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Galactic star formation is limited by how much gas becomes cold, shielded and self-gravitating, and by how long it remains in that state. A useful local estimate isThe star-formation efficiency per free-fall time ${ϵ}_{\mathrm{ff}}$ absorbs the fact that turbulence, magnetic support and stellar feedback prevent all eligible gas from collapsing in one free-fall time of a uniform sphere. Rotation and disk stability influence the supply of dense clouds, while gravitational collapse and gravitational fragmentation operate inside them.

For galaxy-averaged measurements, the Kennicutt–Schmidt law has ${\Sigma }_{\mathrm{SFR}}\propto {\Sigma }_g^N$, with the classic mixed spiral/starburst sample giving $N\simeq 1.4$. This empirical relation was obtained using H-alpha and far-infrared star-formation tracers together with atomic-hydrogen and CO gas measurements.^[ref] Dust attenuation, contamination by older stellar heating, the stellar initial mass function and the CO-to-molecular-gas conversion must be controlled. A disk-averaged total-gas exponent is not automatically a small-scale cloud law.

Young stars then photoionize gas, drive winds and eventually inject supernova energy and momentum. These processes can disrupt clouds, sustain random motions or expel gas; radiative cooling and fresh inflow rebuild the cold supply. Large-scale star formation is a regulated conversion of gas, rather than unimpeded free fall of the entire disk. A long gas-depletion time ${\Sigma }_g/{\Sigma }_{\mathrm{SFR}}$ is compatible with short galactic dynamical times in the dense fraction.

Galactic star formation requires gas to collect into cold dense regions that can become self-gravitating. Disk-scale gravity, turbulent motions, shear, pressure and magnetic fields affect this collection; formation then proceeds within molecular clouds. A useful local parametrization iswhere the star-formation efficiency per free-fall time summarizes inefficient conversion rather than requiring every cloud to collapse at once.

Across galactic disks the empirical Kennicutt–Schmidt law relates star formation rate surface density to gas surface density, ${\Sigma }_{\mathrm{SFR}}\propto {\Sigma }_g^N$. A slope near $1.4$ is a familiar integrated total-gas fit, while molecular-gas relations in ordinary disks can be closer to linear; the slope and normalization depend on tracer, averaging scale and environment. The gas-depletion time $t_{\mathrm{dep}}=M_g/\Psi$ is the corresponding fuel-consumption scale, not a prediction that inflow and recycling cease.

Massive stars supply ionizing radiation, winds and supernova energy and momentum. This stellar feedback can disperse clouds, sustain turbulence and drive outflows, regulating rather than simply extinguishing all future star formation. Fresh accretion and recycled gas replenish the reservoir. UV and recombination-line emission trace young stars, while infrared emission traces absorbed and re-radiated light; extinction, stellar populations and the assumed initial mass function affect inferred rates. A galactic rate reflects supply, cloud formation and feedback together, rather than only the free-fall time of its densest gas.^[ref]

The closed-box model of galactic chemical evolution assumes a fixed total baryonic mass, no gas inflow or outflow, instantaneous and homogeneous mixing, a constant stellar yield, a fixed initial mass function, and usually the instantaneous recycling approximation. It predicts $Z=y\log (1/\mu )$ for gas fraction $\mu$, but real galaxies violate these assumptions.

Evidence for galactic outflows includes blueshifted absorption, broad or split emission lines, extraplanar ionized and molecular gas, X-ray bubbles, and metal-enriched circumgalactic material. The low baryon fractions and low effective yields of dwarf galaxies, together with the galaxy mass--metallicity relation, provide indirect evidence for preferential gas and metal loss. Sustained star formation for longer than a closed reservoir's depletion time, low-metallicity high-velocity clouds, metallicity dilution during starbursts, the G-dwarf problem, and circumgalactic or intergalactic accretion signatures imply continuing galactic gas inflow.

Let $f(t)=A{e}^{-t/\tau }$ be the inflow rate, let the outflow rate be $\lambda \psi$, and let $R$ be the promptly returned fraction. The total baryonic, gas, and metal masses obeyThe first metal term is newly synthesized material; the second locks existing metals into long-lived stars and removes them in an ambient-composition wind. Expanding the final derivative and substituting ${\dot{M}}_g$ cancels those common terms, leaving

The observed Kennicutt–Schmidt law relates star-formation and gas surface densities approximately by ${\Sigma }_{\mathrm{SFR}}\propto {\Sigma }_g^{1.4}$, with a nearly linear relation to molecular gas over many resolved regimes. For the simple integrated model requested here, take a constant depletion coefficient $S$ so thatThen, with $\alpha =S(1-R+\lambda )$,The integrating factor $e^{\alpha t}$ gives, for $\alpha \ne 1/\tau$,At resonance, $\alpha =1/\tau$, the continuous limit isThe first term is depletion of the initial reservoir; the second is gas supplied by the exponentially declining inflow and subsequently consumed or expelled.

The Kennicutt–Schmidt law is the empirical relationfor disk-averaged total gas, with a nearly linear molecular-gas relation in many resolved observations. Atomic gas is mapped through the H I 21-cm line, molecular gas mainly through carbon-monoxide line emission and a CO-to-${\mathrm{H}}_2$ conversion factor, and star formation through combinations of ultraviolet continuum, H-alpha recombination emission, and infrared dust emission. Inclination, dust attenuation, the initial mass function, tracer lifetimes, and conversion factors must be treated consistently.

The gas-depletion time $M_g/{\dot{M}}_{\ast }$ is typically of order a gigayear, whereas a giant molecular cloud has a dynamical or free-fall time of order a few megayears. Star formation is therefore inefficient per collapse time, commonly at the percent level, rather than converting an entire cloud in one free fall.

For the first closed-box model of galactic chemical evolution, neglect returned mass or absorb it into the definitions. Thenand henceThus a region reaching $Z_{\odot }=0.014$ after an enrichment time $t_{\odot }$ with $y_Z=0.006$ hasabout $4.3\mathrm{Gyr}$ for a fiducial $t_{\odot }\simeq 10\mathrm{Gyr}$ enrichment age of the Galactic disk.

The second prescription implies ${\dot{M}}_{\ast }=M_g^2/(M_{g0}{\tilde{\tau }}_{\ast })$. Solving the gas-consumption equation givesTherefore

For long-lived stars, $dN$ is proportional to $d{M}_{\ast }=-d{M}_g$. In the exponential model,In the second model, $1+t/{\tilde{\tau }}_{\ast }=e^{Z/y_Z}$; multiplying its star-formation rate by $dt/dZ$ gives exactly the same result:The metallicity distribution is fixed by the closed-box relation $M_g/M_{g0}=e^{-Z/y_Z}$ and is independent of the star-formation history. Merely changing the time law therefore does not cure the G-dwarf problem; gas inflow, outflow, variable yields, or selection effects must alter the closed-box assumptions.

Robert C. Kennicutt Jr. studies how gas becomes stars in galaxies. His 1998 observational analysis combined normal spiral galaxies and starburst galaxies, finding an approximately $1.4$ power law between disk-averaged star formation rate per unit area and gas surface density. This Kennicutt–Schmidt law connects measurements across whole galaxies to prescriptions used in models of galaxy formation.^[ref]

With Neal J. Evans II, he also reviewed how different observations estimate star formation rates and how the gas–star formation relation changes between molecular clouds and whole galaxies.^[ref]