Simulations of the solar chromosphere in the two-fluid approximation

Abstract

This work presents the study of wave propagation and the Rayleigh-Taylor instability in the solar atmosphere using a two-fluid model. The solar atmosphere is strongly stratified and permeated by magnetic fields with a complex configuration, thus creating very different regimes throughout its layers. Of the different layers of the solar atmosphere the photosphere is the one with the highest density and the strongest magnetic field. The high density makes the plasma collisionally coupled and the magnetohydrodynamic (MHD) assumption valid. Because of the high collision frequencies between different constituents: ions, free electrons and neutral particles, the plasma becomes a perfect conductor. In mathematical terms, the non-ideal terms which appear in the generalized Ohm’s law are very small compared to the ideal term. In the assumption of a perfectly conducting plasma, the field lines are tied to the plasma. The corona is fully ionized, and even if the magnetic fields are weaker than in the photosphere, the very low density of plasma makes the corona a layer dominated by the magnetic field. Because the density decreases, the collision frequencies also decrease from the photosphere towards the corona. In these two extreme collisional regimes, coupled and uncoupled, MHD simulations give good results compared to the observations, but this is not the case for the chromosphere. The solar chromosphere is a complex and dynamic layer located between the photosphere and the corona. It is a transition layer where the properties of plasma change abruptly from gas pressure dominated to magnetic field dominated, and where the collisional coupling of the plasma decreases and the ionization fraction increases. The collisional timescales between ionized and neutral atomic species become equal or larger than the hydrodynamic timescale causing partial decoupling between charges and neutrals. Therefore, classical MHD approach is not valid in the chromosphere. A suitable alternative for this approach is a two-fluid model, numerically implemented in this work. The complexity of the solar atmosphere does not allow to solve the equations analytically, and the problems are solved numerically using simulations. We have extended the non-ideal single-fluid code, Mancha3D, to simultaneously treat neutral and ionized plasma components in the two-fluid approach. The Mancha3D code uses an explicit scheme which has a series of advantages in the case of large- scale parallel simulations in 3D domains. The partial ionization effects are taken into account in the single-fluid approach through a generalized Ohm’s law. However, the two-fluid approach introduces collisional coupling terms which can lead an explicit code to become numerically unstable. For high collision frequencies the equations become stiff. In order to ensure stability when the collisional terms are included in an explicit scheme, the time step needed to integrate the equations in time numerically is of order of the inverse of the collision frequency. When the collisional frequency is high, the time step imposed is very small. This restriction can be overcome by implementing the collisional terms implicitly. In our newly developed code we treat such terms implicitly in a semi implicit scheme. We perform tests of acoustic and Alfvén waves in a uniform atmosphere, where we can compare the numerical solutions to exact analytical solutions, for the purpose of the verification of the code and the determination of the order of accuracy of the scheme. Afterwards, we run more realistic simulations of fast magnetoacoustic waves in a stratified atmosphere, where we have used the VALC model. In both cases we observe damping of the waves, more pronounced when the collision frequency is similar to the wave frequency. These results are consistent with results present in the literature. When the amplitude is large enough, an additional mechanism of damping can be observed, which cannot be predicted by an analytical solution, but it can be shown through numerical simulations. We have performed a simulation using the MHD model, with a setup corresponding to the setup used in the two-fluid approach, where the interaction between neutrals and charges is introduced through the ambipolar term in the induction equation. We observed that, even if the damping of the wave is similar in the two cases, the increase in temperature is several times smaller in the MHD case. In the last part we study Rayleigh-Taylor instability at the interface between a solar prominence and corona. We analyze the growth rate, the decoupling, the energy spectra in several simulations where we want to study the effect of the elastic and inelastic collisions, viscosity and thermal conductivity, compressibility, density contrast, initial perturbation, and the background magnetic field on the devel- opment of the instability in a non uniform medium where the transition between the prominence and the corona is continuous with a characteristic length scale. In these simulations we have considered ideal Ohm’s law (no magnetic diffusivity). We observe that the linear growth rate is considerably smaller than in the ideal incompressible MHD case without viscosity and thermal conductivity. We conclude that the ion-neutral collisions, the viscosity and thermal conductivity have a stabilizing ef- fect. The magnetic field also inhibits the instability. For our equilibrium configuration, in the ideal case without magnetic field, the compressibility increases the linear growth rate.