Measuring relative abundances in the solar corona with optimized linear combinations of spectral lines

National audienceElemental abundances in some coronal structures differ significantly from photospheric abundances, with a dependence on the First Ionization Potential (FIP) of the element. Measuring these FIP-dependent abundance biases is important for coronal and heliospheric physics. We aim at building a method for optimal determination of FIP biases in the corona from spectroscopic observations, in a way that is in practice independent from Differential Emission Measure (DEM) inversions. We optimize linear combinations of spectroscopic lines of low-FIP and high-FIP elements so that the ratio of the corresponding radiances yields the relative FIP bias with a good accuracy, for any DEM in a small set of typical DEMs. These optimized linear combinations of lines allow to retrieve a test FIP bias map with a good accuracy, for all DEMs in the map. The method provides a convenient, fast, and accurate way of computing relative FIP bias maps. It could be used to optimize the use of existing observations and the design of new observations and instruments