Simulated Data Sets for the Megamaser Cosmology Project

The Megamaser Cosmology Project (MCP) is an NRAO Key Science Project to measure the Hubble Constant, $H_0$, by determining geometric distances to circumnuclear 22 GHz $\text{H}_2\text{O}$ megamasers in galaxies well into the Hubble flow. Two independent measurements from VLBI mapping and single-dish spectral monitoring are fitted to a 3 dimensional thin disk model to determine the distance to the megamaser host galaxy. This thesis contributes to the MCP by simulating VLBI data sets through which numerous studies on systematic errors and optimizing observations can be accomplished. As a sample analysis, we investigate the relationship between the a priori uncertainties from the observations and the a posteriori distance uncertainty. In particular, we span the observational error space from $(\delta \nu , \delta A) = (0.2 \text{mJy}, 0.05 \text{km/s/yr})$ to $(2.0 \text{mJy}, 0.25 \text{km/s/yr})$, where $\delta \nu$ represents the VLBI mapping noise and $\delta A$ is the uncertainty in acceleration. The nominal value $(\delta \nu , \delta A) = (1.5 \text{mJy}, 0.2 \text{km/s/yr})$ is accepted as the current position of the MCP in the error space; the simulated data set using this value yields a 14\% a posteriori distance uncertainty. To achieve a 10\% distance uncertainty instead, we conclude that an acceleration uncertainty improvement of 0.15 km/s/yr is needed from the current error values.