Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 55 / 1 / ii / Solution

If the gas can cool appreciably below the virial temperature, radiative cooling removes thermal energy and pressure support. In a dark-matter halo the gas then contracts, dissipating more energy as it falls. Efficient condensation requires the radiative gas cooling time to be short enough compared with the relevant dynamical or assembly time; merely having an available low-temperature transition does not guarantee that the gas reaches it quickly.

The collisionless dark matter cannot lose comparable energy through radiation and remains extended. Gas with appreciable conserved angular momentum stops radial collapse when rotation supports it, often forming a disk; lower-angular-momentum gas reaches a more compact central region. Cold dense gas can fragment into self-gravitating clouds and form stars if its gravitational instability overcomes remaining support. Stellar feedback subsequently reheats or expels gas and regulates the conversion. Efficient cooling enables central baryonic condensation and star formation; angular momentum and feedback determine the resulting galaxy.