Statistical Modeling and Beam Analysis for the Redshifted Global 21 Centimeter Signal

Undergraduate Honors Thesis

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Citeable URL: https://scholar.colorado.edu/concern/undergraduate_honors_theses/41687h81f

Abstract

This thesis explores two aspects of measurements of the global 21 cm signal through analytical simulations. We first attempt to understand how well the global 21 cm signal could be extracted from measurements of the sky. We accomplish this by employing a Fisher matrix analysis to estimate the uncertainties of cosmological parameters for simple measurement models that assume a perfectly calibrated instrument. We find that the assumed parameters of the signal can be constrained to high precision under realistic scenarios of noise and foreground contaminants. We also study the bias in the cosmological parameters due to modeling errors using a Fisher matrix approach. We find that for all cases studied, which correspond to simple frequency independent and frequency dependent model errors smaller than the global 21 cm signal, the bias is not significant. We then examine the spectral structure an instrument beam introduces in measurements of the global 21 cm signal. We simulate realistic beams that vary smoothly over frequency and space, and compute a beam-sky convolution to show how these beams interact with models of the sky. We find that beams that evolve linearly over the frequency range, as well as all bifurcating beams, introduce a spectral structure that is small enough to avoid obstructing measurements of the global 21 cm signal.

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