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Aims. We aim to determine the phase speed of an oscillation in a magnetic pore using only intensity images at one height. The observations were obtained using the CRisp Imaging SpectroPolarimeter at the Swedisch 1-m Solar Telescope and show variations in both cross-sectional area and intensity in a magnetic pore. Methods. We have designed and tested an observational method to extract the wave parameters that are important for seismology. We modelled the magnetic pore as a straight cylinder with a uniform plasma both inside and outside the flux tube and identify different wave modes. Using analytic expressions, we are able to distinguish between fast and slow modes and obtain the phase speed of the oscillations. Results. We found that the observed oscillations are slow modes with a phase speed around 5 km s-1. We also have strong evidence that the oscillations are standing harmonics. [ABSTRACT FROM AUTHOR]

Aims. We aim to calculate the kinetic, magnetic, thermal, and total energy densities and the flux of energy in axisymmetric sausage modes. The resulting equations should contain as few parameters as possible to facilitate applicability for different observations. Methods. The background equilibrium is a one-dimensional cylindrical flux tube model with a piecewise constant radial density profile. This enables us to use linearised magnetohydrodynamic equations to calculate the energy densities and the flux of energy for axisymmetric sausage modes. Results. The equations used to calculate the energy densities and the flux of energy in axisymmetric sausage modes depend on the radius of the flux tube, the equilibrium sound and Alfvén speeds, the density of the plasma, the period and phase speed of the wave, and the radial or longitudinal components of the Lagrangian displacement at the flux tube boundary. Approximate relations for limiting cases of propagating slow and fast sausage modes are also obtained. We also obtained the dispersive first-order correction term to the phase speed for both the fundamental slow body mode under coronal conditions and the slow surface mode under photospheric conditions. [ABSTRACT FROM AUTHOR]

Aims. We present a mathematical framework for the seismology of photospheric flux tubes using a uniform straight cylinder as a flux-tube model. In contrast to the earlier model of Fujimura & Tsuneta (2009, ApJ, 702, 1443), we also include a non-zero gas pressure; we do not use the thin tube approximation and we use an underdense region inside the flux tube. Methods. We used the linearised ideal magnetohydrodynamic equations to describe different wave modes in the photosphere. Using the wave mode polarisations we then obtained phase relations which represent different observables. Those phase relations were used to calculate phase differences and amplitude ratios. Finally we inverted these amplitude ratios to obtain plasma parameters which are not directly observable. Results. The mathematical framework results in phase differences that can be conveniently compared with observational data to distinguish between different wave modes. Once the wave mode has been identified, the inverted amplitude ratios can be used to either analytically or numerically estimate the magnitude of plasma parameters which are not directly observable, such as the vertical wavenumber. Artificial observations of different wave modes have shown that the framework mostly succeeds in identifying the correct wave mode and in reproducing the correct plasma parameters using the inverted amplitude ratios. [ABSTRACT FROM AUTHOR]