Quiet Sun electron densities and their uncertainties derived from spectral emission line intensities

The goal of this paper is to apply statistical methods to determine electrons densities and their errors from measurements of density-sensitive line intensities in the quiet Sun. Three methods are employed. The first is the use of L-function plots to provide a quick visual assessment of the likelihood that a set of line intensities can provide a robust estimate of these quantities. A second methods involves a chi-squared minimization together with a prescription for determining the regions of statistical confidence in addition to the best-fitting value. A third method uses a Bayesian inference technique that employs a Monte-Carlo Markov-chain (MCMC) calculation from which an analysis of the posterior distributions provide estimates of the mean and regions of high probability density. Using these three methods, observations of extreme-ultraviolet spectral lines originating from regions of the quiet Sun have been analyzed. The quantitative chi-squared minimization and MCMC sampling provide results that are generally in good agreement, especially for sets of lines of ions that have L-function plots that suggest that a robust analysis might be possible.