Learning how properties of galaxies such as star formation, galaxy interactions, chemical composition, and others evolve to produce the modern universe has long been a goal of extragalactic astronomy. In recent years, grism spectroscopy from the Hubble Space Telescope (HST) has provided a means to study these properties with spectroscopy while avoiding the limitations of ground-based observation. In this dissertation, I present several studies wherein I used HST G102 grism spectroscopy from the Faint Infrared Grism Survey (FIGS) to investigate these fundamental properties of galaxies and how they interact and evolve. In the first study, I combined the grism spectra with broadband photometry to produce a catalog of redshifts with improved accuracy, reducing the median redshift error from 3\% to 2\%. With this redshift catalog, I conducted a systematic search for galaxy overdensities in the FIGS fields, producing a list of 24 significant candidates. In the second study, I developed a method for identifying emission line galaxy (ELG) candidates from continuum-subtracted 1D spectra, and identified 71 ELGs in one FIGS field. In matching MUSE/VLT spectra, I measured the [OIII]$\lambda$4363 emission line for 14 FIGS ELGs, and used this to measure their $T_e$-based gas-phase metallicities. These ELGs show a low-metallicity offset on the Mass-Metallicity Relation, and I demonstrated that this offset can be explained by recent star formation. In the third study, I expanded the ELG search to all four FIGS fields, identifying 208 H$\alpha$, [OIII]$\lambda\lambda$4959,5007, and [OII]$\lambda\lambda$3727,3729 line emitters. I compiled a catalog of line fluxes, redshifts, and equivalent widths. I combined this catalog with the overdensity study to investigate a possible relationship between line luminosity, star formation, and an ELG's environment. In the fourth study, I usde 15 FIGS H$\alpha$ emitters and 49 ``green pea'' line emitters to compare H$\alpha$ and the far-UV continuum as tracers of star formation. I explored a correlation between the H$\alpha$-FUV ratio and the ratio of [OIII]$\lambda\lambda$4959,5007 to [OII]$\lambda\lambda$3727,3729 and its implications for star formation history.

One of the most fundamental questions in astronomy is how the Universe evolved to become the highly structured system of stars and galaxies that we see today. The answer to this question can be largely uncovered in a relatively unexplored period in the history of the Universe known as the Epoch of Reionization (EoR), where radiation from the first generation of stars and galaxies ionized the neutral hydrogen gas in the intergalactic medium. The reionization process created "bubbles" of ionized regions around radiating sources that perturbed the matter density distribution and influenced the subsequent formation of stars and galaxies. Exactly how and when reionization occurred are currently up for debate. However, by studying this transformative period we hope to unravel the underlying astrophysics that governs the formation and evolution of the first stars and galaxies.

The most promising method to study reionization is 21 cm tomography, which aims to map the 3D distribution of the neutral hydrogen gas using the 21 cm emission lines from the spin-flip transition of neutral hydrogen atoms. Several radio interferometers operating at frequencies below 200 MHz are conducting these experiments, but direct images of the observed fields are limited due to contamination from astrophysical foreground sources and other systematics, forcing current and upcoming analyses to be statistical.

In this dissertation, I studied one-point statistics of the 21 cm brightness temperature intensity fluctuations, focusing on how measurements from observations would be biased by different contaminations and instrumental systematics and how to mitigate them. I develop simulation tools to generate realistic mock 21 cm observations of the Hydrogen Epoch of Reionization Array (HERA), a new interferometer being constructed in the Karoo desert in South Africa, and perform sensitivity analysis of the telescope to one-point statistics using the mock observations. I show that HERA will be able to measure 21 cm one-point statistics with sufficient sensitivity if foreground contaminations can be sufficiently mitigated. In the presence of foreground, I develop a rolling foreground avoidance filter technique and demonstrate that it can be used to obtain noise-limited measurements with HERA. To assess these techniques on real data, I obtain measurements from the legacy data from the first season observation of the Murchison Widefield Array (MWA) and perform additional high-precision radio interferometric simulations for comparison. Through these works, I have developed new statistical tools that are complementary to the power spectrum method that is currently the central focus of the majority of analyses. In addition to confirming power spectrum detections, one-point statistics offer additional information on the distribution of the 21 cm fluctuations, which is directly linked to the astrophysics of structure formation.

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.

The formation of the firsts stars some 100-300 Myr after the Big Bang marked the end of the cosmic darks ages and created the elemental building blocks of not only rocky planets but eventually us. Understanding their formation, lifetimes, and contributions to the evolution of our universe is one of the current frontiers in astronomy and astrophysics.

In this work I present an improved model for following the formation of Pop III stars, their effects on early galaxy evolution, and how we might search for them. I make use of a new subgrid model of turbulent mixing to accurately follow the time scales required to mix supernova (SN) ejecta -- enriched with heavy elements -- into the pristine gas. I implement this model within a large-scale cosmological simulation and follow the fraction of gas with metallicity below a critical value marking the boundary between Pop III and metal enriched Population II (Pop II) star formation. I demonstrate that accounting for subgrid mixing results in a Pop III stars formation rate that is 2-3 times higher than standard models with the same physical resolution.

I also implement and track a new "Primordial metals" (PM) scalar that tracks the metals generated by Pop III SNe. These metals are taken up by second generation stars and likely result in a subclass of carbon-enhanced, metal-poor (CEMP) stars. By tracking both regular metals and PM, I can model, in post-processing, the elemental abundances of simulation stars. I find good agreement between observations of CEMP-no Milky Way halo stars and second generation stars within the simulation when assuming the first stars had a typical mass of 60 M☉, providing clues as to the Pop III initial mass function.

