A long-standing goal of exoplanet astronomy is to understand the physics that determines whether or not a planet could support life. An important, but poorly-understood, aspect of planetary habitability is the role of geophysics. Here on Earth, the decay of radiogenic isotopes heats the interior and drives plate tectonics that support geochemical cycles that maintain the stability of our climate over geologic time scales. Whether such cycles are common or rare among exoplanets is an open question. A further complication is tidal heating — while not significant on Earth, it may provide a large source of heat for potentially habitable planets around low-mass stars. To explore these processes, we simulate the evolution of Earth-like exoplanets over a range of radiogenic and tidal powers. We find that, depending on the radiogenic abundances and magnitude of tidal heating, planets may be unable to support a magnetic field or experience extreme volcanism, both of which could be detrimental to life. These results suggest the geophyisical evolution of exoplanets may be a determining factor in the habitability of some exoplanets, such as Proxima Centauri b and members of the Trappist-1 system.

The Kepler Space Telescope was designed to detect exoplanets by measuring the change in light received as target planets pass between their host stars and Earth. After the failure of two Kepler reaction wheels, the pointing capability required for high-accuracy transit detection was lost. To reduce the noise generated by unstable pointing, the space telescope was aligned to be held stable by the photon pressure from the sun, and the telescope entered a second phase of observation called K2. Although this reconfiguration still detects transits, the precision has decreased resulting in fewer exoplanet discoveries than Kepler. The EVEREST (EPIC Variability Extraction and Removal for Exoplanet Science Targets) pipeline was developed to remove instrumental noise from K2 data and increase the detection capabilities of the telescope. Due to the failed reaction wheels, Kepler targets have motion relative to the detector. EVEREST uses a detrending method called pixel level decorrelation (PLD), which uses the flux measured in each pixel to account for the motion of the star. One possible source of noise is variation in the quantum efficiency between pixels as the star moves across the detector. This includes inter-pixel variation globally on the detector and intra-pixel variation from the center of pixels to their edges. My research characterizes the sensitivity variation of the detector and its impact on the light curves of Kepler targets. I am developing methods using python to simulate a K2 star with a planet, modelling the sensitivity variation, and using this model to test the power of PLD. Preliminary results indicate that defining apertures to limit total flux results in higher accuracy light curves. My research also aims to apply the results to the EVEREST pipeline, as the combination of PLD and sensitivity variation modeling could result in the highest accuracy publicly available K2 data to date.

People have an instinctive understanding of what it means for an object to be three-dimensional: it has height, width, and length. There is similar familiarity with two-dimensional shapes like squares and triangles, as well as one-dimensional shapes such as lines. The dimensions of some objects, on the other hand, cannot be understood in this familiar way. Take, for example, a set of points in the xy-plane that do not form a straight line or any familiar shape from geometry. One way to measure the dimension of these objects is to calculate the Hausdorff dimension of the set of underlying points. Intuitively, the Hausdorff dimension is a measure of how many small boxes it would take to cover an object. Our research aimed to calculate the Hausdorff dimensions of more complicated curves, such as those arising from Brownian motion, which is a probabilistic model for a randomly moving particle. In particular, we set out to corroborate known results about the Hausdorff dimensions of Brownian motion and the Brownian frontier. Further, we wanted to strengthen unsolved conjectures regarding the Hausdorff dimension of the Brownian earthworm model, which is a model of mass redistribution on the d-dimensional integer lattice introduced by Professor Krzysztof Burdzy. We attempted to develop answers to these problems by simulating Brownian motion in two dimensions and performing statistical analysis on our results. Our model correctly calculated the known dimensions and was in line with Professor Burdzy’s previous conjecture regarding the Brownian earthworm. It is our goal that this research will ultimately contribute to a greater understanding of the earthworm model.

At low obliquity, planets like Earth will tend to form permanent ice sheets at the poles, if anywhere. However, at high obliquity, the poles receive more sunlight on average than the tropics, and so ice sheets might be expected to form at the equator. We have used a simple energy balance model for investigating the orbital, atmospheric, and obliquity parameters that allow for the formation of permanent ice at the equator. We find there is a narrow range of semi-major axis and obliquity values that allow for such “ice-belts”. First, we experimented with the range of stability of ice-belt formation by increasing the semi-major axis to the edge of the habitable zone, increasing CO2 levels to counteract the decrease in solar flux. This led to a very small range of conditions that allow for stable ice-belts. To further investigate the cause of this, we decreased the luminosity of the host star while increasing CO2 levels (to simulate the control temperatures). This stabilizes the otherwise unstable system, although the range of ice-belt formation is still narrow. Further, we find that this equatorial ice formation often leads to instability due to the ice-albedo feedback. This work suggests that it should not be common for Earth-like worlds at high obliquity to maintain large ice sheets.