Classical Cepheids, like binary stars, are laboratories for stellar evolution and Cepheids in binary systems are especially powerful ones. About one-third of Galactic Cepheids are known to have companions and Cepheids in eclipsing binary systems have recently been discovered in the Large Magellanic Cloud (LMC). However, there are no known Galactic binary Cepheids with orbital periods less than one year. We compute population synthesis models of binary Cepheids to compare to the observed period and eccentricity distributions of Galactic Cepheids as well as to the number of observed eclipsing binary Cepheids in the LMC. We find that our population synthesis models are consistent with observed binary properties of Cepheids. Furthermore, we show that binary interaction on the red giant branch prevents some red giant stars from becoming classical Cepheids. Such interactions suggest that the binary fraction of Cepheids should be significantly less than that of their main-sequence progenitors, and that almost all binary Cepheids have orbital periods longer than one year. If the Galactic Cepheid spectroscopic binary fraction is about 35%, then the spectroscopic binary fraction of their intermediate mass main sequence progenitors is about 40- 45%.

In this dissertation, we develop new tools for the study of stellar atmospheres, pulsating stellar atmospheres and mass loss from pulsating stars. These tools provide new insights into the structure and evolution of stars and complement modern observational techniques such as optical interferometry and high resolution spectroscopy. In the first part, a new spherically symmetric version of the Atlas program is developed for modelling extended stellar atmospheres. The program is used to model interferometric observations from the literature and to study limb-darkening for stars with low gravity. It is determined that stellar limb-darkening can be used to constrain fundamental properties of stars. When this is coupled with interferometric or microlensing observations, stellar limb-darkening can predict the masses of isolated stars. The new SAtlas program is combined with the plane-parallel hydrodynamic program Hermes to develop a new spherically-symmetric radiative hydrodynamic program that models radial pulsation in the atmosphere of a star to depths including the pulsation-driving regions of the stars. Preliminary tests of this new program are discussed. In the second part, we study the recent observations of circumstellar envelopes surrounding Cepheids and develop a mass-loss hypothesis to explain their formation. The hypothesis is studied using a modified version of the Castor, Abbott, & Klein theory for radiative-driven winds to contain the effects of pulsation. In the theory, pulsation is found to be a driving mechanism that increases the mass-loss rates of Cepheids by up to four orders of magnitude. These mass-loss rates are large enough to explain the formation of the envelopes from dust forming in the wind at large distances from the surface of the star. The mass-loss rates are found to be plausible explanation for the Cepheid mass discrepancy. We also compute mass-loss rates from optical and infrared observations of Large Magellanic Cloud Cepheids from the infrared excess and find mass loss to be an important phenomena in these stars. The amount of infrared excess is found to potentially affect the structure of the infrared Leavitt law.

In this dissertation, we develop new tools for the study of stellar atmospheres, pulsating stellar atmospheres and mass loss from pulsating stars. These tools provide new insights into the structure and evolution of stars and complement modern observational techniques such as optical interferometry and high resolution spectroscopy. In the first part, a new spherically symmetric version of the Atlas program is developed for modelling extended stellar atmospheres. The program is used to model interferometric observations from the literature and to study limb-darkening for stars with low gravity. It is determined that stellar limb-darkening can be used to constrain fundamental properties of stars. When this is coupled with interferometric or microlensing observations, stellar limb-darkening can predict the masses of isolated stars. The new SAtlas program is combined with the plane-parallel hydrodynamic program Hermes to develop a new spherically-symmetric radiative hydrodynamic program that models radial pulsation in the atmosphere of a star to depths including the pulsation-driving regions of the stars. Preliminary tests of this new program are discussed. In the second part, we study the recent observations of circumstellar envelopes surrounding Cepheids and develop a mass-loss hypothesis to explain their formation. The hypothesis is studied using a modified version of the Castor, Abbott, & Klein theory for radiative-driven winds to contain the effects of pulsation. In the theory, pulsation is found to be a driving mechanism that increases the mass-loss rates of Cepheids by up to four orders of magnitude. These mass-loss rates are large enough to explain the formation of the envelopes from dust forming in the wind at large distances from the surface of the star. The mass-loss rates are found to be plausible explanation for the Cepheid mass discrepancy. We also compute mass-loss rates from optical and infrared observations of Large Magellanic Cloud Cepheids from the infrared excess and find mass loss to be an important phenomena in these stars. The amount of infrared excess is found to potentially affect the structure of the infrared Leavitt law.

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.

Measurements of rates of period change of Classical Cepheids probe stellar physics and evolution. Additionally, better understanding of Cepheid structure and evolution provides greater insight into their use as standard candles and tools for measuring the Hubble constant. Our recent study of the period change of the nearest Cepheid, Polaris, suggested that it is undergoing enhanced mass loss when compared to canonical stellar evolution model predictions. In this work, we expand the analysis to rates of period change measured for about 200 Galactic Cepheids and compare them to population synthesis models of Cepheids including convective core overshooting and enhanced mass loss. Rates of period change predicted from stellar evolution models without mass loss do not agree with observed rates, whereas including enhanced mass loss yields predicted rates in better agreement with observations. This is the first evidence that enhanced mass loss as suggested previously for Polaris and δ Cephei must be a ubiquitous property of Classical Cepheids.

