<p> The observation of gravitational waves from compact stars (neutron and quark stars) is a promising method of determining their internal composition. This research presents the details and results for calculations of some of the principal modes of compact star oscillations, by which they radiate gravitational waves. These are: the <i>f</i>-modes, <i>p</i>-modes, and <i>g</i>-modes. We find that for the same stellar mass, the <i> f</i>-modes for quark stars are higher in frequency than for neutron stars. The <i>p</i>-mode frequency of quark stars decrease with stellar mass, displaying an opposite trend to that of neutron stars. Two-component models were also considered. A core-ocean model was examined for a neutron star, using a polytropic equation of state (EOS), and a core-crust model for a quark star, using a bag model EOS. We find that <i>g</i>-mode oscillations in neutron star oceans depend on the dominant chemical species of the ocean as well as the mass of the underlying core. The addition of a solid crust onto a quark star increases the frequencies, attributable to shear stresses between the core and crust. These results pave the way to model and contrast the gravitational wave signals emitted by oscillating compact stars.</p>

<p> The Sun is the best observed object in astrophysics, but despite this distinction the nature of its well-ordered generation of magnetic field in 11-year activity cycles remains a mystery. In this work, we place the solar cycle in a broader context by examining the long-term variability of solar analog stars within 5% of the solar effective temperature, but varied in rotation rate and metallicity. Emission in the Fraunhofer H &amp; K line cores from singly-ionized calcium in the lower chromosphere is due to magnetic heating, and is a proven proxy for magnetic flux on the Sun. We use Ca H &amp; K observations from the Mount Wilson Observatory HK project, the Lowell Observatory Solar Stellar Spectrograph, and other sources to construct composite activity time series of over 100 years in length for the Sun and up to 50 years for 26 nearby solar analogs. Archival Ca H &amp; K observations of reflected sunlight from the Moon using the Mount Wilson instrument allow us to properly calibrate the solar time series to the S-index scale used in stellar studies. We find the mean solar <i>S</i>-index to be 5&ndash;9% lower than previously estimated, and the amplitude of activity to be small compared to active stars in our sample. A detailed look at the young solar analog HD 30495, which rotates 2.3 times faster than the Sun, reveals a large amplitude ~12-year activity cycle and an intermittent short-period variation of 1.7 years, comparable to the solar variability time scales despite its faster rotation. Finally, time series analyses of the solar analog ensemble and a quantitative analysis of results from the literature indicate that truly Sun-like cyclic variability is rare, and that the amplitude of activity over both long and short timescales is linearly proportional to the mean activity. We conclude that the physical conditions conducive to a quasi-periodic magnetic activity cycle like the Sun&rsquo;s are rare in stars of approximately the solar mass, and that the proper conditions may be restricted to a relatively narrow range of rotation rates.</p>

<p> The formation history of galaxy clusters is a powerful probe of cosmology. In particular, one may place strong constraints on the dark energy equation of state by examining the evolution across redshift of the number density of galaxy clusters as a function of mass. In this thesis, I describe my contributions to cluster cosmology, in particular to the development of the richness optical observable mass proxy. </p><p> I introduce <i>redMaPPer</i>, an optical cluster finder which represents an important upstream input for my thesis work. I next introduce the <b>M</b>ass <b>A</b>nalysis <b>T</b>ool for <b>Cha </b>ndra (<i><b>MATCha</b></i>), a pipeline which uses a parallelized algorithm to analyze archival Chandra data. <i>MATCha</i> simultaneously calculates X-ray temperatures and luminosities and performs centering measurements for hundreds of potential galaxy clusters using archival X-ray exposures. I run <i>MATCha</i> on the <i>redMaPPer</i> SDSS DR8 cluster catalog and use <i>MATCha</i>'s output X-ray temperatures and luminosities to analyze the galaxy cluster temperature-richness, luminosity-richness, luminosity-temperature, and temperature-luminosity scaling relations. I investigate the distribution of offsets between the X-ray center and <i>redMaPPer</i> center within 0.1 &lt; <i>z</i> &lt; 0.35 and explore some of the causes of <i>redMaPPer</i> miscentering. I collaborate with members of the Dark Energy Survey in order to repeat this analysis on Dark Energy Survey Year 1 data. I outline the various ways in which <i>MATCha </i> constitutes an important upstream work for a variety of astrophysical applications. These include the calibrations of two separate mass proxies, the study of the AGN fraction of galaxy clusters, and cosmology from cluster number densities and stacked weak lensing masses. Finally, I outline future upgrades and applications for <i>MATCha</i> throughout the lifespan of the Dark Energy Survey and the Large Synoptic Survey Telescope.</p><p>

