## Time damping of non-adiabatic magnetohydrodynamic waves in a partially ionised prominence medium: Effect of a background flow

^{1}
Departament de FísicaUniversitat de les Illes Balears,
07122
Palma de Mallorca,
Spain

^{2}
Departament de Matemàtiques i Informàtica, Universitat de les
Illes Balears, 07122
Palma de Mallorca,
Spain

e-mail: s.barcelo;marc.carbonell@uib.es; joseluis.ballester@uib.es

Received:
29
July
2010

Accepted:
9
October
2010

*Context.* The simultaneous occurrence of flows and time damped
small-amplitude oscillations in solar prominences is a common phenomenon. These
oscillations are mostly interpreted in terms of magnetohydrodynamic (MHD) waves.

*Aims.* We study the time damping of linear non-adiabatic MHD waves in a
flowing partially ionised plasma with prominence-like physical conditions.

*Methods.* Considering non-adiabatic single fluid equations for a
partially ionised hydrogen plasma, we have solved our dispersion relations for the complex
frequency, *ω*, and we have analysed the behavior of the period, damping
time and the ratio of the damping time to the period, versus the real wavenumber
*k*, for Alfvén, fast, slow, and thermal waves.

*Results.* While in the case without flow there is a critical wavenumber
at which the period of Alfvén and fast waves goes to infinite, when a flow is present two
different critical wavenumbers appear. The smaller wavenumber depends on the flow speed
and causes the period of the high-period branch to go to infinite. When the second
critical wavenumber is attained the period of both branches become equal. In general, the
time damping of Alfvén and fast waves is dominated by resistive effects, and its damping
ratio is very inefficient when compared to observations. The damping of slow and thermal
waves is basically dominated by non-adiabatic effects, and for slow waves it is possible
to obtain a damping ratio close to observations, although it would correspond to long
period oscillations with large damping times not often observed. The consideration of a
structured medium produces new features such as the apparition of four critical
wavenumbers for Alfvén waves, and one critical wavenumber for slow waves. For fast waves,
constrained propagation substantially improves, within the range of observed wavelengths,
the ratio of the damping time to period.

*Conclusions.* The presence of a background flow in a partially ionised
plasma gives place to new interesting features when the time damping of MHD waves is
studied. In general, the results point out that ion-neutral collisions are an inefficient
mechanism to explain the observed time damping of prominence oscillations if they are
produced by Alfvén and fast waves. If the oscillations are produced by slow waves, only
long period oscillations with large damping times produce damping ratios in agreement with
observations.

Key words: Sun: oscillations / Sun: filaments, prominences

*© ESO, 2010*