An Atlas of Coronal Electron Density at 5R⊙. II. A Spherical Harmonic Method for Density Reconstruction

This is the second of a series of three papers that present a methodology with the aim of creating a set of maps of the coronal density over a period of many years. This paper describes a method for reconstructing the coronal electron density based on spherical harmonics. By assuming a radial structure to the corona at the height of interest, line-of-sight integrations can be made individually on each harmonic basis prior to determining coefficients, i.e., the computationally expensive integrations are calculated only once during initialization. This approach reduces the problem to finding the set of coefficients that best match the observed brightness using a regularized least-squares approach and is very efficient. The method is demonstrated on synthetic data created from both a simple and an intricate coronal density model. The quality of reconstruction is found to be reasonable in the presence of noise and large gaps in the data. The method is applied to both Large Angle and Spectrometric Coronagraph Experiment C2 and Solar Terrestrial Relations Observatory Cor2 coronagraph observations from 2009 March 20, and the results from both spacecraft compared. Future work will apply the method to large data sets.