<p> Dwarf galaxies present interesting observational challenges for the studies of various galaxy properties: despite their abundance and proximity to the Milky Way, they typically have very low surface brightnesses and small physical sizes. Until now, only the extreme variety of dwarfs &mdash; those undergoing strong bouts of star formation &mdash; have been observed in the FIR, due to observational difficulties. However, this population does not represent the majority of dwarfs, which have only moderate star formation rates and extremely low metallicity (the fraction of heavy elements to hydrogen). The advent of the Herschel Space Telescope, with its superior resolution and sensitivity over previous generations of telescopes, has made it possible to measure FIR spectral lines and broadband continuum in normal dwarf galaxies, expanding the scope of studies beyond the brighter, but more extreme, varieties. </p><p> The general goal of my research was to study the conditions in the interstellar media (ISM) of typical dwarf galaxies. The LITTLE THINGS (Local Irregulars That Trace Luminosity Extremes, TheHI Nearby Galaxy Survey) project aims to unravel many mysteries of nearby dwarfs using a suite of multi-wavelength data, and the new additions from <i>Herschel</i> help provide insight into the physics of these systems. I reduced and analyzed FIR fine-structure spectral line data for the LITTLE THINGS sample to study the different phases of the ISM, as well as FIR photometry data to access the dust properties and infrared continuum emission in these systems. The FIR spectral lines are diagnostics for the conditions in the ISM of galaxies, telling us about heating efficiency, the fraction of gas that resides in photodissociation regions (PDRs), abundance of highly ionized gas from massive stars, and other physical descriptions. The photometric continuum observations enable the modeling of interstellar dust properties &ndash; dust plays an important role in shielding and cooling molecular clouds which form stars, as well as heating via the photoelectric effect. I also utilized neutral hydrogen data to probe the neutral medium in relation to the FIR, as well as optical and UV data to characterize star formation and the emission of starlight.</p>

<p> Mergers of a neutron star and a black hole are interesting because of the dual complexity of the black hole's strong gravity and the neutron star's nuclear-density fluid. Mergers can yield short-lived nuclear accretion disks, emitting copious neutrinos. This radiation may change the thermodynamic state of the disk itself, may drive an ultrarelativistic jet of electrons and positrons, may oscillate in its flavor content, may irradiate surrounding matter, playing a role in nucleosynthesis, and may be detected directly. </p><p> In this thesis I present a model of such a merger, its remnant accretion disk, and its neutrino emission. In particular, we evolve a neutron star&mdash;black hole merger through &sim;100 ms, solving the full general relativistic hydrodynamics equations, from inspiral through merger and accretion epochs. We treat the neutrinos approximately, using a leakage framework, which accounts for local energy losses and composition drift in the fluid due to escaping neutrinos. We use geodesic ray tracing on a late time slice of the model to calculate the full spatial-, angular-, and energy-dependence of the neutrino distribution function around the accretion disk. This distribution then serves in a computation of the energy available to form a jet via neutrino-antineutrino annihilation in the disk funnel. In this scenario, we find that enough energy is deposited to drive a jet of short-gamma-ray-burst-energy by neutrino processes alone.</p>

<p> Solar flares can release ~1e33 ergs of power, accelerate particles to relativistic speeds, heat plasma to ~15 million K and catastrophically reorganize 1e5 km long field structures in 100s&ndash;1000s of seconds. Magnetic reconnection of large-scale field structures in the corona are thought to power flares, but the precise mechanisms that convert the stored magnetic energy into particle kinetic energy are poorly understood. </p><p> Flare spectra in the 20 keV&ndash;10 MeV energy range are rich with information that provide a window into the underlying physics of flare particle acceleration. This hard X-ray (HXR)/gamma-ray emission can be used to understand electron and ion dynamics, particle abundances and the ambient plasma conditions in solar flares. Enhanced imaging, spectroscopy and polarimetry of flare emissions in this energy range are needed to address the current era of particle acceleration and transport questions, including: What causes the spatial separation between HXR emission generated by relativistic electrons and the gamma-ray line emission from energetic ions? How anisotropic are the relativistic electrons, and why can they dominate in the corona? How do the compositions of accelerated and ambient material vary with space and time, and why? </p><p> The <i>Reuven Ramaty High Energy Solar Spectroscopic Imager</i> (RHESSI) instrument, launched in 2002, provided the first combined imaging and high-resolution spectroscopy in the HXR/gamma-ray range. RHESSI's volumes of detailed study on electron-associated emission &lt; 1 MeV is in contrast to comparatively few ion-associated gamma-ray observations. Over the past two solar cycles RHESSI has imaged only five flares at the 2.2 MeV neutron-capture line and has been able to resolve ion lines in ~30 events. My research aims to expand this small set gamma-ray flare observations by (1) using new techniques to study flares obscured by high-background counts in the existing RHESSI dataset and (2) providing new observations through the development and flight of the <i>Gamma-Ray Imager/Polarimeter for Solar Flares</i> (GRIPS) instrument.</p><p>

