Toward detailed prominence seismology I. Computing accurate 2.5D magnetohydrodynamic equilibria

Context. Prominence seismology exploits our knowledge of the linear eigenoscillations for representative magnetohydrodynamic models of filaments. To date, highly idealized models for prominences have been used, especially with respect to the overall magnetic configurations. Aims. We initiate a more systematic survey of filament wave modes, where we consider full multi-dimensional models with twisted magnetic fields representative of the surrounding magnetic flux rope. This requires the ability to compute accurate 2.5 dimensional magnetohydrodynamic equilibria that balance Lorentz forces, gravity, and pressure gradients, while containing density enhancements (static or in motion). Methods. The governing extended Grad-Shafranov equation is discussed, along with an analytic prediction for circular flux ropes for the Shafranov shift of the central magnetic axis due to gravity. Numerical equilibria are computed with a finite element-based code, demonstrating fourth order accuracy on an explicitly known, non-trivial test case. Results. The code is then used to construct more realistic prominence equilibria, for all three possible choices of a free flux-function. We quantify the influence of gravity, and generate cool condensations in hot cavities, as well as multi-layered prominences. Conclusions. The internal flux rope equilibria computed here have the prerequisite numerical accuracy to allow a yet more advanced analysis of the complete spectrum of linear magnetohydrodynamic perturbations, as will be demonstrated in the companion paper.