Empirical Scaling Laws for Coronal Heating

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Abstract
We review the origins and uses of scaling laws in studies of stellar outer atmospheres, with particular emphasis on the properties of coronal loops. The evidence for a fundamental structuring of the Solar corona is reviewed and a discussion of thermodynamic scaling laws is presented. In order to intercompare different theories for coronal formation and heating, it is necessary to recast the theories in terms of observable quantities. As an example, we present a discussion of magnetic field-related heating and scaling laws which can be obtained relating coronal pressure, temperature and magnetic field strength; available data are shown to be consistent with scaling laws obtained in this way. However, some parameters of the theory must be treated as adjustable at the present time and it is necessary to examine data from other stars in order to determine whether these are true parameters in coronal heating. We examine some of the difficulties involved in using unresolved stellar data when dealing with loop atmospheres, by first treating the Sun as an unresolved source. Using the detailed observations now available we examine the limits of applicability of single-loop models. The possibilities and limits of stellar data are then discussed.