The relatively young field of exoplanets promises exciting new discoveries and insights into other planetary systems much like and unlike our own, thanks to the development of advanced instrumentation, observing techniques and analysis techniques. To date, thousands of nearby exoplanets have been discovered via various methods such as transit detection, radial velocity, astrometry, micro-lensing, and direct imaging. Among these methods, direct imaging is the only method to directly receive photons from the sub-stellar companions that are distinguishable from their host stars. As such, it offers unique characterizations to the surface properties of these companions and offer us rich information on the astrometry, mass, atmospheres and evolution of these objects, especially when combined with all other methods.

Throughout my Astrophysics PhD thesis titled "Characterizing Exoplanets, Brown Dwarfs, and Proto-planetary Disks with High Contrast Imaging", I present an exploration into the development of advanced data analysis techniques for high contrast imaging data, alongside their application in characterizing celestial objects. The introductory chapter provides overviews for the subjects covered in each subsequent chapter. In Chapter 2, I contextualize the significance of direct imaging in characterizing these celestial objects, emphasizing the challenges posed by their extreme contrast and close angular separations from their host stars in ground based imaging. Leveraging sophisticated instrumentation and post-processing algorithms, I introduce the pyKLIP-CHARIS Post-Processing Pipeline within the pyKLIP framework, offering a Python-based data analysis tool for reducing and analyzing observation data taken by the CHARIS instrument on the Subaru Telescope in Hawaii. This pipeline incorporates state-of-the-art algorithms and observing techniques like KLIP, ADI, SDI, and forward modeling for PSF subtraction, facilitating the extraction of precise positions and calibrated planet spectra.

In subsequent chapters, I demonstrate the application of various imaging analysis techniques to measure properties of sub-stellar companions and the scientific insights gained from them. In Chapter 3, I delve into the characterization of a binary brown dwarf system, , utilizing long-term relative orbit monitoring and absolute astrometry data from the VLT. This comprehensive analysis yields precise individual dynamical masses for the binary components, shedding light on their mass-luminosity relationship and providing invaluable benchmarks for substellar cooling models.

In Chapter \ref{chap:disk}, my research extends to the investigation of a proto-planetary disk around HD 34700 A. Leveraging CHARIS' unique capability to obtain polarized integral field images, I gain access to the intricate structures of the disk at multiple wavelengths, and explore their implications through 3D Monte Carlo radiative transfer simulations. These simulations, combined with observed polarized intensity data, offer insights into the dust grain properties and scattering mechanisms within the disk, highlighting the complexities inherent in modeling such systems.

Finally, in Chapter \ref{chap:gl504}, I conclude my research with an on-going investigation on the infra-red spectra of two ultra-cool T-dwarfs, Gl~758~B and Gl~504~b. These are two of the coldest brown dwarfs observed so far. They share very similar host star properties and provides invaluable insight to understanding brown dwarfs atmospheres at temperatures of 500-600 K. A special beam-steering mode on the \SCExAO and \CHARIS instrument was required to capture these widely separated companions and poses unique data analysis challenges. I emphasize these challenges and the solutions that employed to address them, along with preliminary results on the astrometry and the extracted spectra of these two brown dwarfs.

Extra-solar planets, brown dwarfs, and low-mass stars are distinct astronomical objects that encompass a wide range of masses, occupying the lower end of the mass and temperature spectrum within the vastness of the Universe. These cool objects’ peak emission occurs at longer wavelengths in the red and infrared regions. They present abundant avenues for observational and theoretical exploration, facilitating the study of their evolutionary pathways. It is believed that stars are born from gravitational collapse of molecular clouds of gas and dust that are scattered throughout most galaxies over thousands to millions of years. The hot core of the collapsing cloud will form a protostar with fast rotation. Some of these spinning clouds of collapsing gas and dust break up into two or three blobs that each form stars which later become multiple systems. The crucial factor setting these objects apart lies in their initial masses, which provide valuable insights into their formation mechanisms and their post-formation evolution. Stars (≥ 80MJup), including low-mass stars like M dwarfs, are self-luminating entities that sustain nuclear fusion in their cores, generating energy through the fusion of hydrogen atoms. Brown dwarfs occupy a mass range between that of the heaviest gas giant planets and the lightest stars (∼ 15− ∼ 80MJup), they fall short of the mass required for sustained hydrogen burning and do not possess a stable energy-generating mechanism. They briefly undergo deuterium burning during their early formation stages, but this process is not sustainable in the long term. Planets (∼ < 15MJup), distinct from stars and brown dwarfs, lack an inherent energy generation process and primarily emit radiation received from their host star and residual internal heat from their formation. Their energy output is primarily determined by the absorbed and reflected light from their parent star. The distinction between these objects is crucial as it helps us classify and study the vast diversity of objects beyond our solar system, providing insights into their formation, evolution, and the conditions that allow for the existence of habitable planets. If one can determine the mass of a detected object empirically and independently, it not only helps confirm the nature of the object but also tests and informs evolutionary models of substellar or sometimes stellar evolution. The work in this thesis expands the sample of planets and brown dwarfs whose dynamical masses and orbits are empirically measured, in order to chart the vast substellar evolutionary landscape spanning the entire range of masses.

