Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/iii/paper-55/1/ii/ii/solution

In the intermediate-temperature interval, atomic line cooling is generally efficient. Collisional excitation of hydrogen and helium followed by photon emission removes thermal energy; collisional ionization and subsequent recombination also contribute. As the gas becomes more ionized, different transitions enter and leave the cooling budget.
For enriched gas, metal-line cooling is often dominant over substantial parts of this interval, because heavy ions provide many ultraviolet and optical transitions. The cooling curve consequently has pronounced peaks rather than one smooth universal power law. Hydrogen/helium atomic processes and metal lines provide the main cooling channels here. Their relative strengths depend on metallicity, ionization state, density and the incident radiation field; these temperature bands describe typical gas, not composition-independent boundaries.

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