Excavating the fossil record of spiral galaxies

Despite spiral galaxies being extremely common in our local neighbourhood, their formation, growth, and dynamics are not fully understood. However, the spatial variation in the properties of stellar populations contained within spiral galaxies are expected to bear the imprint of some of the past and present physical processes driving global and local structure and dynamics. Combining modern integral-field spectroscopic galaxy surveys with spectral fitting methods offers an unprecedented opportunity to peer into the stellar population "fossil record" and how it varies between and within spiral galaxies. By obtaining a full star-formation history at every location, it is possible to construct images denoting the spatial distribution of stars of different ages across the galaxy. In this thesis we explore how such a "time slicing" technique can be applied to data from the SDSS-IV MaNGA survey, and show that this approach can provide insights into the formation and the internal structure of spiral galaxies. While the defining features of spiral galaxies are the beautiful arms that they display, the exact nature of such structure is still an open question. It has been widely assumed that spiral arms in "grand design" systems are the products of density waves that propagate around the disk with an approximately constant angular speed Om_P. We show that it is possible to measure an offset between young stars of a known age and the spiral arm in which they formed in a grand-design spiral galaxy, consistent with predictions of a density wave model. By measuring how this offset varies with radius, we obtain a direct measure of Om_P at a range of radii, and show that the spiral pattern in this galaxy is consistent with being quasi-stationary. We then investigate how the azimuthal structures of the barred spiral galaxy MCG+07-28-064 vary when traced by stars of different ages. Decomposing this galaxy into "time slices", we find evidence for the ongoing growth of the bar, and for