Before the Gaia satellite, the detection of directly imaged brown dwarfs and giant planets orbiting main-sequence stars was a rare occurrence. Merely a small collection of approximately thirty such objects had been identified, and only a fraction of them possessed independently measured masses. These masses, determined through the observation of orbital dynamics, are known as dynamical masses and are regarded as the most reliable and independent measurements, as they do not rely on cooling or evolutionary models. The work undertaken in this thesis focuses specifically on attaining precise mass measurements using the synergistic capabilities of the Hipparcos and Gaia astrometric missions. By combining multiple observation data types, namely Radial Velocity (RV), relative astrometry, and absolute astrometry, one can determine the 3D Keplerian orbit and the precise dynamical mass of a potential, presumably faint companion orbiting a star by measuring the reflex motion of the star in the sky as it responds to the gravitational tug exerted by the unseen companion in orbit.

In Chapter 2, we demonstrate the powerful combination of radial velocities, direct imaging, and Hipparcos and Gaia absolute astrometry via the Hipparcos-Gaia Catalog of Accelerations (HGCA) to achieve highly accurate dynamical mass measurements. To accomplish this, we utilize the Markov-Chain-Monte-Carlo code orvara, along with the epoch astrometry fitting code htof, which enable us to effectively constrain orbits using these three distinct sources of data. By employing orvara, we successfully address the inherent degeneracy in determining an exoplanet’s mass and inclination encountered in RV-only studies by incorporating absolute astrometry in conjunction with radial velocity. Moving on to Chapter 3, we focus on astrometry-only data, using Gaia EDR3 to calibrate ground-based relative and absolute astrometry from VLT/ESO, to precisely determine the barycentric orbit of ε Indi B, one of the closest and the first discovered binary T dwarf systems. These measurements establish them as the most accurately characterized binary brown dwarfs to date, and enable both a relative and absolute test of currently available substellar cooling models. In Chapter 4 and Chapter 5, we present the detection results from our pilot observation program conducted at the Keck/NIRC2 instrument, aiming to identify and image substellar companions around nearby accelerating stars. By utilizing the valuable precursor information from orvara and HGCA, we are able to predict the precise location of the companion a priori, detect the companion with direct imaging, and jointly fit orbits to their data to obtain precise dynamical masses. Our work significantly enhances the success rate of high-contrast imaging surveys, and can serve as a powerful tool for selecting promising follow-up candidates for interferometry and spectroscopic characterizations with instruments like JWST and GRAVITY/KPIC.

It is reasonable to suppose that a typical newborn star or brown dwarf inherits much of its progenitor molecular cloud’s angular momentum. This leads to the suggestion that such an object ought to have a rotational velocity that is close to the Keplerian breakup limit, resulting in significant centrifugal expansion at the equator. According to models of internal energy transport, this expansion ought to make the poles of a rotator significantly hotter than its equator, so that the inclination of its rotational axis greatly affects both the shape of its observed spectrum and its total observed flux. These predictions are consistent with the interferometric and spectroscopic observations of stellar and sub-stellar objects whose rotational speeds are frequently at appreciable fractions of the Keplerian limit.

