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A differential emission measure (DEM) method is used to evaluate therelationship of the electron density and temperature before and after a coronalrain event during an active sun over the period from 20:10 UT on October 6 to02:10 on October 7, 2011. Observational data were obtained from SDO/AIA for sixdifferent extreme ultraviolet (EUV) spectral lines. 240 different coronal loopswere analyzed during this time interval, and the average electron density andtemperature were obtained using 171 {\AA} (Fe IX) and 193 {\AA} (Fe XII)filters. The relationship between the density and temperature made it possibleto estimate the polytropic index in the solar corona before and after thecoronal rain. The polytropic index after the termination of the coronal rainwas estimated to be {\gamma} = 1.3{\pm}0.06, Which shows the usualthermodynamic properties of study-state coronal plasma. The polytropic index atthe time of onset of the coronal rain was, however, estimated to be {\gamma} =2.1{\pm}0.11, which indicates an unstable thermodynamic process, i.e., thermalinstability. It is suggested that the coronal rain is the result of an unstableprocess, and the coronal plasma returns its stable state after the rain.

astrophysics

Measurement of the polytropic index during solar coronal rain using a  diagram of the electron density distribution as a function of the electron  temperature