Exploring Dwarf Galaxies and Their Dark Matter Halos in Diverse Cosmic Environments

A comprehensive study on the formation and evolution of dwarf galaxies, their environments, and corresponding dark matter halos is presented within the framework of the Lambda Cold Dark Matter ($\Lambda$CDM) model. Using advanced cosmological hydrodynamical simulations, and semi-analytic models, this work addresses several critical questions in galaxy formation and evolution. These include the mechanisms driving intra-cluster light (ICL) formation, the role of dwarf galaxies as building blocks of ICL, its reliability as a tracer of the underlying dark matter, and the relation between the dwarf galaxy properties and their corresponding dark matter halo.This research demonstrates that dwarf galaxies exhibit a wide range of relevance in contributing to ICL, with significant implications for upcoming deep observations from the Euclid and Roman space telescopes. Findings show that systems with minimal contributions from dwarf galaxies (M${\star}$ $<$ $10^{10}$ M${\odot}$) display shallower ICL metallicity profiles. Moreover, intra-cluster globular clusters (ICGCs) are identified as valuable tracers of halo assembly histories, particularly when observing ICL is challenging. The shape and orientation of ICL and ICGCs show a reasonable correlation with those of the dark matter in the outskirts of halos, underscoring their common origin and potential as luminous tracers.In addition, this dissertation explores the ICL component of Virgo-like clusters by analyzing ICL fractions, density profiles, and star formation rates. The simulation results predict an ICL component comparable to the brightest cluster galaxy in mass and star formation rate, with an in-situ stellar component present at all redshifts. The in-situ component, accounting for approximately 8--28\% of the ICL stellar mass at $z=0$, is attributed to widespread star formation along filamentary structures tracing the distribution of neutral gas in the cluster host halo.Additionally, a modified semi-analytic model, Galacticus, was developed to reproduce the ...