Formation of solar filaments by steady and nonsteady chromospheric heating

It has been established that cold plasma condensations can form in a magnetic loop subject to localized heating of its footpoints. In this paper, we use grid-adaptive numerical simulations of the radiative hydrodynamic equations to investigate the filament formation process in a pre-shaped loop with both steady and finite-time chromospheric heating. Compared to previous works, we consider low-lying loops with shallow dips and use a more realistic description for radiative losses. We demonstrate for the first time that the onset of thermal instability satisfies the linear instability criterion. The onset time of the condensation is roughly similar to 2 hr or more after the localized heating at the footpoint is effective, and the growth rate of the thread length varies from 800 km hr(-1) to 4000 km hr(-1), depending on the amplitude and the decay length scale characterizing this localized chromospheric heating. We show how single or multiple condensation segments may form in the coronal portion. In the asymmetric heating case, when two segments form, they approach and coalesce, and the coalesced condensation later drains down into the chromosphere. With steady heating, this process repeats with a periodicity of several hours. While our parametric survey confirms and augments earlier findings, we also point out that steady heating is not necessary to sustain the condensation. Once the condensation is formed, it keeps growing even after the localized heating ceases. In such a finite-heating case, the condensation instability is maintained by chromospheric plasma that gets continuously siphoned into the filament thread due to the reduced gas pressure in the corona. Finally, we show that the condensation can survive the continuous buffeting of perturbations from photospheric p-mode waves.