Supermassive black holes (SMBH) are now thought to exist at the center nearly all massive galaxies. Not only are they thought to be ubiquitous, but it was also discovered nearly two decades ago that the mass of these SMBHs correlate strongly with properties of their host galaxies including bulge stellar velocity dispersion (MBH-sigma) and bulge luminosity (MBH-Lbulge). This correlation was not expected due to the tiny size of the SMBH gravitational sphere of influence compared to the size of the host galaxy, and imply a connection between the two, but this connection is still not well-understood. One step toward understanding this connection is to accurately measure the masses of these black holes. Two of the most common direct SMBH mass measurement techniques are stellar dynamical modeling (SDM), which generally only applies to quiescent galaxies, and reverberation mapping (RM), which can only be applied to active galactic nuclei (AGN) that exhibit broadened emission lines. Due to the unknown geometry of the region that produces these broad lines, the whole RM sample of black hole masses generally needs to be multiplied by a constant called the f-factor to bring it into agreement with the SDM sample on the MBH-sigma relation. It is unknown how well this f-factor, being a population average, applies to individual RM masses. It would therefore be useful to measure an SMBH mass with both methods simultaneously to test whether they produce the same black hole mass. However, because the RM and SDM techniques usually apply to galaxies that are not possible for both, this has only been attempted twice before (NGC 3227 and NGC 4151). The purpose of this dissertation is to apply SDM to the SMBH at the center of NGC 6814 for which there already exists an RM mass. This makes it only the third broad-lined AGN for which an SDM mass has been derived. In order to perform SDM accurately, the distance to the galaxy needs to be well-constrained as the error in the SDM mass scales linearly with distance. Because no adequate distance measurements already exist, the first half of this dissertation is devoted to deriving a Cepheid distance to NGC 6814 from V- and I-band HST WFC3 time series photometry. We measure the distance to NGC 6814 to be 17.54 +1.44/-1.33 Mpc. In the second half, we incorporate that distance measurement into our stellar dynamical modeling on Gemini NIFS+Altair IFU data of NGC 6814's central 1.55''x1.55''. We derive a mass of 1.19 +37.57/-1.17 x108 solar masses, and best fit mass-to-light ratio of 0.948 +0.032/-0.208 in solar units. This mass is nearly an order of magnitude larger than the RM mass but has a 3-sigma range spanning nearly three orders of magnitude. We describe possible reasons for our larger-than-expected mass value, such as the existence of a bar, which would not be well-modeled by an axisymmetric dynamical code. Finally, we describe future steps that may be taken to better constrain the mass, such as creating more models to further explore parameter space.

Using high resolution optical spectra from Mount John University Observatory, Mount Stromlo Observatory and the Anglo-Australian Observatory, new, high accuracy radial velocity curves have been obtained for the two bright southern Cepheids l carinae (HR 3884) and beta doradus (HR 1922). An indepth investigation into period variations, cycle-to-cycle and long-term variations in the velocity curves and the reliability of the combination of velocity data from different observatories is carried out. Evidence for shock waves in the atmosphere of l car and resonance in beta dor is discussed. A grid of static model atmospheres incorporating plane-parallel geometry is compared with the observational spectra of both Cepheids, using line depth ratios, to determine the variation in effective temperature, surface gravity and microturbulence with phase. This information is used to determine the phase dependence of the surface-brightness for both Cepheids. The surface brightness variation with phase was found to follow an almost linear relationship. The distance to and radius of the Cepheids are determined using both a near-infrared version of the Barnes-Evans method and the Fourier Baade-Wesselink (BW) method. The derived radii and distances agree within the limits of the errors for both methods. The Fourier BW method was found to be very sensitive to phase shifts between the photometric and spectroscopic data and the derived distance highly dependent on the assumed reddening. An investigation into line profile variations in l car and beta dor has revealed the magnitude of these phenomena increase as the pulsational period of the Cepheid increases. It is estimated that line level variations introduce an additional uncertainty into derived radii of approximately 4 per cent for beta dor and 10 per cent in lcar. The uncertainty introduced into derived distances and radii by line profile asymmetries was estimated to be of the order of 6 per cent in beta dor and 10 per cent in l car. A comparative analysis is made of the hydrogen line radial velocity curves of l car and beta dor. A trend in the properties of these radial velocity curves with period has been revealed. In longer period Cepheids, the Halpha line seems to be forming in a region that does not partake in the pulsation as a whole, probably in a chromospheric shell. A quantitative analysis of the asymmetries in these lines reveal large redward asymmetries near maximum infall velocity. The magnitude of these asymmetries and the period for which they are present are larger in l Car than in beta dor. The blueward asymmetries in the Halpha line in l Car are comparable in magnitude to the redward asymmetries while the other lines exhibit only small blueward asymmetries. A qualitative analysis of these line profiles with phase reveal no conclusive evidence for line doubling in these Cepheids. Evidence of emission is found in the Halpha and H Beta lines of beta dor and l car. The strength and duration of the emission is found to be greater in the longer period Cepheid. Although it is likely that this emission is shock-related, theoretical work is needed to determine the exact origin of the emission. A non-LTE radiative hydrodynamic model for l Car has been created. This atmosphere will be used in further work to calculate synthetic spectral line profiles which will aid the interpretation of our observational results.

