Limb darkening is a fundamental ingredient for interpreting observations of planetary transits, eclipsing binaries, optical/infrared interferometry and microlensing events. However, this modeling traditionally represents limb darkening by a simple law having one or two coefficients that have been derived from plane-parallel model stellar atmospheres, which has been done by many researchers. More recently, researchers have gone beyond plane-parallel models and considered other geometries. We previously studied the limb-darkening coefficients from spherically symmetric and plane-parallel model stellar atmospheres for cool giant and supergiant stars, and in this investigation we apply the same techniques to FGK dwarf stars. We present limb-darkening coefficients, gravity-darkening coefficients and interferometric angular diameter corrections from Atlas and SAtlas model stellar atmospheres. We find that sphericity is important even for dwarf model atmospheres, leading to significant differences in the predicted coefficients.

Mira and semi-regular variable stars have been studied for centuries but continue to be enigmatic. One unsolved mystery is the presence of polarization from these stars. In particular, we present 40 years of polarization measurements for the prototype o Ceti and V CVn and find very different phenomena for each star. The polarization fraction and position angle for Mira is found to be small and highly variable. On the other hand, the polarization fraction for V CVn is large and variable, from 2-7%, and its position angle is approximately constant, suggesting a long-term asymmetric structure. We suggest a number of potential scenarios to explain these observations.

Both pulsation and mass loss are commonly observed in stars and are important ingredients for understanding stellar evolution and structure, especially for massive stars. There is a growing body of evidence that pulsation can also drive and enhance mass loss in massive stars and that pulsation-driven mass loss is important for stellar evolution. In this review, I will discuss recent advances in understanding pulsation-driven mass loss in massive main-sequence stars, classical Cepheids and red supergiants and present some challenges remaining.

New results are described for the use of the Hanle effect in the photospheres of oblique magnetic rotators and of the Zeeman effect in stellar wind emission lines.

The Hanle effect has been proposed as a new diagnostic of circumstellar magnetic fields for early-type stars, for which it is sensitive to field strengths in the 1-300 G range. In this paper we compute the polarized P Cygni line profiles that result from the Hanle effect. For modeling the polarization, we employ a variant of the "last scattering approximation." For cases in which the Sobolev optical depths are greater than unity, the emergent line intensity is assumed to be unpolarized, while for smaller optical depths, the Stokes source functions for the Hanle effect with optically thin line scattering are used. For a typical P Cygni line, the polarized emission forms in the outer wind, because the Sobolev optical depth is large at the inner wind. For low surface field strengths, weak P Cygni lines are needed to measure the circumstellar field. For high values of the surface fields, both the Zeeman and Hanle diagnostics can be used, with the Zeeman effect probing the photospheric magnetic fields and the Hanle effect measuring the magnetic field in the wind flow. Polarized line profiles are calculated for a self-consistent structure of the flow and the magnetic geometry based on the WCFields model, which is applicable to slowly rotating stellar winds with magnetic fields drawn out by the gas flow. For surface fields of a few hundred gauss, we find that the Hanle effect can produce line polarizations in the range of a few tenths of a percent up to about 2%.

