Galaxy evolution

Galaxy evolution studies how galaxies acquire mass, form stars, enrich their gas, exchange material with their surroundings, change morphology, and merge over cosmic time.

Stellar feedback is the transfer of energy, momentum, mass, and newly formed elements from stars to surrounding matter through radiation, winds, supernovae, and cosmic rays.

If a virialized, well-mixed self-gravitating system instantaneously retains mass fraction $ϵ>1/2$, homologous revirialization gives $R^{\prime }/R=ϵ/(2ϵ-1)$. At or below one half, the idealized remnant is unbound.

If a self-gravitating system loses mass slowly compared with its orbital times, adiabatic invariance gives $MR=\text{constant}$ in the homologous approximation, so retaining fraction $ϵ$ expands the system by $R^{\prime }/R=1/ϵ$.

A galactic outflow carries gas, metals, energy, and momentum away from a galaxy under stellar or active-galactic-nucleus feedback. Whether the material escapes or later returns depends on its speed and the galactic potential.

The mass-loading factor is the ratio of outflow rate to star-formation rate, $\lambda ={\dot{M}}_{\mathrm{out}}/{\dot{M}}_{\ast }$. Its value can depend on galaxy mass, radius, gas phase, and the surface through which the flow is measured.

Galactic chemical evolution follows the production, transport, dilution, locking, and loss of chemical elements as stars form and die and gas enters or leaves a galaxy.

Galactic metallicity measures the abundance of elements heavier than helium in a galaxy. Gas and stars retain different time-weighted records of enrichment.

Gas-phase metallicity is the heavy-element abundance of interstellar gas. In star-forming galaxies it is commonly inferred from nebular emission lines in H II regions, often through oxygen abundance $12+{\log }_{10}(\mathrm{O}/\mathrm{H})$.

Stellar metallicity is the heavy-element abundance locked in stars. Integrated-light measurements are luminosity weighted unless a stellar-population reconstruction converts them to a mass-weighted quantity.

The galaxy mass--metallicity relation is the empirical tendency for galaxies with greater galaxy stellar mass to have higher gas-phase metallicity and stellar metallicity. Mass-dependent metal loss, gas inflow, star-formation efficiency, and recycling all contribute.

The instantaneous recycling approximation treats short-lived stars as returning their ejecta immediately after formation while long-lived stars retain their mass indefinitely. It turns delayed chemical enrichment into local differential equations.

The stellar yield is the newly synthesized metal mass returned to gas per unit mass locked into long-lived stars, under a specified recycling convention and initial mass function.

The closed-box model evolves a fixed total baryonic mass with no inflow or outflow. Under instantaneous recycling and constant yield it predicts $Z=y\log (1/\mu )$ for gas fraction $\mu$.

The leaky-box model adds a galactic outflow to the closed box. If the outflow has the ambient gas metallicity and constant mass-loading factor $\lambda$, its effective yield is reduced to $y/(1+\lambda )$ when returned fractions are absorbed into the definitions.

The effective yield is the yield that a simple closed-box relation would need to reproduce an observed gas fraction and metallicity. Outflow and pristine inflow generally lower it below the nucleosynthetic yield.

The G-dwarf problem is the deficit of low-metallicity long-lived G dwarfs near the Sun relative to the prediction of a constant-yield closed-box model. Prolonged accretion of metal-poor gas is a standard ingredient in its resolution.

A metallicity distribution function gives the number or mass of stars per metallicity interval. Its interpretation depends on sample selection, stellar lifetimes, spatial migration, and whether metallicity means total heavy-element abundance or a particular abundance ratio.