Using high resolution optical spectra from Mount John University Observatory, Mount Stromlo Observatory and the Anglo-Australian Observatory, new, high accuracy radial velocity curves have been obtained for the two bright southern Cepheids l carinae (HR 3884) and beta doradus (HR 1922). An indepth investigation into period variations, cycle-to-cycle and long-term variations in the velocity curves and the reliability of the combination of velocity data from different observatories is carried out. Evidence for shock waves in the atmosphere of l car and resonance in beta dor is discussed. A grid of static model atmospheres incorporating plane-parallel geometry is compared with the observational spectra of both Cepheids, using line depth ratios, to determine the variation in effective temperature, surface gravity and microturbulence with phase. This information is used to determine the phase dependence of the surface-brightness for both Cepheids. The surface brightness variation with phase was found to follow an almost linear relationship. The distance to and radius of the Cepheids are determined using both a near-infrared version of the Barnes-Evans method and the Fourier Baade-Wesselink (BW) method. The derived radii and distances agree within the limits of the errors for both methods. The Fourier BW method was found to be very sensitive to phase shifts between the photometric and spectroscopic data and the derived distance highly dependent on the assumed reddening. An investigation into line profile variations in l car and beta dor has revealed the magnitude of these phenomena increase as the pulsational period of the Cepheid increases. It is estimated that line level variations introduce an additional uncertainty into derived radii of approximately 4 per cent for beta dor and 10 per cent in lcar. The uncertainty introduced into derived distances and radii by line profile asymmetries was estimated to be of the order of 6 per cent in beta dor and 10 per cent in l car. A comparative analysis is made of the hydrogen line radial velocity curves of l car and beta dor. A trend in the properties of these radial velocity curves with period has been revealed. In longer period Cepheids, the Halpha line seems to be forming in a region that does not partake in the pulsation as a whole, probably in a chromospheric shell. A quantitative analysis of the asymmetries in these lines reveal large redward asymmetries near maximum infall velocity. The magnitude of these asymmetries and the period for which they are present are larger in l Car than in beta dor. The blueward asymmetries in the Halpha line in l Car are comparable in magnitude to the redward asymmetries while the other lines exhibit only small blueward asymmetries. A qualitative analysis of these line profiles with phase reveal no conclusive evidence for line doubling in these Cepheids. Evidence of emission is found in the Halpha and H Beta lines of beta dor and l car. The strength and duration of the emission is found to be greater in the longer period Cepheid. Although it is likely that this emission is shock-related, theoretical work is needed to determine the exact origin of the emission. A non-LTE radiative hydrodynamic model for l Car has been created. This atmosphere will be used in further work to calculate synthetic spectral line profiles which will aid the interpretation of our observational results.

Classical Cepheids form one of the foundations of modern cosmology and the extragalactic distance scale; however, cosmic microwave background observations measure cosmological parameters and indirectly the Hubble Constant, H 0, to unparalleled precision. The coming decade will provide opportunities to measure H0 to 2% uncertainty thanks to the Gaia satellite, JWST, ELTs and other telescopes using Cepheids and other standard candles. In this work, we discuss the upcoming role for variable stars and asteroseismology in calibrating the distance scale and measuring H0 and what problems exist in understanding these stars that will feed back on these measurements.

Measurements of secular period change probe real-time stellar evolution of classical Cepheids making these measurements powerful constraints for stellar evolution models, especially when coupled with interferometric measurements. In this work, we present stellar evolution models and measured rates of period change for two Galactic Cepheids: Polaris and l Carinae, both important Cepheids for anchoring the Cepheid Leavitt law (period-luminosity relation). The combination of previously-measured parallaxes, interferometric angular diameters and rates of period change allows for predictions of Cepheid mass loss and stellar mass. Using the stellar evolution models, We find that l Car has a mass of about 9 M S™ consistent with stellar pulsation models, but is not undergoing enhanced stellar mass loss. Conversely, the rate of period change for Polaris requires including enhanced mass-loss rates. We discuss what these different results imply for Cepheid evolution and the mass-loss mechanism on the Cepheid instability strip.