Abstract
Abstract Thermal nonequilibrium (TNE) is a fascinating situation that occurs in coronal magnetic flux tubes (loops) for which no solution to the steady-state fluid equations exists. The plasma is constantly evolving even though the heating that produces the hot temperatures does not. This is a promising explanation for isolated phenomena such as prominences, coronal rain, and long-period pulsating loops, but it may also have much broader relevance. As known for some time, TNE requires that the heating be both (quasi-)steady and concentrated at low coronal altitudes. Recent studies indicate that asymmetries are also important, with large enough asymmetries in the heating and/or cross-sectional area resulting in steady flow rather than TNE. Using reasonable approximations, we have derived two formulae for quantifying the conditions necessary for TNE. As a rough rule of thumb, the ratio of apex to footpoint heating rates must be less than about 0.1, and asymmetries must be less than about a factor of 3. The precise values are case-dependent. We have tested our formulae with 1D hydrodynamic loop simulations and find a very acceptable agreement. These results are important for developing physical insight about TNE and assessing how widespread it may be on the Sun.
Highlights
Thermal non-equilibrium (TNE) is one of the most fascinating phenomena in solar physics, in part because it is so counter-intuitive
The conditions for TNE are: (1) the heating must be sufficiently concentrated at low coronal altitudes, and (2) asymmetries in the heating and/or cross-sectional area cannot be too great
Tests should be made with more realistic models having more complex variations of heating rate and crosssectional area with position along the loop
Summary
Thermal non-equilibrium (TNE) is one of the most fascinating phenomena in solar physics, in part because it is so counter-intuitive. Temperature and density are uniform to within 50% along the coronal section of a symmetric equilibrium loop (Klimchuk et al 2008; Cargill et al 2012), so the radiative losses can be approximated by RRcc ≈ nn2ΛΛ0TTababLL , where n is the average electron number density and Λ(T) = Λ0Tb is a simplified form of the optically-thin radiative loss function. Heating Sufficiently Concentrated at Low Altitudes As we have discussed, TNE requires that the energy input to the upper corona be too small to balance the local radiative losses, a situation that occurs when the heating decreases rapidly with height. With heating that is strongly height dependent, the equilibrium temperature profile has two distinctive knees where a steep rise in the lower legs rolls over rather rapidly into a long flat section This is shown schematically in the sketch at the middle-right of Figure 2. We use Qλ and Γλ for the strongly heated leg when applying the formula
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