Nebular emission-lines offer a powerful tool for studying the physical properties and chemical compositions of galaxies in the near and distant universe. They are excellent tracers of star formation activity in galaxies as well as efficient probes of intergalactic medium in the early universe. This dissertation presents findings from three different studies of emission-line galaxies (a.k.a. line emitters) at low and high redshifts, based on imaging and spectroscopic observations. The first study explores Hα emitters at z ~ 0.6 from the Cosmic Deep And Wide Narrow-band (DAWN) survey, providing robust measurements of the Hα luminosity function (LF) and the star-formation rate density (SFRD) at z ~ 0.6. The effects of different dust-extinction corrections on the measured LF were also investigated in this study. Owing to the observing strategy employed in this survey, this study demonstrates the importance of performing deep and wide-field observations, in order to robustly constrain the entire LF. In the second study, 21 Lyman-α emitter (LAE) candidates at z ~ 7 from the Lyman-Alpha Galaxies in the Epoch of Reionization (LAGER) survey were followed up spectroscopically, using Low Resolution Imaging Spectrometer (LRIS) on the Keck telescope. 15 of these were confirmed to be LAEs, obtaining a spectroscopic confirmation success rate of ~ 80% for LAGER LAE candidates. Apart from Lyman- α, no other rest-frame ultra-violet (UV) nebular lines were detected, with a 2σ upper limit for the ratio of NV/Lyα ≲ 0.27. These confirmations help validate the neutral Hydrogen fraction estimates from LAGER, which is consistent with a fully ionized universe at z ~ 7. The final study investigated the presence of black hole/active galactic nuclei (AGN) signatures among Green Pea (GP) galaxies, using mid-infrared (MIR) observations from the Wide-field Infrared Survey Explorer (WISE) mission. 31 GPs were selected as candidate AGN based on a stringent MIR color-color diagnostic including two GPs exhibiting notable variability in the shorter two WISE bandpasses. Given that GPs are one of the best analogs of high-redshift galaxies, findings from this study suggest that AGN activity could be responsible for the hard ionizing radiation observed in some GPs, which has crucial implications on the sources likely to have contributed towards cosmic reionization.

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.

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.

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.

Lyman-alpha (Lyα) galaxies (LAEs) and Lyα blobs (LABs) are objects identified and studied due to their bright Lyα emission lines. This bright emission allows LAEs and LABs to be studied in the distant universe, providing a glimpse into the physical processes occuring in the early universe. This dissertation presents three complementary studies of LAEs and LABs at z ~ 3.1. The two main foci of this work are (1) to understand the gas kinematics in both classes of objects and (2) to improve spectral energy distribution (SED) fitting processes to better determine the physical characteristics of LAEs. Gas kinematics in this dissertation means looking for signatures of large-scale winds. This is an exciting astrophysical endeavor, because the results can provide insight into how Lyα photons escape distant galaxies and traverse the IGM, and the results have implications for how the epoch of reionization can be studied with the Lyα line and because winds can be a signature of powerful star formation events. In the first two studies we find signatures of winds in three LAEs by measuring the velocity offset between the redshifts of [OIII] and Lyα in these galaxies. The first two LAEs presented here represent the first ever measurements of [OIII] in Lyα-selected field galaxies. The third study reports no velocity offset between [OIII] and Lyα when the methodology is transferred to a z ~ 3.1 LAB. This lack of velocity offset is an interesting result, however, as powerful outflows and star formation events, which should impart a velocity offset, have been hypothesized as power sources for LABs. In addition to understanding the kinematics of these objects, we introduce a new parameter into the SED fitting process typically used to characterize LAEs. This new parameter enables better determination of characteristics like the age, mass, metallicity, dust content and star formation history of the galaxies in our sample. These characteristics provide a snapshot of galaxies in the universe ~ 11 billion years ago and also provide insight into how these characteristics compare to galaxies at other epochs.