M dwarf stars are the most abundant stars in the Galaxy and appear to host the vast majority of temperate, Earth-sized planets. Investigations into their detailed compositions are important for inferring the chemical evolution of the Galaxy and for understanding relationships between stellar composition and planet occurrence. However, detailed characterization of M dwarfs is hampered by a unique set of challenges due to their lower effective temperatures. Previous attempts to measure the compositions of M dwarfs relied on observations of M dwarfs with F-, G-, or K-type companions to calibrate metallicity-sensitive features in their near-infrared spectra. These methods are indirect tracers of metallicity, using sodium and calcium lines to estimate iron abundance and overall metallicity. As such, they are not suited for detailed chemical analysis. Utilizing state-of-the-art stellar atmosphere models, I showed that previous M dwarf metallicity calibrations are more sensitive to carbon and oxygen abundances than they are to overall metallicity. By accounting for the effects of carbon and oxygen, I developed the first calibrated method to directly measure the abundances of individual elements in M dwarfs. I showed that the abundances of iron and titanium can be measured directly from iron and titanium lines in high-resolution Y-band spectra. The relative abundance of titanium to iron correlates with stellar age due to the chemical evolution of the Galaxy. I showed that titanium enhancement combined with kinematics can constrain the ages of individual field M dwarfs. I developed a method to measure chemo-kinematic ages of M dwarfs and used it to investigate the tidal evolution of planets on eccentric, short-period orbits around M dwarfs. I found that short-period planets around M dwarfs can maintain non-zero eccentricities for at least 9 Gyr. Detailed chemical analysis of Sun-like stars is now being carried out by the hundreds of thousands thanks to numerous high-resolution spectroscopic surveys at optical wavelengths. In this dissertation, I reviewed current and planned spectroscopic surveys at near-infrared wavelengths that are amenable to M dwarf abundance analysis and presented a case study design of a compact, high-resolution, near-infrared spectrometer for 5-meter class telescopes.

A major goal of the field of Galactic archeology is to understand the formation and evolution of the Milky Way disk. Stars migrate to different Galactic radii throughout their lifetimes, often leaving little dynamical signature of their initial orbits. Therefore, we need to look at the archaeological record preserved in stellar chemical compositions, which is indicative of their birth environment. In this thesis, we use the measurable properties of stars (chemical compositions and ages) to reconstruct the Milky Way disk's past. First, using hydrodynamical simulations, we find that a star's birth radius and age are linked to its chemical abundances. Subsequently, we learn that even with current-day measurement uncertainty and sample sizes, chemical abundances of Milky Way stars provide a route to reconstructing its formation over time. Extending the insights from hydrodynamical simulations to 30,000 stars observed across the Milky Way disk in the APOGEE survey reveals the importance of using the high-dimensional chemical abundance space. Specifically, we determine that we can use groups of chemically similar stars with 19 measured abundances to trace different underlying formation conditions. Using the high-dimensional abundance data for 10,000 stars from two spectroscopic surveys, APOGEE and GALAH, we empirically describe the chemical abundance trends across a vast radial extent of the Milky Way disk. To do this, we employ a novel approach of quantifying radial variations for individual abundances conditioned on supernovae enrichment history. This enables us to assess the information content in each of the 15 abundances examined and capture the fine-grained signatures in the disk's chemical evolution history. This thesis outlines the potential of using stellar chemistry to trace different evolutionary events of the Milky Way disk, particularly in a time where survey data sample size and precision are growing rapidly.

