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Time domain astronomy is a thriving field, allowing astronomers to discover and characterize variables such as exoplanets, quasars, stellar variables, and more. However, with the advent of wide-field sensitive surveys at high observing cadence, analyzing these data present unique challenges. This dissertation considers methods of detecting and characterizing variables and exoplanets in computationally efficient ways and explores their statistical sensitivity.
I consider the Vera Rubin Observatory (VRO) Legacy Survey of Space and Time (LSST), which is set to start regular operations in 2024. This survey will observe a large area of the southern sky over 10 years, detecting 17 billion resolved stars. LSST is not optimized for exoplanet science but presents a unique opportunity to contribute to this field as a secondary science objective. As the transit depth of a super-Earth exoplanet around an M6V dwarf star is as deep as a Hot Jupiter transiting a solar-type star, I explore the likelihood that LSST will be able to detect an M dwarf system with transiting exoplanets given the scientific importance of such systems. Short transit duration exoplanets of this type present a computationally expensive detection problem given the required sampling in orbital phase and frequency when using a common algorithm such as the Box Least Squares (BLS) method.
I show that this computational complexity can be mitigated using scientifically and mathematically supported sampling mitigations. Using this modified application of BLS in a high performance computing (HPC) setting, I find that up to 83.7\% of $2.5 R_{\oplus}$ planets orbiting an M6 star at a distance $d=100$ pc and with periods $P\leq 3$ days are recoverable in the LSST Deep Drilling observing cadence.
Furthermore, I conservatively estimate that it is possible to detect transits of $\gtrsim$ 7 closely orbiting super-Earths and Earths around nearby M6V stars over the 10 year LSST survey.
I also consider the identification and characterization of variable objects in the Dark Energy Survey (DES) Supernova fields (DES-SN), which have higher observing cadences. Identifying variable astrophysical objects is crucial to current and future wide-field astronomical surveys, as these objects provide a rich opportunity to provide limits for physical constraints on inherent variability mechanisms. The Damped Random Walk (DRW) algorithm that leverages the Kalman filter was used to generate a unique Dark Energy Survey Variability catalog (DESVAR\_DR2, accessible via Github). This catalog yields a complete census of single-band and multi-band variables within the DES-SN fields. This catalog characterizes stellar variables and active galactic nuclei, finding a total of 61,898 robust variable objects.
Finally, I explore an application of the BLS method to simulated exoplanet light curves with cadences matching the DES-SN fields. This assessment of the sensitivity and bias of this method for the DES-SN observing cadence and DES photometric noise model is a crucial first step in understanding the potential contribution of DES to exoplanet science. This work shows that cadences in the DES-SN fields with the minimum number of observations are not ideal for exoplanet identification, with a maximum exoplanet recovery rate of only $\sim 30\%$. I further find in these simulation studies that only $\sim42\%$ of all Warm Neptunes around K7V stars would be detected with a maximal shallow field DES-SN cadence. However, DES is more suited to detecting either Hot Jupiters around solar-type stars or super-Earths orbiting M dwarf stars for cadences that have either the median or maximum number of observations for the DES-SN shallow fields.
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