Galaxies in the universe are surrounded by a hot medium called the Circum-Galactic Medium (CGM). Present the CGM is gas that forms up clouds which travel within the CGM at speeds that approximately range between 100 km/s and 300 km/s. These gas clouds are very interesting because they play a crucial in the formation of stars within the galaxies and also in the overall evolution of galaxies. The clouds could in fact be thought of as mobile "gas stations" whose sole purpose is facilitate the ionization of elements and ultimately supply gas to galaxies. My thesis project is a follow-up study on CGM gas cloud observations that were made by Borthakur et. al. (2016). Using Cosmic Origins Spectrograph (COS) data from the Hubble Space Telescope (HST), Borthakur et. al. (2016) observed the presence of both Carbon IV (C IV) and Oxygen VI (O IV) but did not observe any Nitrogen V (N V) in the gas cloud when expected to be observable. Therefore, the ultimate goal of my research was to determine whether indeed CGM gas clouds have an actual shortage of the N V ion. My research involves the generation of cosmological simulations of a cold gas cloud that has a radius of 98 parsecs, relative velocity of 200 km/s, density range of 10-3 to -5 and a temperature in the range of ~104 to 5 K, and also a hot CGM that has density in the range of 10-4.5 to -6 particles/cm3 and temperature of approximately 106 K. Traces of N v are observed in my simulations.

The Universe transitioned from a state of neutral hydrogen (HI) shortly after recombination to its present day ionized state, but this transition, the Epoch of Reionization (EoR), has been poorly constrained by observational data. Estimates place the EoR between redshifts 6 < z <13 (330-770 Myr).

The interaction of the 21 cm hyperfine ground state emission/absorption-line of HI with the cosmic microwave background (CMB) and the radiation from the first luminous sources in the universe can be used to extract cosmological information about the EoR. Theorists have created global redshifted 21 cm EoR models of this interaction that predict the temperature perturbations to the CMB in the form of a sky-averaged difference temperature, Tb. The difficulty in measuring Tb is that it is

predicted to be on the order of 20 to 100 mK, while the sky foreground is dominated

by synchrotron radiation that is 105 times brighter. The challenge is to subtract the much brighter foreground radiation without subtracting the Tb signal and can only be done when the data has small error levels.

The Experiment to Detect the Global EoR Signature (EDGES) is an effort to measure Tb with a single wide field-of-view well-calibrated antenna. This dissertation focuses on reducing systematic errors by quantifying the impact of the chromatic nature of the antenna’s beam directivity and by measuring the variability of the spectral index of the radio sky foreground. The chromatic beam study quantified the superior qualities of the rectangular blade-shaped antenna and led to its adoption over the previously used fourpoint-shaped antenna and determined that a 5 term polynomial was optimum for removing the foreground. The spectral index, β, of the sky was measured, using 211 nights of data, to be −2.60 > β > −2.62 in lower LST regions, increasing to −2.50 near the Galactic plane. This matched simulated results using the Guzm´an et al. (2011) sky map (∆β < 0.05) and demonstrated the exceptional stability of the EDGES instrument. Lastly, an EoR model by Kaurov & Gnedin (2016) was shown to be inconsistent with measured EDGES data at a significance level of 1.9.

The goal of this thesis is to extend the astrophysical jet model created by Dr.
Gardner and Dr. Jones to model the surface brightness of astrophysical jets. We attempt to accomplish this goal by modeling the astrophysical jet HH30 in the spectral emission lines [SII] 6716Å, [OI] 6300Å, and [NII] 6583Å. In order to do so, we used the jet model to simulate the temperature and density of the jet to match observational data by Hartigan and Morse (2007). From these results, we derived the emissivities in these emission lines using Cloudy by Ferland et al. (2013). Then we used the emissivities to determine the surface brightness of the jet in these lines. We found that the simulated surface brightness agreed with the observational surface brightness and we conclude that the model could successfully be extended to model the surface brightness of a jet.

The LOw Frequency ARray (LOFAR) is a new and innovative radio telescope designed and constructed by the Netherlands Institute for Radio Astronomy (ASTRON). LOFAR unique capable of operating in very low frequencies (10-240 MHz) and consists of an extensive interferometry array of dipole antenna stations distributed throughout the Netherlands and Europe which allows it to achieve superb angular resolution. I investigate a part of the northern sky to search for rare radio objects such as radio haloes and radio relics that may have not been able to have been resolved by other radio telescopes.

Radio astronomy is a subfield in astronomy that deals with objects emitting frequencies around 10 MHz to 100 GHz. The Low Frequency Array (LOFAR) is a array of radio antennas in Europe that can reach very low frequencies, roughly between 10-240 MHz. Our project was to image and clean a field from LOFAR. The data was a 10 degree square in the sky centered at a right ascension of 10:19:34.608 and a declination +49.36.52.482. It was observed for 600 seconds at 141 MHz. To clean the field, we had to flag and remove any stations that were not responding. Using a program called FACTOR, we cleaned the image and reduced the residuals. Next we checked the validity of our sources. We checked positional offsets for our sources using the TGSS survey at 150 MHz, and corrected the declination of our LOFAR sources by a factor of 0.0002 degrees. We also fixed the LOFAR fluxes by a factor of 1.15. After this systematic check, we calculated the spectral index of our sources using the FIRST survey at 1435 MHz. We plotted this spectral index against LOFAR flux as well as redshift of the sources, and compared these to literature.