Isothermal Bias of the ``Filter Ratio'' Method for Observations of Multithermal Plasma

Abstract

An early result from the Transition Region and Coronal Explorer (TRACE) was that the EUV filter ratios for many narrow coronal loops (widths of a few arcseconds) were found to cluster within the small range 0.50-1.70, as functions of position along loop length. The most common interpretation is that the temperature along the loop is in fact nearly constant with a value between 1.1 and 1.3 MK. This interpretation has resulted in a class of TRACE loop models with heating close to the footpoints. We analyze the filter ratio method to show that the constant TRACE 195 Å/173 Å ratios can be reproduced by multithermal differential emission measures (DEMs) along the line of sight over a wide range of peak temperatures, so long as the distribution is relatively flat and spans the temperature response of both channels. Furthermore, in the limit of flat (i.e., very multithermal) DEMs, the filter ratio method is biased toward the ratio of the integrals of the temperature response functions. This result is general to any measurement of intensity ratios that are formed over a nonzero temperature range (e.g., narrow passbands and ion emission lines).