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Abstract
Aims. Motivated by recent observations of oscillations in coronal arcad arcades, we investigate analytically the influence of longitudinales, structuring on the modes of oscillation of a straight coronal loop arcade. As a first step towards more complicated models, we use a simple structure to obtain analytical solutions.
Methods. A partial differential equation is derived for the total pressure perturbation of the fast modes in a zero beta plasma and it is solved analytically. We first recover the results for a homogeneous structure, and the then study an equilibrium with an exponentially n structured density profile, solving it in terms of Bessel functions of noninteger order and exponential argument, thus obtaining a disdispersion relation. The properties of this dispersion relation are discussed and some limits studied, leading to analytical approximations persion to the eigenfrequencies.
Results. The introduction of longitudinal structuring results in a modification to the oscillatory frequencies of the modes of oscillatory oscillation in such structures when compared with the uniform case. Regarding the oscillatoryperiodstion Pn, n = 1, 2,...,., the period ratios, P1/2P(2) and P1/3P(3) are both shifted from unity. Other properties described in structured coronal loops are also found in an arcade: the occurrence of avoided crossings in the dispersion diagram and the displacement of the extrema towards the footpoints in the spatial structure of the eigenmodes.
Conclusions. We show analytically for simple arcade modes that the shift in the fundamental period proves to be small, but the ratio P1/2P(2) depends strongly on the density structure. Moreover, transversal propagation also shifts the ratio P1/2P(2) from unity, so it can be used in the coronal seismology of arcades in which transversal propagation is present. We use the currently available observational data to illustrate this application.
Original language  English 

Pages (fromto)  999 
Number of pages  13 
Journal  Experimental Astronomy 
Volume  471 
DOIs  
Publication status  Published  Sept 2007 
Keywords
 sun : oscillations
 sun : magnetic fields
 sun : corona
 FAST MAGNETOHYDRODYNAMIC OSCILLATIONS
 FAST MAGNETOACOUSTIC WAVES
 LOOP OSCILLATIONS
 TRANSVERSE OSCILLATIONS
 KINK OSCILLATIONS
 MHD OSCILLATIONS
 STRATIFICATION
 MODES
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Solar&Magnetospheric Plasma Theory PP/E1: Solar and Magnetospheric Plasma Theory
Neukirch, T., Hood, A. W., Parnell, C. E., Priest, E., Roberts, B. & Wright, A. N.
1/04/07 → 31/03/12
Project: Standard