Three‐dimensional Magnetohydrodynamic Wave Behavior in Active Regions: Individual Loop Density Structure

Abstract

We present the numerical results from a three-dimensional (3D) nonlinear MHD simulation of wave activity in an idealized active region in which individual, realistic loop density structure is included. The active region is modeled by an initially force-free, dipole magnetic configuration with gravitationally stratified density and contains a loop with a higher density than its surroundings. This study represents an extension to the model of Ofman & Thompson. As found in their work, we see that fast wave propagation is distorted by the Alfvén speed profile and that the wave propagation generates field line oscillations, which are rapidly damped. We find that the addition of a high-density loop significantly changes the behavior inside that loop, specifically in that the loop can support trapped waves. We also find that the impact of the fast wave impulsively excites both horizontal and vertical loop oscillations. From a parametric study of the oscillations, we find that the amplitude of the oscillations decreases with increasing density contrast, whereas the period and damping time increase. This is one of the key results presented here: that individual loop density structure can influence the damping rate, and specifically that the damping time increases with increasing density contrast. All these results were compared with an additional study performed on a straight coronal loop with similar parameters. Through comparison with the straight loop, we find that the damping mechanism in our curved loop is wave leakage due to curvature. The work performed here highlights the importance of including individual loop density structure in the modeling of active regions and illustrates the need for obtaining accurate density measurements for coronal seismology.

Impulsively generated oscillations in a 3D coronal loop

“…In fact, Selwa et al (2006Selwa et al ( , 2007a as well as point out that (in 2D) the leakage is "too efficient" to explain the observed damping rates. Analysing 3D numerical simulations of coronal loop oscillations in a magnetic dipole, McLaughlin & Ofman (2008) also find very rapid damping, which (using a comparison with a straight cylinder) they attribute to the loop curvature. However, due to the aspect ratio of our loop (a relatively "fat" loop with a/L ≈ 0.035) the effect of curvature is probably stronger than it would be in realistic coronal loops.…”

“…8c (curved loop) and Fig. 9c (straight loop) of McLaughlin & Ofman (2008), this scaling also seems to be present (although it was not investigated in detail by these authors). This strong modification of the period due to the curvature appears to contradict the result of Van Doorsselaere et al (2004), who found that the periods of oscillations were only marginally affected by the curvature.…”

“…Ofman (2005 demonstrated the potential of such models: that the analysis of such three-dimensional wave propagation can serve as a diagnostic of active region parameters. McLaughlin & Ofman (2008) extended these studies with the inclusion of an individual loop density structure. This creates a density contrast between the loop and the ambient plasma, and this can support trapped MHD modes , as well as phase mixing (Heyvaerts & Priest 1983) and resonant absorption (e.g.…”

Solar flares and focused energy transport by MHD waves

“…Separately, significant work has gone into modelling coronal waves in active regions to improve understanding of observed coronal oscillations (e.g. Ofman & Thompson 2002;Terradas & Ofman 2004;Brady & Arber 2005;Ofman 2005Ofman , 2007Díaz et al 2006;Verwichte et al 2006;McLaughlin & Hood 2006;McLaughlin & Ofman 2008;Pascoe et al 2009;Schmidt & Ofman 2010), but little attention has been given to focused transport as relevant to flares. This paper seeks to bridge the gap between the sub-disciplines of flare physics and MHD waves by investigating whether, and under what conditions, MHD waves can deliver spatially localised energy fluxes to the chromosphere, and by highlighting for the flare community the wave concepts applicable to this problem.…”

Selective spatial damping of propagating kink waves due to resonant absorption

“…The observed post-flare kink waves in coronal loops have two main defining characteristics; firstly, they are standing modes, and secondly, they are strongly damped oscillations (in about 1−4 periods, see e.g., Aschwanden et al 2003). Initially there were several physical mechanisms proposed to explain the observed damping, e.g., footpoint leakage (Berghmans & de Bruyne 1995;De Pontieu et al 2001), lateral wave leakage (Smith et al 1997;Brady & Arber 2005;Verwichte et al 2006;Selwa et al 2005Selwa et al , 2007McLaughlin & Ofman 2008), phase mixing (Heyvaerts & Priest 1983;Roberts 2002;Ofman & Aschwanden 2002), resonant absorption (Ruderman & Roberts 2002;Goossens et al 2002), and more recently loop cooling (Morton & Erdélyi 2009). Thus far, resonant absorption, caused by plasma inhomogeneity in the direction transverse to the magnetic field (see Ionson 1978;Hollweg & Yang 1988;Steinolfson & Davila 1993;Ofman & Davila 1995), has proved the most likely candidate for explaining the observed short damping times in coronal loops (see Goossens 2008, for review).…”