Theory & Observation of High-Order Radio Recombination Lines

This dissertation resolves a mystery in cosmic radio recombination line observations reported by Bell et al. (2000). This is accomplished by rigorously “reverse-engineering” the novel data processing technique they used and through independent observations of high-order RRLs (radio recombination lines) of cosmic origin to test the theory of Stark broadening in plasmas. The findings of this dissertation are summarized in two papers published during the dissertation and reproduced in Chapter 4. I discovered that the apparent hydrogen RRL narrowing first reported by Bell et al. is an artifact of their data processing. I accomplished this by creating a theoretical model of the multiple FS (frequency shifting) technique, originally developed by Bell (1997), which I then implemented as a computer simulation. This technique copies a spectral line bandpass, shifts it in frequency by an offset, and adds it to the unshifted bandpass. The output of this process is then fed back to itself multiple times. I then co-created a theoretical model of the Orion nebula which includes mechanisms of spectral line broadening and non-equilibrium thermodynamics effects. This model is used to numerically solve the radiative transfer problem to simulate hydrogen RRLs. These simulated lines are then processed through the multiple FS model, the results of which are called “processed” lines. Finally, I used Monte Carlo simulation to estimate how noise influences the processed line widths and amplitudes. From these models and simulations, I discovered that multiple FS does not preserve broadening when the original line width is greater than the FS-offset. In this case, I find the processed results manifest the narrowing reported by Bell et al., by reducing broad spectral wings characteristic of Stark broadened RRLs. I also discovered that the S/N of processed lines reduces weakly with the number of overlaps as a result of adding dependent samples. This means the S/N of processed lines as a function of ∆n (transition-order), at fixed frequency, decreases faster than for unprocessed lines, such that a given statistical insignificance level is reached more quickly. Given this analysis, I argue Bell et al.’s ∆n > 11 lines are artifacts of their technique. I conclude that their reported findings, upon re-examination of their novel data processing technique, do not indicate a need to change Stark broadening theory. I present original observations of high-order RRLs from the Orion nebula to test the theory of Stark broadening in cosmic plasmas. I use a wide 1 GHz bandpass centered at 6 GHz to significantly improve the accuracy of measurements by stacking up to eleven hydrogen RRLs of the same ∆n and find no evidence of spectral line narrowing. I show that all statistically significant data from my observations and four-sets of previous observations of high-order hydrogen RRLs (Smirnov et al., 1984; Bell et al., 2011) are in agreement and demonstrate how Stark broadening theory is consistent with these observations. I find that Lockman and Brown (1975)’s RRL model of the Orion nebula over a large range of radio frequencies and ∆n ≤ 2 requires the addition of small-scale density inhomogeneities (clumps) and turbulence to adequately predict my observed hydrogen RRLs for ∆n ≤ 5. I demonstrate that the power law predicted by electron-impact Stark broadening theory is consistent with the five-sets of high-order hydrogen RRLs analyzed here. My data do not allow distinguishing between two approaches to the cut-off parameters (nearest neighbor versus Debye radius) when predicting line broadening from electron impacts. Specifically, the data does not allow an unambiguous choice between the theoretical results of Griem (1967); Gee et al. (1976) and Watson (2006); Peach (2015). This ambiguity arises from small differences in the radiative transfer nebula model parameters. It is currently impossible to independently determine turbulent velocities and other physical & geometric parameters of the Orion nebula with enough accuracy to choose between the two predications of electron-impact broadening theory. This situation represents an ill-posed inverse problem that is currently unsolvable (Brown et al., 1978). However, I am able to show that Peach’s model for electron-plus-proton impacts significantly deviates from the Lorentz-width trend in my data