Coronal loop kink oscillation periods derived from the information of density, magnetic field, and loop geometry

Context. Coronal loop oscillations can be triggered by solar eruptions, for example, and are observed frequently by the Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO). The Helioseismic and Magnetic Imager (HMI) on board SDO offers us the opportunity to measure the photospheric vector magnetic field and carry out solar magneto-seismology (SMS).

Aims. By applying SMS, we aim to verify the consistency between the observed period and the one derived from the information of coronal density, magnetic field, and loop geometry, that is, the shape of the loop axis.

Methods. We analysed the data of three coronal loop oscillation events detected by SDO/AIA and SDO/HMI. First, we obtained oscillation parameters by fitting the observational data. Second, we used a differential emission measure (DEM) analysis to diagnose the temperature and density distribution along the coronal loop. Subsequently, we applied magnetic field extrapolation to reconstruct the three-dimensional magnetic field and then, finally, used the shooting method to compute the oscillation periods from the governing equation.

Results. The average magnetic field determined by magnetic field extrapolation is consistent with that derived by SMS. A new analytical solution is found under the assumption of exponential density profile and uniform magnetic field. The periods estimated by combining the coronal density and magnetic field distribution and the associated loop geometry are closest to the observed ones, and are more realistic than when the loop geometry is regarded as being semi-circular or having a linear shape.

Conclusions. The period of a coronal loop is sensitive to not only the density and magnetic field distribution but also the loop geometry.