Twisted coronal loops in uniform gravity

Coronal loop emission profiles are often of remarkably constant width along their entire lengths, contradicting expectations based on model coronal magnetic field strengths decreasing with height. Meanwhile Paul Bellan has produced a theoretical model in which an initially empty, twisted force-free loop, on being filled with plasma via upflow at each foot point, in the absence of significant gravitational effects, forms a narrow, filamentary loop of constant cross-section. In this paper, we focus on equilibrium states that include stratification by uniform gravity while retaining the effects of magnetic field twist. Comparing these with related force-free equilibria, it is found that injection of low-$β$ plasma under coronal conditions is not likely to change the shape of a loop significantly. These linear equilibria apply to the interiors and boundaries of loops only, with external influences modeled by boundary total pressures. The effects of total pressure balance with surroundings and of gravitational stratification are to inhibit the pinching of a loop to a constant cross-section. Only if the plasma $β$ were high enough for the plasma to reconfigure the external field and the hydrostatic scale height much greater than the loop size could the final state have nearly constant cross section. We do not expect this to occur in the corona.