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J.A. Klimchuk (NRL), P. Demoulin (Obs Paris, Meudon, France), C.H. Mandrini (IAFE, Argentina)
Ever since it was realized, some 60 years ago, that the solar corona is two orders of magnitude hotter than the underlying photosphere, scientists have puzzled over the reason for these extreme conditions. A number of plausible ideas have been proposed, including the dissipation of MHD waves (AC models) and the dissipation of stressed, current-carrying magnetic fields (DC models), but it has proved difficult to establish which, if any, is correct. One approach to answering this fundamental question is to determine scaling laws relating the heating rate to observable physical parameters. Klimchuk & Porter (1995, Nature, 377, 131) showed that the heating rate varies inversely with the square of the length of coronal loops observed by Yohkoh. To compare this with the predictions of coronal heating theories, it is necessary to know also how the magnetic field strength in the loops varies with their length.
By computing magnetic field extrapolation models based on both observed and synthetic distributions of active region surface fields, we have found that B \propto ( L2 + S2 )c/2, where B is the coronal field strength averaged along a loop, L is the loop length, S is the characteristic size of the active region, and -3 \leq c \leq -1, depending on the complexity of the region. More importantly, for the range of loop lengths studied by Klimchuk & Porter, 50 < L < 300 Mm, there is a universal scaling law of the form B \propto L\delta, where \delta = -0.98 ±0.3. The details of these results will be presented, and their implications for theories of coronal heating will be discussed. It will be shown that DC models are in better agreement with the observations than are AC models.
This work was supported in part by NASA grant W-19,200.
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