ENERGY-BALANCE IN CORONAL FUNNELS

Semi-analytic models are used to explore the energy balance in magnetic flux tubes over wide ranges of areal constriction, shape, length, and maximum temperature. Models in which thermal conduction balances radiation are emphasized, but enthalpy transport is also considered. The main results for conduction-dominated models are (1) magnetic constriction does not greatly alter the overall energy budget of the solar corona. Except for some funnels that undergo most of their constriction near the hot end, the downward heat flux at the 10(6) K level is typically within a factor of 2 of the value for an unconstricted flux tube of the same length, even for areal constrictions of 100 or more. (2) The empirical differential emission measure over the range 5.3 less-than-or-similar-to log T less-than-or-similar-to 6.0 is closely matched by a bowl-shaped funnel with a constriction factor of 4. The same model reproduces the observation that plasma at log T almost-equal-to 5.8 covers at most 40% of the surface. (3) "Loop" scaling relationships of the form T(h) proportional-to (pL)1/3, where p is the gas pressure, L is the length of the tube and T(h) is the temperature at the hot end, are derived for the full range of models, showing the dependence of the constant of proportionality on the properties of the magnetic constriction. The result that the magnetic constriction between the levels log T = 6.2 and log T = 4.5 is less than a factor of 10 in area is consistent with observational evidence for canopy-type magnetic fields that fan out rapidly above the photosphere. For a simple flow-dominated model, constriction can reduce the total energy requirement of the funnel by a factor of 5 in extreme cases but does not influence the differential emission measure.