This thesis presents a starburst model for far-infrared/sub-millimeter/millimeter (FIR/sub-mm/mm) line emission of molecular and atomic gas in an evolving starburst region, which is treated as an ensemble of non-interacting hot bubbles which drive spherical shells of swept-up gas into a surrounding uniform gas medium. These bubbles and shells are driven by winds and supernovae within massive star clusters formed during an instantaneous starburst. The underlying stellar radiation from the evolving clusters affects the properties and structure of photodissociation regions (PDRs) in the shells, and hence the spectral energy distributions (SEDs) of the molecular and atomic line emission from these swept-up shells and the associated parent giant molecular clouds (GMCs) contains a signature of the stage evolution of the starburst.

The physical and chemical properties of the shells and their structure are computed using a a simple well known similarity solution for the shell expansion, a stellar population synthesis code, and a time-dependent PDR chemistry model. The SEDs for several molecular and atomic lines (¹²CO and its isotope ¹³CO, HCN, HCO⁺, C, O, and C⁺) are computed using a non-local thermodynamic equilibrium (non-LTE) line radiative transfer model.

By comparing our models with the available observed data of nearby infrared bright galaxies, especially M 82, we constrain the models and in the case of M 82, provide estimates for the age of the recent starburst activity. We also derive the total H₂ gas mass in the measured regions of the central 1 kpc starburst disk of M 82. In addition, we apply the model to represent various stages of starburst evolution in a well known sample of nearby luminous infrared galaxies (LIRGs). In this way, we interpret the relationship between the degree of molecular excitation and ratio of FIR to CO luminosity to possibly reflect different stages of the evolution of star-forming activity within their nuclear regions.

We conclude with an assessment of the strengths and weaknesses of this approach to dating starbursts, and suggest future work for improving the model.