As discussed above, and as illustrated in Fig. 1., the formation of an individual galaxy in the standard, hierarchical formation scenario involves the following processes: the collapse and virialization of dark matter halos, the cooling and condensation of gas within the halo, and the conversion of cold gas into stars and a central supermassive black hole. Evolving stars and AGN eject energy, mass and heavy elements into the interstellar medium, thereby determining its structure and chemical composition and perhaps driving winds into the intergalactic medium. Finally, galaxies can merge and interact, reshaping their morphology and triggering further starbursts and AGN activity. In general, the properties of galaxies are determined by the competition among all these processes, and a simple way to characterize the relative importance of these processes is to use the time scales associated with them. Here we give a brief summary of the most important time scales in this context.
Fig. 1. A logic flow chart for galaxy formation. In the standard scenario, the initial and boundary conditions for galaxy formation are set by the cosmological framework. The paths leading to the formation of various galaxies are shown along with the relevant physical processes. Note, however, that processes do not separate as neatly as this figure suggests.
- Hubble time: This is an estimate of the time scale on which the Universe as a whole evolves. It is defined as the inverse of the Hubble constant , which specifies the current cosmic expansion rate. It would be equal to the time since the Big Bang if the Universe had always expanded at its current rate. Roughly speaking, this is the time scale on which substantial evolution of the galaxy population is expected.
- Dynamical time: This is the time required to orbit across an equilibrium dynamical system. For a system with mass M and radius R, we define it as
, where 
. This is related to the free-fall time, defined as the time required for a uniform, pressure-free sphere to collapse to a point, as 
- Cooling time: This time scale is the ratio between the thermal energy content and the energy loss rate (through radiative or conductive cooling) for a gas component.
- Star-formation time: This time scale is the ratio of the cold gas content of a galaxy to its star-formation rate. It is thus an indication of how long it would take for the galaxy to run out of gas if the fuel for star formation is not replenished.
- Chemical enrichment time: This is a measure for the time scale on which the gas is enriched in heavy elements. This enrichment time is generally different for different elements, depending on the lifetimes of the stars responsible for the bulk of the production of each element .
- Merging time: This is the typical time that a halo or galaxy must wait before experiencing a merger with an object of similar mass, and is directly related to the major merger frequency.
- Dynamical friction time: This is the time scale on which a satellite object in a large halo loses its orbital energy and spirals to the center, this time scale is proportional to
, where 
is the mass of the satellite object and 
is that of the main halo. Thus, more massive galaxies will merge with the central galaxy in a halo more quickly than smaller ones.
These time scales can provide guidelines for incorporating the underlying physical processes in models of galaxy formation and evolution, as we describe in later chapters. In particular, comparing time scales can give useful insights. As an illustration, consider the following examples:
- Processes whose time scale is longer than the Hubble time can usually be ignored. For example, satellite galaxies with mass less than a few percent of their parent halo normally have dynamical friction times exceeding the Hubble time . Consequently, their orbits do not decay significantly. This explains why clusters of galaxies have so many ‘satellite’ galaxies – the main halos are so much more massive than a typical galaxy that dynamical friction is ineffective.
- If the cooling time is longer than the dynamical time, hot gas will typically be in hydrostatic equilibrium. In the opposite case, however, the gas cools rapidly, losing pressure support, and collapsing to the halo center on a free-fall time without establishing any hydrostatic equilibrium.
- If the star formation time is comparable to the dynamical time, gas will turn into stars during its initial collapse, a situation which may lead to the formation of something resembling an elliptical galaxy. On the other hand, if the star formation time is much longer than the cooling and dynamical times, the gas will settle into a centrifugally supported disk before forming stars, thus producing a disk galaxy .
- If the relevant chemical evolution time is longer than the star-formation time, little metal enrichment will occur during star formation and all stars will end up with the same, initial metallicity. In the opposite case, the star-forming gas is continuously enriched, so that stars formed at different times will have different metallicities and abundance patterns .
o far we have avoided one obvious question, namely, what is the time scale for galaxy formation itself? Unfortunately, there is no single useful definition for such a time scale. Galaxy formation is a process, not an event, and as we have seen, this process is an amalgam of many different elements, each with its own time scale. If, for example, we are concerned with its stellar population, we might define the formation time of a galaxy as the epoch when a fixed fraction (e.g. 1% or 50%) of its stars had formed. If, on the other hand, we are concerned with its structure, we might want to define the galaxy’s formation time as the epoch when a fixed fraction (e.g. 50% or 90%) of its mass was first assembled into a single object. These two ‘formation’ times can differ greatly for a given galaxy, and even their ordering can change from one galaxy to another. Thus it is important to be precise about definition when talking about the formation times of galaxies.
