Kink oscillations of cooling coronal loops with variable cross-section

Abstract

We study kink waves and oscillations in a thin expanding magnetic tube in the presence of flow. The tube consists of a core region and a thin transitional region at the tube boundary. In this region the plasma density monotonically decreases from its value in the core region to the value outside the tube. Both the plasma density and velocity of background flow vary along the tube and in time. Using the multiscale expansions we derive the system of two equations describing the kink oscillations. When there is no transitional layer the oscillations are described by the first of these two equations. We use this equation to study the effect of plasma density variation with time on kink oscillations of an expanding tube with a sharp boundary. We assume that the characteristic time of the density variation is much greater than the characteristic time of kink oscillations. Then we use the Wentzel-Kramer-Brillouin (WKB) method to derive the expression for the adiabatic invariant, which is the quantity that is conserved when the plasma density varies. The general theoretical results are applied to the kink oscillations of coronal magnetic loops. We consider an expanding loop with the half-circle shape and assume that the plasma temperature inside a loop decays exponentially with time. We numerically calculated the dependences of the fundamental mode frequency, the ratio of frequencies of the first overtone and fundamental mode, and the oscillation amplitude on time. We obtained that the oscillation frequency and amplitude increase and the frequency ratio decreases due to cooling. The amplitude increase is stronger for loops with a greater expansion factor. This effect is also more pronounced for higher loops. However, it is fairly moderate even for loops that are quite high.

The Effect of Cooling on Driven Kink Oscillations of Coronal Loops

“…In the model applied here, we consider a loop of half-circular shape, where the curvature affects only the density distribution. The temperature is modelled to be exponentially decaying in time (similar to the profiles studied in, for example, Aschwanden and Terradas [2008]; Morton and Erdélyi [2010]; Ruderman [2011b]; Ruderman et al [2017]) and is approximated by:…”

“…where T0 is the constant external temperature and t cool is the cooling time (assumed to be the total lifetime of the oscillation here). Additionally, we describe the variation of the loop crosssection with height, z, in a manner similar to that discussed by Ruderman et al 2008Ruderman et al , 2017. This takes the form:…”

“…In order to obtain results comparable with observed amplitude profiles, we set At = A(0)A Ob (0), where A Ob (0) is the measured initial amplitude of the observed oscillation, At is the factor by which the dimensionless amplitude is scaled, and set L/Lc = 6 (similar to the values used by Ruderman et al 2008Ruderman et al , 2017. This allows us to obtain results for loop expansion factors in the range of 1-1.5, consistent with values discussed in the literature for coronal loops (see, for example, Klimchuk 2000;Watko and Klimchuk 2000).…”

“…This work was expanded upon in Ruderman [2011b] with the inclusion of a resonant layer, where it was found that cooling could cancel out the damping due to resonant absorption in some cases. The effects of loop expansion were considered for cooling coronal loops when no resonant layer was observed by Ruderman et al [2017]. Again it was found that amplification of the coronal loop oscillations could occur.…”

Evolution of the Transverse Density Structure of Oscillating Coronal Loops Inferred by Forward Modeling of EUV Intensity

“…Large amplitude kink waves have been shown to produce plasma flows along the field, and the ponderomotive force can cause accumulation of density at the loop top (e.g Terradas & Ofman 2004;Clack & Ballai 2009;Vasheghani Farahani et al 2012). The effect of a time-varying crosssection was recently investigated analytically in Ruderman et al (2017). In it was observed that the quality factor of kink oscillations decreases as the oscillation amplitude increases, indicating that finite amplitude effects are playing some role in modifying the damping time and/or period.…”