<p> Currently, we lack a means of identifying the type of matter at the core of compact stars, but in the future, we may be able to use gravitational wave signals produced by fluid oscillations inside compact stars to discover new phases of dense matter. To this end, we study the fluid perturbations inside compact stars such as Neutron Stars (NS) and Strange Quark Stars (SQS), focusing on modes that couple to gravitational waves (GWs). Using a modern equation of state for quark matter that incorporates interactions at moderately high densities, we implement an efficient computational scheme to solve the oscillation equations in the framework of General Relativity, and determine the complex eigenfrequencies that describe the oscillation and damping of the non-radial fluid modes. We find that the <i>f</i>- mode frequency only weakly distinguishes NS from SQS. However, we do find that the <i> p</i>- mode has a strong discriminating signature between the two models. In addition we study the impact of parameters of the SQS equation of state on the oscillation spectra. Finally, we discuss the significance of our results for future detection of these modes through gravitational waves.</p><p>

<p> Through their connection with dark matter structures, galaxies act as tracers of the underlying matter distribution in the Universe. Their observed spatial distribution allows us to precisely measure large scale structure and effectively test cosmological models that explain the content, geometry, and history of the Universe. Current observations from galaxy surveys such as the Baryon Oscillation Spectroscopic Survey have already probed vast cosmic volumes with millions of galaxies and ushered in an era of precision cosmology. The next surveys will probe over an order of magnitude more. With this unprecedented statistical power, the bottleneck of scientific discovery is in the methodology. </p><p> In this dissertation, I address major methodological challenges in constraining cosmology with the large-scale distribution of galaxies. I develop a robust framework for treating systematic effects, which significantly bias galaxy clustering measurements. I apply new innovative approaches to probabilistic parameter inference that challenge and test the in- correct assumptions of the standard approach. Furthermore, I use precise predictions of structure formation from cosmology and observations of galaxies during the last eight billion years to develop detailed models of how galaxies are impacted by their host dark matter structures. These models provide key insight into the galaxy-halo connection, which bridges the gap between cosmology theory and observations. They also answer crucial questions of how galaxies form and evolve. The developments in this dissertation will help unlock the full potential of future observations and allow us to precisely test cosmological models, General Relativity and modified gravity scenarios, and even particle physics theory beyond the Standard Model.</p><p>

<p> Gamma-ray astronomy is the study of very energetic photons, from <i> E</i> = <i>m_ec</i>² &ap;0.5&times;10⁶ eV to > &ge;10²⁰eV. Due to the large span of the energy range, the field focuses on non-thermal processes that include the acceleration and propagation of relativistic particles, which can be found in extreme environments such as pulsars, supernova remnants, molecular clouds, black holes, etc.</p><p> The High Altitude Water Cherenkov (HAWC) observatory is an instrument designed for the study of gamma rays in the energy range of &sim;100 GeV to 100 TeV. Using data from the HAWC observatory, a study for the search of very high energy gamma rays in the northern <i>Fermi</i> Bubble region was made. The <i>Fermi</i> Bubbles are large extended regions in the gamma-ray sky located above and below the galactic plane that present a hard emission between 1 GeV and 100 GeV. No significant excess is found an upper bounds at 95% C.L. are obtained. The implications of this result are that certain processes explaining the Fermi Bubble formation from the center of our galaxy are excluded. I will discuss and compare the scenarios that still present a possible hypothesis of the Fermi Bubble origin.</p>