In particular, the oblate shapes, surface temperature variations, and spectral line broadening of many early-type stars indicate large rotational velocities. Via its effects on surface temperature and shape, rotation has a significant effect on these stars’ spectra. Thus, in order to infer the structural and life history parameters of these objects from their spectra, one must carefully integrate specific intensity over the two-dimensional surfaces of corresponding stellar models. Toward this end, in Chapter 2, we offer PARS (Paint the Atmospheres of Rotating Stars) – an integration scheme based on models that incorporate solid body rotation, Roche mass distribution, and collinearity of gravity and energy flux (Lipatov & Brandt, 2020a). The scheme features a closed-form expression for the azimuthal integral, a high-order numerical approximation of the longitudinal integral, and a precise calculation of surface effective temperature at rotation rates up to 99.9% of the Keplerian limit. Extensions of the scheme include synthetic color-magnitude diagrams and planetary transit curves. An important input to PARS in Chapter 2 is a grid of specific intensities for stellar plane-parallel atmosphere models, ATLAS9.

Much like the observations of early-type stars, spectroscopy and time-resolved photometry of brown dwarfs are frequently indicative of rotational velocities that are comparable to the breakup limit. Accordingly, in Chapter 3, we apply PARS to parameter inference in the case of rotating brown dwarfs, exploring the dependence of these sub- stellar objects’ observables on rotational speed and axis inclination. In this case, instead of specific intensities for stellar atmosphere models, we feed PARS an intensity grid that is appropriate for brown dwarfs, computed by PICASO (a Planetary Intensity Code for Atmospheric Spectroscopy Observations) from Sonora brown dwarf 1D climate and chemistry models. We find that the specific flux of a typical fast-rotating brown dwarf can increase by as much as a factor of 1.5 with movement from an equator-on to a pole-on view. On the other hand, the distinctive effect of rotation on spectral shape increases toward the equator-on view. The latter effect also increases with lower effective temperature. The bolometric luminosity estimate for a typical fast rotator at extreme inclinations has to be adjusted by as much as ∼ 20% due to the anisotropy of the object’s observed flux. We provide a general formula for the calculation of the corresponding adjustment factor in terms of rotational speed and inclination.

Rotation does not only directly affect the spectra of present-day stars, it also significantly alters the evolution of stars throughout their lives, chiefly via its effect on stellar internal transport. By means of both the direct and the evolutionary effects, stellar rotation is possibly responsible for the fact that the color-magnitude diagrams (CMDs) of intermediate-age star clusters (≲2 Gyr) are much more complex than those predicted by coeval, non-rotating stellar evolution models. The clusters’ observed extended main sequence turnoffs (eMSTOs) could result from variations in stellar age, stellar rotation, or both. The physical interpretation of eMSTOs is largely based on the complex mapping between stellar models—themselves functions of mass, rotation, orientation, and binarity—and the CMD. In Chapter 4, we compute continuous probability densities in three-dimensional color, magnitude, and vsini (i.e., projected equatorial velocity) space for individual stars in a cluster’s eMSTO, based on a rotating stellar evolution model. These densities enable the rigorous inference of cluster properties from a stellar model, or, alternatively, constraints on the stellar model from the cluster’s CMD. We use the MIST stellar evolution models to jointly infer the age dispersion, the rotational distribution, and the binary fraction of the Large Magellanic Cloud cluster NGC 1846. We derive an age dispersion of ∼ 70 − 80 Myr, approximately half the earlier estimates due to non-rotating models. This finding agrees with the conjecture that rotational variation is largely responsible for eMSTOs. However, the MIST models do not provide a satisfactory fit to all stars in the cluster and achieve their best agreement at an unrealistically high binary fraction. The lack of agreement near the main-sequence turnoff suggests specific physical changes to the stellar evolution models, including a lower mass for the Kraft break and potentially enhanced main sequence lifespans for rapidly rotating stars.

