The influence of flux rope heating models on solar prominence formation

Context. Prominences are cool, dense clouds suspended within the solar corona. Their in situ formation through the levitation-condensation mechanism is a textbook example of the thermal instability, where a slight energy imbalance leads to a runaway process resulting in condensed filamentary structures embedded within the concave-up portions of a flux rope. The detailed interplay between local radiative losses and the global heating of the solar corona is investigated here for prominence-forming flux rope structures. Aims. We begin by exploring the influence of two classes of commonly adopted heating models on the formation behaviour of solar prominences. These models consider either an exponential variation dependent on height alone, or local density and magnetic field conditions. We highlight and address some of the limitations inherent to these early approximations by proposing a new, dynamic 2D flux rope heating model that qualitatively accounts for the 3D topology of the twisted flux rope field. Methods. We performed 2.5D grid-adaptive numerical simulations of prominence formation via the levitation-condensation mechanism. A linear force-free arcade is subjected to shearing and converging motions, leading to the formation of a flux rope containing material that may succumb to thermal instability. The eventual formation and subsequent evolution of prominence condensations was then quantified as a function of the specific background heating prescription adopted. For the simulations that consider the topology of the flux rope, reduced heating was considered within a dynamically evolving ellipse that traces the flux rope cross-section. This ellipse is centred on the flux rope axis and tracked during runtime using an approach based on the instantaneous magnetic field curvature. Results. We find that the nature of the heating model is clearly imprinted on the evolution and morphology of any resulting prominences: one large, low-altitude condensation is obtained for the heating model based on local parameters, while the exponential model leads to the additional formation of smaller blobs throughout the flux rope which then relocate as they tend towards achieving hydrostatic equilibrium. Finally, a study of the condensation process in phase space reveals a non-isobaric evolution with an eventual recovery of uniform pressure balance along flux surfaces