Two-dimensional simulations of coronal rain dynamics. I. Model with vertical magnetic field and an unbounded atmosphere

Abstract

Aims. We aim to improve the understanding of the physical mechanisms behind the slower than free-fall motion and the two-stage evolution (an initial phase of acceleration followed by an almost constant velocity phase) detected in coronal rain events. Methods. Using the Mancha3D code, we solve the 2D ideal MHD equations. We represent the solar corona as an isothermal vertically stratified atmosphere with a uniform vertical magnetic field and the plasma condensation as a density enhancement described by a 2D Gaussian profile. We analyse the temporal evolution of the descending plasma and study its dependence on parameters such as density and magnetic field strength. Results. We confirm previous findings that the pressure gradient is the main force that opposes the action of gravity and slows down the blob descent and that larger densities require larger pressure gradients to reach the constant speed phase. We find that the shape of a condensation with a horizontal variation of density is distorted as it falls, due to the denser parts of the blob falling faster than the lighter ones. This is explained by the fact that the duration of the initial acceleration phase, and therefore the maximum falling speed attained by the plasma, increases with the ratio of blob to coronal density. We also find that the magnetic field plays a fundamental role in the evolution of the descending condensations. A strong enough magnetic field (greater than 10 G in our simulations) forces each plasma element to follow the path given by a particular field line, which allows to describe the evolution of each vertical slice of the blob in terms of 1D dynamics, without influence of the adjacent slices. In addition, under the typical conditions of the coronal rain events, the magnetic field prevents the development of the Kelvin-Helmholtz instability.