The effect of spatially dependent heating on the thermal equilibria of coronal loops

The thermal equilibria along a symmetric coronal loop with constant cross-sectional area is investigated in the absence of gravity. A coronal heating function that depends on distance along the loop is considered and the effects of varying the values of the parameters involved in the governing equations are studied. It is found that there is a critical decay length of the heating below which a hot coronal loop does not exist. It is suggested that thermal non-equilibrium occurs, allowing the existence of catastrophic cooling and it is shown that prominence-type equilibria are possible. A study of the stability of the equilibrium up to a second order approximation is presented, and it is found that the response of the structure not only depends on the amplitude of the disturbance, but also on whether the disturbance increases or decreases the equilibrium temperature.