SOFT-X-RAY LOOPS AND CORONAL HEATING

We have measured the temperatures, pressures, and lengths of 47 nonfla ring coronal loops observed by the Soft X-Ray Telescope on the Yohkoh satellite. The median temperature is 5.7 x 10(6) K, and the median pre ssure is 1.6 x 10(16) cm(-3) K. We have carefully examined the possibl e random and systematic errors in the measurements and have found, thr ough simulated observations, that the errors produced by photon statis tical noise can sometimes greatly exceed the values given by commonly used error expressions, derived here and elsewhere. Furthermore, the m easurements are not normally distributed and therefore are not amenabl e to standard statistical analysis. We have used nonparametric methods to look for statistical relationships and find that temperature and l ength 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 wit h length to approximately the second power. This is an important const raint for distinguishing among competing theories of coronal heating, and we discuss the results in the context of three specific models.