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We investigate the effect of a variable, i.e. time-dependent, background onthe standing acoustic (i.e. longitudinal) modes generated in a hot coronalloop. A theoretical model of 1D geometry describing the coronal loop isapplied. The background temperature is allowed to change as a function of timeand undergoes an exponential decay with characteristic cooling times typicalfor coronal loops. The magnetic field is assumed to be uniform. Thermalconduction is the dominant mechanism of cooling the hot background plasma inthe presence of an unspecified thermodynamic source that maintains the initialequilibrium. The influence of the rapidly cooling background plasma on thebehaviour of standing acoustic (longitudinal) waves is investigatedanalytically. The temporally evolving dispersion relation and wave amplitudeare derived by using the WKB theory. An analytic solution for thetime-dependent amplitude that describes the influence of thermal conduction onthe standing longitudinal (acoustic) wave is obtained by exploiting theproperties of Sturm-Liouville problems. Next, numerical evaluations furtherillustrate the behaviour of the standing acoustic waves in a system withvariable, time dependent background. The results are applied to a number ofdetected loop oscillations. We find a remarkable agreement between thetheoretical predictions and the observations. The cooling of the backgroundplasma due to thermal conduction is found to cause a strong damping for theslow standing magneto-acoustic waves in hot coronal loops in general. Furtherto this, the increase in the value of thermal conductivity leads to a strongdecay in the amplitude of the longitudinal standing slow MHD waves.

The Effect of Variable Background on Oscillating Hot Coronal Loop due to Thermal Conduction