We develop and apply an enhanced regularization algorithm, used inRHESSI X-ray spectral analysis, to constrain the ill-posed inverseproblem that is determining the DEM from solar observations. Wedemonstrate this computationally fast technique applied to a range ofDEM models simulating broadband imaging data from SDO/AIA and highresolution line spectra from Hinode/EIS, as well as actual activeregion observations with Hinode/EIS and XRT. As this regularizationmethod naturally provides both vertical and horizontal (temperatureresolution) error bars we are able to test the role of uncertaintiesin the data and response functions. The regularization method is ableto successfully recover the DEM from simulated data of a variety ofmodel DEMs (single Gaussian, multiple Gaussians and CHIANTI DEMmodels). It is able to do this, at best, to over four orders ofmagnitude in DEM space but typically over two orders of magnitude frompeak emission. The combination of horizontal and vertical error barsand the regularized solution matrix allows us to easily determine theaccuracy and robustness of the regularized DEM. We find that thetypical range for the horizontal errors is DeltalogTapprox 0.1-0.5 and this is dependent on the observed signal to noise,uncertainty in the response functions as well as the source model andtemperature. With Hinode/EIS an uncertainty of 20% greatly broadensthe regularized DEMs for both Gaussian and CHIANTI models althoughinformation about the underlying DEMs is still recoverable. Whenapplied to real active region observations with Hinode/EIS and XRT theregularization method is able to recover a DEM similar to that foundvia a MCMC method but in considerably less computational time.
Download page contains links to both the preprint in arXiv
as well as the codes used.