The distribution of galaxies traces the structure of underlying dark matter, and carries signatures of both the cosmology that evolved the universe as well as details of how galaxies interact with their environment and each other. There are many ways to measure the clustering of galaxies, each with unique strengths, uses, theoretical background, and connection to other physical concepts. One uncommon clustering statistic is the Void Probability Function (VPF): it simply asks, how likely is a circle/sphere of a given size to be empty in your galaxy sample? Simple and efficient to calculate, the VPF is tied to all higher order volume-averaged correlation functions as the 0$^{\text{th}}$ moment of count-in-cells, and encodes information from higher order clustering that the robust two-point correlation function cannot always capture. Using simulations of Lyman-alpha emitting galaxies across either redshift history or the epoch of reionization, this work asks: how powerful is the VPF itself? When can and should it be used for galaxy clustering? What unique constraints or guidelines can it give for the pacing of reionization, in the Lyman-$\alpha$ Galaxies in the Epoch of Reionization (LAGER) narrowband survey or across the Roman Space Telescope grism? This work provides practical guidelines for creating and carrying out clustering studies using the the VPF, and motivates the use of the VPF for reionization. The VPF of LAEs can complement LAGER constraints for the end of reionization, and thoroughly inform the timing and pace of reionization with Roman.

Galaxy structural properties such as size, morphology, and surface brightness bear the imprint of galaxies' evolutionary histories, and so are related with other properties such as stellar mass, star formation rate, and emergent spectra. In this dissertation, I present three studies exploring such relationships. In the first, I investigated the relationships between 4000 Å break (D4000) strength, colors, stellar masses, and morphology in a sample of 352 galaxies at intermediate redshifts based on photometric and spectroscopic data from the Hubble Space Telescope (HST). I explored several diagrams such as UVJ color space combined with the D4000 strengths and the structural parameters of sample galaxies. The analysis shows that the presence of a bulge component is a necessary but not sufficient requirement for star formation quenching at intermediate redshifts. In the second study, I investigated the central 250 pc UV star formation intensity (SFI, star formation rate per unit area) of a sample of 40 Green Pea (GP) galaxies and 15 local Lyman Break Galaxy Analogs (LBAs) to understand the Lyα escape mechanisms and the associations with the SFI in Lyα-emitters (LAEs). I utilized the Cosmic Origins Spectrograph near-ultraviolet (COS/NUV) images from the HST. I found that the Lyα equivalent width (EW(Lyα)) and the Lyα escape fraction are positively correlated with the ratio of SFI to galaxy stellar mass. These correlations suggest the importance of the central SFI in Lyα photon escape. In the third study, I investigated the UV photometric properties of a sample of 40 GPs and the possible associations with Lyα escape mechanisms. I measured the UV-continuum size and luminosity of the sample galaxies by employing the COS/NUV images. The circularized half-light radius of GPs shows compact sizes and it further shows the statistically significant anti-correlations with EW(Lyα) and the Lyα escape fraction. The size comparison of GPs to those of high-redshift LAEs shows that their sizes are similar, once spatial resolution effects are properly considered. These results show that a compact size is crucial for escape of Lyα photons, and that Lyα emitters show constant characteristic size independent of their redshift. Therefore, the results presented in this dissertation emphasize the importance of galaxy structural properties in star formation quenching and in Lyα escape.

Green pea galaxies are a class of rare, compact starburst galaxies that have powerful optical emission line [OIII]$\lambda$5007. They are the best low-redshift analogs of high-redshift (z$>$2) Lyman-alpha emitting galaxies (LAEs). They provide unique opportunities to study physical conditions in high-redshift LAEs in great detail. In this dissertation, a few physical properties of green peas are investigated. The first study in the dissertation presents star formation rate (SFR) surface density, thermal pressure in HII regions, and a correlation between them for 17 green peas and 19 Lyman break analogs, which are nearby analogs of high-redshift Lyman break galaxies. This correlation is consistent with that found from the star-forming galaxies at z $\sim$ 2.5. In the second study, a new large sample of 835 green peas in the redshift range z = 0.011 -- 0.411 are assembled from Data Release 13 of the Sloan Digital Sky Survey (SDSS) with the equivalent width of the line [OIII]$\lambda$5007 $>$ 300\AA\ or the equivalent width of the line H$\beta$ $>$ 100\AA. The size of this new sample is ten times that of the original 80 star-forming green pea sample. With reliable T$_e$-based gas-phase metallicity measurements for the 835 green peas, a new empirical calibration of R23 (defined as ([OIII]$\lambda$$\lambda$4959,5007 + [OII]$\lambda$$\lambda$3726,3729)/H$\beta$) for strong line emitters is then derived. The double-value degeneracy of the metallicity is broken for galaxies with large ionization parameter (which manifests as log([OIII]$\lambda$$\lambda$4959,5007/[OII]$\lambda$$\lambda$3726,3729) $\geq$ 0.6). This calibration offers a good way to estimate metallicities for extreme emission-line galaxies and high-redshift LAEs. The third study presents stellar mass measurements and the stellar mass-metallicity relation of 828 green peas from the second study. The stellar mass covers 6 orders of magnitude in the range 10$^{5}$ -- 10$^{11}$ M$_{\odot}$, with a median value of 10$^{8.8}$ M$_{\odot}$. The stellar mass-metallicity relation of green peas is flatter and displays about 0.2 - 0.5 dex offset to lower metallicities in the range of stellar mass higher than 10$^{8}$ M$_{\odot}$ compared to the local SDSS star-forming galaxies. A significant dependence of the stellar mass-metallicity relation on star formation rate is not found in this work.