Large stellar surveys are revealing the chemodynamical structure of the Galaxy across a vast spatial extent. However, the many millions of low-resolution spectra observed to date have not yet been fully leveraged. In chapters 2 and 3, we employ data-driven spectroscopic models to the low-resolution LAMOST survey (𝑅 = 1800). In chapter 2, we employ The Cannon, a data-driven approach for estimating chemical abundances, to obtain detailed abundances, using the GALAH survey as our reference. We deliver five (for dwarfs) or six (for giants) estimated abundances representing five different nucleosynthetic channels, for 3.9 million stars, to a precision of 0.05 - 0.23 dex. Using wide binary pairs, we demonstrate that our abundance estimates provide chemical discriminating power beyond metallicity alone. We show the coverage of our catalogue with radial, azimuthal and dynamical abundance maps, and examine the neutron capture abundances across the disk and halo, which indicate different origins for the in-situ and accreted halo populations. LAM- OST has near-complete Gaia coverage and provides an unprecedented perspective on chemistry across the Milky Way. Stars with unusual levels of enrichment in a particular element are of great interest, but often pose a problem for data-driven methods. In chapter 2, we present a simple method, for the de- tection of 𝑋-enriched stars, for arbitrary elements ?, even from blended lines. Our method does not require stellar labels, but instead directly estimates the counterfactual unrenriched spectrum from other unlabelled spectra. We apply this method to the 6708 Å Li doublet in LAMOST DR5, identifying 8,428 Li-enriched stars seamlessly across evolutionary state. We comment on the ex- planation for Li-enrichement for different subpopulations, including planet accretion, nonstandard mixing, and youth. The Galactic disk exhibits complex chemical and dynamical substructure thought to be induced by the bar, spiral arms, and satellites. In chapter 4, rather than calculating spectroscopic quantities, we use them to understand the Milky Way. We explore the chemical signatures of bar resonances in action and velocity space and characterize the differences between the signatures of corotation and higher-order resonances using test particle simulations. Thanks to recent surveys, we now have large datasets containing metallicities and kinematics of stars outside the solar neighborhood. We compare the simulations to the observational data from Gaia EDR3 and LAMOST DR5 and find weak evidence for a slow bar with the “hat” moving group (250 km s⁻¹ ≲ 𝑣_𝜑i ≲ 270 km s⁻¹) associated with its outer Lindblad resonance and “Hercules” (170 km s⁻¹ ≲ 𝑣_𝜑 ≲ 195 km s⁻¹) with corotation. While constraints from current data are limited by their spatial footprint, stars closer in azimuth than the Sun to the bar’s minor axis show much stronger signatures of the bar’s outer Lindblad and corotation resonances in test particle simulations. Future datasets with greater azimuthal coverage, including the final Gaia data release, will allow reliable chemodynamical identification of bar resonances. Finally, in chapter 5, we present KORG, a new package for 1D LTE (local thermal equilib- rium) spectral synthesis, which computes theoretical spectra from the near-ultraviolet to the near- infrared, and implements both plane-parallel and spherical radiative transfer. It is compatible with automatic differentiation libraries, and easily extensible, making it ideal for statistical inference and parameter estimation applied to large data sets. We outline the inputs and internals of KORG, and compare its output spectra to those produced by other codes. We use five example wavelength regions across 3660 Å – 15050 Å to show that the residuals between KORG and the other codes are no larger than that between existing codes themselves. We show that KORG is 1–100 times faster than other codes in typical use.

Galactic Archaeology aims to understand the formation history of the Milky Way (MW). Observations from large spectroscopic and photometric surveys in the recent over the last decade have revolutionized this field. Many substructures and stellar populations have been discovered thanks to full sky surveys, such as Gaia, suggesting the MW is out of equilibrium. However, with numerous missions providing high-quality spectra and photometric time series for billions of stars, it has become increasingly difficult to interpret multidimensional data. One way to address the challenge of large data ensembles is to convey multidimensional information in a more compact way. This can be done by constructing a set of key summary statistics. In my thesis, I use photometric and abundance data to obtain the ages and birth radii of stars in the MW. These two physical quantities of stars, along with stellar abundances and kinematic measurements provide a ``Galactic timetable'' that marks the locations and times of occurrence of different events including mergers and enhancements in the star formation rate. To infer stellar ages, I use gyrochronology, one of the only viable methods to age-date main-sequence (especially for low-mass K/M dwarfs) stars. This technique uses stellar rotation periods and temperature measurements as age indicators. Due to the complexity of magnetic fields in stars, no purely theoretical gyrochronology model currently exists. As a result, gyrochronology relies strongly on empirical calibrations to known stellar ages using other methods. However, none of the age-dating methods for single field stars are suitable for low-mass main sequence stars, as they are faint and their physical properties evolve slowly. To get ages for these stars, I apply the simple assumption that the velocity dispersion of stars increases over time and adopt an age--velocity--dispersion relation (AVR) to estimate average stellar ages, which we called gyro-kinematic ages, for groupings of stars with similar period, temperature, absolute G magnitude, and Rossby number values. Since calculating gyro-kinematic ages requires a large number of stars with period and kinematic measurements, I measured rotation periods for K and M dwarfs using the Zwicky Transient Facility (ZTF). With conservative vetting criteria, I created the largest rotation period catalog (~ 40,000) for low-mass dwarf stars. By combining open cluster ages from literature and gyro-kinematic ages inferred from stars with 6-D kinematic from Gaia DR3 and rotation periods from Kepler and ZTF, I calibrated a fully empirical gyrochronology relation using Gaussian Processes. This approach is suitable for age-dating dwarf stars between 0.67 - 14 Gyr. Using this newly calibrated relation, I provide the community with the largest and most precise stellar ages for ~ 100,000 low-mass dwarf stars. This is the first time that the approach of gyrochronology has been used to date stars older than 4 Gyr. This sample can be used to study exoplanet evolution and the kinematic sub-structure in the solar neighborhood. Stars move away from their birthplaces over time via a process known as radial migration, which blurs chemo-kinematic relations used for reconstructing the MW formation history. One of the ultimate goals of Galactic Archaeology, therefore, is to understand stars’ birth locations. In my thesis, I first tested the reliability and limitation of the only method \cite{Minchev2018} that is able to infer star by star birth radius. I do so by testing the underlying assumption --- the metallicity gradient is linear at all times --- using the cosmology zoomed-in simulation NIHAO-UHD. This analysis concluded that for the MW, we can infer birth radii with an uncertainty of ~0.5 kpc if the metallicity gradient evolution is known and after the rotationally supported stellar disk has started to form. I then developed a method to recover the time evolution of the stellar birth metallicity gradient, d[Fe/H](R, t)/dR, through its inverse relation to the metallicity range as a function of age today. This allows me to place any star with age and metallicity measurements back to its birthplace, Rb. Applying this method to a high-precision large data set of MW disk subgiant stars, I find a steepening of the birth metallicity gradient from 11 to 8 Gyr ago, which coincides with the time of the last major merger, Gaia-Sausage-Enceladus (GSE). By dissecting the disk into mono-Rb populations, clumps in the low-[alpha/Fe] sequence appear, which are not seen in the total sample and coincide in time with known star-formation bursts.

