The Effect of Thermal Misbalance on Slow Magnetoacoustic Waves in a Partially Ionized Prominence-Like Plasma

Abstract

Solar prominences are partially ionized plasma structures embedded in the solar corona. Ground- and space-based observations have confirmed the presence of oscillatory motions in prominences, which have been interpreted in terms of standing or propagating MHD waves. Some of these observations suggest that slow magnetoacoustic waves could be responsible for these oscillations and have provided us with evidence about their damping/amplification with very small ratios between damping/amplifying times and periods, which have been difficult to explain from a theoretical point of view. Here we investigate the temporal behavior of non-adiabatic, slow, magnetoacoustic waves when a heating–cooling misbalance is present. The influence of optically thin losses and of a general heating term, in which density and temperature dependence can be modified, as well as the effect of partial ionization have been considered. Furthermore, a tentative example of how, using observational data, the observed ratio between damping/amplifying times and periods could be matched with those theoretically obtained is shown. In summary, different combinations of radiative losses, heating mechanisms, and typical wavenumbers, together with the effect of partial ionization, could provide a theoretical tool able to reproduce observational results on small-amplitude oscillations in prominences.

Nonlinear Coupling of Alfvén and Slow Magnetoacoustic Waves in Partially Ionized Solar Plasmas: The Effect of Thermal Misbalance

“…The stronger damping corresponds to the highest temperature (red curve), while the weaker damping is associated with the lowest temperature (brown curve). Following [32,49], this behavior can be understood by means of the thermal time, τ T , related, in this case, to radiative losses and heating. In the nonlinear case, no analytical expression exists for the thermal damping/amplifying time; however, one can get some help from the linear case [32].…”

“…Following [32,49], this behavior can be understood by means of the thermal time, τ T , related, in this case, to radiative losses and heating. In the nonlinear case, no analytical expression exists for the thermal damping/amplifying time; however, one can get some help from the linear case [32]. In this case-and assuming small wavenumbers, such as those that are considered in these calculations-the imaginary part of the approximate analytical solution corresponding to slow waves [32] is:…”

“…On the other hand, once exponent b is fixed, using Equation (32), one also obtains an expression for the threshold value of exponent a, which is…”

“…A polynomial fit to these tables, up to third order in pressure, p, temperature, T, together with product terms or interactions was performed, which allows us to compute the ionization degree for any combination of pressure and temperature. For the rest of the parameters, the values for the magnetic field, density and temperature are those typical of quiescent prominences, respectively: B 0 = 5 × 10 −4 T, oriented along the z-axis, ρ 0 = 5 × 10 −11 kg • m −3 , considered constant in the calculations here, while the considered temperature, T, is in the interval of 4000-12,000 K. Single-fluid equations constituted our starting set of equations, with ambipolar diffusion, radiative losses and heating included, while thermal conduction is neglected, because under prominence conditions thermal conduction times are much longer than radiative times [20,32]. Furthermore, in order to characterize the radiative losses, two optically thin radiative-loss functions, such as Hildner [42] and CHIANTI7 [43][44][45] ones are considered.…”

“…Regarding partially ionized prominence plasmas, this approach was taken into account in Ref. [32], which considered single-fluid equations and a partially ionized hydrogen plasma, in which different radiative losses as well as ambipolar diffusion were taken into account. Then, the temporal behaviors of the linear slow magnetoacoustic waves, propagating parallel to the magnetic field, and of thermal waves were studied.…”