<p>Hierarchical structure formation in the standard &Lambda;+cold dark matter (CDM) model produces gravitationally bound clumpy halos with abundant substructure. These subhalos are the remnants of dark matter halos that have been accreted by their host halo over cosmic time, and have survived tidal destruction. Understanding halo substructure is extremely important, as subhalos are believed to host satellite galaxies, boost the dark matter annihilation signal, cause tidal heating of fragile structures such as stellar streams and disks, and are potentially responsible for interesting phenomena in gravitational lensing. Most importantly, the demographics of subhalos contain information of the Universe, thus providing a stringent testbed for the cosmological model.</p><p> This thesis provides a comprehensive study of dark matter subhalos, using a combination of cosmological <i>N</i>-body simulations and semi-analytic modeling. We start with developing a new, semi-analytic model describing halo assembly and subhalo evolution. The model combines Monte-Carlo techniques of generating halo merging histories and simple analytical descriptions for the evolution of subhalos, thus offering extremely fast computation, the agility to experiment with different cosmologies, and the control of specific physical processes. The model accurately predicts the distributions of subhalo mass and structural parameters in cosmological simulations, and outperforms simulations in terms of mass resolution and statistical power. Taking advantage of the speed and agility of the model, we present universal fitting formulae for subhalo mass and maximum circular velocity (^&ngr;max) functions that are valid for a broad range in host halo mass, redshift and CDM cosmology. </p><p> The remainder of the dissertation makes use of the model, together with a number of state-of-the-art <i>N</i>-body simulations, to study the statistics of halo substructure. Recent high-resolution CDM simulations reveal ~10 massive Galactic subhalos whose central potential wells are too deep to be consistent with those of the ~10 brightest Milky-Way (MW) satellite galaxies. This inconsistency, dubbed the `too-big-to-fail' problem (TBTF), has become a persistent challenge to the standard ACDM cosmology. However, the number of well resolved Galactic halos in simulations is too small to fully capture the halo-to-halo variance in substructure content, which hinders the interpretation of the inconsistency. Unleashing the power of the semi-analytic model, we generate thousands of MW-size halos with well-resolved subhalo populations, and explicitly demonstrate that a reliable assessment of TBTF requires such large samples. We argue that existing statistics used to address TBTF suffer from the look-elsewhere effect and/or disregard certain aspects of the data on the MW satellite population. We devise a new statistic that is not hampered by these shortcomings, and, using data of the MW satellites with vmax > 15 km s<sup>-1</sup>, demonstrate that 1.4<sup>+3.3</sup>-1.1% of MW-size host halos have a subhalo population in statistical agreement with that of the MW. We also discuss how the severity of TBTF depends on halo mass and cosmology.</p><p> We conclude the thesis with a study of unprecedented statistical power regarding the halo-to-halo variance of substructure. First, we study the mass fraction (<i>f</i><sub>sub</sub>) in subhalos as a function of host halo mass, formation redshift, and halo-centric distance. We note that recent measurements of <i>f</i><sub>sub</sub> from gravitational lensing are much higher than the average but within the 90th percentile of the <i> f</i><sub>sub</sub> distribution. Second, we quantify the deviation of the occupation statistics of subhalos from Poissonian statistics, which is widely assumed in halo occupation distribution (HOD) models. In particular, we clearly reveal the sub-Poissonian statistics at [special characters omitted] &le; 3, aside from the already-known super-Poissonity at [special characters omitted] &raquo; 1, with [special characters omitted] the average number of subhalos. we also quantify the effect of the sub-Poissonity on the galaxy clustering predictions from HOD models. We further show that the extent of nonPoissonity depends on subhalo selection and on halo formation time - selecting subhalos by their mass or vmax at accretion yields weaker super-Poissonity for large [special characters omitted] but stronger sub-Poissonity for small [special characters omitted], compared to selecting by their present-day mass or vmax; earlier-formed halos exhibit less non-Poissonity than later-formed ones. Finally, we use the occupation statistics of the most massive satellites of the MW to put constraint on the mass and formation redshift of the MW halo. In particular, the `^&ngr;_max gap' of MW satellites between ~ 30 km s^-1 and 60 km s^-1 favors a low-mass, late-formed MW halo, with 0.25 &lt; <i>M</i>_vir/10¹² <i> h</i>^-1M[special characters omitted] &lt; 1.4 and 0.1 &lt; <i>z</i>_f &lt; 1.4 at 90% confidence.</p>