Analysis of Overtones in Transverse Oscillations of Coronal Loops of an Active Region

We investigate the fundamental mode and overtones in the transverse oscillations of coronal loops associated with an active region using intensity observations taken by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). The fundamental periods of the two selected coronal loops are found to be 17.0 minutes and 15.2 minutes, respectively. The first loop oscillated in the first and second overtones, with periods of around 6.9 minutes and 4.3 minutes, respectively. However, the second loop was detected only with the first overtone of approximately 7.7 minutes period. The period ratios of the fundamental to the first overtones of these loops are 1.24 and 0.99, respectively, while the fundamental-to-second-overtone period ratio of the first loop is 1.33. Thus, the deviation of period ratios from unity helps estimate the density scale height and the loop expansion factor. We obtained a density scale height of 11 Mm for the second loop and a loop expansion factor of 1.5 for the first coronal loop, considering that coronal loops have a greater effect on the loop expansion factor than on longitudinal density stratification associated with a sigmoidal active region. Using their lengths and periods of oscillations, we estimated a reasonable average magnetic field strength within a range of \(20-30\) G in the coronal loops.