High Resolution Radio Observations of Energetically Dominant Regions in Local Luminous Infrared Galaxies

Luminous and Ultra-luminous Infrared galaxies (U/LIRGs) are one of the most powerful classes of extragalactic objects in the local universe, and they provide a unique opportunity to study star formation and feedback processes in extreme environments. They are primarily observed to be interacting or merging disk galaxies. During the interaction, large amounts of gas are funneled to the central few kpc, triggering high star formation rates (SFR) and dust production. The absorption of UV and optical radiation from stars, or active galactic nuclei (AGN), by dust produces their observed high infrared luminosities. The high level of dust obscuration intrinsic to U/LIRGs makes them difficult to study. Radio interferometry is thus the perfect tool for revealing the nature of these systems -- it provides the high spatial resolution needed to resolve energetically dominant regions in U/LIRGs at wavelengths that have both diagnostic power and transparency to dust. In this thesis, 6 and 33 GHz radio continuum interferometric observations with the upgraded Karl G. Jansky Very Large Array (VLA) are used to study a sample of 22 local U/LIRGs. First, a detailed analysis of the 6 and 33 GHz radio continuum emission from the closest ULIRG, Arp 220, is presented. This late stage merger is highly obscured, being optically thick even at mid-infrared wavelengths. Further, due to its extreme environment, it is often used as a template for high redshift starbursts. Arp 220 hosts two distinct nuclei that are separated by \(\sim\) 370 pc. The nuclei are well resolved with the 33 GHz observations (i.e., with a spatial resolution of $\sim$ 30 pc). The deconvolved radii enclosing half of the total 33 GHz light are approximately 50 and 35 pc for the eastern and western nucleus, respectively. Literature values of the gas mass and infrared luminosity are combined with the 33 GHz sizes under the assumption of co-spatiality to show that Arp 220 has one of the highest molecular gas surface densities (\(\Sigma_{\rm mol} \sim 10^{5.3}\) (east) and \(10^{5.7}\) (west) \(\mathrm{M_\odot~pc^{-2}}\)) and SFR surface densities (\(\mathrm{\Sigma_{SFR} \sim 10^{4.0}~(east)~and~10^{4.0}~(west)~M_{\odot}~yr^{-1}~kpc^{-2}}\)) measured for any star-forming system. Despite these high values, the nuclei of Arp 220 are not maximal starbursts (i.e., under the assumption that the main feedback mechanism is radiation pressure on dust). The small derived sizes for the nuclei indicate Arp 220 is only optically thin in a narrow frequency range, \(\sim\) 5 to 350 GHz. The analysis of a larger sample of 22 U/LIRGs at 33 GHz with the VLA is also presented. It is found that, for most of these galaxies, the integrated radio flux densities correlate well with those at infrared wavelengths, indicating these systems follow the radio-IR correlation and that the emission at 33 GHz is primarily produced by star formation activity. The radio emission from most of these galaxies are resolved, with deconvolved half-light radii ranging from 20 pc to 1.7 kpc. Similar assumptions for Arp 220 above are used here to estimate SFR surface densities of \(\Sigma_{\rm SFR}\) from \(10^{0.5}\) to \(10^{4.5}\) \(\mathrm{M_{\odot}~yr^{-1}~kpc^{-2}}\) and molecular gas surface densities \(\Sigma_{\rm mol}\) of \(\mathrm{10^{2.5}~to~10^{5.7}~M_{\odot}~pc^{-2}}\). These values are among the highest values measured for any galaxies. The star formation-gas scaling relation is used to compare the U/LIRGs with regions within normal spiral galaxies. The presence of two ``modes" of star formation is inferred in the comparison, although this result is extremely dependent on the CO-to-\(\rm{H_{2}}\) conversion factor. The local U/LIRGs studied in this survey show high infrared surface brightnesses, however 19 of the 22 sources are not maximal starbursts. Finally, those targets showing the flattest 1.5--6 GHz spectral indices and the highest surface brightnesses exhibit the strongest [{\sc Cii}] deficits, which supports the idea that deficit is associated with the most highly obscured, high energy density star-forming regions. In order to determine the true limit for star formation in galaxies (e.g., through Eddington limit analysis), better measures of the gas content, opacity and velocity dispersion of U/LIRGs are needed. The last study presented in this thesis is an analysis of the first high spatial resolution ALMA observations of the mm continuum and dense molecular gas tracers in Arp 220. A spatial resolution of 30 pc is achieved using the most extended configuration available in Cycle 3. An optically thin model of the spectral flux density distribution is found to predict the continuum emission at 92 GHz, within the uncertainties of the measurement and accounting for extended emission that is potentially filtered out. At 92 GHz, the western nucleus is dominated by dust emission, while the eastern nucleus by free-free emission. High critical gas density tracers HCN, HCO\(^{+}\), their isotopologues, and the shock tracer SiO are detected. P-Cygni profiles are observed in the central beam of both nuclei, with a cleaner profile shape in the eastern nucleus. The western nucleus shows strong absorption in the center, which makes determination of the profile line shapes more complicated. These P-Cygni features indicate the presence of outflowing gas. The derived mass loading factors are 18 (east) and 35 (west), which may be an indication that active galactic nuclei help to boost the outflow mass rates. However, these numbers are strongly dependent on the highly uncertain HCN-to-gas mass conversion factor and should only be considered as upper limits. In addition to signatures of outflowing gas, clear evidence of gas rotation in both nuclei are observed