Soft X-Ray Loops and Coronal Heating

Abstract

We have measured the temperatures, pressures, and lengths of 47 nonflaring coronal loops observed by the Soft X-Ray Telescope on the Yohkoh satellite. The median temperature is 5.7 x 106 K, and the median pressure is 1.6 x 1016 cm-3 K. We have carefully examined the possible random and systematic errors in the measurements and have found, through simulated observations, that the errors produced by photon statistical noise can sometimes greatly exceed the values given by commonly used error expressions, derived here and elsewhere. Furthermore, the measurements are not normally distributed and therefore are not amenable to standard statistical analysis. We have used nonparametric methods to look for statistical relationships and find that temperature and length are uncorrelated and that pressure varies inversely with length to approximately the first power. The observed lifetimes of the loops are much longer than their computed cooling times, suggesting that the loops are in a state of quasi-static equilibrium. This has allowed us to use simple scaling law theory to infer that the volumetric heating rate in the loops (averaged along the loop axis) varies inversely with length to approximately the second power. This is an important constraint for distinguishing among competing theories of coronal heating, and we discuss the results in the context of three specific models.