 observed. To convert between volume and surface densities, a constant disk scale height must also be assumed. This is however not the physical basis for the Kennicutt-Schmidt law, but simply a plausibility argument. Recent progressKennicutt’s seminal 1998 paper combined with rapidly improving observational facilities in the early 2000’s led to a burgeoning in this field. Increased resolution has now allowed resolved studies within galaxies, and the ΣSFR-Σgas relation appears to hold at kpc scales within disk galaxies, as well as amongst entire disk galaxies. Interestingly, the majority of work at these kpc scales finds a linear relation — N ≈ 1 – instead of the superlinear relation Kennicutt originally derived. Furthermore, the role of the molecular gas has now been isolated: the correlation between the SFR and H2 is much tighter than that between the SFR and HI+H2. Additionally, modern studies typically use multiple star formation tracers, e.g. Hα (to trace recombination radiation that escapes the galaxy) plus mid-infrared (to trace the portion absorbed by dust). For interested readers, Kennicutt & Evans (2012) provide a detailed and comprehensive (though dense) review of this subject in a review paper, which I highly recommend.There has been incredible progress over the last two decades in understanding the fundamental process of star formation. However, it is important to remember that the Kennicutt-Schmidt law is an empirical one. It is widely cited, widely studied, and widely used as a prescription in simulations. But the physical basis for a power law relation between the star formation rate and gas density has not yet been clearly determined. And that is why, as they say, this is still a very relevant topic of active research today.“Astrophysical classics” is a series of articles that delves into seminal papers from the astronomical past and places them in the context of modern research.