Damped kink motions in a system of two solar coronal tubes with elliptic cross sections

Aims. This study is motivated by observations of coordinated transverse displacements in neighboring solar active region loops, addressing specifically how the behavior of kink motions in straight two-tube equilibria is impacted by tube interactions and tube cross-sectional shapes. Methods. We worked with linear, ideal, pressureless magnetohydrodynamics. Axially standing kink motions were examined as an initial value problem for transversely structured equilibria involving two identical, field-aligned, density-enhanced tubes with elliptic cross sections (elliptic tubes). Continuously nonuniform layers were implemented around both tube boundaries. We numerically followed the system response to external velocity drivers, largely focusing on the quasi-mode stage of internal flows to derive the pertinent periods and damping times. Results. The periods and damping times that we derive for two-circular-tube setups justify the available modal results found with the T-matrix approach. Regardless of cross-sectional shapes, our nonuniform layers feature the development of small-scale shears and energy accumulation around Alfvén resonances, indicative of resonant absorption and phase mixing. As with two-circular-tube systems, our configurational symmetries still make it possible to classify lower-order kink motions by the polarization and symmetric properties of the internal flows; hence, such motions are labeled as S ​ x and A x . However, the periods and damping times for two-elliptic-tube setups further depend on cross-sectional aspect ratios, with A x motions occasionally damped less rapidly than S ​ x motions. We find uncertainties up to ∼20% (∼50%) for the axial Alfvén time (the inhomogeneity lengthscale) if the periods (damping times) computed for two-elliptic-tube setups are seismologically inverted with canonical theories for isolated circular tubes. Conclusions. The effects of loop interactions and cross-sectional shapes need to be considered when the periods, and in particular the damping times, are seismologically exploited for coordinated transverse displacements in adjacent coronal loops.