On the properties of slow mhd sausage waves within small-scale photospheric magnetic structures

The presence of magneto-acoustic waves in magnetic structures in the solar atmosphere is well-documented. Applying the technique of solar magneto-seismology (SMS) allows us to infer the background properties of these structures. Here, we aim to identify properties of the observed magneto-acoustic waves and study the background properties of magnetic structures within the lower solar atmosphere. Using the Dutch Open Telescope (DOT) and Rapid Oscillations in the Solar Atmosphere (ROSA) instruments, we captured two series of high-resolution intensity images with short cadence of two isolated magnetic pores. Combining wavelet analysis and empirical mode decomposition (EMD), we determined characteristic periods within the cross-sectional (i.e., area) and intensity time series. Then, by applying the theory of linear magnetohydrodynamics (MHD), we identified the mode of these oscillations within the MHD framework. Several oscillations have been detected within these two magnetic pores. Their periods range from 3 to 20 minutes. Combining wavelet analysis and EMD enables us to confidently find the phase difference between the area and intensity oscillations. From these observed features, we concluded that the detected oscillations can be classified as slow sausage MHD waves. Further, we determined several key properties of these oscillations such as the radial velocity perturbation, magnetic field perturbation and vertical wavenumber using solar magnetoseismology. The estimated range of the related wavenumbers reveals that these oscillations are trapped within these magnetic structures. Our results suggest that the detected oscillations are standing harmonics, and, this allows us to estimate the expansion factor of the waveguides by employing SMS. The calculated expansion factor ranges from 4-12