A new type of astronomical polarimeter is presented that incorporates a fused silica stress-birefringent modulator which simultaneously allows the selection of chopping frequency (≤ 5 Hz) and spectral tuning (1 ≤ λ ≤ 2.5 μm) with very high modulation efficiency. Two integrating detector packages are discussed. The first uses a single germanium photodiode and HR polaroid analyzer and achieves σᵥ = 1% for a J = 14.5 object in 0.5 hr with the MMT. The second package uses a 12 x 30 pixel HgCdTe array and MgF₂ Wollaston prism to provide four simultaneous polarimetric channels that properly eliminate the systematic errors resulting from "staring" mode operation. The instrumental polarizations of the MMT are calculated using Mueller calculus and experimentally verified. It is found that the hexagonal symmetry of the telescope cancels the large amplitude spurious polarizations that arise from the single "arms" and results in a polarimetric efficiency term that is a function only of spectral bandpass and not sky position. Therefore, the MMT behaves essentially like a clean Cassegrain telescope. The continuum polarizations of five isolated highly magnetic white dwarfs are investigated both observationally and theoretically. The most complete broad-band polarimetric survey throughout the spectral region 0.35 ≤ λ ≤ 1.65 μm is performed. An apparent correlation in the linear polarizations of Grw + 70°8247, GD229, and G240-72 is discovered. In addition, no evidence for time-dependent rotation of position angle is found for any of the stars. Hydrogen Balmer photoionization occurring from the magnetically-perturbed bound states into the Coulomb-Lorentz mixed quasi-Landau continuum is investigated with the aid of recent high field calculations. Finally, the continuum polarization of Grw + 70°8247 is compared to models for cyclotron and inverse magnetobremsstrahlung absorptions in a dipolar field. The conclusion is that the continuum polarizations of these objects still eludes an exact description. New observations of BG C Mi reveal the first definitive discovery of polarized cyclotron emission in any intermediate polar and confirms that the long-held basic model of a magnetically accreting white dwarf is correct. The wavelength dependence of circular polarization is found to increase rapidly into the near-infrared, from V(I) = -0.25±0.06% to V(J) = -1.74±0.26% and suggests a field strength in the cyclotron emission region near 5-10 MG if the system scales directly with the AM Her stars.