Brown dwarfs are sub-stellar objects that span the enormous range in mass from $\sim15\Mjup$ to $\sim80\Mjup$. The internal physics and temporal evolution of these objects are remarkably similar across the entire range of mass, albeit massive brown dwarfs cool to a given luminosity more slowly than lighter ones. Giant planets (masses between $\sim1$ and $\sim15\Mjup$) behave very similarly. Electron degeneracy causes these objects to all have similar radii, almost independent of both mass and temperature. These objects do not fuse hydrogen. Thus, the luminosity of a brown dwarf simply decreases over time due to the steady radiative loss of the brown dwarf's internal energy. Most observational evidence points to these objects forming ``hot'' (so-called hot-starts), whereby most the energy of their formation is retained and so their internal energy is set at birth and is solely a function of their initial mass, much like how the number of grains in an hourglass is fixed. Under the hourglass analogy, the mass is the total amount of sand trapped the hourglass and the observed luminosity is akin to the number of grains remaining in the top reservoir. Adding in knowledge of the energy-loss (sand-grain) rate from cooling models, one can calculate the age of the companion (i.e., when the hourglass was flipped). Thus, brown dwarfs have a unique advantage compared to e.g., rocky planets. If one has a precisely measured luminosity and a stellar age, one can predict from the cooling-models what the mass of that object ought to be. Conversely, if one has a precisely measured mass and luminosity, one can determine when the brown dwarf was born and hence age date the host system and every planet therein. Unfortunately, both those above scenarios are subject to uncertainties in, and slight differences between, the various models of brown dwarf evolution. The goal is not to use cooling models to infer the third quantity when two are known, but rather to measure all three: the mass, luminosity, and the age of the brown dwarf, \textit{independent} of evolutionary models. Then one can actually test and inform models of brown dwarf evolution. The work in this thesis moves towards that end goal: expanding the sample of brown dwarfs and giant planets where all three quantities are measured so that we may advance our understanding of sub-stellar evolution across the entire mass range of $\sim1\Mjup$ to $\sim80\Mjup$.

In the decade preceding the launch of the \gaia satellite, directly imaged brown dwarfs and giant planets (which orbited main-sequence stars) were rare. Of order twenty were known, and only a small fraction had an independently measured mass. Masses measured via observing the orbit of the companion are referred to as dynamical masses, because the mass measurement relies only on Newtonian dynamics. These are the gold-standard of independent mass measurements (``independent'' because they do not rely on cooling/evolutionary models).

In order to: 1. test models of brown dwarf and giant planet evolution; 2. provide independent age estimates of a stellar system; and 3. test models of brown dwarf atmospheres; one needs not only more brown dwarfs, but a dynamical mass for each. On one front, \gaia enabled the discovery and subsequent confirmation of many more brown dwarfs companions (of-order 100 in only 4 years; by 2025, \gaia alone is expected to detect 20,000-70,000 companions across a broad range of mass). The work in this thesis has worked precisely towards the second front of producing precise mass measurements, independent ages, and tests of brown dwarf evolutionary models. The key is leveraging the synergy between the \hipparcos and \gaia astrometric missions, which allows us to measure a precise mass for companions around stars by measuring the reflex motion of the star in the sky as the unseen, orbiting companion tugs the star.

In Chapter \ref{chap:betapicbc}, we resolve a tension between the dynamical mass of the giant planet $\beta$~Pictoris~b and the model-predicted mass based on its luminosity and host-star age. We showcase how one can combine the radial-velocities of the star, direct imaging, and \hipparcos and \gaia reflex motion (via the Hipparcos-Gaia Catalog of Accelerations), to obtain an excellent dynamical mass measurement. We utilize the Markov-Chain-Monte-Carlo code, \texttt{orvara}, and the astrometry parsing code \texttt{htof}, to constrain orbits using those three separate sources of data. In Chapter \ref{chap:HR8799}, we use those same methods to obtain the mass, for the first time ever, of the planet HR~8799~e. From the mass, we obtain a measure of the planet's age and thereby the age of the star. HR~8799 is a star whose cluster membership is uncertain, and so an independently measured age is one way to finally assign the birthplace of the HR~8799 system. In Chapter \ref{chap:BrownDwarfs}, we use all the aforementioned techniques to update the masses and orbits of six brown dwarfs, including the cornerstone and puzzling ``over-massive'' system, Gl~229. This thesis concludes with a detailed recalibration of \hipparcos, in Chapter \ref{chap:HipMerger}, to enable better mass measurements in future works. In addition, Chapter \ref{chap:HipMerger} addresses a long standing question surrounding overfitting in the second \hipparcos data reduction.