Scaling Laws for Dynamic Solar Loops

Abstract

The scaling laws which relate the peak temperature $T_M$ and volumetric heating rate $E_H$ to the pressure $P$ and length $L$ for static coronal loops were established over 40 years ago; they have proved to be of immense value in a wide range of studies. Here we extend these scaling laws to {\it dynamic} loops, where enthalpy flux becomes important to the energy balance, and study impulsive heating/filling characterized by upward enthalpy flows. We show that for collision-dominated thermal conduction, the functional dependencies of the scaling laws are the same as for the static case, when the radiative losses scale as $T^{-1/2}$, but with a different constant of proportionality that depends on the Mach number $M$ of the flow. The dependence on the Mach number is such that the scaling laws for low to moderate Mach number flows are almost indistinguishable from the static case. When thermal conduction is limited by turbulent processes, however, the much weaker dependence of the scattering mean free path (and hence thermal conduction coefficient) on temperature leads to a limiting Mach number for return enthalpy fluxes driven by thermal conduction between the corona and chromosphere.

arXiv comment14 pages, 3 figures

References in corpus (6)

• Highly Efficient Modeling of Dynamic Coronal Loops
• Solar UV and X-Ray Spectral Diagnostics
• The influence of numerical resolution on coronal density in hydrodynamic models of impulsive heating
• Scaling Laws and Temperature Profiles for Solar and Stellar Coronal Loops with Non-uniform Heating
• Heating and cooling of coronal loops with turbulent suppression of parallel heat conduction
• Coronal Loop Scaling Laws for Various Forms of Parallel Heat Conduction

Cited by in corpus (4)

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• A statistical study of propagating MHD kink waves in the quiescent corona
• Temperature and Differential Emission Measure Profiles in Turbulent Solar Active Region Loops
• Coronal Loops with Different Metallicities and Generalized RTV Scaling Laws