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Stars form in giant molecular clouds, and feedback from massive stars within these clouds results in a star formation efficiency (SFE) of about 2%: only in the dense molecular cores does the SFE rise to about ~ 30%, as confirmed with the prestellar core mass function. In other words, there is a constant fraction of molecular gas turned into stars per free-fall timescale, as in fig. 17. A similar global SFE is observed in star-forming disk galaxies, in which the star formation rate SFR can be described by:

Equation 48 (48)

where ρgas is the gas density and tdyn is the dynamical time of the rotating disk.

Figure 17

Figure 17. Observed star formation efficiency per dynamical time as a function of mean gas density. Each data point represents a different method of measuring the gas, which is sensitive to different densities. GMC indicates giant molecular clouds, IRDCs indicates infrared dark clouds, ONC is the Orion Nebula cluster, HCN represents extragalactic measurements. Figure from [94].

The reason for these relations resides in the gravitational instability of cold disks, while feedback physics, such as supernovae-driven turbulence, provides the observed efficiency of ~ 2% which reproduces the normalization, SFE, of the global star formation law in eq. 48. The star formation rate per unit area, ΣSFR, obeys the Kennicutt-Schmidt (KS) law, which can be expressed as:

Equation 49 (49)

where Σgas is the surface density of gas. Such a global law applies also to starburst galaxies, as in fig. 18.

Figure 18

Figure 18. Star formation surface density versus gas surface density per dynamical time. The slope of the solid line represents the star formation efficiency SFE. Figure from [95].

It is a remarkable coincidence that the SFE observed in giant molecular clouds is similar to that seen globally in nearby (as well as in distant) disk galaxies. Massive OB stars provide a common link, but grain photoheating, winds and photo-ionization dominate in the former case, and SNe in the latter case.

An investigation of the KS law reveals that the key ingredient that regulates star formation is molecular gas, H2, with an evident "knee" in the ΣSFR - ΣHI+H2 distribution at the transition point from a HI to an H2-dominated interstellar medium, as in fig. 19. Because of the saturation of ΣHI at ~ 9Modot pc-2, this quantity as well as the total ΣHI+H2 cannot be used to predict either ΣSFR or the SFE in spiral galaxies [96]. Indeed, in the outer parts of galaxies, where the molecular gas H2 is reduced due to the UV radiation field and lower surface density, the star formation rate per unit gas mass also declines.

Figure 19

Figure 19. ΣSFR vs ΣHI+H2. Diagonal dotted lines show lines of constant star formation efficiency SFE. Figure from [96].

Disk instabilities result in cloud formation and subsequent star formation, and one needs to supply cold gas in order to maintain such a cold disk. There is evidence for spiral galaxies to have reservoirs of HI in their outer regions, for example in NGC 6946 [97] and UGC 2082 [98], pointing to recent gas accretion. In particular, the deep neutral hydrogen survey HALOGAS with WSRT, presented in [98], has the goal of revealing the global characteristics of cold gas accretion onto spiral galaxies in the local Universe. Recent examples of extraplanar and HI gas reservoirs are [99, 100, 101].

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