On the period ratio P1/2P2 in the oscillations of coronal loops

Aims. With strong evidence of fast and slow magnetoacoustic modes arising in the solar atmosphere there is scope for improved determinations of coronal parameters through coronal seismology. Of particular interest is the ratio P1/2P2 between the period P1 of the fundamental mode and the period P2 of its first harmonic; in an homogeneous medium this ratio is one, but in a more complex configuration it is shifted to lower values. Methods. We consider analytically the effects on the different magnetohydrodynamic modes of structuring and stratification, pointing out that transverse or longitudinal structuring or gravitational stratification modifies the ratio P1/2P2. Results. The deviations caused by gravity and structure are studied for the fast and slow modes. Structure along the loop is found to be the dominant effect. Conclusions. The departure of P1/2P2 from unity can be used as a seismological tool in the corona. We apply our technique to the observations by Verwichte et al. (2004), deducing the density scale height in a coronal loop.