In this dissertation, I use infrared spectral maps of star-forming regions to explore the circumstances of star formation in the centers of cool-core galaxy clusters. Using Spitzer's IRS and MIPS instruments, we present a rich spectral map of the nearest super star cluster, 30 Doradus, which acts as as a laboratory for extreme modes of star formation. Photoionization from local hot stars dominates in the region. We present IRS spectra based on sparse spectral maps of BCGs in nine cool-core

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... y clusters. Eight of the nine targets show optical and ultraviolet evidence of star formation. We compare MIR indicators of obscured star formation to evidence of exposed star formation. We find that the BCGs have weaker thermal dust continuum emission than expected for normal star-forming galaxies, relative to several metrics. In six of the targets, we find that star formation is progressing in an unusually exposed environment, consistent with a model of extended filaments with fine substructure containing star-forming knots. Two other galaxies in the sample evidently have vigorous star formation in a normal disk or nuclear starburst. The efficiency of star formation is high, assuming that the cooling gas is the source of fuel. We find temperatures and masses of the warm H 2 and contrast with other luminous sources of H 2 associated with shocks. We find that star formation powers the PAH and dust emission, but another source of heat (perhaps associated with the surrounding hot ICM) is responsible for the molecular gas emission in the galaxies in at least some targets. We consider shocks and energetic particle heating for the H 2 . There are inconsistencies between our data and the type of shocks that power other MOHEGs, and our data are consistent with the particle heating model, but we do not rule out shock heating. iii Acknowledgements The composite image of Hydra A on the cover page shows 10 million degree Xray-emitting gas in blue and jets of radio emission in pink. Optical observations in yellow show galaxies in the cool core cluster. Image credit: Chandra Photo Album. X-ray: NASA/CXC/U.Waterloo/Kirkpatrick et al. (2009). Radio: NSF/NRAO/VLA. Optical: Canada-France-Hawaii-Telescope/DSS. Professional I gratefully thank the many scientists who have taken the time to advise me on my work and to discuss their research and mine. Any errors in this work are mine alone. Foremost on the list is my excellent advisor, R.W. O'Connell, closely followed by my thesis committee (R. Indebetouw, A. Evans, M. Donahue, and P. Arnold) and my co-authors, particularly R. Indebetouw, M. Donahue, B.R. McNamara, G.M. Voit, M.W. Wise, A. Hoffer, and the SAGE team. Thanks as well to the anonymous referees who have made a number of useful suggestions, and to R. Antonucci (for discussions including the emission profile of large vs small dust grains at a given radiation field). P. Appleton (especially for help with 24 µm diagnostics), L. Armus (for discussing the relationship of star formation and dust formation, and the role of emission lines as coolants to enable star formation), D. Calzetti and A. Crocker (for supplying tabulated plot data and discussion of star formation rates including the complications of star formation rates based on PAH emission), M. Cluver (for discussions on fitting the 7.7 µm PAH and for giving additional context on her work on Stephan's Quintet), A. Hicks (for valuable discussions and for significant assistance in determining UV-based evidence of star formation), D.C. Kim (for providing extensive discussion of the GOALS survey), P. Ogle (for iv taking extensive time to discuss the cool-core galaxy cluster spectra and their implications, their relationship to radio galaxies, and especially for his consultation on the warm H 2 ), J.D. Smith (who contributed significant software assistance), and M. Sun (for discussions on star formation in cool core galaxy clusters). Those who have loaned data, contributed helpful discussions and suggestions, or assisted with software in the course of this project include in part J. Carlberg, J.