The first part of this dissertation presents the implementation of Bayesian statistics with galaxy surface luminosity (SL) prior probabilities to improve the ac- curacy of photometric redshifts. The addition of the SL prior probability helps break the degeneracy of spectro-photometric redshifts (SPZs) between low redshift 4000 A break galaxies and high redshift Lyman break galaxies which are mostly catas- trophic outliers. For a sample of 1138 galaxies with spectroscopic redshifts in the GOODS North and South fields at z < 1.6, the application of the surface luminosity prior reduces the fraction of galaxies with redshift deviation sigma(z) > 0.2 from 15.0% to 10.4%. The second part of this dissertation presents the study of the chemical evolution of the star-forming galaxies. The Hubble Space Telescope Probing Evolution and Reionization Spectroscopically (PEARS) grism Survey effectively selects emission line galaxies (ELGs) to mAB ~ 27. Follow-up Magellan LDSS3+IMACS spectroscopy of the HST/ACS PEARS ELGs confirms an accuracy of sigma_z = 0.006 for the HST/ACS PEARS grism redshifts. The luminosity-metallicity (L-Z) relation and the mass-metallicity (M-Z) relation of the PEARS ELGs at z ~ 0.6 are offset by ~ - 0.8 dex in metallicity for a given rest-frame B absolute magnitude and stellar mass relative to the local relations from SDSS galaxies. The offsets in both relations are ~ - 0.4 dex larger than that given by other samples at same redshifts, which are demonstrated to be due to the selection of different physical properties of the PEARS ELGs: low metallicities, very blue colors, small sizes, compact disturbed morphologies, high SSFR > 10^-9 yr^-1 , and high gas fraction. The downsizing effect, the tidal interacting induced inflow of metal-poor gas, and the SNe driven galactic winds outflows, may account for the significant offset of the PEARS galaxies in the L-Z and the M-Z relations relative to the local relations. The detection of the emission lines of ELGs down to m ~ 26 mag in the HST/ACS PEARS + HST/WCF3 ERS NIR composit grism spectra enables to extend the study of the evolution of the L-Z and M-Z relations to 0.6 < z < 2.4.

Galaxies with strong Lyman-alpha (Lya) emission line (also called Lya galaxies or emitters) offer an unique probe of the epoch of reionization - one of the important phases when most of the neutral hydrogen in the universe was ionized. In addition, Lya galaxies at high redshifts are a powerful tool to study low-mass galaxy formation. Since current observations suggest that the reionization is complete by redshift z~ 6, it is therefore necessary to discover galaxies at z > 6, to use their luminosity function (LF) as a probe of reionization. I found five z = 7.7 candidate Lya galaxies with line fluxes > 7x10-18 erg/s/cm/2 , from three different deep near-infrared (IR) narrowband (NB) imaging surveys in a volume > 4x104Mpc3. From the spectroscopic followup of four candidate galaxies, and with the current spectroscopic sensitivity, the detection of only the brightest candidate galaxy can be ruled out at 5 sigma level. Moreover, these observations successfully demonstrate that the sensitivity necessary for both, the NB imaging as well as the spectroscopic followup of z~ 8 Lya galaxies can be reached with the current instrumentation. While future, more sensitive spectroscopic observations are necessary, the observed Lya LF at z = 7.7 is consistent with z = 6.6 LF, suggesting that the intergalactic medium (IGM) is relatively ionized even at z = 7.7, with neutral fraction xHI≤ 30%. On the theoretical front, while several models of Lya emitters have been developed, the physical nature of Lya emitters is not yet completely known. Moreover, multi-parameter models and their complexities necessitates a simpler model. I have developed a simple, single-parameter model to populate dark mater halos with Lya emitters. The central tenet of this model, different from many of the earlier models, is that the star-formation rate (SFR), and hence the Lya luminosity, is proportional to the mass accretion rate rather than the total halo mass. This simple model is successful in reproducing many observable including LFs, stellar masses, SFRs, and clustering of Lya emitters from z~ 3 to z~ 7. Finally, using this model, I find that the mass accretion, and hence the star-formation in > 30% of Lya emitters at z~ 3 occur through major mergers, and this fraction increases to ~ 50% at z~7.