In my second semester at UT Austin, I joined the White Dwarf Group as part of the Freshman Research Initiative (FRI). FRI is a pioneering two-semester program that enables first-year undergraduates to participate in real-world research projects. Drs. Michael Montgomery and Zachary Vanderbosch, the PIs of the White Dwarf Group, were collecting near-nightly images of a patch of sky over a period of ∼1.5 years to investigate a white dwarf showing signs of transiting planetary debris. However, these observations simultaneously captured nearly 2000 stars in the telescope’s field of view, none of which were being studied as part of the program.

There was a unique opportunity to leverage the exquisite high-cadence dataset of 1560 images and conduct a deep search for short- and long-term variability in these “background” stars. Variable stars and eclipsing binary stellar systems have profound implications in astronomy. Pulsating variable stars are a fundamental part of the cosmic distance ladder, which forms the foundation of cosmology by enabling astronomers to measure distances to galaxies across the universe. Eclipsing binary stellar systems are unique environments to explore their formation, mass transfer, and accretion phenomena.

I performed aperture photometry on 2000+ stars and assembled their light curves. Using the light curves, I generated Lomb-Scargle periodograms and developed an automated procedure to search for high-significance periodicities. I discovered and characterized 27 previously unknown variable stars and eclipsing binaries, a factor of ∼2.5 increase in the number known from previous generations of surveys of the same patch of sky. My work demonstrates the potential for the discovery of new transient objects in long-term imaging observations with next-generation survey facilities like the Vera C. Rubin Observatory.

Associated Papers:
(1) Sanghi, A., Vanderbosch, Z. P., Montgomery, M. H., 2021, AJ, 162, 133

Finding the roots of functions is central to the study of their behavior. Complex roots hold importance in topics such as circuit theory and signal processing. Given any function in the co-ordinate plane, the points at which it intersects the x-axis represent the real roots of the function. However, a function’s complex roots cannot be found by this approach. I deduced that these could be obtained graphically using a complex input. However, a 2D complex input results in a 2D complex output, requiring four-dimensions of space to represent the graph of the function. I developed a dimensionality reduction technique that utilizes the 2D complex input while restricting the output to 1D, i.e., to real numbers. This allows 3D graphical visualization of the complex roots of quadratic and cubic functions in MATLAB. My novel visualization method enhances classroom learning, stimulates original thinking, and offers unique perspectives on topics in undergraduate mathematics.

Associated Papers:
(1) Sanghi, A., 2021, The College Mathematics Journal, 52(5), 373-379