Dynamics of flaring loops. I - Thermodynamic decay scaling laws

A simple analytical approximate solution for the hydrodynamic equations describing the decay of a flaring loop is derived. It is found that, independent of chemical composition of the plasma, the entropy per particle at the top of the loop undergoes an initial phase of linear decay, with a slope related to the initial loop conditions. The characteristic decay time is shorter than conductive or radiative times for typical solar flare conditions. The analytical solution is compared with numerical solutions of the full set of hydrodynamic equations for loop flares, and it is shown that its validity extends over a large fraction of the decay. Also the decay times of temperature, density and pressure are related to the entropy decay time.