We investigate torsional Alfvén modes of relativistic stars with a global dipole magnetic field .
It has been noted recently ( Glampedakis et al .
2006 ) that such oscillation modes could serve as as an alternative explanation ( in contrast to torsional crustal modes ) for the SGR phenomenon , if the magnetic field is not confined to the crust .
We compute global Alfvén modes for a representative sample of equations of state and magnetar masses , in the ideal MHD approximation and ignoring \ell \pm 2 terms in the eigenfunction .
We find that the presence of a realistic crust has a negligible effect on Alfvén modes for B > 4 \times 10 ^ { 15 } G. Furthermore , we find strong avoided crossings between torsional Alfvén modes and torsional crust modes .
For magnetar-like magnetic field strengths , the spacing between consecutive Alfvén modes is of the same order as the gap of avoided crossings .
As a result , it is not possible to identify modes of predominantly crustal character and all oscillations are predominantly Alfvén-like .
Interestingly , we find excellent agreement between our computed frequencies and observed frequencies in two SGRs , for a maximum magnetic field strength in the range of ( 0.8–1.2 ) \times 10 ^ { 16 } G .