Bibcode
McEwan, M. P.; Díaz, A. J.; Roberts, B.
Referencia bibliográfica
Astronomy and Astrophysics, Volume 481, Issue 3, 2008, pp.819-825
Fecha de publicación:
4
2008
Revista
Número de citas
51
Número de citas referidas
48
Descripción
Context: In transverse coronal loop oscillations, two periodicities have
been measured simultaneously and are interpreted as the fundamental kink
mode (with period P_1) and the first harmonic (with period P_2).
Deviations of the period ratio P1/2P2 from unity
provide information about the extent of longitudinal structuring within
the loop. Aims: Here we develop an analytical approximation that
describes the shift in P1/2P2 in terms of the
ratio L/Λc of the length 2L of a coronal loop and the
density scale height Λ_c. Methods: We study the MHD wave
equations in a low β plasma using the thin tube approximation.
Disturbances are described by a differential equation which may be
solved for various equilibrium density profiles, obtaining dispersion
relations in terms of Bessel functions. These dispersion relations may
be used to obtain analytical approximations to the periods P1
and P2. We also present a variational approach to determining
the period ratio and show how the WKB method may be used. Results: Analytical approximations to the period ratio
P1/2P2 are used to shed light on the magnitude of
longitudinal structuring in a loop, leading to a determination of the
density scale height. We apply our formula to the observations in
Verwichte et al. (2004) and Van Doorsselaere et al. (2007), obtaining
the coronal density scale height. Conclusions: Our simple formula
and approximate approaches highlight a useful analytical tool for
coronal seismology. We demonstrate that P1/2P2 is
linked to the density scale height, with no need for estimates of other
external parameters. Given the accuracy of current observations, our
formula provides a convenient means of determining density scale
heights.