Title: Properties of radiatively cooling coronal loops

Abstract: I will discuss the robust $T \propto$ n^\delta$ power-law
relationship between the temperature and the density that arises in
numerical studies of cooling coronal loops when they enter the radiative
cooling phase. Through analytical and numerical hydrodynamic models I
will show that the radiative energy loss from the transition region is
the dominant physical process in establishing this relationship and so
governs the dynamics and evolution of the entire loop. There is limited
(though some) observational evidence for the physical existence of this
power-law relationship. Observational verification would be an important
step forward for two reasons: (1) it would serve to validate (or
otherwise) several of the assumptions upon which our numerical models
are based and from which so many results are extrapolated; and (2) it
has recently been suggested that loops in the 1 MK temperature range, as
observed by instruments such as TRACE and EIT, are actually cooling. If
the latter is true and the existence of a $T \propto$ n^\delta$ -type
relationship is established then we may claim a substantial
understanding of the physics governing these ubiquitous structures
during a significant part of their life-cycle. Finally, I will describe
an observing plan for Hinode-EIS that has been designed to address these
matters.