Scaling Laws for Dynamic Solar Loops.

The scaling laws which relate the peak temperature and volumetric heating rate to the pressure and length 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 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 , but with a different constant of proportionality that depends on the Mach number of the flow.