Issue 
A&A
Volume 591, July 2016



Article Number  A131  
Number of page(s)  10  
Section  The Sun  
DOI  https://doi.org/10.1051/00046361/201628713  
Published online  28 June 2016 
Damping of prominence longitudinal oscillations due to mass accretion
^{1} School of Mathematics and Statistics (SoMaS), The University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
email: m.s.ruderman@sheffield.ac.uk
^{2} Space Research Institute (IKI) Russian Academy of Sciences, 117810 Moscow, Russia
^{3} Instituto de Astrofísica de Canarias, 38200 La Laguna, Tenerife, Spain
^{4} Universidad de La Laguna, Dept. Astrofísica, 38206 La Laguna, Tenerife, Spain
Received: 14 April 2016
Accepted: 9 May 2016
We study the damping of longitudinal oscillations of a prominence thread caused by the mass accretion. We suggested a simple model describing this phenomenon. In this model we considered a thin curved magnetic tube filled with the plasma. The prominence thread is in the central part of the tube and it consists of dense cold plasma. The parts of the tube at the two sides of the thread are filled with hot rarefied plasma. We assume that there are flows of rarefied plasma toward the thread caused by the plasma evaporation at the magnetic tube footpoints. Our main assumption is that the hot plasma is instantaneously accommodated by the thread when it arrives at the thread, and its temperature and density become equal to those of the thread. Then we derive the system of ordinary differential equations describing the thread dynamics. We solve this system of ordinary differential equations in two particular cases. In the first case we assume that the magnetic tube is composed of an arc of a circle with two straight lines attached to its ends such that the whole curve is smooth. A very important property of this model is that the equations describing the thread oscillations are linear for any oscillation amplitude. We obtain the analytical solution of the governing equations. Then we obtain the analytical expressions for the oscillation damping time and periods. We find that the damping time is inversely proportional to the accretion rate. The oscillation periods increase with time. We conclude that the oscillations can damp in a few periods if the inclination angle is sufficiently small, not larger that 10°, and the flow speed is sufficiently large, not less that 30 km s^{1}. In the second model we consider the tube with the shape of an arc of a circle. The thread oscillates with the pendulum frequency dependent exclusively on the radius of curvature of the arc. The damping depends on the mass accretion rate and the initial mass of the threads, that is the mass of the thread at the moment when it is perturbed. First we consider small amplitude oscillations and use the linear description. Then we consider nonlinear oscillations and assume that the damping is slow, meaning that the damping time is much larger that the characteristic oscillation time. The thread oscillations are described by the solution of the nonlinear pendulum problem with slowly varying amplitude. The nonlinearity reduces the damping time, however this reduction is small. Again the damping time is inversely proportional to the accretion rate. We also obtain that the oscillation periods decrease with time. However even for the largest initial oscillation amplitude considered in our article the period reduction does not exceed 20%. We conclude that the mass accretion can damp the motion of the threads rapidly. Thus, this mechanism can explain the observed strong damping of largeamplitude longitudinal oscillations. In addition, the damping time can be used to determine the mass accretion rate and indirectly the coronal heating.
Key words: hydrodynamics / waves / Sun: chromosphere / Sun: corona / Sun: filaments, prominences / Sun: oscillations
© ESO, 2016
Current usage metrics show cumulative count of Article Views (fulltext article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 4896 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.