A Method for Smooth Merging of Electron Density Distributions at the Chromosphere-Corona Boundary

Abstract

The electron number density N_e distributions in solar chromosphere and corona are usually described with models of different nature: exponential for the former and inverse power law for the latter. Moreover, the model functions often have different dimensionality, e.g. the chromospheric distribution may depend solely on solar altitude, while the coronal number density may be a function of both altitude and latitude. For applications which need to consider both chromospheric and coronal models, the chromosphere-corona boundary, where these functions have different values as well as gradients, can lead to numerical problems. We encountered this problem in context of ray tracing through the corona at low radio frequencies, as a part of effort to prepare for the analysis of solar images from new generation radio arrays like the Murchison Widefield Array (MWA), Low Frequency Array (LOFAR) and Long Wavelength Array (LWA). We have developed a solution to this problem by using a {\em patch} function, a thin layer between the chromosphere and the corona which matches the values and gradients of the two regions at their respective interfaces. We describe the method we have developed for defining this patch function to seamlessly "stitch" chromospheric and coronal electron density distributions, and generalize the approach to work for any arbitrary distributions of different dimensionality. We show that the complexity of the patch function is independent of the stitched functions dimensionalities. It always has eight parameters (even four for univariate functions) and they may be found without linear system solution for every point. The developed method can potentially be useful for other applications.