New measurements of the Hα luminosity function (LF) and star formation rate

(SFR) volume density are presented for galaxies at z∼0.62 in the COSMOS field.

These results are part of the Deep And Wide Narrowband Survey (DAWN), a unique

infrared imaging program with large areal coverage (∼1.1 deg 2 over 5 fields) and

sensitivity (9.9 × 10 −18 erg/cm 2 /s at 5σ).

The present sample, based on a single DAWN field, contains 116 Hα emission-

line candidates at z∼0.62, 25% of which have spectroscopic confirmations. These

candidates have been selected through comparison of narrow and broad-band images

in the infrared and through matching with existing catalogs in the COSMOS field.

The dust-corrected LF is well described by a Schechter function with L* = 10 42.64±0.92

erg s −1 , Φ* = 10 −3.32±0.93 Mpc −3 (L* Φ* = 10 39.40±0.15 ), and α = −1.75 ± 0.09. From

this LF, a SFR density of ρ SF R =10 −1.37±0.08 M○ yr −1 Mpc −3 was calculated. An

additional cosmic variance uncertainty of ∼ 20% is also expected. Both the faint

end slope and luminosity density that are derived are consistent with prior results at

similar redshifts, with reduced uncertainties.

An analysis of these Hα emitters’ sizes is also presented, showing a direct corre-

lation between the galaxies’ sizes and their Hα emission.

Understanding the properties and formation histories of individual stars in galaxies remains one of the most important areas in astrophysics. The impact of the Hubble Space Telescope<\italic> (HST<\italic>) has been revolutionary, providing deep observations of nearby galaxies at high resolution and unprecedented sensitivity over a wavelength range from near-ultraviolet to near-infrared. In this study, I use deep HST<\italic> imaging observations of three nearby star-forming galaxies (M83, NGC 4214, and CGCG 269-049) based on the HST<\italic> observations, in order to provide to construct color-magnitude and color-color diagrams of their resolved stellar populations. First, I select 50 regions in the spiral arm and inter-arm areas of M83, and determine the age distribution of the luminous stellar populations in each region. I developed an innovative method of star-by-star correction for internal extinction to improve stellar age and mass estimates. I compare the extinction-corrected ages of the 50 regions with those determined from several independent methods. The young stars are much more likely to be found in concentrated aggregates along spiral arms, while older stars are more dispersed. These results are consistent with a scenario where star formation is associated with the spiral arms, and stars form primarily in star clusters before dispersing on short timescales to form the field population. I address the effects of spatial resolution on the measured colors, magnitudes, and age estimates. While individual stars can occasionally show measurable differences in the colors and magnitudes, the age estimates for entire regions are only slightly affected. The same procedure is applied to nearby starbursting dwarf NGC 4214 to study the distributions of young and old stellar populations. Lastly, I describe the analysis of the HST<\italic> and Spitzer Space Telescope<\italic> observations of the extremely metal-poor dwarf galaxy (XMPG) CGCG 269-049 at a distance of 4.96 Mpc. This galaxy is one of the most metal-poor known with 12+log(O/H)=7.43. I find clear evidence for the presence of an old stellar population in CGCG~269-049, ruling out the possibility that this galaxy is forming its first generation of stars, as originally proposed for XMPGs. This comprehensive study of resolved stellar populations in three nearby galaxies provides detailed view of the current state of star formation and evolution of galaxies.

A thorough exploration of star formation necessitates observation across the electromagnetic spectrum. In particular, observations in the submillimeter and ultra-violet allow one to observe very early stage star formation and to trace the evolution from molecular cloud collapse to stellar ignition. Submillimeter observations are essential for piercing the heart of heavily obscured stellar nurseries to observe star formation in its infancy. Ultra-violet observations allow one to observe stars just after they emerge from their surrounding environment, allowing higher energy radiation to escape. To make detailed observations of early stage star formation in both spectral regimes requires state-of-the-art detector technology and instrumentation. In this dissertation, I discuss the calibration and feasibility of detectors developed by Lawrence Berkeley National Laboratory and specially processed at the Jet Propulsion Laboratory to increase their quantum efficiency at far-ultraviolet wavelengths. A cursory treatment of the delta-doping process is presented, followed by a thorough discussion of calibration procedures developed at JPL and in the Laboratory for Astronomical and Space Instrumentation at ASU. Subsequent discussion turns to a novel design for a Modular Imager Cell forming one possible basis for construction of future large focal plane arrays. I then discuss the design, fabrication, and calibration of a sounding rocket imaging system developed using the MIC and these specially processed detectors. Finally, I discuss one scientific application of sub-mm observations. I used data from the Heinrich Hertz Sub-millimeter Telescope and the Sub-Millimeter Array (SMA) to observe sub-millimeter transitions and continuum emission towards AFGL 2591. I tested the use of vibrationally excited HCN emission to probe the protostellar accretion disk structure. I measured vibrationally excited HCN line ratios in order to elucidate the appropriate excitation mechanism. I find collisional excitation to be dominant, showing the emission originates in extremely dense (n&sim10;11 cm-3), warm (T&sim1000; K) gas. Furthermore, from the line profile of the v=(0, 22d, 0) transition, I find evidence for a possible accretion disk.