Spatial damping of compressional MHD waves in prominences

Abstract

Aims.We study the spatial damping of linear compressional MHD waves in a homogeneous, isothermal, and unbounded prominence. Methods.We derive a general dispersion relation invoking the Newtonian radiation and turbulent viscosity. The turbulent viscosity is derived from SUMER and CDS observations for Kraichnan and Kolmogorov turbulences. Since we are interested in the spatial damping, the dispersion relation is solved numerically considering $\omega$ as real and k as complex corresponding to slow, fast, and thermal modes. Results.Both the slow and fast modes show strong damping, but the thermal mode is absent. The turbulent viscosity derived from observations can be a viable mechanism for the spatial damping of slow and fast modes. For a wave period of 1 s, the damping length for slow and fast modes is found to be $1.1 \times 10^{2}$ km for the Kolmogorov turbulence. Correspondingly, the damping length of slow modes is $1.3 \times 10^{1}$ km and for fast modes $1.9\times 10^{2}$ km for the Kraichnan turbulence. From the damping length study of slow modes, it is found that Kraichnan turbulence dominates for short wave periods between 10-7 to 102 s, and the Kolmogorov turbulence dominates for longer wave periods between 103 to 105 s. From the damping length of fast modes, it is found that the Kraichnan turbulence dominates from very short to long wave periods. Conclusions.The Kraichnan and Kolmogorov turbulence can be a viable damping mechanism for the spatial damping of short-period oscillations. In particular, the short-period oscillations (5-15 min) observed in quiescent limb prominences, which seem to be due to internal fundamental slow modes, have damping lengths in the range $1.9{-}3.7\times 10^{3}$ km for Kolmogorov turbulence and $3.5 \times 10^3.1 \times 10^{4}$ km for Kraichnan turbulence. Correspondingly, for fast modes, the damping length is in the range $2.6\times 10^2.3\times 10^{6}$ km for Kolmogorov turbulence and $1.7 \times 10^1.5\times 10^{8}$ km for Kraichnan turbulence. This study underlines the importance of turbulent viscosity for explaining the damping of both slow and fast modes, which, hitherto, has not been explored.