Validity of the Isobaric Assumption to the Solar Corona

Many coronal heating mechanisms have been suggested to balance the losses from this tenuous medium by radiation, conduction, and plasma mass flows. A previous paper (Walsh, Bell, and Hood, 1995) considered a time-dependent heating supply where the plasma evolved isobarically along the loop length. The validity of this assumption is investigated by including the inertial terms in the fluid equations making it necessary to track the sound waves propagating in a coronal loop structure due to changes in the heating rate with time. It is found that the temperature changes along the loop are mainly governed by the variations in the heating so that the thermal evolution can be approximated to a high degree by the simple isobaric case. A typical isobaric evolution of the plasma properties is reproduced when the acoustic time scale is short enough. However, the cooling of a hot temperature equilibrium to a cool one creates supersonic flows which are not allowed for in this model.